WO2016123719A1 - Reshaping of optical waveguides by refractive index modification - Google Patents

Abstract

A method of modifying an optical waveguide wherein a pre-existing core waveguide and/or the surrounding (evanescent) volume is irradiated with external radiation in a preferentially shaped beam with sufficient intensity to create permanent refractive index changes of a controlled cross-sectional shape and pattern along the axial length of the pre-existing core waveguide. This reshaping of the waveguide serves in several ways, for example, to modify the mode profile, the propagation constant of each permitted mode, the birefringence, and the radiation mode losses of the pre-existing guided modes. Further, the reshaping can enable a change in the number of modes permitted to propagate in selected portions of an optical waveguide. In this way, a Multimode Interference (MMI) waveguide section can be introduced selectively into the pre-existing waveguide.

Description

TITLE: RESHAPING OF OPTICAL WAVEGUIDES BY REFRACTIVE INDEX MODIFICATION

CROSS-REFERENCE

This application claims the benefit of priority to U.S. Provisional Patent Application No. 62/112,625 filed February 5, 2015 entitled RESHAPING OF OPTICAL WAVEGUIDES BY REFRACTIVE INDEX MODIFICATION, the contents of which are hereby incorporated by reference in the Detailed Description of Example Embodiments, herein below.

FIELD

At least some example embodiments relate generally to the formation of permanent refractive index structures in waveguide materials by external radiation and, more particularly, within or in close proximity to a pre-existing optical waveguide to create multimode interference (MMI) waveguides and devices.

BACKGROUND In the field of optical waveguides, a multimode waveguide of a particular length defines a Multimode Interference (MMI) device which confines and propagates light on the principle of self-imaging known as the Talbot effect, first disclosed in waveguides by Bryngdahl in US. Pat. 3,832,029 and extended further by Ulrich in US. Pat. 4,078, 159. The different values of propagation constant (or equivalently, phase velocity) for each mode leads to modal interference that realigns in relative phase to reproduce the guided transverse intensity pattern on self and multiple images that appear periodically along the length of the multimode waveguide.

A typical MMI device will usually contain one or more input waveguides that define an input optical field to the multimode waveguide section in which a number of higher-ordered modes propagate to produce a length-dependent interference pattern. In optical fiber technology, a single mode fiber (SMF) could serve as the input waveguide when fusion spliced to a multimode fiber, where the distribution of input light into the individual modes of the multimode light will be generated with specific amplitudes and specific phases according to an overlap integral as described, for example, by Soldano et al., J. Lightwave Technol. 13 (4), pp. 615-627 (1995). Hence, the geometric and refractive index properties of single mode and multimode waveguides can be designed and tailored individually to strongly affect these amplitude and phases in their combination as an MMI device. In planar lightwave circuits, one or more input waveguides that are typically single mode can be preferentially positioned against a MMI waveguide section in order to control the amplitude and phase of each of the excited modes (Soldano et al., J. Lightwave Technol. 13 (4), pp. 615-627 (1995)).

Alternatively, Kwakernaak and Wada, (US Pat. No 8,532,447 Bl) disclosed an alternative method of varying the angle between an input waveguide and the MMI section as a means for controlling the amplitude and phase excitation of the MMI modes.

A common form of MMI device will further include output waveguides. In the case of optical fibers, for example, where a multimode fiber (MMF) is fusion spliced between two SMFs, a bandpass filter for coarse wavelength division multiplexing may be designed with spectral response controlled by the length of the MMF (Mohammed et al., Opt. Lett. 31 (17), pp. 2547-2549 (2006)). The output waveguide may also be different from the input waveguide, where the MMF length is designed to preferentially shape the co-propagating modes into a profile shape optimized for the on-axis coupling to this output waveguide (Mohammed et al. in paper JThC92 of the Proceedings of the Conference on Lasers and Electro-Optics, (2006)). In planar lightwave circuits, multiple output waveguides can be readily connected to an MMI waveguide and give way to optical MMI couplers (Pennings et al., Appl. Phys. Lett. 59, pp. 1926-1928, (1996)), 1 xN MMI splitters (Heaton et al., Appl. Phys. Lett. 61, 1754-1756 (1992)) wavelength splitters (US Pat. 5,852,691) which offer advantages in integrated optics. Furthermore, the presence of birefringence in a MMI waveguide introduces polarization dependent responses such as the polarization splitter disclosed by Mackie in US Pat. No 5,838,842. Here, an input single mode waveguide that supports two orthogonal polarizations (TE and TM) is offset from the center of a birefringent MMI waveguide such that each polarization will excite two or more propagation modes. The birefringence causes different self imaging lengths that can over several cycles position the TE and TM modes to replicate in direct (also know as bar) and mirrored (as also known as cross) positions, respectively, and thus couple separately into appropriately positioned cross and bar output waveguides to complete the polarization separation. To practitioners of the art of optical waveguide technology, there are several well established and known methods for designing and combining single and multimode waveguides. In planar lightwave circuits, waveguide of selected length can be widened or the refractive index can be increased by material composition tuning in order to create multimode sections. In optical fibers, multimode guiding is available when the core guiding region is increased in size as part of the design of the preform, chemically doped to increase the refractive index, or microstructured (as in photonics crystal fibers) to create a strong stopband. Such multimode fibers may then be connected to other single mode or multimode fiber types by fusion splicing, epoxy bonding, or various types of mechanical mounting.

An alternative method of directly manipulating the waveguide refractive index is by using light, preferentially from lasers, to modify the refractive index inside transparent materials. One method relies on driving photochemical and other changes within the core waveguide by using laser light (US Pat. No 4,474,427 A), leading to a controllable patterning of the refractive index along the waveguide. In this way, Bragg grating filters can be formed by laser interference with a phase mask as taught by K. Hill in US. Pat. No 5,367,588 A or by point-by-point writing as reported by Hill et al. (Hill et al., Electron. Lett. 26 (16), pp. 1270- 1272 (1990)). Stronger refractive index responses can be induced in standard optical fiber by hydrogen loading (US 5287427 A) or by using higher concentration of dopants in the glass that increase the photochemical reactions. In bulk glasses, focused ultraviolet (UV) laser light can increase the refractive index by similar photochemical change, compaction and other means, with the benefit of localizing the index change within the focal volume without the need for a pre-existing core waveguide to provide a strong photochemical response. Borrelli et al. (US Pat. No US6796148 Bl) and Wei et al. in Photon Processing in Microelectronics and Photonics, SPIE Proc. 4637, Photonics West pp. 251-257 (2002) disclosed a UV and deep UV laser direct-write method, respectively, of ultraviolet laser formation of light guiding structures in bulk silica-based glass substrates. Alternatively, femtosecond laser internal microstructuring has emerged as a more attractive methodology for generating three-dimensional photonics devices in transparent materials that are confined only within or near the focal volume of the focused laser pulses to provide a highly localized modification. Unlike the prior ultraviolet methods that were driven principally by concentrating linear absorption at the focal position, the short pulsed laser light is transparent in propagation through the whole glass, expect when nonlinear absorption is induced in the focal volume. In this way, Davis et al. (Opt. Lett. 21 (21), pp. 1729-1731 (1996)) reported that femtosecond lasers can modify the refractive index of bulk dielectric materials only within the highly localized focal volume, and demonstrated optical guiding along the buried optical waveguides formed by scanning the laser focus within the material. Borrelli et al. (US Pat. No. 6977137 B2) disclosed an improved femtosecond laser direct- write method of waveguide writing in a silica-based material substrate that induced a desired refractive index change while avoiding damage or other changes that could negatively affect the waveguide properties. Stronger laser exposure by using slow scanning speed (lower than 0.08 mm/s) was taught by Will et al., in Commercial and Biomedical Applications of Ultrafast and Free-Electron Lasers, SPIE Proc. 4633, Photonics West pp. 99-106 (2002) to control the number of guided modes in femtosecond direct laser written waveguides for guiding visible wavelength light. Laser exposure of fused silica glass by means of femtosecond laser transverse (Liu et al., Chinese Phys. Lett. 25 (7), pp. 2500-2503 (2008)) and longitudinal (Wantanabe et al., Opt. Lett. 30 (21), pp. 2888-2890 (2005)) writing was applied to increase the cross-sectional exposure area of a single waveguide and demonstrate multimode guiding. In both approaches, laser induced filaments (self-channeling) created elongated refractive index structures that were closely stitched together in multi-pass laser scans to increase the waveguide area and form multimode interference waveguides for guiding in the visible spectrum By fabricating a single mode input waveguide that couples light into this multimode waveguide, Wantanabe (Wantanabe et al., Opt. Lett. 30 (21), pp. 2888-2890 (2005)) further demonstrated a 1 x 3 MMI coupler. Refractive index structuring of pre-existing waveguides by femtosecond laser exposure has become an increasingly useful technique in bulk glasses as well as for optical fiber devices. Long period gratings have been formed in the pre-existing optical fiber core waveguide by a point-by-point writing method using a focused femtosecond ultraviolet light source as reported by Kalachev et al. (J. Lightwave Technol. 23 (8), pp. 2568-2578 (2005)). Martinez et al. (Electron. Lett. 40 (19), (2004)) further demonstrated how shorter period fiber gratings with Bragg resonances could also be fabricated with a femtosecond laser by the point-by- point writing technique while Mihailov et al. (U.S Pat. No 6,993,221) further extended the fiber Bragg grating writing by ultrafast laser exposure through a phase mask. Sezerman et al. (US Pat. No 7 8,107,782) disclosed a method of fabricating optical fiber taps and attenuators by scanning a focused femtosecond laser through a SMF core waveguide to create a refractive index zone at a controlled angle such that a portion of the core waveguide light can be extracted externally out of the fiber cladding. Dugan et al. (US Pat. No 7,382,952) disclosed an ultrafast laser method of refractive index modification to form refractive index tracks within or in close proximity to pre-existing waveguides and thus trim the optical circuit response, for example, by controlling the coupling between two parallel waveguides with the laser formation of a 'facilitator segment' centrally between the two waveguides. DiGiovanni et al. (US Pat. No US8591777 B2) disclosed a method of modifying the longitudinal properties of optical fibers such as waveguide chromatic dispersion, dispersion slope, zero dispersion wavelength, cutoff wavelength, polarization mode dispersion, birefringence, and SBS characteristics, that involves a repeated measurement of the waveguide property while a refractive index-modifying treatment is applied on the same monitoring length of the optical fiber.

