WO2002047128A1 - Patterned phase shift layers for wavelength-selectable vertical-cavity surface-emitting laser (vcsel) arrays - Google Patents

Abstract

A method is provided, the method comprising forming a first of n masking layers (1165) for a device (900) and forming a first of nphase-shift layers (970) for the device (900) using the first of the n masking layers (1165). The method also comprises forming a second of n masking layers (1165) for a device (900), and forming a second of n phase-shift layers (1070) for the device (900) using the second of the n masking layers (1165) and forming at least n + 1 and at most 2' different optical thicknesses for the device (900) using the n masking layers (1165) and the n phase-shift layers (1170).

Description

PATTERNED PHASE SHIFT LAYERS FOR

WAVELENGTH-SELECTABLE VERTICAL-CAVITY

SURFACE-EMITTING LASER (VCSEL) ARRAYS

BACKGROUND OF THE INVENTION

1. FIELD OF THE INVENTION

This invention relates generally to laser manufacturing and, more particularly, to vertical-cavity surface-emitting lasers (VCSELs).

2. DESCRIPTIONOFTHERELATEDART In many applications, it is desirable to have lasers capable of producing light at several different wavelengths that are closely spaced. In particular, for optical communication applications, such as wavelength division multiplexing (WDM), many wavelengths spaced a few nanometers apart are useful. There are several possible ways to make wavelength-selectable arrays with edge-emitting semiconductor lasers. However, edge-emitting semiconductor lasers that meet specifications for telecommunication applications are typically complex and expensive to manufacture. Monolithic edge-emitting semiconductor laser arrays with large numbers of wavelengths are impractical technically and economically.

Vertical-cavity surface-emitting lasers (VCSELs) provide a more cost effective solution for many applications. VCSELs can be made using wafer-scale processing and testing, dramatically lowering the cost in comparison to edge-emitting semiconductor lasers, for example. In a VCSEL, the wavelength may be determined by the optical cavity length. The optical cavity length is the effective distance between the two generally parallel mirrors, typically distributed Bragg reflectors (DBRs), enclosing the active region of the VCSEL. Since the optical cavity length is typically set by the epitaxial growth, which should be uniform across the entire wafer or workpiece, the wavelength is uniform.

Tunable VCSELs are desired in order to provide different wavelengths on the same wafer or workpiece. One conventional approach to providing tunable VCSELs uses a top mirror that is suspended on a micromachined cantilever. With this conventional structure, any given VCSEL can be tuned to any wavelength within the tuning range. However, this conventional approach involves a micromachined structure that is difficult to fabricate, has reliability problems and is susceptible to mechanical vibrations. A more reliable way of providing monolithically integrated VCSEL arrays is still needed.

In a VCSEL, the lasing wavelength may be determined by the length of a Fabry-Perot cavity formed by two DBRs separated by the semiconductor optical cavity active region that includes layers with optical gain. The optical gain in a VCSEL is typically provided by quantum wells. Each quantum well has a gain spectrum with a single peak wavelength, and some spectral width over which gain is present. Each DBR is composed of quarter-wave layers of alternating high and low refractive indices. The DBR reflectivity is characterized by a complex amplitude and phase spectrum. The amplitude spectrum exhibits a high reflectivity region at the center of which the reflectivity is highest. The width of the high reflectivity region is referred to as the DBR stop-band width. The phase characteristic of the DBR varies approximately linearly over the stop-band width. The lasing wavelength of a VCSEL is determined by the optical length of the semiconductor cavity and the phase characteristics of the DBRs. The gain provided by the active layer, necessary to achieve lasing (threshold gain) is determined by the roundtrip cavity loss that includes material absoφtion and the DBR transmission. A monolithic multiple-wavelength VCSEL array requires side-by-side fabrication of VCSELs with varying lasing wavelengths, but otherwise uniform laser characteristics, such as threshold gain and current, and efficiency. This implies that the vertical structure of the lasers must vary from device to device on the same wafer, while the cavity losses, material gain, and the DBR transmission remain largely unchanged. The lasing wavelength variation is most commonly realized by changing the optical length of the semiconductor cavity.

One conventional method of making a monolithic multiple wavelength VCSEL array uses non-uniform growth due to a thermal gradient. The backside of a substrate is patterned prior to epitaxial growth in a molecular beam epitaxy (MBE) reactor. The resulting backside pattern produces a thermal gradient on the surface of the substrate when the wafer is heated. Because growth rate is temperature dependent, there is a variable material thickness and, hence, a variable laser wavelength along the thermal gradient. One disadvantage of this conventional approach is the fact that the arrays are limited to linear geometries. To date, it has been difficult to control the wavelengths precisely and repeatedly over large areas of the wafer.

Another conventional method is to grow a partial VCSEL structure including the lower DBR, the active region, and some part of the upper DBR. The wafer is masked and anodically oxidized to some controlled oxide thickness over the exposed portions. A selective etch is then used to remove the oxide. This process is repeated to create different effective cavity lengths for each laser in an array. The remainder of the VCSEL structure is regrown over the patterned wafer. However, each selective etch is sensitive to voltage and concentration variations that may affect the depth, resulting in reduced control over wavelength spacing between devices in the array. Yet another conventional method of making a monolithic multiple wavelength VCSEL array is described, for example, in U.S. Patent No. 6,117,699 to Lemoff et al. ("the Lemoff et al. '699 patent"), describing an array of N- wavelength VCSELs that can be grown with wavelength control. First, as shown in Figure 1, a foundation VCSEL structure 100 is grown on a gallium arsenide (GaAs) substrate 105. The foundation VCSEL structure 100 includes a lower DBR 110 in an optical cavity 145. The lower DBR 110 includes M pairs of layers 115, 120, 125, 130, 135 and 140 (M = 6, in Figure 1), each member of each pair having an index of refraction differing from the other member of each pair. For example, the lower member 115a of the pair 115 may comprise aluminum arsenide (AlAs) and the upper member 115b of the pair 115 may comprise aluminum gallium arsenide (Al_ΛGaι- As, where

0.15<x<l).

The optical cavity 145 also includes a first intrinsic (non-doped) layer 150, an optical gain layer 155 and a second intrinsic (non-doped) layer 160. The optical cavity 145 also includes N-paired semiconductor phase shift epitaxially grown layers 165, 170, 175 and 180 (N = 4 in Figure 1) of aluminum gallium arsenide (AlGaAs) and indium gallium phosphide

(InGaP), where N is the desired number of different wavelengths.

Next, a region of one of the N-paired semiconductor phase shift layers is lithographically patterned (masked and etched). For example, as shown in Figure 1, a mask 185 is formed and portions 190 and 195 (shown in phantom) of the paired semiconductor phase shift epitaxially grown layer 180 are removed by selective etching. The steps of patterning (masking and etching) are repeated for a total of at least (N-l)/2 patterning (masking and etching) steps until regions of at least N-l of the N-paired semiconductor phase shift layers are etched. For example, as shown in Figure 2, a mask 200 is formed and portions 205 and 210 (shown in phantom) of the paired semiconductor phase shift epitaxially grown layers 170, 175 and 180 are removed by selective etching, forming 4 different effective optical cavity lengths corresponding to 4 different lasing wavelengths.

Finally, an upper VCSEL structure (not shown) is grown. The upper VCSEL structure may include an upper DBR similar to the lower DBR 110, but typically having fewer than M pairs of layers, each member of each pair having an index of refraction differing from the other member of each pair. The upper DBR typically has fewer than M pairs of layers so that the reflectivity of the upper DBR is less than the reflectivity of the lower DBR 110. Equivalently, the transmissivity of the upper DBR is greater than the transmissivity of the lower DBR 110. Consequently, more laser photons are emitted from the upper surface (not shown) of the VCSEL than into the substrate 105. However, this Lemoff et al. '699 patent method necessarily requires at least (N-l)/2 masking steps, to produce an array of N-wavelength VCSELs. For a large number N of wavelengths, such methods may become expensive, unwieldy, impractical, and inefficient and may suffer from a loss of yield. For example, as shown in Figure 3, a foundation VCSEL structure 300 is grown on the gallium arsenide (GaAs) substrate 105. The foundation VCSEL structure 300 includes the lower DBR 110 and an optical cavity 345. The optical cavity 345 includes the first intrinsic (non-doped) layer 150, the optical gain layer 155 and the second intrinsic (non-doped) layer 160. The optical cavity 345 also includes N-paired semiconductor phase shift epitaxially grown layers 165, 170, 175, 180, 365, 370, 375 and 380 (N = 8 in Figure 3) of aluminum gallium arsenide (AlGaAs) and indium gallium phosphide (InGaP), where N is the desired number of different wavelengths.

Next, a region of one of the N-paired semiconductor phase shift layers is lithographically patterned (masked and etched). For example, as shown in Figure 3, a mask 305 is formed and portions 390 and 395 (shown in phantom) of the paired semiconductor phase shift epitaxially grown layer 380 are removed by selective etching. The steps of patterning (masking and etching) are repeated for a total of at least (N-l)/2 patterning (masking and etching) steps until regions of at least N-l of the N-paired semiconductor phase shift layers are etched. For example, as shown in Figure 4, a mask 400 is formed and portions 405 and 410 (shown in phantom) of the paired semiconductor phase shift epitaxially grown layers 370, 375 and 380 are removed by selective etching. Then, as shown in Figure 5, a mask 500 is formed and a portion 505 (shown in phantom) of the paired semiconductor phase shift epitaxially grown layer 365 is removed by selective etching. Finally, two more patterning steps (similar to those shown in Figures 1 and 2) may be performed to remove respective portions (similar to the portions 190, 195, 205 and 210 shown in Figures 1 and 2) from the paired semiconductor phase shift epitaxially grown layers 170, 175 and 180 by selective etching, forming 8 different effective optical cavity lengths corresponding to 8 different lasing wavelengths, but using as many as 5 patterning steps.

In many monolithic multiple wavelength VCSEL arrays, the tuning range of the individual VCSELs in the array may be low. For example, each VCSEL in the array may be able to cover only a four-wavelength range (λ_l,λ₂,λ_{i >}λ_Λ, with 100 GHz spacing). To cover a range of eight wavelengths, conventionally two such VCSELs would typically be needed in the array, one for wavelengths

and the other for wavelengths λ₅,λ₆,λ_η,λ_Si, for example. However, if one of these two VCSELs in such an array fails, all of the wavelengths covered by that particular VCSEL would be missing from that array. The present invention is directed to overcoming, or at least reducing the effects of, one or more of the problems set forth above.

SUMMARY OF THE INVENTION In one aspect of the present invention, a method is provided, the method comprising forming a first of n masking layers for a device and forming a first of n phase-shift layers for the device using the first of the n masking layers. The method also comprises forming a second of n masking layers for a device, and forming a second of n phase-shift layers for the device using the second of the n masking layers and forming at least n + l and at most 2" different optical thicknesses for the device using the n masking layers and 'the n phase-shift layers.