Mihailov et al. (US Pat. No 7,689,087) taught a method of tuning the birefringence of an optical waveguide that is especially effective in an SMF. The method builds on Mihailov et al. (US. Pat. No. 6,993,221) technique that moves the region of femtosecond laser periodic modification from inside the core waveguide to the nearby external cladding region. The resulting cladding modification track is preferentially positioned sufficiently far away (2 to 5 um) from the core waveguide in order to avoid significant overlap with the fundamental guided mode, while induced birefringence in the core waveguide.

The potential for creating symmetric and asymmetric all-fiber mode converters were proposed by Savolainen et al. {IEEE Photonics Technol. Lett. 26 (14), (2014)) that teaches how femtosecond laser direct writing can form refractive index structures inside or in the proximity of the core waveguide and induce preferential phase delays that on passing the laser modification zone will reshape the mode profile.

Thomas et al. (US Pat. No. 2012/0237162 Al) applied femtosecond laser writing to form two fiber Bragg grating and define a Fabry-Perot cavity in a multimode optical fiber. The method of femtosecond laser writing of refractive index tracks were further applied in preferential positions in the guiding region, located between the two Bragg gratings, to induce different optical path lengths for different modes so that only selected modes would become filtered by the Fabry-Perot cavity. In this way, preferably in a large mode area fiber, the combination of gratings and laser tracks can selectively attenuate light propagating, for example, in higher order modes such as desired in maintaining only fundamental mode guiding in high powered fiber lasers.

Voigtlander et al. (Pat. WO2013045097 Al) disclosed a mode filter for preferentially removing higher-order modes of a multimode fiber. Refractive index modification tracks are written with a femtosecond laser axially along the fiber and either within the core waveguide or in the near-cladding region and preferentially cause the higher order modes to expand to larger mode size. After propagating a certain track length, the larger diameter profile of the higher order modes will be become preferentially lossy when meeting with the unmodified waveguide due to a larger mismatch with the smaller mode size of the unmodified waveguide. In this way, only the lowest order mode or modes will propagate with high efficiency through the laser-fabricated device, which is desirable in high powered fiber lasers, for example. Further, when the refractive index modification tracks are asymmetrically positioned to break the cylindrically symmetry of the waveguide, the two orthogonal linear polarized modes will experience a different refractive index change, which can result in the selective filtering of a single polarization.

Additional difficulties with existing systems may be appreciated in view of the Detailed Description of Example Embodiments, below.

SUMMARY

MMI waveguide devices (e.g. couplers, wavelength and polarization splitters, and wavelength and polarization filters) have found use in the field of integrated optical circuits. Further, there has been considerable development in using refractive index microstructuring both within pre-existing core waveguides (e.g. fiber Bragg gratings and long period gratings) and within the area surrounding pre-existing core waveguides (e.g. optical attenuators, birefringence tuning, mode shaping and mode filtering). The refractive index microstructuring of pre-existing waveguides for the formation of MMI devices is a desirable fabrication approach for expanding the functionality of integrated optical circuit technology. An example embodiment discloses a method of modifying the number of modes as well as reshaping the modes of an optical waveguide wherein a pre-existing core waveguide and/or the surrounding (evanescent) volume is irradiated with external radiation in a preferentially shaped beam with sufficient intensity to create permanent refractive index changes of a controlled shape that are patterned along the axial length of the pre-existing core waveguide to create an MMI waveguide section. The resulting waveguide modes that propagate through the MMI section, each with different values of propagation constant, are thereby tailored to interfere and realign periodically in phase to reproduce the guided transverse intensity patterns on self and multiple images that reappear along the length of the multimode waveguide due to the self-imaging principle of the Talbot effect. In an additional aspect, the permanent refractive index changes may be preferentially formed in a region preceding the MMI section in order to adiabatically reshape the original mode profile of the unmodified waveguide prior to meeting with and being projected onto the guided modes in the multimode section. In this way, the amplitude and phase of the light appearing at each mode of the MMI section can be controlled to tailor the spectral and polarization response at the output waveguide(s). Similarly, permanent refractive index changes may also be preferentially formed in a region following after the MMI section to control the amplitude and phase projection of each mode in the MMI onto the mode or modes of the output waveguide(s).

In one embodiment, an MMI splitter is formed with laser radiation by modifying a pre- existing single mode waveguide to couple light from the single-mode waveguide into a laser- formed multimode section, which further couples in to multiple output waveguides that are pre-existing and/or laser- formed. Optical routing through this MMI structure is preferentially tuned by the laser modification length and spatial pattern in the multimode section to control the splitting ratio over the output waveguides.

In another embodiment, an in-line optical fiber polarizer is formed consisting of a preexisting single mode waveguide in which a birefringent multimode section is fabricated with laser radiation, causing the self-imaging lengths of each mode to be polarization dependent. An optimal length of the birefringent multimode section may be selected such that TE and TM states of linear polarization become bar and cross self-imaged, respectively, and hence, preferentially couple only one polarization state (e.g. TE) to the output waveguide, leaving the other polarization (e.g. TM) to be cross self- imaged and coupled to either the cladding waveguide, the cladding, radiation modes, or fractional combinations, to define a polarization splitter or tap. This principle can be applied to either a single mode optical fiber, or to a, already birefringent, polarization maintaining fiber.

In an example embodiment, there is provided a method of modifying an optical waveguide, wherein the optical waveguide includes a core waveguide and a surrounding volume, the method including: irradiating at least one of the core waveguide and the surrounding volume with external radiation in a preferentially shaped beam with an intensity to create permanent refractive index changes of a controlled shape that are patterned along an axial length of the core waveguide to add or shape at least one mode of the optical waveguide, wherein the irradiated optical waveguide forms a MMI waveguide.

In an example embodiment, there is provided a MMI waveguide formed from a pre-existing optical waveguide, the modified optical waveguide including: a core waveguide; and a surrounding volume, wherein at least one of the core waveguide and the surrounding volume, from a respective pre-existing core waveguide or pre-existing surrounding volume, has permanent refractive index changes from external radiation of a controlled shape that are patterned along an axial length of the core waveguide to add or shape at least one mode of the MMI waveguide, wherein an interface between a permanent refractive index change and a pre-existing refractive index is unitary.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described by way of examples with reference to the accompanying drawings, in which like reference numerals are used to indicate similar features, and in which:

FIGS 1(a) and 1(b) (sometimes collectively referred to as FIG. 1) provides perspective schematic, in FIG. 1(a), of an optical device consisting of a pre-existing core waveguide 1, surrounded by a cladding region 2. A permanent refractive index structure 3 of length (L) is formed alongside and offset at a center-to-center distance (S) from the pre-existing core waveguide 1 by focusing radiation 4 through a lens 5 to a radiation interaction volume 6. The cross-sectional refractive index profile 7 through the pre-existing core waveguide and the radiation-modified structure is shown in FIG. 1(b).

FIG. 2 illustrates end-view schematics which are presented as example embodiments consisting of a pre-existing core waveguide 1, surrounded by a cladding region 2 with a permanent refractive index structure or structures 3 formed in a single track: (a)

symmetrically in the center of the pre-existing core waveguide; (b) off-centered inside in the pre-existing core waveguide; (c) at the core-cladding boundary; and (d) within the cladding region in close proximity to the pre-existing core waveguide; or in multiple tracks: (e) in pairs on opposite sides of the pre-existing core waveguide; (f) in four tracks symmetrically around and outside the pre-existing core waveguide; and (g) in multiple tracks that align both inside a pre-existing core waveguide and outside in the cladding region; or in multiple overlapping tracks that: (h) exactly overlap in a single track; (i) partially overlap in an extended track; and partially overlap to form a near-continuous or continuous modification surface, for example, forming as a (j) continuous half-cylindrical, (k) continuous full- cylindrical, or (1) discontinuous elliptical shell around the pre-existing core waveguide.

FIG. 3 illustrates top or side-view schematics which are presented as example embodiments consisting of a pre-existing core waveguide 1, surrounded by a cladding region 2 and with a permanent refractive index structure 3 formed of length (L) that: (a) is uniform and positioned in the center of the pre-existing core waveguide; (b) is uniform and positioned at an offset distance S from the center of the pre-existing core waveguide; (c) is adiabatically varying from lower refractive index on the left and right ends to reach a maximum in the middle, while positioned in the center of the pre-existing core waveguide; (d) is adiabatically varying from lower refractive index on the left and right ends to reach a maximum in the middle, while positioned offset at a distance S from the center of the pre-existing core waveguide; (e) is adiabatically changed from higher refractive index on the left and right ends to reach a minimum in the middle, while positioned in the center of the pre-existing core waveguide; (f) is uniform, and begins positioned offset by S from the pre-existing core waveguide, and bends to meet in the center of the pre-existing core waveguide along an S- bend path; (g) is uniform, and begins positioned in the center of the pre-existing core waveguide and bends to extend to a position offset by a distance (S) from the pre-existing core waveguide along an S-bend path; (h) starts outside the pre-existing core waveguide offset by a distance (Si), and proceeds into and back out of the pre-existing core waveguide to an offset distance (S₂) using S-bends; (i) is uniform, and begins positioned offset by S from the pre-existing core waveguide, and bends to meet in the center of the pre-existing core waveguide along a bend angle; (j) begins positioned in the center of the pre-existing core waveguide and then follow an S-bend path that extends into a straight section, with a refractive index profile that is scaled from high to low index contrast, at a position offset by a distance (S) from the pre-existing core waveguide; (k) begins with a straight section, with a refractive index profile that is scaled from high to low index contrast, positioned at a position offset by a distance (S) from the pre-existing core waveguide and then follows an S-bend path that extends into a straight section in the center of the pre-existing core waveguide; and (1) is uniform and positioned at an offset distance S from the center of the pre-existing core waveguide in two symmetrical tracks, and where the modified waveguide section is connected to a dissimilar waveguide.

FIGS. 4(a), 4(b), 4(c), and 4(d) (sometimes collectively referred to as FIG. 4) illustrate a top view schematic of a multimode interference device consisting of a surrounding cladding region 2 and a pre-existing core waveguide 1 which serves as the input (Port 1) and output (Port 2) ports, and is radiation modified to create a multimode interference waveguide section 8 of length (L) formed with the technique of the described example embodiments. In FIG. 4(a) the multimode interference waveguide section is symmetrically in-line with the pre- existing core waveguide, while in FIG. 4(b), the MMI section is tilted to laterally shift and angle tune the input and output port waveguides with respect to the MMI interfaces. The MMI waveguide section may also be connected to an additional waveguide at the output (Port 3) as in FIG. 4(c) wherein the radiation-formed uniform refractive index modification track 3 extents with an S-Bend shape into the cladding region 2 to connect to a straight waveguide section, defining a second output port (Port 3). More generally, the MMI waveguide may be connected to multiple waveguides to form N input and M output ports as shown in FIG. 4(d). FIG. 5 is a graph plotting the unpolarized optical transmission as a function of MMI waveguide length (L) as expected through an MMI device of uniform cross-section for three separate wavelengths (λι < λ₂ < λ₃). FIG. 6 is a graph plotting the unpolarized optical transmission spectra expected through similar MMI devices having three different MMI section lengths (Li > L₂ > L₃).

FIG. 7 is a graph showing transmission as a function of the MMI section length for TE (solid line) and TM (dashed line) polarized light of a fixed wavelength when propagated independently (FIG. 7(a)) or simultaneously (FIG. 7(b)) through a birefringent MMI device.

FIG. 8(a) is a graph showing the transmission (T; solid line) and reflection (R; dotted line) spectra recorded of unpolarized light propagating through an SMF where a femtosecond laser had modified the refractive index profile periodically along a 19.5 mm length of the pre- existing core waveguide to create a Bragg resonance for each of the LP₀i (1551.3 nm wavelength) LPn (1547.77 nm wavelength) and LP₀i^→LPn (1549.6 nm wavelength) modes, and further seen in higher resolution (inset image) when recorded with light polarized in the TE (solid line) and TM (dashed line) states of the LP₀i, LPn, and LP₀i^→LPn modes. The LP01 and LPn mode field intensity profiles recorded at 1560 nm wavelength are shown in FIG. 8(b) and FIG. 8(c), respectively.

FIG. 9 presents graphs of the normalized optical transmission of unpolarized light (solid line) measured at 1550 nm wavelength through an SMF core waveguide recorded in-situ during femtosecond laser writing of a straight and uniform refractive index track positioned parallel with and offset to the pre-existing core waveguide at an offset distance of 6 μηι. In FIG. 9(a), the decrease of the guided light, averaged over each beat cycle, is followed (dashed line) by an exponential decay function of 0.015 dB/cm. Inset, the recorded (solid circles) and modeled (solid line) transmission spectra found after eliminating the propagation loss and plotted over MMI waveguide lengths of L = 8.4 mm to 23.3 mm. FIG. 9(b) shows an expanded scale of the gray region in FIG. 9(a) with examples of points representing a 3 dB coupler (point A), a 97% coupler (point B), and a polarizer (point C) are noted.

FIG. 10 presents a graph of the normalized optical transmission of unpolarized light (solid line) measured at 1550 nm wavelength through an SMF core waveguide recorded in-situ during femtosecond laser writing of a straight and uniform refractive index track positioned parallel with and approximately centered within the pre-existing core waveguide. The decrease of the guided light, averaged over each beat cycle, is followed (dashed line) by an exponential decay function of 0.045 dB/cm. Inset, the recorded (solid circles) and modeled (solid line) transmission spectra found after eliminating the propagation loss and plotted over MMI waveguide lengths of L = 1.71 mm to 4.44 mm.