In one embodiment, the device comprises a first VCSEL of a monolithic VCSEL array, the first VCSEL being tunable to a first plurality of wavelengths, and a second VCSEL of the monolithic VCSEL array, the second VCSEL being tunable to a second plurality of wavelengths, wherein at least one wavelength is in both the first plurality of wavelengths and the second plurality of wavelengths.

In another aspect of the present invention, a device is provided, the device comprising a first VCSEL of a monolithic VCSEL array, the first VCSEL being tunable to a first plurality of wavelengths. The device also comprises a second VCSEL of the monolithic VCSEL array, the second VCSEL being tunable to a second plurality of wavelengths, wherein at least one wavelength is in both the first plurality of wavelengths and the second plurality of wavelengths.

BRIEF DESCRIPTION OF THE DRAWINGS The invention may be understood by reference to the following description taken in conjunction with the accompanying drawings, in which the leftmost significant digit(s) in the reference numerals denote(s) the first figure in which the respective reference numerals appear, and in which:

Figures 1-5 schematically illustrate conventional methods and devices for manufacturing monolithic multiple wavelength VCSEL arrays; and

Figures 6-17 schematically illustrate various embodiments of a method and a device according to the present invention.

While the' invention is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS Illustrative embodiments of the invention are described below. In the interest of clarity, not all features of an actual implementation are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure.

Illustrative embodiments of a method and a device according to the present invention are shown in Figures 6-17. As shown in Figure 6, a VCSEL structure 600 may be grown on a substrate 605, such as a gallium arsenide (GaAs) substrate or an indium phosphide (InP) substrate. The VCSEL structure 600 may comprise a lower DBR 610 and an optical cavity 645. In various illustrative embodiments, the lower DBR 610 may be n-doped. The lower DBR 610 may comprise M pairs of layers 615, 620, 625, 630, 635 and 640 (M = 6, in Figure 6), each member of each pair having an index of refraction differing from the other member of each pair. In various illustrative embodiments, the number of pairs M may be in a range of about 4 to about 60. The lower DBR 610 may by formed, for example, on the substrate 605 by molecular beam epitaxy (MBE). For example, when the substrate 605 is gallium arsenide (GaAs), the lower member 615a of the pair 615 may comprise aluminum arsenide (AlAs) and the upper member 615b of the pair 615 may comprise aluminum gallium arsenide (Al^Gai-^As, where 0.15< <l). In various illustrative embodiments, x = 0.3. In various alternative illustrative embodiments, for example, the lower DBR 610 may comprise a wide variety of suitable materials that may be chosen for various reasons including cost, reliability, manufacturability, and the like.

The optical cavity 645 includes a first intrinsic (non-doped) layer 650, formed of aluminum gallium arsenide (AlGaAs), indium gallium phosphide (InGaP), gallium arsenide

(GaAs) or indium phosphide (InP), an optical gain layer 655 and a second intrinsic (non-doped) layer 660, formed of aluminum gallium arsenide (AlGaAs), indium gallium phosphide (InGaP), gallium arsenide (GaAs) or indium phosphide (InP). While the layers 650 and 660 may be intrinsic, non-doped, and/or undoped (also known as unintentionally doped), there is a trade-off between electrical conductivity and free-carrier absoφtion. This trade-off requires a lower relative doping in these layers 650 and 660, but for electrical pumping, these layers 650 and 660 may have to have some non-zero amount of doping.

In various illustrative embodiments, having a first intrinsic (non-doped) layer 650 lattice matched to a gallium arsenide (GaAs) substrate 605, the optical gain layer 655 may comprise about a 2200 A layer of aluminum gallium arsenide (A^Ga^As, where x = 0.3) interspersed with about 3 aluminum gallium arsenide (Al_ΛGaι-_ΛAs, where x = 0.12) quantum wells (QWs) or about 3 gallium arsenide (GaAs) quantum wells (QWs), suitable for wavelengths in a range of about 0.6 microns to about 1.0 microns. In various alternative illustrative embodiments, having a first intrinsic (non-doped) layer 650 lattice matched to an indium phosphide (InP) substrate 605, the optical gain layer 655 may comprise about a 2200 A layer of indium gallium arsenide phosphide

where x is about 0.8 and y is about 0.4, for example) interspersed with about 3 indium phosphide (InP) quantum wells (QWs) or about 3 indium gallium arsenide (friyGai-yAs, where y = 0.2) quantum wells (QWs), suitable for wavelengths in a range of up to about 1.6 microns.

The optical cavity 645 may also comprise a phase shift layer 670. The phase shift layer 670 may have a thickness t_x in a range of about 10-1000 A. The phase shift layer 670 may be formed using a lithographically patterned masking or lift-off layer 665 comprising photoresist, for example, capable of being selectively removed with respect to the phase shift layer 670. The lithographically patterned masking or lift-off layer 665 may cover a fraction of the area of the upper surface of the VCSEL structure 600. In various illustrative embodiments, for example, the lithographically patterned masking or lift-off layer 665 may cover about half the area of the upper surface of the VCSEL structure 600. In various illustrative embodiments, for example, the phase shift layer 670 comprises silicon dioxide (SiO₂). In various alternative illustrative embodiments, for example, the phase shift layer 670 may comprise a wide variety of suitable materials that may be chosen for various reasons including cost, reliability, manufacturability, and the like. When the phase shift layer 670 is formed, a phase shift layer 675 is also formed on the lithographically patterned masking or lift-off layer 665 comprising photoresist. When the lithographically patterned masking or lift-off layer 665 comprising photoresist is removed by being lifted off, for example, the phase shift layer 675 is also removed, leaving the phase shift layer 670 formed as a portion of the optical cavity 645 for at least a portion of the VCSEL structure 600.

As shown in Figure 7, an optical cavity 745 may also comprise a phase shift layer 770. The phase shift layer 770 may have a thickness t₂ in a range of about 10-1000 A. The phase shift layer 770 may be formed using a lithographically patterned masking or lift-off layer 765 comprising photoresist, for example, capable of being selectively removed with respect to the phase shift layer 770. The lithographically patterned masking or lift-off layer 765 may cover about half the area of the upper surface of the VCSEL structure 600. The lithographically patterned masking or lift-off layer 765 may comprise a plurality of portions each covering about half the area of each portion of the lithographically patterned masking or lift-off layer 665.

In various illustrative embodiments, for example, the phase shift layer 770 comprises silicon dioxide (SiO₂). The phase shift layer 770 may comprise a plurality of portions each covering about half the area of each portion of the phase shift layer 670. When the phase shift layer 770 is formed, a phase shift layer 775 is also formed on the lithographically patterned masking or lift-off layer 765 comprising photoresist. When the lithographically patterned masking or lift-off layer 765 comprising photoresist is removed by being lifted off, for example, the phase shift layer 775 is also removed, leaving the phase shift layer 770 formed as a portion of the optical cavity 745 for at least a portion of the VCSEL structure 600. The optical cavity 745 of the VCSEL structure 600 has 4 different effective optical cavity lengths formed, corresponding to 4 different lasing wavelengths. One effective optical cavity length includes no additional phase shift layer thickness, another effective optical cavity length includes the phase shift layer 770 having a thickness t₂ , another effective optical cavity length includes the phase shift layer 670 having a thickness t. , and another effective optical cavity length includes the phase shift layers 670 and 770 having a combined thickness t. + t₂ , corresponding respectively to the 4 different lasing wavelengths for 4 VCSELs 840, 850, 860 and 870 (Figure 8) in a monolithic array. Note that while the 4 VCSELs 840, 850, 860 and 870 in the monolithic array illustrated in Figures 7 and 8 are linearly arranged, other non-linear geometries are possible, of course, as one of ordinary skill in the art having the benefit of the present disclosure would know.

Finally, as shown in Figure 8, an upper VCSEL structure 810 is deposited. The upper VCSEL structure 810 may include an upper DBR similar to the lower DBR 610 (Figure 6), but typically having L pairs of layers 815, 820, 825 and 830 (L = 4, in Figure 8), each member of each pair having an index of refraction differing from the other member of each pair. In various illustrative embodiments, the number of pairs L may be in a range of about 4 to about 60. The upper DBR 810 may by formed, for example, on the optical cavity 745 by sputtering. For example, the lower member 815a of the pair 815 may comprise titanium oxide

(TiO₂) and the upper member 815b of the pair 815 may comprise silicon oxide (SiO₂).

Alternatively, for example, the lower member 815a of the pair 815 may comprise aluminum gallium arsenide (A^Ga^As, where 0.15<jc<l) and the upper member 815b of the pair 815 may comprise aluminum arsenide (AlAs). In various alternative illustrative embodiments, for example, the upper DBR 810 may comprise a wide variety of suitable materials that may be chosen for various reasons including cost, reliability, manufacturability, and the like.

As shown in Figure 9, a VCSEL structure 900 may be grown on a substrate 605, such as a gallium arsenide (GaAs) substrate or an indium phosphide (InP) substrate. The VCSEL structure 900 may comprise a lower DBR 610 and an optical cavity 945. In various illustrative embodiments, the lower DBR 610 may be as described above in conjunction with Figure 6. The optical cavity 945 includes a first intrinsic (non-doped) layer 650, formed of aluminum gallium arsenide (AlGaAs), indium gallium phosphide (InGaP), gallium arsenide (GaAs) or indium phosphide (InP), an optical gain layer 655 and a second intrinsic

(non-doped) layer 660, formed of aluminum gallium arsenide (AlGaAs), indium gallium phosphide (InGaP), gallium arsenide (GaAs) or indium phosphide (InP). In various illustrative embodiments, having a first intrinsic (non-doped) layer 650 lattice matched to a gallium arsenide (GaAs) substrate 605, the optical gain layer 655 may comprise about a 2200 A layer of aluminum gallium arsenide (A^Ga^As, where JC = 0.3) interspersed with about 3 aluminum gallium arsenide (Al_xGa _xAs, where Λ = 0.12) quantum wells (QWs) or about 3 gallium arsenide (GaAs) quantum wells (QWs), suitable for wavelengths in a range of about 0.6 microns to about 1.0 microns. In various alternative illustrative embodiments, having a first intrinsic (non-doped) layer 650 lattice matched to an indium phosphide (InP) substrate 605, the optical gain layer 655 may comprise about a 2200 A layer of indium gallium arsenide phosphide

where x is about 0.8 and y is about 0.4, for example) interspersed with about 3 indium phosphide (InP) quantum wells (QWs) or about 3 indium gallium arsenide (In jai-yAs, where y = 0.2) quantum wells (QWs), suitable for wavelengths in a range of up to about 1.6 microns. The optical cavity 945 may also comprise a phase shift layer 970. The phase shift layer 970 may have a thickness t_t in a range of about 10-1000 A. The phase shift layer 970 may be formed using a lithographically patterned masking or lift-off layer 965 comprising photoresist, for example, capable of being selectively removed with respect to the phase shift layer 970. The lithographically patterned masking or lift-off layer 965 may cover a fraction, such as about an eighth or about a quarter or about half, of the area of the upper surface of the

VCSEL structure 900. In various illustrative embodiments, for example, the phase shift layer 970 comprises silicon dioxide (SiO₂). When the phase shift layer 970 is formed, a phase shift layer 975 is also formed on the lithographically patterned masking or lift-off layer 965 comprising photoresist. When the lithographically patterned masking or lift-off layer 965 comprising photoresist is removed by being lifted off, for example, the phase shift layer 975 is also removed, leaving the phase shift layer 970 formed as a portion of the optical cavity 945 for at least a portion of the VCSEL structure 900.