FIG. 11 presents a graph of the normalized optical transmission of unpolarized light measured at 1550 nm wavelength through an SMF core waveguide recorded in-situ during femtosecond laser writing of a uniform refractive index track crossing approximately through the center of the SMF core waveguide in the (a) horizontal (xy) and (b) vertical (xz) plane with respect to the vertical writing laser beam at an angle of 0.24 mrad. FIG. 12 is a graph plotting the average and the difference between Δβ_ΤΕ and Δβ_ΤΜ as a function of the center-to-center offset distance (S) between the SMF core waveguide and the laser- formed refractive index track written uniformly and parallel with the pre-existing core waveguide. The average between Δβτε and ΔβτΜ (ΔβΑν₈) is plotted for the horizontal (b) and vertical (d) offset distances with respect to the writing laser propagation direction. The difference between Δβ_ΤΕ and Δβ_ΤΜ is plotted for the horizontal (a) and vertical (c) offset distances with respect to the writing laser propagation direction. The two vertical dashed lines indicate the physical boundary between the SMF core waveguide and the cladding region.

FIG. 13 is a graph of the normalized optical transmission of unpolarized light recorded through an MMI device, consisting of an SMF core waveguide modified with a femtosecond laser to form a straight refractive index modification track parallel with the pre-existing core waveguide at an offset distance of 5 μηι and with MMI section lengths of Li = 4.5 mm (dashed line) and L₂ = 10 mm (solid line). FIG. 14 is a graph of the TE (solid line) and TM (dashed line) polarized optical transmission of light as measured through a SMF core waveguide (Port 2) with a MMI section created by placing a laser-formed uniform refractive index track of 8.74 mm length (L) at a 5 μηι offset distance (S) as defined in FIG. 3(b). The inset presents an expanded spectrum near 1403 nm wavelength demonstrating a strong polarization extinction ratio of >20 dB in a narrow 3 nm spectrum

FIG. 15 is a graph of the optical transmission of unpolarized light recorded in the bar-port (Port 2) of the SMF core waveguide (solid line) and the cross-port (Port 3) of the

femtosecond (fs) laser-formed waveguide (dashed line) for the MMI device design shown in FIG. 4(c) as femtosecond laser written to form an MMI waveguide length (L) of 0.099 mm and an offset distance (S) of 6 μηι. Vertical and horizontal dotted lines demark a

representative example of a balanced 3 dB MMI coupler providing 38% transmission into each output port (Port 2 and Port 3) at 1486.5 nm wavelength after accounting for overall losses.

FIG. 16 is a graph of the spectral dependence of the TE (solid line) and TM (dashed line) polarized light coupling ratios as measured for the MMI splitter device shown in FIG. 4(c) with a MMI waveguide length (L) of 7.519 mm and an offset distance (S) of 6 μηι. The arrows indicate wavelengths where the MMI splitter functions as a polarization selective tap (PST).

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

Example embodiments generally provide a method of modifying the number of modes and reshaping the mode(s) of an optical waveguide. In some example embodiments, there are no restrictions on the type of waveguide that can be considered for modification. In some example embodiments, various compositions of materials that harness total internal reflection to guide light in a waveguide include dielectrics such as glasses and doped glasses (e.g. fused silica, germanosilicate, borosilicate, chalcogenide), crystals (eg. lithium niobate, sapphire, LBO, BBO, and diamond), and further include semiconductors (e.g. silicon, germanium, AlGaAs, InP and their various admixtures), and polymers (e.g. poly (methylmethacrylate) (PMMA), poly (ethylmethacrylate) (PEMA), polystyrene, epoxy (Su8), polydimethylsiloxane (PDMS), polytetrafluoroethylene (PTFE), polycarbonate, and sol-gel). An example embodiment also provides the radiative modification of plasmonic waveguides, that mix dielectric or semiconductor materials with thin metal coatings, for example, of Au, Ag, and Cu. Modifying hybrid waveguides based on plasmonic and total internal reflection are further provided by an example embodiment. These material compositions can be further arranged in a myriad of structural configurations, as well known by a practitioner of the art, that can be formed into waveguides, for example, including single mode, mulitmode, single core, multicore, step-index, graded-index, and photonic crystal fiber, and nano-fibers, while extending to planar lightwave or 3D volume circuits that include slab, strip, rib, slot, ridge, embedded, graded, and planar waveguides, and plasmonic waveguides.

In an example embodiment, there is provided a method of modifying an optical waveguide, wherein the optical waveguide includes a core waveguide and a surrounding volume, the method including: irradiating at least one of the core waveguide and the surrounding volume with external radiation in a preferentially shaped beam with an intensity to create permanent refractive index changes of a controlled shape that are patterned along an axial length of the core waveguide to add or shape at least one mode of the optical waveguide, wherein the irradiated optical waveguide forms a MMI waveguide.

In an example embodiment, there is provided a MMI waveguide formed from a pre-existing optical waveguide, the modified optical waveguide including: a core waveguide; and a surrounding volume, wherein at least one of the core waveguide and the surrounding volume, from a respective pre-existing core waveguide or pre-existing surrounding volume, has permanent refractive index changes from external radiation of a controlled shape that are patterned along an axial length of the core waveguide to add or shape at least one mode of the MMI waveguide.

In an example embodiment, an interface between a permanent refractive index change and a pre-existing refractive index is unitary. For example, unitary can mean the interface not having any adhesive, fusion splicing, or other connections between materials of different refractive index.

A non-limiting example depiction of an optical waveguide consisting of a pre-existing core waveguide 1 and a surrounding cladding region 2 is presented in FIG. 1(a). This depiction is an illustrative example as the example embodiment provides that the waveguide and cladding could have any shape and consist of multiple materials or sections. The methodology of the present example embodiment is further depicted in FIG. 1(a) whereby a permanent refractive index structure 3 of length (L) is being formed alongside the pre-existing core waveguide 1 at an offset distance (S) by transverse or longitudinal scanning of radiation 4 focused through a lens 5. The intensity of the focused radiation in the focal volume of the lens defines a radiation interaction zone 6 in which a permanent refractive index modification is created to meet a controlled shape of positive and/or negative change according to the power, duration, and beam shape of the source, following methods as well known to practitioners in the field. The scanning of the focal volume over length (L) creates a multimode interference (MMI) waveguide section by modifying the refractive index profile 7 as depicted in the cross section shown in FIG. 1(b). Here, the profile of pre-existing core waveguide and the radiation modification track are shown with refractive index values of IICORE and n_MoDiFiED, respectively, against the background refractive index of the surrounding cladding, ncL ADDING- The example embodiment provides creating a wide range of refractive index profiles of nMODiFiED, beyond the step-index example here, including but not limited to enhanced, depressed, Gaussian, elliptical, parabolic, and apodized.

The source of radiation to drive sufficiently strong interaction in the focal zone 6 may include laser(s), for example particularly ultraviolet, C0₂, ultrafast (femtosecond) pulsed lasers, and picosecond pulsed lasers that are well known to a practitioner of the art to create permanent changes in refractive index. Other forms of radiation may include electron or ion beams, and x-rays. The resulting changes in the refractive index can be a result of mechanisms such as but not limited to, densification of the material (Ponader et al., J. Appl. Phys. 103 (6), 063516 (2008)), generation of color centers or stress-relief (Hirao et al., J. Non-Cryst. Solids 239, pp. 91-95 (1998)), as well as restructuring of the material to form volume nanogratings, or nanopores (Zimmermann et ,, ΑρρΙ. Phys. Lett. 104 (21), 211107 (2014)).