As shown in Figure 10, an optical cavity 1045 may also comprise a phase shift layer 1070. The phase shift layer 1070 may have a thickness t₂ in a range of about 10-1000 A. The phase shift layer 1070 may be formed using a lithographically patterned masking or lift-off layer 1065 comprising photoresist, for example, capable of being selectively removed with respect to the phase shift layer 1070. The lithographically patterned masking or lift-off layer 1065 may cover about half the area of the upper surface of the VCSEL structure 900. The lithographically patterned masking or lift-off layer 1065 may comprise a plurality of portions each covering about half the area of each portion of the lithographically patterned masking or lift-off layer 965.

In various illustrative embodiments, for example, the phase shift layer 1070 comprises silicon dioxide (SiO₂). The phase shift layer 1070 may comprise a plurality of portions each covering about half the area of each portion of the phase shift layer 970. When the phase shift layer 1070 is formed, a phase shift layer 1075 is also formed on the lithographically patterned masking or lift-off layer 1065 comprising photoresist. When the lithographically patterned masking or lift-off layer 1065 comprising photoresist is removed by being lifted off, for example, the phase shift layer 1075 is also removed, leaving the phase shift layer 1070 formed as a portion of the optical cavity 1045 for at least a portion of the VCSEL structure 900.

As shown in Figure 11, an optical cavity 1145 may also comprise a phase shift layer 1170. The phase shift layer 1170 may have a thickness t₃ in a range of about

10-1000 A. The phase shift layer 1170 may be formed using a lithographically patterned masking or^' lift-off layer 1165 comprising photoresist, for example, capable of being selectively removed with respect to the phase shift layer 1170. The lithographically patterned masking or lift-off layer 1165 may cover about half the area of the upper surface of the VCSEL structure 900. The lithographically patterned masking or lift-off layer 1165 may comprise a plurality of portions each covering about half the area of each portion of the lithographically patterned masking or lift-off layer 1065. In various illustrative embodiments, for example, the phase shift layer 1170 comprises silicon dioxide (SiO₂). The phase shift layer 1170 may comprise a plurality of portions each covering about half the area of each portion of the phase shift layer 1070. When the phase shift layer 1170 is formed, a phase shift layer 1175 is also formed on the lithographically patterned masking or lift-off layer 1165 comprising photoresist. When the lithographically patterned masking or lift-off layer 1165 comprising photoresist is removed by being lifted off, for example, the phase shift layer 1175 is also removed, leaving the phase shift layer 1170 formed as a portion of the optical cavity 1145 for at least a portion of the VCSEL structure 900.

The optical cavity 1145 of the VCSEL structure 900 has 8 different effective optical cavity lengths formed, corresponding to 8 different lasing wavelengths. One effective optical cavity length includes no additional phase shift layer thickness, another effective optical cavity length includes the phase shift layer 1170 having a thickness t₃ , another effective optical cavity length includes the phase shift layer 1070 having a thickness t₂ , another effective optical cavity length includes the phase shift layers 1070 and 1170 having a combined thickness t₂ +t₃ , another effective optical cavity length includes the phase shift layer 970 having a thickness t. , another effective optical cavity length includes the phase shift layers 970 and 1170 having a combined thickness t. +t₃ , another effective optical cavity length includes the phase shift layers 970 and 1070 having a combined thickness t, +t₂ and another effective optical cavity length includes the phase shift layers 970, 1070 and 1170 having a combined thickness t_x +t₂ +t₃, corresponding to the 8 different lasing wavelengths for 8 VCSELs in a monolithic array. Note that while the 8 VCSELs in the monolithic array illustrated in Figure 11 are linearly arranged, other non-linear geometries are possible, of course, as one of ordinary skill in the art having the benefit of the present disclosure would know. Finally, an upper VCSEL structure (not shown) is deposited. The upper VCSEL structure may include an upper DBR similar to the upper DBR 810, as shown in Figure 8. The upper DBR may have fewer than the M pairs of layers of the lower DBR 610, each member of each pair having an index of refraction differing from the other member of each pair. In various illustrative embodiments, the number of pairs of layers in the upper DBR may be in a range of about 4 to about 60. The upper DBR may have fewer than M pairs of layers so that the reflectivity of the upper DBR is less than the reflectivity of the lower DBR 610. Equivalently, the transmissivity of the upper DBR is greater than the transmissivity of the lower DBR 610. Consequently, more laser photons are emitted from the upper surface of the VCSEL structure 900 than into the substrate 605. Figures 12-17 schematically illustrate particular embodiments of respective methods 1200-1700 practiced in accordance with the present invention. Figures 6-11 schematically illustrate various exemplary particular embodiments with which the methods 1200-1700 may be practiced. For the sake of clarity, and to further an understanding of the invention, the methods 1200-1700 shall be disclosed in the context of the various exemplary particular embodiments shown in Figures 6-11. However, the present invention is not so limited and admits wide variation, as is discussed further below.

In various illustrative embodiments, forming at least n + l and at most 2" different optical thicknesses for a device, such as a monolithic array of optical devices, using n masking layers and n phase-shift layers, may be accomplished as follows. The n phase-shift layers may have thicknesses t_1;t₂,K ,t_n where t_{ > t₂ >L > t_π__[ ≥ t_n . The total number θ of different optical thicknesses formed using the n phase-shift layers, having thicknesses

t t₂,K ,t_n where tj = t₂ =L = t„_₁ = t„ may be calculated as follows: θ ^ i = n + l . The

1=0 total number θ of different optical thicknesses formed using the n phase-shift layers, having

thicknesses t_{,t₂,K ,t„ where t. > t₂ >L > t_n__λ > t_n and t_t > t_} for t = l,2,K ,n-2 , may be y=.+l

calculated as follows: = (l + l)" = 2" . The total number θ of

different optical thicknesses formed using the n phase-shift layers, having thicknesses t.,t₂,K ,t_n where t, > t₂ >L > t„_, > t„ , is in the range of n + l ≤ θ ≤ 2" . The n phase-shift layers, having thicknesses t t₂,K ,t„ where t. > t₂ >L > t_B_, ≥ t_n , may be formed in any of n\ = (n)(n - l)(ra -2)L (3)(2)(l) different ways, each corresponding to one of the n\ permutations of the order of forming the n phase-shift layers.

As shown in Figure 12, the method 1200 begins, as set forth in box 1210, by forming a first of n masking layers for a device. The first of the n masking layers (similar to the lithographically patterned masking or lift-off layer 665 shown in Figure 6 and the lithographically patterned masking or lift-off layer 965 shown in Figure 9) may be formed above a first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich, similar to the first intrinsic (non-doped) layer 650, optical gain layer 655 and second intrinsic (non-doped) layer 660 shown in Figures 6-11.

The method 1200 proceeds, as set forth in box 1220, by forming a first of n phase-shift layers for the device using the first of the n masking layers. The first of the n phase shift layers (similar to the phase shift layer 670 shown in Figure 6 and the phase shift layer 970 shown in Figure 9) may be formed using the lithographically patterned first of the n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the first of the n phase shift layers. The lithographically patterned first of the n masking layers may cover about half the area of the upper surface of the monolithic

VCSEL array. In various illustrative embodiments, for example, the first of the n phase shift layers comprises silicon dioxide (SiO₂). When the first of the n phase shift layers is formed, a phase shift layer (similar to the phase shift layer 675 shown in Figure 6 and the phase shift layer 975 shown in Figure 9) is also formed on the lithographically patterned first of the n masking layers comprising photoresist. When the lithographically patterned first of the n masking layers- comprising photoresist is removed by being lifted off, for example, the overlying phase shift layer is also removed, leaving the first of the n phase shift layers formed as a portion of the optical cavity for at least a portion of the monolithic VCSEL array. The method 1200 proceeds, as set forth in box 1230, by forming a second of n masking layers for a device. The second of the n masking layers (similar to the lithographically patterned masking or lift-off layer 765 shown in Figure 7 and the lithographically patterned masking or lift-off layer 1065 shown in Figure 10) may be formed above the first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich and the first of the n phase shift layers. The method 1200 proceeds, as set forth in box 1240, by forming a second of n phase-shift layers for the device using the second of the n masking layers. The second of the n phase shift layers (similar to the phase shift layer 770 shown in Figure 7 and the phase shift layer 1070 shown in Figure 10) may be formed using the lithographically patterned second of the n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the second of the n phase shift layers. The lithographically patterned second of the n masking layers may cover about half the area of the upper surface of the monolithic VCSEL array. The lithographically patterned second of the n masking layers may comprise a plurality of portions each covering about half the area of each portion of the lithographically patterned first of the n masking layers. In various illustrative emb'odiments, for example, the second of the n phase shift layers comprises silicon dioxide (SiO₂). When the second of the n phase shift layers is formed, a phase shift layer (similar to the phase shift layer 775 shown in Figure 7 and the phase shift layer 1075 shown in Figure 10) is also formed on the lithographically patterned second of the n masking layers comprising photoresist. When the lithographically patterned second of the n masking layers comprising photoresist is removed by being lifted off, for example, the overlying phase shift layer is also removed, leaving the second of the n phase shift layers formed as a portion of the optical cavity for at least a portion of the monolithic VCSEL array.

The method 1200 proceeds, as set forth in box 1250, by forming at least ra + 1 and at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers. In various illustrative embodiments, at least n+1 and at most 2" different optical thicknesses for optical cavities for a monolithic VCSEL array using n masking layers and n phase-shift layers may be formed, as described above. The n phase-shift layers may have thicknesses t,,t₂,K ,t_B where t. > t₂ >L > t„_, ≥ t_π . The total number θ of different optical thicknesses for the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, having thicknesses t t₂,K ,t_n where t_l = t₂ =L = t_n__l = t_π may be

calculated as follows: θ = i = n + l . The total number θ of different optical thicknesses for

1=0 the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, j=n having thicknesses t,,t₂,K ,t„ where t. > t₂ >L > t_n__x > t„ and t. > ^T t. for z =l,2,K ,n -2 , j=M

may be calculated as follows: θ = = 2" . The total number θ of

different optical thicknesses for the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, having thicknesses t₁₅t₂,K ,t„ where t, > t₂ >L > t_n_, ≥ t_n is in the range of n + l ≤ θ ≤ 2" .