The methodology of an example embodiment provides the formation of permanent refractive index modifications where the position, shape, and profile, together with birefringence and stress modification, can be manipulated by the focused radiation. Additionally, this refractive index modification may be favorably applied inside or in the vicinity of the pre-existing waveguide core to alter the waveguide properties, such as birefringence, number of allowed guiding modes, cut-off wavelength, and mode shape. In formation of the MMI section, an example embodiment provides many flexible arrangements for positioning and pattering of the radiation-modified structure 3 with respect to the pre-existing waveguide 1. For example, FIG. 2 illustrates end-view schematics of several non-limiting example embodiments, offering a preferential geometry of the modified structure 3 to the pre-existing core waveguide 1. The induced permanent refractive index changes 3 can be symmetrically centered within the pre-existing waveguide, off-centered within the pre-existing waveguide, on the waveguide-cladding boundary, or entirely within in the cladding region 2, but adjacent and in close proximity to the pre-existing core waveguide 1, as shown in FIG. 2(a), 2(b), 2(c), and 2(d), respectively. The example embodiment may also consist of a plurality of refractive index modifications 3 that together modify the number of modes and/or reshape the mode(s). The multiple refractive index modifications 3 can be positioned as a pair on opposite sides of the pre-existing core waveguide 1, in a set of four symmetrically around and outside of the pre-existing core waveguide, or in multiple tracks that align both inside a preexisting core waveguide and outside in the cladding region, as shown in FIG. 2(e), 2(f), and 2(g), respectively. Fully or partially overlapping refractive index modifications 3 are also provided that can form stronger and/or larger refractive index modifications as arranged in FIG. 2(h) and FIG. 2(i), respectively. The refractive index modifications 3 can also be patterned with multiple scans of the focal volume or modification of the focal beam shape and form into continuous, near-continuous, or varying shaped structures that form as half- cylindrical, full-cylindrical, or discontinuous elliptical shell around the pre-existing core waveguide 1 as depicted in FIG. 2(j), 2(k), and 2(1), respectively. An example embodiment provides the shapes and refractive index profile of the pre-existing core waveguide, surrounding cladding region, and the refractive index modifications to extend beyond those of these non-limiting, but illustrative, examples to represent symmetric and non-symmetric profiles of continuous, pseudo-continuous, periodic, aperiodic and discontinuous structures. A further aspect of an example embodiment includes the ability to control the magnitude and shape of the refractive index structure along the path of the pre-existing waveguide. FIG. 3(a) and FIG. 3(b) are top or side view depictions of a pre-existing core waveguide 1 surrounded by a cladding region 2, in which a uniform refractive index modification 3 is positioned in the center and adjacent, respectively, to the pre-existing core waveguide offset by a distance (S). Modifying a section of a pre-existing core in this way is applied advantageously to change the number of guided modes in this waveguide section as well as to reshape the mode(s) with respect to that in the pre-existing waveguide. The projections of the modes from the preexisting waveguide onto the modified section can be controlled by the offset distance (S) as well as by the strength induced to form the refractive index modification.

An example embodiment further provides a method of refractive index modification, that when applied over sufficient length, can adiabatically modify the mode profile along a length of the waveguide propagation direction and thereby advantageously enhance or reduce modal mismatch loss. Such modal mismatch loss arises at abrupt waveguide transitions, for example, where the MMI waveguide interfaces with the pre-existing waveguide sections. Further, the transition of power from modes in the pre-existing waveguide to modes in the MMI section, as well as from the MMI section to the output pre-existing waveguide, is governed by an overlap integral.

In one approach of adiabatic mode tuning of a waveguide section, FIG. 3(c) and FIG. 3(d) provides a gentle scaling of the refractive index from low to high contrast, beginning on the left and right ends of the MMI waveguide, and reaching a maximum contrast in the middle of the MMI waveguide section for modified structures positioned both inside and offset, respectively, by a distance (S) to the pre-existing core waveguide. The high to low refractive index scaling is tuned by exposure control to enable an adiabatic transition towards smaller and more confined modes at the center position of the MMI section. Alternatively, the refractive index modification 3 can be gently scaled from higher refractive index on the left and right ends of the MMI waveguide to reach a minimum in the middle of the MMI waveguide as shown in FIG. 3(e), providing an adiabatic transition to larger and less confined modes at the center of the MMI section. The adiabatic tuning may also be obtained by scaling the cross-sectional size of the modification tracks 3 in FIG. 3(c), 3(d), and 3(e), where increasing/decreasing refractive index may be exchanged with increasing/decrease track diameter or increasing/decreasing track area. Any combination of these changes to modification track, as presented along the length of the pre-existing waveguide, can be provided in example embodiments to increase or decrease the overall guiding strength of this waveguide and provide adiabatic mode tuning to advantageously control the MMI device properties. The example embodiment also provides that the changes to the modification tracks can be asymmetric and/or non-uniformly distributed along the path of the pre-existing waveguide. Gentle scaling of the refractive index change and the diameter or the area of the modification track can be generated by controlling the exposure parameters of the radiation, for example, by adjusting the power level or the relative scan speed in the direct write process, or changing the number and relative positions of overlapping or partially

overlapping tracks as depicted in Fig. 2(h) and Fig. 2(i), respectively. These methods of exposure control are well known by a practitioner of the art. Another aspect of an example embodiment is the ability to independently control the projection of modes at the input and output interfaces, using a transverse scanning sweep to vary the offset distance (S) with propagation along the MMI waveguide section. For example, a uniform refractive index modification 3 offset by a distance (S) from the pre-existing core waveguide 1 bends to meet the center of the pre-existing core waveguide 1 along an S-bend path as shown in FIG. 3(f), or starts in the center of the pre-existing core waveguide 1 and bends along an S-bend path to extend to an offset distance (S) away from the pre-existing core waveguide 1 as shown in FIG. 3(g). This approach can be combined at both the input and output sections where the uniform refractive index modification 3 starts outside the preexisting core waveguide 1 at an offset distance (Si), proceeds into and back out of the pre- existing core waveguide 1 at an offset distance (S₂) following an S-bends path as shown in FIG. 3(h). The values for Si and S₂ may be the same or different. In another embodiment, the uniform refractive index modification 3 can be extended outside of the waveguide using a straight segment as shown in FIG. 3(i). As a non-limiting example for the adiabatic mode shaping at the output of an MMI a refractive index modification 3 can begin positioned in the center of the pre-existing core waveguide 1 and then follow an S-bend path that extends into a straight section, having a refractive index profile that is scaled from high to low index contrast, at a position offset by a distance (S) from the pre-existing core waveguide 1 as shown in FIG. 3(j). The input modes of an MMI can also be adiabatically reshaped in this way as show in FIG. 3(k), where a straight refractive index modification section 3, with a refractive index profile that is scaled from high to low index contrast, is positioned at a position offset by a distance (S) from the pre-existing core waveguide 1 and then follows an S-bend path that extends into a straight section in the center of the pre-existing core waveguide 1. An example embodiment provides the input and output waveguide ports to the radiation- formed MMI waveguide section can also be nonidentical, for example, where a single mode waveguide is fused to a multimode waveguide, as depicted in the example in FIG. 3(1). The choice of input and output waveguides is not limited to the example shown in FIG. 3(1) and could also include connecting to planar lightwave circuits for example.

The various types of radiation modified refractive index tracks 3 at the input and/or output of an MMI depicted in FIG. 3(a) through FIG. 3(k) can advantageously tune the MMI beat length, the waveguide birefringence and hence the polarization beat length, as well as the spectral, modal, and power transfer properties, while adiabatically maintaining constant power in the modes. In this way, the MMI section can have applications in mode shaping and mode filtering. The multimode phenomena resulting from the example embodiments can be understood and explained by MMI theory (Soldano et al., J. Lightwave Technol. 13 (4), pp. 615-627 (1995)). The number of modes allowed to propagate in a waveguide or MMI waveguide is controllable, and is generally known to increase with an increase in the physical cross- sectional size of the waveguide as well as an increase in the refractive index contrast between the waveguide and cladding regions. Amongst a total of Q modes that are designed to propagate in an MMI waveguide 8, each mode q (q = 0, 1, 2, ... , Q-l) will propagate with a specific propagation constant (β_¾) such that an overall transverse intensity profile at the input port can reform periodically to reproduce as direct (bar) and mirrored (cross) images as well as multiple images of the input profile that follows with the self-imaging principle of the Talbot effect.

Any mode (q = 1...Q) will beat with the fundamental mode (q = 0) on a beating distance that scales inversely with the difference in the propagation constants, (βο-Pq). Generally, modal dispersion will cause a dephasing amongst the various pairs of the MMI waveguide modes, leading to the eventual blurring of the self images, particularly for the combination of high mode capacity waveguides with low index contrast (Z. Jin and G.D. Peng, Opt. Commun. 241 pp. 299-308 (2004)). This condition is relaxed in high index contrast slab waveguides such that general, paired, and symmetric interference in an MMI device provides exact self-images at distances of 3nL_n, nL_n, and 3/4nL_n, respectively, where n is an integer (n = 0, 1, 2, ...) with even and odd values of n resulting in direct and mirrored self-images, respectively. The MMI beat length (L„) is defined as L„ = π/(Δβ), where Δβ is the difference in the propagation constants of the two lowest order modes (βο-βι). N-fold images of the guided transverse intensity pattern will then appear at distances of 3«L„/N, «L„/N, and 3/4«L„/N, respectively, for the cases of general, paired, and symmetric interference. (Soldano et al., J. Lightwave Technol. 13 (4), pp. 615-627 (1995))

When the MMI section 8 is sandwiched between an input (Port 1 in FIG. 4(a)) and output (Port 2 in FIG. 4(a)) waveguide that support a total of P and R modes, respectively, the total power coupling efficiency (η) of light from all the input modes (index p = 0, 1, 2, ... , P-l) of Port 1 to all of the R output modes (index r = 0, 1, 2, ... , R-l) of Port 2 may be represented by Equation (1), which is an extension from Mohammed et al. (Mohammed et al., J. Mod.