The total number of at least θ = n + 1 and at most 9 = 2" different optical thicknesses for the optical cavities corresponds to the total number of at least θ = n + l and at most θ = 2" different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers formed by using the n masking layers, as described above. The total number 0 = 2" of different optical thicknesses for the optical cavities also corresponds to the power set (the set of all subsets) of the set of the thicknesses t,,t₂,K ,t_n. of the n phase-shift =« layers, where t, > t₂ >L > t„__! > t„ and t_; > ∑ t₇ for . = 1,2,K ,ra-2 , the empty set

]=M corresponding to the optical thickness derived using none of the n phase-shift layers for the optical cavities.

As shown in Figure 13, the method 1300 begins, as set forth in box 1310, by forming n masking layers for a device. The n masking layers (similar to the lithographically patterned masking or lift-off layers 665 and 765 shown in Figures 6 and 7, and the lithographically patterned masking or lift-off layers 965, 1065 and 1165 shown in Figures 9, 10 and 11) may be formed above a first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich, similar to the first intrinsic (non-doped) layer 650, optical gain layer 655 and second intrinsic (non-doped) layer 660 shown in Figures 6-11. The method 1300 proceeds, as set forth in box 1320, by forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective thicknesses t t₂,K ,t_n where t. > t₂ >L ≥ t_n__λ ≥ t_n . The n phase shift layers (similar to the phase shift layers 670 and 770 shown in Figures 6 and 7, and the phase shift layers 970, 1070 and 1170 shown in Figures 9, 10 and 11) may be formed using the lithographically patterned n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the n phase shift layers. The lithographically patterned n masking layers may cover about half the area of the upper surface of the monolithic VCSEL array.

In various illustrative embodiments, for example, the n phase shift layers comprise silicon dioxide (SiO₂). When the n phase shift layers are formed, phase shift layers (similar to the phase shift layers 675 and 775 shown in Figures 6 and 7, and the phase shift layers 975, 1075 and 1175 shown in Figures 9, 10 and 11) are also formed on the lithographically patterned n masking layers comprising photoresist. When the lithographically patterned n masking layers comprising photoresist are removed by being lifted off, for example, the overlying phase shift layers are also removed, leaving the n phase shift layers formed as portions of the optical cavity for at least portions of the monolithic VCSEL array.

The method 1300 proceeds, as set forth in box 1330, by forming at least « + l and at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers. In various illustrative embodiments, at least /_ +1 and at most 2" different optical thicknesses for optical cavities for a monolithic VCSEL array using n masking layers and n phase-shift layers may be formed, as described above. The n phase-shift layers may have thicknesses t.,t₂,K ,t_B where t. ≥ t₂ >L > t_B_, > t_B . The total number θ of different optical thicknesses for the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, having thicknesses t ,t₂,K ,t_n where t. = t₂ =L =t„__I = t„ may be

calculated as follows: θ = i = n + l . The total number θ of different optical thicknesses for

1=0 the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, j=n having thicknesses t₁₅t₂,K ,t_B where t. > t₂ >L > t_B_. > t_n and t. > ^ t_y. for t = l,2,K ,n-2 ,

;=.+ι

may be calculated as follows: θ = = (l + 1)" = 2" . The total number θ of

different optical thicknesses for the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, having thicknesses t,,t₂,K ,t_B where t, > t₂ >L > t_π_. > t_n is in the range of n + \ ≤ θ ≤ 2" . The total number of at least θ - n -X and at most θ = 2" different optical thicknesses for the optical cavities corresponds to the total number of at least θ = n+l and at most 0 = 2" different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers formed by using the n masking layers, as described above. The total number θ = 2" of different optical thicknesses for the optical cavities also corresponds to the power set (the set of all subsets) of the set of the thicknesses t₁₅t₂,K ,t_n of the n phase-shift

layers, where t, > t₂ >L > t_n__l > t_n and t,- > ∑ t, for z = l,2,K ,n-2 , the empty set

;=.+_ corresponding to the optical thickness derived using none of the n phase-shift layers for the optical cavities. As shown in Figure 14, the method 1400 begins, as set forth in box 1410, by forming n masking layers for a device. The n masking layers (similar to the lithographically patterned masking or lift-off layers 665 and 765 shown in Figures 6 and 7, and the lithographically patterned masking or lift-off layers 965, 1065 and 1165 shown in Figures 9, 10 and 11) may be formed above a first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich, similar to the first intrinsic (non-doped) layer 650, optical gain layer 655 and second intrinsic (non-doped) layer 660 shown in Figures 6-11.

The method 1400 proceeds, as set forth in box 1420, by forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective thicknesses t_!,t₂,K ,t_B where t_x = rt₂ > t₂ >L > t_B-1 = rt„ > t„ for r ≥ 1 , where r may be any real number greater than or equal to one. The n phase shift layers (similar to the phase shift layers 670 and 770 shown in Figures 6 and 7, and the phase shift layers 970, 1070 and 1170 shown in Figures 9, 10 and 11) may be formed using the lithographically patterned n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the n phase shift layers. The lithographically patterned n masking layers may cover about half the area of the upper surface of the monolithic VCSEL array.

In various illustrative embodiments, for example, the n phase shift layers comprise silicon dioxide (SiO₂). When the n phase shift layers are formed, phase shift layers (similar to the phase shift layers 675 and 775 shown in Figures 6 and 7, and the phase shift layers 975, 1075 and 1175 shown in Figures 9, 10 and 11) are also formed on the lithographically patterned n masking layers comprising photoresist. When the lithographically patterned n masking layers comprising photoresist are removed by being lifted off, for example, the overlying phase shift layers are also removed, leaving the n phase shift layers formed as portions of the optical cavity for at least portions of the monolithic VCSEL array. The method 1400 proceeds, as set forth in box 1430, by forming at least n+1 and at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers. In various illustrative embodiments, at least n+1 and at most 2" different optical thicknesses for optical cavities for a monolithic VCSEL array using n masking layers and n phase-shift layers may be formed, as described above. The n phase-shift layers may have thicknesses t₁₃t₂,K ,t_n where t_l=rt₂≥t₂≥L ≥ t_n__λ = rt_n ≥t_n for r≥l, where r may be any real number greater than or equal to one. The total number θ of different optical thicknesses for the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, having thicknesses t.,t₂,K ,t„ where t,=t₂=L =t_n__γ=t_n may be l=n calculated as follows: θ = ∑/ = n +1. The total number θ of different optical thicknesses for

1=0 the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers,

having thicknesses t t₂,K ,t_n where t. >t₂ >L >t_n__l >t_n and t. > ∑ t_y for t = l,2,K ,n-2,

_=»^•+!

may be calculated as follows: θ = = 2" . The total number θ of

different optical thicknesses for the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, having thicknesses t t₂,K ,t_B where t >t₂ >L >t_B_, >t_B is in the range of n + l≤θ≤2" .

The total number of at least θ = n + 1 and at most θ = 2" different optical thicknesses for the optical cavities corresponds to the total number of at least θ = n+l and at most θ = 2" different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers formed by using the n masking layers, as described above. The total number θ = 2" of different optical thicknesses for the optical cavities also corresponds to the power set (the set of all subsets) of the set of the thicknesses t t₂,K ,t_n of the n phase-shift

layers, where t_t>t₂>L >t„_₁>t„ and t,- > for t = l,2,K,n-2, the empty set

corresponding to the optical thickness derived using none of the n phase-shift layers for the optical cavities.

In various illustrative embodiments, the n phase-shift layers may have thicknesses t,,t₂,K,t,₍ where t, =rt₂ >t₂ >L >t„_, =rt_B >t„ for r>2 and

t_i=rt_M=r²t_i+2=r"^~it_n> for r>2, since , or

i = 1, 2,K , n - 2. For example, for r = 2 , t_t = 2t₂ > t₂ >L > t_B_, = 2t„ > t_B and

t. = 2t 'i.,+,l = 2²t_;+2 = 2-'t„ > g _tj since ∑ _tj = t_{n j} 2^ = ~^t_n = (2"^ -l)t„ < 2"^"'t„ , for j=ι+l j=M j=i+l t i = l,2,K ,n-2. Similarly, for r = 3, t. = 3t₂ > t₂ >L > t„_ι = 3t„ > t„ and

ti = 3t_M

i - = 1,2,K ,n-2. Likewise, for r = 4, t. = 4t₂ > t₂ >L > t_n__! = 4t„ > t_n and

< A^**t, , for

= 1, 2,K , n - 2. Similarly, for r = 5 , t, = 5t₂ > t₂ >L > t„__[ = 5t_B > t_B and

<5"^~it_n , for

/ = 1, 2,K , n - 2. Likewise, for r = 10 , t, = 10t₂ > t₂ >L > t_B_, = 10t_B > t_B and

t, = 10t_;+1 = 10²t,.₊₂ = 10-'t„ > t„ < 10^»-'t„ , for

Ϊ = 1,2,K ,n-2.

In various illustrative embodiments, the total number of at least θ = n + 1 and at most θ = 2" different optical thicknesses for optical cavities of a monolithic VCSEL array formed using the n phase-shift layers may correspond to the total number of at least θ = n + l and at most θ = 2" different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers. In various alternative illustrative embodiments, the total number of at least θ = n + l and at most θ = 2" different optical thicknesses for a monolithic array of optical filters formed using the n phase-shift layers may correspond to the total number of at least θ = n + l and at most 0 = 2" different filterable wavelengths of the monolithic array of • optical filters formed using the n phase-shift layers.

In various other alternative illustrative embodiments, the total number of at least θ = n + 1 and at most θ = 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices formed using the n phase-shift layers may correspond to the total number of at least θ = n + 1 and at most θ = 2" different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices formed using the n phase-shift layers. In still other various alternative illustrative embodiments, the total number of at least θ = n + 1 and at most 9 = 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors formed using the n phase-shift layers may correspond to the total number of at least 9 = n+1 and at most 9 = 2" different detectable resonant modes of the monolithic array of resonant cavity photodetectors formed using the n phase-shift layers.