Opt. 55 (7), (2008))

(Equation 1)

The field excitation coefficient (α_Μ) from mode p with transverse mode field distribution Ψ_ρ to mode q with transverse mode field distribution Ψ_ρ can be represented by Equation (2)

(Soldano et al., J. Lightwave Technol. 13 (4), pp. 615-627 (1995)):

(Equation 2)

It should also be noted that power may also be coupled to the radiating modes, which have not been accounted for in Equation (1) and thus lead to power coupling efficiency falling below 100%. The overall power coupling efficiency will therefore depend on the a_m and a_v values, which may now be manipulated by the radiation modified tracks 3 and patterns that are preferentially positioned and/or tapered in the MMI waveguide section, for example, as described in the embodiments presented in FIG. 2 to FIG. 3.

An aspect of an example embodiment applies a radiation exposure to modify the number of modes (Q) permitted to propagate in a section of a pre-existing core waveguide and thereby create an MMI device as well as to manipulate the values of the field excitation coefficients for propagating into (α_Μ) and out of (a_¾r) the MMI device. The unmodified pre-existing core waveguide 1 sections on either side of the MMI waveguide section 8 serve as both the input (Port 1) and output (Port 2) waveguides to form an MMI device as depicted in FIG. 4(a) and FIG. 4(b). The MMI section can be positioned parallel (FIG. 4(a)) or at an angle (FIG. 4(b))

to the pre-existing waveguide to control the magnitude of the input and output coupling.

Additional ports can be connected to the MMI waveguide section as in FIG. 4(c) where the

radiation-induced refractive index modification 3 is extended along an S-bend path away

from the pre-existing waveguide 1 to form an additional output port (Port 3). More generally,

the MMI waveguide section can be extended to connected to N input and M output ports as

shown in FIG. 4(d).

As a non-limiting, illustrative example, a section of a single mode waveguide can be

modified by radiation to increase the number of guided modes to two (Q = 2). The

unmodified waveguide sections on either side of the radiation modified section serve as the

input and output ports as an example of the configuration shown in FIG. 4(a), where for this

example P = R = 1, and Q = 2. For this case, the total power coupling efficiency from the

input waveguide through the MMI waveguide and into the output waveguide can be

simplified from Equation (1) as follows:

η(Δ

For a special case of complete and equal coupling to the guided modes (|αο,ι| = |«i,o|) the

power coupling efficiency in Equation (3) will oscillate fully between 0 and 1 as a function of

the MMI waveguide length (L) as plotted in FIG. 5 for three different wavelengths, where

λ₁ < λ₂ < λ₃. The wavelength dependent power transfer of this MMI device permits one to

define different wavelength filter functions with variable waveguide length, for example,

passing λ₁ and λ₂ while rejecting λ₃ for an MMI waveguide length of 2.0. Here, λ₃ has been

lost to radiation or cladding modes and no longer propagates in the core waveguide.

As a result of the dispersion in the p_q values and the field excitation coefficients, the power

coupling efficiency may also have a strong wavelength dependency, η(λ), as seen in FIG. 6

for three examples of different MMI device lengths, where Li > L₂ > L₃ For the case of an

MMI waveguide length of L₂, a bandpass and band-reject filter that demonstrates a

wavelength division multiplexing (WDM) device is noted at wavelengths of 1550 nm and

1375 nm, respectively. Comparing with the other MMI waveguide lengths (Li and L₃), the

pass and rejection bands of the filters as well as their bandwidth may be controlled by this

MMI waveguide length. Since the power coupling efficiency (η) can vary from zero to 100%, couplers and attenuators may be designed at any wavelength by changing the length of the MMI waveguide section. Shorter MMI waveguide lengths may be applied advantageously for broader band spectral responses as well as to minimize any polarization dependence if there is any birefringence in the MMI waveguide.

In another aspect of an example embodiment, a birefringent MMI waveguide section can be introduced by the radiation-formed refractive index modification, or be inherent in the original waveguide design (e.g. polarization maintaining fiber or silica-on-silicon planar lightwave circuits), or be present in the waveguide material (e.g. lithium niobate or calcite). Any form of such birefringence removes the polarization degeneracy to create two distinct

oTE linearly polarized modes (e.g. TE and TM), each with unique propagation constants (^μι and ΤΜ J E T TM

μ<ι ) and hence unique MMI beat lengths and ). This birefringence may also lead

TE TE

to polarization sensitivity in the field excitation coefficient ΡΛ and P,Q for TE and TM modes, respectively.

In the non-limiting example of an MMI device in which two modes (Q = 2) are supported in the MMI section and only single mode input (P = 1) and output (R = 1) modes are permitted, the introduction of birefringence will cause the power coupling efficiency in Equation (3) separate into TE (solid line) and TM (dashed line) polarized components, ητΕ and ητκι , that follow Equations 4(a) and 4(b) and are plotted as a function of the MMI waveguide length in FIG. 7(a). ηΤΕ(ΔβτΕ)— O(o, l TE) + ^a(l,0 TE) + ^2a(0, l T\E) ^a(l ,0 TE) ^cos (^T E L) (Equation η_ΤΜ (Αβ_ΤΜ) — a,o₀,l₁ T_TM_M)₎ ++ ^aa(,l₁ ,0₀ T_TM_M)₎ ++ 22aaf₍o₀, l₁ T_TM_M)₎ ^aa(₍li,_,0o TTMM) ^C0S(^TML) (Equation 4b)

When both the TE and TM polarizations are simultaneously present in the MMI device, the resulting transmission is the superposition of the individual TE and TM transmissions. For the case of unpolarized light launched into the fundamental (p = 0) mode of the input waveguide with equal amounts of TE and TM polarization, the total power transfer (T|TOTAL) of the MMI will oscillate periodically as a function of MMI waveguide length according to

Equation (5) with the average beta difference

as shown in FIG.

7(b). VTOTAL = VTE + VTM (Equation 5)

The MMI waveguide birefringence causes a periodic beating with a polarization beat length of (L_p = 2π/(ΔβχΕ - ΔβτΜ) as the phase of the TE and TM polarization modes progressively move in and out of phase periodically with the MMI waveguide length. A polarization filter or splitter may be defined for MMI lengths where the two polarizations modes have

accumulated a net (2m+\) phase delay, where m is an integer (m = 0, 1, 2,...). For the present case with only two modes (Q = 2), this condition occurs when one polarization is bar self-imaged and the other is cross self-imaged according to the the condition

where u and v are integers and u+v = odd. In other words, this condition occurs when one of the polarization modes (e.g. TE) coupled with maximum efficiency from the MMI back into the single mode section, while the other mode (e.g. TM) is coupled into radiations mode, or cladding modes.

For example, a minimum length (m = 0) TE polarization pass filter may be defined at point C in FIG. 7(b), where ^{u v} , and ^½ are 14, 13, 2.8 rad/mm and 2.6 rad/mm, respectively, yielding an MMI length of L_p/2 = 15.71 mm. Alternatively, the shortest lengths at which a 3 dB or 100% coupler can be achieved, possibly with minimal birefringence dependence, are also labeled on FIG. 7(b) as points A and B, respectively.

Application of the methodology

The following non-limiting examples demonstrate the application of the disclosed

methodology of modifying the number of modes and/or reshaping the modes in an SMF. As mentioned previously, permanent refractive index modifications can be formed with various forms of radiation as well known by a practitioner of the art. One exemplary example of such radiation comes from lasers, particularly laser with short pulse durations less than 10 ps that have the advantage of producing localized 3D modifications as contained near or within the focal volume. Such lasers are exploited here for the purposes of constructing an MMI waveguide, tailoring the number of modes and mode shapes to control the amount,

polarization and spectrum of light coupled through the MMI device. Examples of MMI devices are presented to serve as polarization selective taps, in-line polarizers, couplers, and wavelength filters. In the following examples, a ytterbium-doped fiber chirped pulse amplified femtosecond laser (IMRA America; uJewel D-400-VR) set to 500 kHz pulse repetition rate and frequency doubled to 522 nm and 200 fs pulse duration was employed to create permanent refractive index modifications in the pre-existing core and cladding region of SMFs. The optical fiber was stripped of the acrylate buffer and mounted onto air-bearing motion control stages (Aerotech ABLIOOO) having 2.5 nm resolution and 50 nm repeatability to translate the sample with respect to the focused laser beam position. The core waveguide of the stripped fiber was aligned with respect to the laser focus to ±1 μηι accuracy over 10 cm fiber length by monitoring the back-reflected laser beam profile from the fiber surfaces. Accurate and undistorted positioning of the laser focus into any region of the cylindrically shaped fiber was made possible with oil-immersion lens focusing into a fiber clamped taut with a suspension tool. Here, focusing with a ΙΟΟ^χ, 1.25 numerical aperture (NA) oil-immersion lens overcame both spherical and astigmatic optical aberrations at the cylindrical glass-air interface while also confining the laser interaction more tightly to create higher contrast and smaller, more symmetric refractive index structures.

It is important to re-emphasize that the following non-limiting examples serve as illustrative examples that put the disclosed methodology into practice. The radiation source used here for refractive index modification is from a femtosecond pulsed laser, however, this could be from any laser or source of radiation capable of modifying the refractive index of a material as mentioned previously. In addition, a SMF is selected here as the pre-existing waveguide, however, such a pre-existing waveguide can come in many different forms, sizes, materials and can contain any number of pre-existing modes as previously mentioned. As well this pre- existing waveguide can also be formed by the same mechanism suggested here for the refractive index modification. In other words, this waveguide can be produced by the same laser used to further inscribe the modification described here.

Example 1

In an example embodiment, the femtosecond laser pulses were used to create refractive index modifications near to the center (< ±1 μηι) of the core waveguide of SMF for the purpose of defining a multimode interference waveguide section. The number of modes and their associated propagating constants in the resulting MMI waveguide structure were assessed by modulating the laser writing beam to form a strong Bragg grating structure and permit the spectral recording of Bragg resonances of the relevant propagating MMI modes. A laser exposure of 130 nJ energy per pulse at 500 kHz repetition rate, square-wave modulated by an acousto-optic modulator with 60% duty cycle to generate 500 Hz burst trains which were focused through a ΙΟΟ^χ, 1.25 NA lens and translated at 0.268 mm/s speed inside the waveguide, was used to generate an MMI waveguide section of 19.5 mm length together with a fiber Bragg grating with 536.3 nm grating periodicity (Λ). The resulting unpolarized transmission (T) and reflection (R) spectra recorded through the MMI-embedded fiber are shown in FIG. 8(a). Here, three Bragg stopbands have been identified in both reflection and transmission that correspond to fundamental (LP₀i) and first higher-order mode (LPn) reflections as well as a cross-coupling (LPoi→ LPn) reflection, found at 1551.4 nm, 1549.6 nm, and 1547.8 nm wavelengths, respectively. One also finds cladding mode resonances. Hence, two modes are confirmed to be propagating in the MMI section. The existence of two guiding modes is further noted at 1560 nm wavelength by the preferential excitation of the LPoi (FIG. 8(b)) and LPn (FIG. 8(c)) mode field intensity profiles by varying the input fiber position when end-fired directly into a cleaved MMI section.

When probed with linearly polarized TE and TM light, the LPoi, LPn and LPoi^→LPn Bragg stopbands of the same MMI device (FIG. 8(a)) were each found to split into two separate TE and TM polarized stopbands as seen in the spectrum inset of FIG. 8(a). The wavelength separation between the TE and TM modes was measured to be ·½ ^{~~ =} 0.44 nm, 0.16 nm, and 0.18 nm for the LPoi, LPn and LPoi^→LPn modes, respectively. The Bragg formulae, λ_Β = 2n_eff0iA, λ_Β = 2n_effnA, and λ_Β = (n_{eff 0}i+ n_eff η)Λ, provides birefringence values of 4.1 l0^"4, 1.5 lO^"4 and 1.7 lO^"4 respectively, for the LP₀i, LPn and LP₀i^LPn modes. This birefringence is induced from the anisotropy of the laser- formed structure and the stress of the refractive index modification on the pre-existing core waveguide (US Pat. No 7,689,087, Fernandes et al., Opt. Express 20 (22), pp. 24103-24114 (2012)). The

birefringence and hence the polarization beat length of the MMI device is provided to be further controlled with the femtosecond laser waveguide exposure conditions such as power, focusing numerical aperture, scan speed, and polarization. In the latter case, perpendicular polarization can align nanogratings parallel with the waveguide to induce a strong form birefringence (Mills et ., Αρρί Phys. Lett. 81 (2), p.196 (2002)). Further, laser modification stress tracks (US Pat. No 7,689,087, Fernandes et al., Opt. Express 20 (22), pp. 24103-24114 (2012)) can be formed around the waveguide structures which is also provided to control the birefringence and polarization beating properties of the MMI.

Example 2

In another aspect of an example embodiment, femtosecond laser pulses with 130 nJ energy per pulse at 500 kHz repetition rate were focused through a ΙΟΟ^χ, 1.25 NA lens and scanned at a constant speed of 0.268 mm/s to create a uniform refractive index modification track 3 parallel to the pre-existing core waveguide of an SMF at an offset distance of S = 6 μηι (FIG. 3(b)) away from the center of the pre-existing core waveguide 1 to form a MMI waveguide section 8 between two unmodified SMF sections. The normalized optical transmission (solid line) through the resulting MMI device was recorded in-situ at a 1550 nm wavelength as a function of the MMI waveguide length and is presented in FIG. 9(a). In this case, the offset distance (S) of 6 μηι proved a nearly balanced power coupling (i.e., a_0,o= <¾i) of the input single mode light (Port 1) into nearly equal power levels into each of the LPoi and LPn modes of the MMI section. When this MMI propagating light was coupled back to the SMF output (Port 2), deep modulations reaching almost to zero amplitude were observed as predicted by Equation (5). A small 0.43 dB insertion loss is identified on the first instance of laser writing (zero length MMI) to arise from cladding and/or radiation mode losses occurring at the abrupt starting and ending point of the MMI waveguide section. The data in FIG. 9(a) also followed an exponential decay function (dashed line) of 0.015 dB/cm, owing to the scattering loss of guided light overlapping with the laser-formed track. This loss is much smaller than the 0.65 dB/cm otherwise seen from guiding in a single laser track formed in fused silica with the same exposure condition but is much larger than the pre-existing core waveguide loss of 0.2 dB/km The inset in FIG. 9(a) plots the measured transmission efficiency (solid circles), normalized to the loss, for L = 8.4 mm to 23.3 mm MMI length. By accounting for these losses, a calculated efficiency (solid line) according to Equation 5 is found to well represent the observed data, confirming the expected MMI response. This close representation was found for differences in the polarized propagation constants, Δβ_ΤΕ = 5.78 rad/mm and Δβ_ΤΜ= 5.36 rad/mm, yielding an average beta difference of Δβ_Ανο = 5.57 rad/mm, and an MMI beating length of L_n = 0.56 mm. The polarization beating of L_p = 14.9 mm as identified in FIG. 9(a) matches with the expected L_p = 2π/(ΔβτΕ - Δβτΐνΐ) = 14.96 mm value. In order to minimize the device losses, polarization sensitivity, and wavelength sensitivity, one may consider the application of short-length MMI sections as depicted by the gray shaded area in FIG. 9(a). The transmission efficiency over this length (8.4 mm) is replotted on an expanded scale in FIG. 9(b). Point C shows the minimum length at which Δβ_ΤΕ - Δβ_ΤΜ has evolved to put the TE and TM modes in opposing bar and cross positions. In this example the self-imaging lengths for TE and TM polarizations are 0.543 mm and 0.586 mm, respectively, and do not yield integer values for u and v according to the condition

T E T Ivl

^UL-K = vL^ _^ where u+v = odd. However, this condition may be found at select wavelengths depending on the overall dispersion of the MMI waveguide section.