In various alternative illustrative embodiments, forming 2" different optical thicknesses for a device, such as a monolithic array of optical devices, using n masking layers and n phase-shift layers, may be accomplished as follows. The n phase-shift layers

}=" may have thicknesses t.,t₂,K ,t_B where t- > t₂ >L > t„_₁ > t„ and t. > ∑ t. for j=ι+l i = 1,2,K ,n -2. The total number 9 of different optical thicknesses for the monolithic array of optical devices formed using the n phase-shift layers, having thicknesses t_j,t₂,K ,t_B where

t_[ > t₂ >L > t„__! > t„ and t_i > ∑ t. for = l,2,K ,»-2 , may. be calculated as follows:

As shown in Figure 15, the method 1500 begins, as set forth in box 1510, by forming a first of n masking layers for a device. The first of the n masking layers (similar to the lithographically patterned masking or lift-off layer 665 shown in Figure 6 and the lithographically patterned masking or lift-off layer 965 shown in Figure 9) may be formed above a first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich, similar to the first intrinsic (non-doped) layer 650, optical gain layer 655 and second intrinsic (non-doped) layer 660 shown in Figures 6-11.

The method 1500 proceeds, as set forth in box 1520, by forming a first of n phase-shift layers for the device using the first of the n masking layers. The first of the n phase shift layers (similar to the phase shift layer 670 shown in Figure 6 and the phase shift layer 970 shown in Figure 9) may be formed using the lithographically patterned first of the n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the first of the n phase shift layers. The lithographically patterned first of the n masking layers may cover about half the area of the upper surface of the monolithic

VCSEL array.

In various illustrative embodiments, for example, the first of the n phase shift layers comprises silicon dioxide (SiO₂). When the first of the n phase shift layers is formed, a phase shift layer (similar to the phase shift layer 675 shown in Figure 6 and the phase shift layer 975 shown in Figure 9) is also formed on the lithographically patterned first of the n masking layers comprising photoresist. When the lithographically patterned first of the n masking layers comprising photoresist is removed by being lifted off, for example, the overlying phase shift layer is also removed, leaving the first of the n phase shift layers formed as a portion of the optical cavity for at least a portion of the monolithic VCSEL array. The method 1500 proceeds, as set forth in box 1530, by forming a second of n masking layers for a device. The second of the n masking layers (similar to the lithographically patterned masking or lift-off layer 765 shown in Figure 7 and the lithographically patterned masking or lift-off layer 1065 shown in Figure 10) may be formed above the first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich and the first of the n phase shift layers. The method 1500 proceeds, as set forth in box 1540, by forming a second of n phase-shift layers for the device using the second of the n masking layers. The second of the n phase shift layers (similar to the phase shift layer 770 shown in Figure 7 and the phase shift layer 1070 shown in Figure 10) may be formed using the lithographically patterned second of the n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the second of the n phase shift layers. The lithographically patterned second of the n masking layers may cover about half the area of the upper surface of the monolithic VCSEL array. The lithographically patterned second of the n masking layers may comprise a plurality of portions each covering about half the area of each portion of the lithographically patterned first of the n masking layers. In various illustrative embodiments, for example, the second of the n phase shift layers comprises silicon dioxide (SiO₂). When the second of the n phase shift layers is formed, a phase shift layer (similar to the phase shift layer 775 shown in Figure 7 and the phase shift layer 1075 shown in Figure 10) is also formed on the lithographically patterned second of the n masking layers comprising photoresist. When the lithographically patterned second of the n masking layers comprising photoresist is removed by being lifted off, for example, the overlying phase shift layer is also removed, leaving the second of the n phase shift layers formed as a portion of the optical cavity for at least a portion of the monolithic VCSEL array.

The method 1500 proceeds, as set forth in box 1550, by forming 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers. In various illustrative embodiments, 2" different optical thicknesses for optical cavities for a monolithic VCSEL array using n masking layers and n phase-shift layers may be formed, as described above. The n phase-shift layers may have thicknesses t_y,t₂,K ,t_B where t. > t₂ >L > t_B__j > t_n j=» and ti > ∑ t_j for z = l,2,K ,n-2. The total number θ of different optical thicknesses for

./=ι+l the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers,

having thicknesses t_lst₂,K ,t_B where t. > t₂ >L > t_B__! > t„ and t,. > for z = l,2,K ,n-2 ,

may be calculated as follows: The total number

9 = 2" of different optical thicknesses for the optical cavities corresponds to the total number

9 = 2" of different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers formed by using the n masking layers, as described above. The total number 9 = 2" of different optical thicknesses for the optical cavities also corresponds to the power set (the set of all subsets) of the set of the thicknesses t,,t₂,K ,t_n of the n phase-shift j=n layers, where t. > t₂ >L > t„__I > t„ and t, > ∑ t_y for z' = l,2,K ,n-2 , the empty set

;=ι+l corresponding to the optical thickness derived using none of the n phase-shift layers for the optical cavities.

As shown in Figure 16, the method 1600 begins, as set forth in box 1610, by forming n masking layers for a device. The n masking layers (similar to the lithographically patterned masking or lift-off layers 665 and 765 shown in Figures 6 and 7, and the lithographically patterned masking or lift-off layers 965, 1065 and 1165 shown in Figures 9,

10 and 11) may be formed above a first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich, similar to the first intrinsic (non-doped) layer 650, optical gain layer 655 and second intrinsic (non-doped) layer 660 shown in Figures 6-11. The method 1600 proceeds, as set forth in box 1620, by forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective j=n thicknesses t_γ,t₂,¥L ,t_n where t. > t₂ >L > t_B__j > t_B and t,. > ∑ t. for z = l,2,K ,n-2. The n =ι+l phase shift layers (similar to the phase shift layers 670 and 770 shown in Figures 6 and 7, and the phase shift layers 970, 1070 and 1170 shown in Figures 9, 10 and 11) may be formed using the lithographically patterned n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the n phase shift layers. The lithographically patterned n masking layers may cover about half the area of the upper surface of the monolithic VCSEL array. In various illustrative embodiments, for example, the n phase shift layers comprise silicon dioxide (SiO₂). When the n phase shift layers are formed, phase shift layers (similar to the phase shift layers 675 and 775 shown in Figures 6 and 7, and the phase shift layers 975, 1075 and 1175 shown in Figures 9, 10 and 11) are also formed on the lithographically patterned n masking layers comprising photoresist. When the lithographically patterned n masking layers comprising photoresist are removed by being lifted off, for example, the overlying phase shift layers are also removed, leaving the n phase shift layers formed as portions of the optical cavity for at least portions of the monolithic VCSEL array.

The method 1600 proceeds, as set forth in box 1630, by forming 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers. In various illustrative embodiments, 2" different optical thicknesses for optical cavities for a monolithic

VCSEL array using n masking layers and n phase-shift layers may be formed, as described above. The n phase-shift layers may have thicknesses t_1;t₂,K ,t„ where t, > t₂ >L > t_B_. > t_B

7=» and t,. > ∑ t_j for t = l,2,K ,n-2. The total number 9 of different optical thicknesses for

7=;+l the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, j=n having thicknesses t₁₅t₂,K ,t_B where t. > t₂ >L > t_B_, > t_B and t,- > ∑ t_} for z = l,2,K ,n-2 ,

7=ι+ι

may be calculated as follows: The total number

9 = 2" of different optical thicknesses for the optical cavities corresponds to the total number 9 = 2" of different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers formed by using the n masking layers, as described above. The total number 9 = 2" of different optical thicknesses for the optical cavities also corresponds to the power set (the set of all subsets) of the set of the thicknesses t_{I 5}t₂,K ,t_B of the n phase-shift

layers, where t. > t₂ >L > t„_ι > t„ and t,- > l,2,K ,n -2 , the empty set

corresponding to the optical thickness derived using none of the n phase-shift layers for the optical cavities.

As shown in Figure 17, the method 1700 begins, as set forth in box 1710, by forming n masking layers for a device. The n masking layers (similar to the lithographically patterned masking or lift-off layers 665 and 765 shown in Figures 6 and 7, and the lithographically patterned masking or lift-off layers 965, 1065 and 1165 shown in Figures 9, 10 and 11) may be formed above a first intrinsic (non-doped) layer/optical gain layer/second intrinsic (non-doped) layer sandwich, similar to the first intrinsic (non-doped) layer 650, optical gain layer 655 and second intrinsic (non-doped) layer 660 shown in Figures 6-11.

The method 1700 proceeds, as set forth in box 1720, by forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective thicknesses t_l3t₂,K ,t„ where t, = rt₂ > t₂ >L > t_n__x = rt_n > t_n for r > 2 and

t_i , for

z' = l,2,K ,n-2. The n phase shift layers (similar to the phase shift layers 670 and 770 shown in Figures 6 and 7, and the phase shift layers 970, 1070 and 1170 shown in Figures 9, 10 and 11) may be formed using the lithographically patterned n masking layers comprising photoresist, for example, capable of being selectively removed with respect to the n phase shift layers. The lithographically patterned n masking layers may cover about half the area of the upper surface of the monolithic VCSEL array.

In various illustrative embodiments, for example, the n phase shift layers comprise silicon dioxide (SiO₂). When the n phase shift layers are formed, phase shift layers (similar to the phase shift layers 675 and 775 shown in Figures 6 and 7, and the phase shift layers 975,

1075 and 1175 shown in Figures 9, 10 and 11) are also formed on the lithographically patterned n masking layers comprising photoresist. When the lithographically patterned n masking layers comprising photoresist are removed by being lifted off, for example, the overlying phase shift layers are also removed, leaving the n phase shift layers formed as portions of the optical cavity for at least portions of the monolithic VCSEL array.

The method 1700 proceeds, as set forth in box 1730, by forming 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers. In various illustrative embodiments, 2" different optical thicknesses for optical cavities for a monolithic VCSEL array using n masking layers and n phase-shift layers may be formed, as described above. The n phase-shift layers may have thicknesses t_{1 ;}t₂,K ,t_π where

t_l = rt₂ > t₂ >L > t_n_, = rt„ > t„ for r > 2 for r > 2 , with

t_n , for z^' = l,2,K ,n-2. The total number θ of different optical

thicknesses for the optical cavities of the monolithic VCSEL array formed using the n phase-shift layers, having thicknesses t_l3t₂,K ,t_B where t, = rt₂ > t₂ >L > t_n__l = rt_n > t_n for

r ≥ 2 and t, = rt_M = r%₂ = r"X > , for

i = 1, 2,K , n - 2 , may be calculated as follows: θ = =(l + 1)" = 2" . The

total number 0 = 2" of different optical thicknesses for the optical cavities corresponds to the total number 9 = 2" of different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers formed by using the n masking layers, as described above. The total number 9 = 2" of different optical thicknesses for the optical cavities also corresponds to the power set (the set of all subsets) of the set of the thicknesses t₁₅t₂,K ,t_B of j=n the n phase-shift layers, where t. >t₂ >L >t_B__[ >t_B and t, > ∑ t. for t = l,2,K ,n-2, the

J=M empty set corresponding to the optical thickness derived using none of the n phase-shift layers for the optical cavities. In various illustrative embodiments, the n phase-shift layers may have thicknesses t,t₂,K. ,t_n where t_{ = rt₂ > t₂ > > t_n__{ = rt_n > t_n for r>2 and

t_l=rt,_+l=r²t_l+2=r"^~'t_n>∑t_J for r>2, since ∑ t_} =t_n ∑ r"^~J = — →_B, for =ι+l 7=ι+l 7=1+1 1 i = 1, 2,K , n - 2. For example, for r = 2 , t, = 2t₂ > t₂ >L > t_n_, = 2t_B > t„ and

t, = 2t,₊₁ = 2²t_I+2 = (T^~> -l)t„ < l^»t. , for

i = l,2,K,n-2. Similarly, for r = 3, t_{ =3t₂ >t >L >t_B_, =3t_B >t_B and

;,=3t,_+I=3²t,₊₂=3"-*t„> ∑t, since ∑ t_} =t_n ∑ 3^ = ^→, <3"-t„, for

7=ι+l 7=ι+l 7=1+1 ^ i = l,2,K,n-2. Likewise, for r = 4, t, =At₂ >t₂ >L >t_n_, =4t_B >t„ and

t, for

z^' = l,2,K ,n-2. Similarly, for r = 5, t, =5t₂ >t₂ >L >t_B__t = 5t„ >t_n and

',=5t_i+1=5²t,₊₂=5-'t_B>∑t, since ∑ t, =t_n ∑ 5"^"' = ^-→„ <5"^"'t_B, for

7=ι+l 7=1+1 7=1+1 ^ z = 1,2,K ,n -2. Likewise, for r = 10 , t_! = 10t₂ > t₂ >L > t_n_. = 10t_B > t_n and

t, <10"-'t_B, for

/ = 1,2,K ,n-2. In various illustrative embodiments, the total number

of different optical thicknesses for optical cavities of

a monolithic VCSEL array formed using the n phase-shift layers may correspond to the total number 9 = 2" of different lasing wavelengths of the monolithic VCSEL array formed using the n phase-shift layers. In various alternative illustrative embodiments, the total number

9 = 2" of different optical thicknesses for a monolithic array of optical filters formed using the n phase-shift layers may correspond to the total number 9 = 2" of different filterable wavelengths of the monolithic array of optical filters formed using the n phase-shift layers.

In various other alternative illustrative embodiments, the total number 9 = 2" of different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices formed using the n phase-shift layers may correspond to the total number 9 = 2" of different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices formed using the n phase-shift layers. In still other various alternative illustrative embodiments, the total number 9 = 2" of different optical thicknesses for a monolithic array of resonant cavity photodetectors formed using the n phase-shift layers may correspond to the total number 9 = 2" of different detectable resonant modes of the monolithic array of resonant cavity photodetectors formed using the n phase-shift layers.

By contrast with the conventional Lemoff et al. '699 patent method, described above

in the Description of the Related Art, which necessarily requires at least masking

steps to produce an array of 2" -wavelength VCSELs, methods according to various illustrative embodiments of the present invention only require n masking steps to produce an array of 2" -wavelength VCSELs. For a large number 2" of wavelengths, whenever n is greater than 2, for example, methods according to various illustrative embodiments of the present invention are less expensive, more manageable, more practical, more efficient and have an increased yield as compared to conventional methods such as the Lemoff et al. '699 patent method.

As described above, in many monolithic multiple wavelength VCSEL arrays, the tuning range of the individual VCSELs in the array may be low. For example, each VCSEL in an array (similar to the array 600, as shown in Figure 8) may be able to cover only a four- wavelength range (for example,

with spacing in a range of about 50-400 GHz; in various illustrative embodiments, the spacing may be about 100 GHz). In various illustrative embodiments, the tuning may be accomplished by controlling the temperature of the whole array of the vertical cavity surface-emitting lasers (VCSELs) and/or by controlling the electric current supplied to each vertical cavity surface-emitting laser (VCSEL) in the array. Controlling the temperature of the whole array of the vertical cavity surface-emitting lasers (VCSELs) may provide tuning over a range of about 1.5 nm, whereas controlling the electric current supplied to each vertical cavity surface-emitting laser (VCSEL) in the array may provide tuning over a range of about 2.5 nm. The tunability of the vertical cavity surface-emitting lasers (VCSELs) in the array over these ranges may be particularly useful for "C" band telecommunication applications to cover a range of about 30 nm.

In various illustrative embodiments, to cover a range R of wavelengths X,,^J ,λ_R , where R = mk + p; m = 1,2,3, ; p < k, about 2(m + l) VCSELs able to cover a k -wavelength range (for example, ,λ^ ,λ_k, with spacing in a range of about 50-400 GHz; in various illustrative embodiments, the spacing may be about 100 GHz) may be used in the array. In various alternative illustrative embodiments, to cover a range R of wavelengths Λ-,Λ-,K ,λ_R, where R = 2mj; m = l,2,3,K , about 2m + 1 VCSELs able to cover a 2j -wavelength range (for example, ,^, L , l-_y, with spacing in a range of about 50-400 GHz; in various illustrative embodiments, the spacing may be about 100 GHz) may be used in the array, a first for wavelengths λ__J+l,λ__J+2,K , _j ,X_j (where λ__J+l,λ__J+2,K ,λ_ λ₀ are wavelengths outside the desired range R of wavelengths -,_. -_2.K ,λ_R), a second for wavelengths

a third for wavelengths ^ ₊₁.^ ₊₂-K- -^₇-ι.^ - ^a f^ourm f°^r wavelengths λ_2jJi,_l,λ_2jΛ.₂₎ ^~~ ,λ^__x,λ _j and so forth until a (2ro + l)-th for wavelengths

(^where

^are wavelengths outside the desired range R of wavelengths , λ^ ,K , λ_R ), for example.

If any one of these (2m + 1) VCSELs in such an array fails, none of the wavelengths covered by that particular VCSEL would be missing from that array. For example, if the second VCSEL for wavelengths

fails, the first VCSEL for wavelengths - ₊₁, l_₇.₊₂,K , l₇-. l₇ may be tuned to cover the wavelengths

,λ ,λ_j and the third VCSEL for wavelengths λ_j+1,λ_j÷2,K _.^-.i_.^- may be tuned to cover the wavelengths λ_J+l,λ_J+2,K ^_j^,^ . Similarly, if the third VCSEL for wavelengths λ_J+1,λ_J+2,K , -_3y_ι, l₃₇ fails, the second VCSEL for wavelengths A^A^K , -_2y-._I, -₂ may be tuned to cover the wavelengths λ_j+l,λ ,¥L ^_j^,^ and the fourth VCSEL for wavelengths

. Likewise, if the 2 -th VCSEL for wavelengths A,_2ffl__{2 +1},A,_2m__{2 +2},K , _mj-_{\> mj} ϊά s, ^me (2m - 1) -th VCSEL for wavelengths _2m__3)j+ , A_(2m_₃₎,.₊₂ ,K , λ_2m_ _)j_ , A_(2nι__l may be tuned to cover the wavelengths A_(2m_₂₎ .₊₁,A_(2ra__2)y+2,K ,2_(2m_₁₎ ._₁, _(2m__1)/ and the (2m + l)-th VCSEL for wavelengths _(2ra_₁₎₇.₊₁, _(2ra__1)y.₊₂,K , _2m+x) , _2m+x)j may be tuned to cover the wavelengths

^(2n.-l)7+l' ^(2m-l)7+2'^- > ^2mj- ^2mj ^•

For example, in various illustrative embodiments, to cover a range of eight wavelengths A^A^K ,λ_i , five 4-wavelength VCSELs may be used in the array, a first for wavelengths λ^λ^,?^,?^ (where λ__x,λ₀ are wavelengths outside the desired range of eight wavelengths A.,A-,K ,λ_% ), a second for wavelengths

a third for wavelengths λ_i,λ_A,λ_s,λ₆, a fourth for wavelengths A₅ , λ₆ , A, , and the fifth for wavelengths λ_j , , A, , t_[0

(where _g,^_Q are wavelengths outside the desired range of eight wavelengths I., --,,]<£ , ), for example.

If any one of these five 4-wavelength VCSELs in such an array fails, none of the wavelengths covered by that particular 4-wavelength VCSEL would be missing from that array. For example, if the second VCSEL for wavelengths

fails, the first VCSEL may be tuned to cover the wavelengths A-, and the third VCSEL may be tuned to cover the wavelengths A₃,A₄. Similarly, if the third VCSEL for wavelengths A₃,A₄,A₅,A₆ fails, the second VCSEL may be tuned to cover the wavelengths ₃, A₄ and the fourth VCSEL may be tuned to cover the wavelengths λ₅,λ₆. Likewise, if the fourth VCSEL for wavelengths λ₅,λ₆,λ_?,λ_s fails, the third VCSEL may be tuned to cover the wavelengths λ_s,λ₆ and the fifth VCSEL may be tuned to cover the wavelengths A- , Ag . In various alternative illustrative embodiments, to cover a range R of wavelengths λ_x,λ₂,K ,λ_R, where R = 2mj; m = l,2,3,K , about 2m VCSELs able to cover a 2j -wavelength range (for example, A.,A-,,K jA-_y, with spacing in a range of about 50-400 GHz; in various illustrative embodiments, the spacing may be about 100 GHz) may be used in the array, two 2j -wavelength VCSELs for wavelengths λ_x,λ₂,K ^_j, two 2j -wavelength VCSELs for wavelengths A_2y+1,A_2y+2,K ,λ_4j__x,λ_4J , two 2j -wavelength

VCSELs for wavelengths λ_4j+x,λ_4J+2,¥L ,λ_6j__x,λ_6J , two 2 -wavelength VCSELs for wavelengths A₆₇₊₁,A_6;+2,K , _X, . and so forth until two 2j -wavelength VCSELs for wavelengths λ_{2m__x)J+x, A_(2m__{l +2},K

, for example. If any one of these 2m VCSELs in such an array fails, none of the wavelengths covered by that particular VCSEL would be missing from that array. For example, if one of the first 2 -wavelength VCSELs for wavelengths

fails, the other one of the first 2j -wavelength VCSELs for wavelengths ApA-_pK

remains to cover the wavelengths

Similarly, if one of the second 2/ -wavelength VCSELs for wavelengths for wavelengths

,λ_4j_ ,λ_4j fails, the other one of the second

2j -wavelength VCSELs for wavelengths

,λ_4j__x,λ_4j remains to cover the wavelengths A_2j._+pA_2;+2,K ,λ_4J_ ,λ_4j . Likewise, if one of the 2m -th 2j -wavelength VCSELs for wavelengths A_(2m__2)/+ A_(2m_₂₎ .₊₂,K

fails, other one of the 2m -th 2j -wavelength VCSELs for wavelengths ,_2m_₂ .₊ A/_2m__{2) +2},K , A₂„_y._p _2my. remains to cover the wavelengths λ_(2m__2)J+x, A₍₂„,__2)y+2,K ,λ_2mj__x,λ_2mj .

For example, in various illustrative embodiments, to cover a range of eight wavelengths A_p -.,K ,λ_% , four 4-wavelength VCSELs may be used in the array, two

4-wavelength VCSELs for wavelengths λ ,λ₂,λ_i,λ₄ and two 4-wavelength VCSELs for wavelengths A₅ , A₆ , A- , , for example. If any one of these four 4-wavelength VCSELs in such an array fails, none of the wavelengths covered by that particular 4-wavelength VCSEL would be missing from that array. For example, if the one of the VCSELs for wavelengths λ_x,λ₂,λ_i,λ₄ fails, the other one of the VCSELs for wavelengths A₁,A₂,A₃,A₄ remains to cover the wavelengths

A₁,A₂,A₃,A₄. Similarly, if one of the VCSELs for wavelengths λ₅,λ₆,λ_J,λ_s fails, the other one of the VCSELs for wavelengths A^A^ -^ remains to cover the wavelengths

In various other alternative illustrative embodiments, to cover a range R of wavelengths

,λ_R, where R = 1,2,3,K , about 2 R; rø = l,2,3,K , VCSELs able to cover a 1 -wavelength range may be used in the array. At least 2m 1 -wavelength VCSELs may be provided for each of wavelengths A₁,A₂,K ,λ_R . If any one of the 2m 1 -wavelength VCSELs used in the array fails, the other 2m -1 of the 1 -wavelength VCSELs remain to cover that 1 -wavelength range.

The burgeoning metro telecommunications network has created new challenges for service providers. Many of the illustrative embodiments described above allow the introduction of a multi- wavelength 1.55 μm VCSEL array that will enable equipment manufactures to better meet the needs of service providers. Steadily rising bandwidth demands are driving the expansion of metro networks. However, the economics of the metro network are changing. In today's metro network the price/performance balance is tilting towards lower costs and greater agility, in contrast to the performance-obsessed long-haul network.

Equipment providers have responded to this shift with new lines targeted at the emerging metro arena, but suppliers of optical components, particularly laser transmitter producers, have typically been slow to adapt. They have been unable to deliver an intermediate reach laser at an affordable price. Equipment manufactures have had to choose either expensive high-performance 1.55 μm DFB lasers or cheaper, and less advantageous, wavelengths (i.e. 1.3 μm) and laser technologies (e.g. Fabry-Perot).

The new "C" and "L" band VCSEL arrays according to many of the illustrative embodiments described above will give equipment manufacturers a new alternative for metro core and edge applications, each laser working at a different ITU wavelength with about 200 GHz spacing. This VCSEL array will help equipment suppliers meet the metro challenge by providing an economical and robust intermediate reach (2-50 km) laser.

VCSEL arrays according to many of the illustrative embodiments described above have a number of advantages. Compared to the incumbent 1.55 μm DFB edge-emitting laser technology, VCSEL arrays according to many of the illustrative embodiments described above are considerably less expensive to produce because they are grown and processed monolithically. Moreover, the ability to make cost effective, multi-wavelength arrays opens technological avenues unavailable to edge-emitting lasers. This innovation promises to significantly reduce equipment costs, giving a significant price advantage to equipment suppliers who can incoφorate it into their equipment. VCSEL arrays according to many of the illustrative embodiments described above reduce equipment costs in two ways. For example, a four-wavelength VCSEL array is less expensive than four DFB lasers. But the VCSEL arrays according to many of the illustrative embodiments described above enable a much large saving beyond simple component costs. Traditionally, each laser in a system resides on one line card, filling one slot in a telecommunications bay. A four- wavelength VCSEL according to many of the illustrative embodiments described above can eliminate the need for three of four line cards, radically expanding the capacity of a telecommunications bay. The four- VCSEL array according to many of the illustrative embodiments described above also is appropriate for applications such as multiprotocol lambda switching (MPLS), routing, optical cross-connects and switching. Higher array counts, higher power levels and/or different spacing options according to many of the illustrative embodiments described above are further advantages.

The particular embodiments disclosed above are illustrative only, as the invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope and spirit of the invention. In particular, every range of values (of the form, "from about a to about b," or, equivalently, "from approximately a to b," or, equivalently, "from approximately a-b") disclosed herein is to be understood as referring to the power set (the set of all subsets) of the respective range of values, in the sense of Georg Cantor. Accordingly, the protection sought herein is as set forth in the claims below.

Claims

CLAIMSWHAT IS CLAIMED:

1. A method comprising: forming a first of n masking layers for a device; forming a first of n phase-shift layers for the device using the first of the n masking layers; forming a second of the n masking layers for the device; forming a second of the n phase-shift layers for the device using the second one of the n masking layers; and forming at least n + 1 and at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers.

2. The method of claim 1, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for optical cavities of a monolithic vertical-cavity surface-emitting laer (VCSEL) array, the at least n + 1 and the at most 2" different optical thicknesses for the optical cavities corresponding to a total number of at least n + 1 and at most 9 = 2" different lasing wavelengths of the monolithic VCSEL array.

3. The method of claim 1, wherein forming the at least n+1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of optical filters, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different filterable wavelengths of the monolithic array of the optical filters.

4. The method of claim 1, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

5. The method of claim 1, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most

9 = 2" different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

6. The method of claim 1, wherein forming the first of n masking layers for the device comprises forming the first of n masking layers to cover about half a first area of the device and wherein forming the second of n masking layers for the device comprises forming the second of n masking layers to cover about half a second area of the device.

7. The method of claim 6, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the at least n + 1 and the at most 2" different optical thicknesses for the optical cavities corresponding to a total number of at least n + 1 and at most θ = 2" different lasing wavelengths of the monolithic VCSEL array.

8. The method of claim 6, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n+1 and the at most 2" different optical thicknesses for a monolithic array of optical filters, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different filterable wavelengths of the monolithic array of the optical filters.

9. _. The method of claim 6, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n+1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

10. The method of claim 6, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

11. A method comprising: forming n masking layers for a device; forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective thicknesses tpt₂,K ,t_B where t, ≥ t₂ >L > t„__I > t_B ; and forming at least n + 1 and at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers.

12. The method of claim 11, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the at least n + 1 and the at most 2" different optical thicknesses for the optical cavities corresponding to a total number of at least n + 1 and at most 9 = 2" different lasing wavelengths of the monolithic VCSEL array.

13. The method of claim 11 , wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of optical filters, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different filterable wavelengths of the monolithic array of the optical filters.

14. The method of claim 11, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

15. The method of claim 11 , wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

16. The method of claim 11, wherein forming the n masking layers for the device comprises forming each of the n masking layers to cover at most about half an area of the device.

17. The method of claim 16, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n+1 and the at most 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the at least n+1 and the at most 2" different optical thicknesses for the optical cavities corresponding to a total number of at least n+1 and at most 9 = 2" different lasing wavelengths of the monolithic VCSEL array.

18. The method of claim 16, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of optical filters, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different filterable wavelengths of the monolithic array of the optical filters.

19. The method of claim 16, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

20. The method of claim 16, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

21. A method comprising: forming n masking layers for a device; forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective thicknesses t_pt₂,K ,t_n where t, = rt₂ > t₂ >L > t„_. = rt„ > t_n for r > 1 ; and forming at least n + 1 and at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers.

22. The method of claim 21, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the at least n + 1 and the at most 2" different optical thicknesses for the optical cavities corresponding to a total number of at least n + 1 and at most 9 = 2" different lasing wavelengths of the monolithic VCSEL array.

23. The method of claim 21, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of optical filters, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different filterable wavelengths of the monolithic array of the optical filters.

24. The method of claim 21, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n+1 and at most 9 = 2" different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

25. The method of claim 21, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

26. The method of claim 21, wherein forming the n masking layers for the device comprises forming each of the n masking layers to cover at most about half an area of the device.

27. The method of claim 26, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the at least n + 1 and the at most 2" different optical thicknesses for the optical cavities corresponding to a total number of at least n + 1 and at most θ = 2" different lasing wavelengths of the monolithic VCSEL array.

28. The method of claim 26, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n+1 and the at most 2" different optical thicknesses for a monolithic array of optical filters, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different filterable wavelengths of the monolithic array of the optical filters.

29. The method of claim 26, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most 9 = 2" different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

30. The method of claim 26, wherein forming the at least n + 1 and the at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the at least n + 1 and the at most 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the at least n + 1 and the at most 2" different optical thicknesses corresponding to a total number of at least n + 1 and at most

9 = 2" different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

31. A method comprising: forming a first of n masking layers for a device; forming a first of n phase-shift layers for the device using the first of the n masking layers; forming a second of the n masking layers for the device; forming a second of the n phase-shift layers for the device using the second_. one of the n masking layers; and forming 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers.

32. The method of claim 31, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the 2" different optical thicknesses for the optical cavities corresponding to a total number 9 = 2" of different lasing wavelengths of the monolithic VCSEL array.

33. The method of claim 31, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of optical filters, the 2" different optical thicknesses corresponding to a total number 9 = 2" of different filterable wavelengths of the monolithic array of the optical filters.

34. The method of claim 31, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the 2" different optical thicknesses corresponding to a total number 9 = 2" of different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

35. The method of claim 31, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the 2" different optical thicknesses corresponding to a total number 9 = 2" of different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

36. The method of claim 31, wherein forming the first of n masking layers for the device comprises forming the first of n masking layers to cover about half a first area of the device and wherein forming the second of n masking layers for the device comprises forming the second of n masking layers to cover about half a second area of the device.

37. The method of claim 36, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the 2" different optical thicknesses for the optical cavities corresponding to a total number 0 = 2" of different lasing wavelengths of the monolithic VCSEL array.

38. The method of claim 36, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the

2" different optical thicknesses for a monolithic array of optical filters, the 2" different optical thicknesses corresponding to a total number 0 = 2" of different filterable wavelengths of the monolithic array of the optical filters.

39. The method of claim 36, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the 2" different optical thicknesses corresponding to a total number 0 = 2" of different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

40. The method of claim 36, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the 2" different optical thicknesses corresponding to a total number 0 = 2" of different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

41. A method comprising: forming n masking layers for a device; forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective thicknesses tpt₂,K ,t„ where j=n t_x > t₂ >L > t„_ι > t„ and t_i > ∑ t_j for t = l,2,K ,n-2 ; and

7=ι+ι forming 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers.

42. The method of claim 41, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the 2" different optical thicknesses for the optical cavities corresponding to a total number 0 = 2" of different lasing wavelengths of the monolithic VCSEL array.

43. The method of claim 41, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of optical filters, the 2" different optical thicknesses corresponding to a total number 0 = 2" of different filterable wavelengths of the monolithic array of the optical filters.

44. The method of claim 41, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the 2" different optical thicknesses corresponding to a total number 0 = 2" of different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

45. The method of claim 41, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the

2" different optical thicknesses corresponding to a total number 0 = 2" of different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

46. The method of claim 41, wherein forming the n masking layers for the device comprises forming each of the n masking layers to cover about half an area of the device.

47. The method of claim 46, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the 2" different optical thicknesses for the optical cavities corresponding to a total number 0 = 2" of different lasing wavelengths of the monolithic VCSEL array.

48. The method of claim 46, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of optical filters, the 2" different optical thicknesses corresponding to a total number 0 = 2" of different filterable wavelengths of the monolithic array of the optical filters.

49. The method of claim 46, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the 2" different optical thicknesses corresponding to a total number

0 = 2" of different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

50. The method of claim 46, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the

2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the 2" different optical thicknesses corresponding to a total number 0 = 2" of different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

51. A method comprising: forming n masking layers for a device; forming n phase-shift layers for the device using the n masking layers, the n phase-shift layers having respective thicknesses t_pt₂,K ,t_B where ti = rt₂ > t₂ >L > t_n__x = rt_n > t_n for r > 2 and

^■ t_i = rt_M = r%₂ = r"-ⁱt_n > for r 2 , with

t„ , for i = 1,2,K ,n-2 ; and

forming 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers.

52. The method of claim 51, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the 2" different optical thicknesses for the optical cavities corresponding to a total number 0 = 2" of different lasing wavelengths of the monolithic VCSEL array.

53. The method of claim 51, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of optical filters, the 2" different optical thicknesses corresponding to a total number 9 = 2" of different filterable wavelengths of the monolithic array of the optical filters.

54. The method of claim 51, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the 2" different optical thicknesses corresponding to a total number 9 = 2" of different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

55. The method of claim 51, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the

2" different optical thicknesses corresponding to a total number 9 = 2" of different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

56. The method of claim 51, wherein forming the n masking layers for the device comprises forming each of the n masking layers to cover about half an area of the device.

57. The method of claim 56, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for optical cavities of a monolithic VCSEL array, the 2" different optical thicknesses for the optical cavities corresponding to a total number 9 = 2" of different lasing wavelengths of the monolithic VCSEL array.

58. The method of claim 56, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of optical filters, the 2" different optical thicknesses corresponding to a total number 9 = 2" of different filterable wavelengths of the monolithic array of the optical filters.

59. The method of claim 56, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the 2" different optical thicknesses for a monolithic array of resonant cavity-based optical and opto-electronic devices, the 2" different optical thicknesses corresponding to a total number

9 = 2" of different resonant modes of the monolithic array of resonant cavity-based optical and opto-electronic devices.

60. The method of claim 56, wherein forming the 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers comprises forming the

2" different optical thicknesses for a monolithic array of resonant cavity photodetectors, the 2" different optical thicknesses corresponding to a total number 9 = 2" of different detectable resonant modes of the monolithic array of resonant cavity photodetectors.

61. A device comprising: a first vertical-cavity surface-emitting laser (VCSEL) of a monolithic VCSEL array, the first VCSEL being tunable to a first plurality of wavelengths; and a second VCSEL of the monolithic VCSEL array, the second VCSEL being tunable to a second plurality of wavelengths, wherein at least one wavelength is in both the first plurality of wavelengths and the second plurality of wavelengths.

62. The device of claim 61, wherein a third plurality of wavelengths are in both the first plurality of wavelengths and the second plurality of wavelengths.

63. The device of claim 61, wherein the monolithic VCSEL array covers a range R of wavelengths A- , A-, ,K , λ_R , where R = mk + p; m = 1, 2, 3,K ; p < k , and comprises about

2(m + l) VCSELs capable of covering a k -wavelength range.

64. The device of claim 62, wherein the monolithic VCSEL array covers a range R of wavelengths A. , A-. ,K , λ_R , where R = mk + p; m = 1, 2, 3,K ; p < k, and comprises about

2 (m + 1) VCSELs capable of covering a k -wavelength range.

65. The device of claim 61, wherein the monolithic VCSEL array covers a range R of wavelengths λ_x,λ₂,K ,λ_R, where R = 2mj; m = l,2,3,K , and comprises about 2m + 1 VCSELs capable of covering a 2/ -wavelength range.

66. The device of claim 62, wherein the monolithic VCSEL array covers a range

R of wavelengths λ_x,λ₂,K ,λ_R, where R = 2mj; m = l,2,3,K , and comprises about 2/n + l VCSELs capable of covering a 2/ -wavelength range.

67. The device of claim 61, wherein the monolithic VCSEL array covers a range R of wavelengths A₁,A₂,K ,A_R, where R = 2mj; m = l,2,3,K , and comprises about 2m

VCSELs capable of covering a 2j -wavelength range.

68. The device of claim 62, wherein the monolithic VCSEL array covers a range R of wavelengths λ_l,λ₂^ ,λ_R, where R = 2mj; m = 1,2,3 fi , and comprises about 2m VCSELs capable of covering a 2j -wavelength range.

69. The device of claim 61, wherein the monolithic VCSEL array covers a range R of wavelengths p -,,K , _j; , where R = 1,2,3,K , and comprises about 2mR m = 1,2,3,K , VCSELs capable of covering a 1 -wavelength range.

70. The device of claim 62, wherein the monolithic VCSEL array covers a range R of wavelengths

where R = 1,2,3,K , and comprises about 2mR; m = 1,2,3,K , VCSELs capable of covering a 1 -wavelength range.

71. A device comprising: a first VCSEL of a monolithic VCSEL array, the first VCSEL being tunable by at least one of temperature control and electric current control to a first plurality of wavelengths; and a second VCSEL of the monolithic VCSEL array, the second VCSEL being tunable by at least one of temperature control and electric current control to a second plurality of wavelengths, wherein at least one wavelength is in both the first plurality of wavelengths and the second plurality of wavelengths.

72. The device of claim 71, wherein a third plurality of wavelengths are in both the first plurality of wavelengths and the second plurality of wavelengths.

73. The device of claim 71, wherein the monolithic VCSEL array covers a range

R of wavelengths ,λ^^ ,λ_R, where R = mk + p; m = 1, 2, 3,K ; p < k , and comprises about

2(m + 1) VCSELs capable of covering a k -wavelength range.

74. The device of claim 72, wherein the monolithic VCSEL array covers a range R of wavelengths A, , A- ,K , λ_R , where R = mk + p; m = 1, 2, 3,K ; p < k, and comprises about

2 (in + 1) VCSELs capable of covering a k -wavelength range.

75. The device of claim 71, wherein the monolithic VCSEL array covers a range R of wavelengths A_p -,,K ,λ_R, where R = 2mj; m = 1,2,3, . , and comprises about 2m + 1 VCSELs capable of covering a 2j -wavelength range.

76. The device of claim 72, wherein the monolithic VCSEL array covers a range R of wavelengths A_pA^K ^, where R = 2mj; m = l,2,3,K , and comprises about 2m + 1 VCSELs capable of covering a 2j -wavelength range.

77. The device of claim 71, wherein the monolithic VCSEL array covers a range R of wavelengths A ,A₂,K ,A_β, where R = 2mj; m = 1,2,3, K. , and comprises about 2m VCSELs capable of covering a 2j -wavelength range.

78. The device of claim 72, wherein the monolithic VCSEL array covers a range

R of wavelengths

where R = 2mj; m = l,2,3,YL , and comprises about 2m VCSELs capable of covering a 2j -wavelength range.

79. The device of claim 71, wherein the monolithic VCSEL array covers a range R of wavelengths

,λ_R, where R = 1,2,3,K , and comprises about 2mR; m = 1,2,3,K , VCSELs capable of covering a 1 -wavelength range.

80. The device of claim 72, wherein the monolithic VCSEL array covers a range

R of wavelengths A_pA-,K ,A_Λ, where R = 1,2,3,K , and comprises about 2 R; m = 1,2,3,K , VCSELs capable of covering a 1 -wavelength range.

81. A method comprising: forming a first of n masking layers for a device; forming a first of n phase-shift layers for the device using the first of the n masking layers; forming a second of the n masking layers for the device; forming a second of the n phase-shift layers for the device using the second one of the n masking layers; and forming at least n + 1 and at most 2" different optical thicknesses for the device using the n masking layers and the n phase-shift layers wherein the device comprises: a first VCSEL of a monolithic VCSEL array, the first VCSEL being tunable, to a first plurality of wavelengths; and a second VCSEL of the monolithic VCSEL array, the second VCSEL being tunable to a second plurality of wavelengths, wherein at least one wavelength is in both the first plurality of wavelengths and the second plurality of wavelengths.

82. The method of claim 81, wherein a third plurality of wavelengths are in both the first plurality of wavelengths and the second plurality of wavelengths.

83. The method of claim 81, wherein the monolithic VCSEL array covers a range R of wavelengths A, , A-, ,K , λ_R , where R = mk + p; m = l, 2, 3,K ; p < k , and comprises about

2( + l) VCSELs capable of covering a k -wavelength range.

84. The method of claim 82, wherein the monolithic VCSEL array covers a range R of wavelengths A, , λ^ ,K , λ_R , where R = mk + p; m = 1, 2, 3,K ; p < k , and comprises about

2(m + l) VCSELs capable of covering a k -wavelength range.

85. The method of claim 81, wherein the monolithic VCSEL array covers a range

R of wavelengths λ_x,λ_2>K ,λ_R, where R = 2mj; m = l,2,3,K , and comprises about 2m + 1 VCSELs capable of covering a 2j -wavelength range.

86. The method of claim 82, wherein the monolithic VCSEL array covers a range R of wavelengths ApA-,K ,λ_R , where R = 2mj; m = l,2,3,K , and comprises about 2 + 1

VCSELs capable of covering a 2j -wavelength range.

87. The method of claim 81, wherein the monolithic VCSEL array covers a range R of wavelengths λ_x,λ₂,J^~. ,λ_R, where R = 2m ; m = l,2,3,K , and comprises about 2m VCSELs capable of covering a 2j -wavelength range.

88. The method of claim 82, wherein the monolithic VCSEL array covers a range R of wavelengths λ ,λ₂fl ,λ_R, where R = 2m ; m = l,2,3,K , and comprises about 2m VCSELs capable of covering a 2j -wavelength range.

89. The method of claim 81, wherein the monolithic VCSEL array covers a range R of wavelengths ApApK

where R = 1,2,3,K , and comprises about 2mR; m = 1,2,3,K , VCSELs capable of covering a 1 -wavelength range.

90. The method of claim 82, wherein the monolithic VCSEL array covers a range

R of wavelengths ^^ ,λ_R, where R = 1,2,3,K , and comprises about 2mR; m = 1,2,3,K , VCSELs capable of covering a 1 -wavelength range.