T TE i

Alternatively, the exposure conditions can be tuned to vary the and L_n values such that the condition uL_n = vL_n and u+v = odd are met at any selected wavelength.

In FIG. 9(b) the length corresponding to the first MMI beat length at L_n = 0.68 mm takes the transmission efficiency through the MMI device from 100% to approximately 3% at Point B, while half this length defines a 3 dB attenuator at Point A. In this way, MMI devices with controllable attenuation can be designed that will have little polarization and wavelength sensitivity in contrast with the polarization splitting seen at Point C. In an example embodiment, it is also provided that the placement of additional output waveguides, 0_1; 0₂, . . . OM as represented in FIG. 4(d), may result in formation of N ^χ M couplers of controllable coupling and polarization ratios.

Example 3

In extending on the prior example, the offset distance (S) selected between the pre-existing waveguide core and the radiation-modified track is provided to strongly vary the values of the field excitation coefficients (α_ΡΛ and a_v), MMI beating length (L,,), and the birefringence beating length (L_p). The following non-limiting example applies the same exposure conditions applied in Example 2 to create a uniform refractive index track 3 positioned parallel with and closely centered (S ~ 0) within the pre-existing core waveguide 1, creating the device as depicted in FIG. 3(a) that positions an MMI waveguide section between two unmodified SMF sections. The normalized optical transmission (solid line) observed through the resulting MMI device was recorded in-situ at a fixed 1550 nm wavelength as a function of the MMI waveguide length and is presented in FIG. 10. For a laser modification track precisely centered and symmetric inside of the pre-existing waveguide, only coupling to the symmetric LP₀i mode would be expected, yielding a zero field excitation coefficient (a 0,1 = 0) from the input LP₀i mode to the LPn mode in the MMI waveguide section. However, in this example, an asymmetric waveguide profile together with the ±1 μηι uncertainty in the centering alignment enabled an asymmetric coupling from the LP01 input mode (Port 1) into the LP 11 MMI waveguide mode. As a result, the transmission through the MMI section into the output SMF (Port 2) yielded weaker interference contrast, with the first half oscillation attenuating to 27% at the first MMI beat length of ]_,„_□= 0.170 mm. A stronger 0.71 dB insertion loss is inferred to have coupled light to cladding or radiation modes as compared with the 0.43 dB case in Example 2 (S = 6 μηι). The data in FIG. 10 also followed an exponential decay function (dashed line) of 0.045 dB/cm, showing a three-fold increase in scattering loss as compared with the case in Example 2 (S =6 μηι). Stronger overlap of the light in the LP01 and LPn modes are provided when the higher loss laser-formed refractive index track 3 is positioned near the pre-existing core waveguide 1 center (S = 0) in comparison with the S = 6 um offset case of Example 2. The inset spectrum shows the measured transmission efficiency (solid circles), normalized to the loss, and the calculated efficiency (solid line) according to Equation 5 for MMI waveguide lengths of L = 1.71 mm to 4.44 mm. The positioning of the refractive index modification directly inside the germanium- doped core region gave way to much larger differences in the propagation constants of Δβ_Ανο = 18.49 rad/mm, resulting in a shorter observed MMI beat length (L,, = 0.170 mm). The centralized laser structuring also increased the birefringence, seen from the large difference in the Δβχ_Ε = 19.64 rad/mm and Δβ_ΤΜ = 1 .34 rad/mm values as obtained from the theoretical representation of the data in the inset spectrum (FIG. 10). The polarization beating length of L_p = 2π/(Δβ_ΤΕ - Δβ_ΤΜ) = 2.73 mm in FIG. 10 presents a ~5.5-fold decrease in the polarization beat length as compared with the case in Example 2 (S = 6 μηι) which is beneficial to produce shorter and hence more broadband polarization sensitive MMI devices. The fast MMI beat frequency and hence shorter MMI beat length also results in shorter MMI lengths for 3 dB and maximum value coupling lengths (points A and B in FIG. 7(b)). However, the unbalanced coupling of light into and out of the MMI waveguide modes limits the maximum coupling to 27% in this example, which can be tuned by controlling the amount of light coupled into and out of each of the MMI modes using the embodiments presented in FIG. 2 and FIG. 3. Example 4

The MMI beat length (L„), beating frequency (Δβ_Ανο) and field excitation coefficients (a_PA and a_v) of the transmission through the MMI device can be advantageously controlled, for example, by varying the center to center offset distance (S) (FIG. 3(b)) as well as the angle (FIG. 3(i)) between the laser formed refractive index modification and the SMF core waveguide. In another example embodiment, a uniform refractive index modification track 3 was formed at an angle of 0.24 mrad to a pre-existing SMF core waveguide 1 as shown on the left side of FIG. 3(i). The same laser exposure conditions in Example 2 were applied to begin the track at an approximate offset of S = 12 μπι, and cross through the center of the pre-existing core waveguide to a symmetric offset position of S = -12 μηι on the other side of the core waveguide, resulting in a continuously varying offset distance (S) along a 100 mm segment of the SMF. The normalized optical transmission of unpolarized light at 1550 nm wavelength through the SMF core waveguide was recorded in-situ during laser writing along the vertical axis, and while scanning in the horizontal (xy) and vertical (xz) plane at the targeted angle of 0.24 mrad, yielding the results in FIG. 11(a) and FIG. 11(b), respectively. The zero offset distance corresponds to the laser focus positioned at the center of the SMF core waveguide. To correct for the centering of the laser focus positioning, the abscissa where shifted in FIG. 11(a) and FIG. 11(b) by -0.78 μηι and -3.77 μηι, respectively, in order to place the maximum value of Δβ_Ανο to the expected center waveguide position at S = 0 μηι offset. These corrections fall within the ±1 μηι random centering error as well as the onesided ~4 μηι vertical shift of the waveguide mode position found with respect to the measured focal plane of the laser. The MMI beat frequency is fastest when laser writing at the center of core waveguide (i.e. the zero offset positions) and is also symmetric both vertically (FIG. 11(b)) and horizontally (FIG. 11(a)) about this point. Similarly, the waveguide birefringence is highest with the laser modification centered within the preexisting SMF core waveguide as seen by the short polarization beat lengths (L_p ~ 2.7). The modulation depths also follow the trend of decreasing with the offset distance applied either horizontally (FIG. 11(a)) or vertically (FIG. 11(b)) at the start position of the MMI. First cycle modulation to is approximately 79% with 7.5 μηι vertical offset (FIG. 11(b)) decrease to 29% at 10.9 μηι horizontal offset (FIG. 11(b)) owing to the weaker coupling to the LPn mode with increasing offset distance. The weak modulation amplitude found after the laser modification reaches near the center of the SMF core region (at offset positions greater than - 1 μηι in FIG. 11) is provided by Equation 2 when the a_1;0 field excitation coefficient falls dramatically for coupling of the asymmetric LPn MMI mode to the LPoi fiber core mode. Three sets of transmission responses similar to each of FIG. 11(a) and FIG. 11(b) were recorded and analyzed to generate MMI beating frequency values as a function of the track offset distance (S), yielding the data plotted in FIG. 12(b) and FIG. 12(d), respectively for the horizontal (xy-plane) and vertical (xz-plane) planes. The difference between Δβ_ΤΕ and Δβ_ΤΜ is also plotted in FIG. 12(a) and FIG. 12(c), respectively for the horizontal (xy-plane) and vertical (xz-plane) planes. The two vertical dashed lines indicate the boundary between the SMF core waveguide and the cladding region. The MMI beat frequency (Δβ_Ανο) is seen to be have a Gaussian- like shape with similar values for each the horizontal and vertical scanning offset, scaling from low values of 1.8 rad/mm at large offsets of 12 μπι, to values peaking at 23.5 rad/mm for the centrally positioned laser track at S = 0. The vertically elongated laser modification tracks here are likely responsible for broadening the profile in the vertical offset case (FIG. 12(d)) over the horizontal case (FIG. 12(b)). For these examples, the MMI beat frequency follows an exponential fall off with offset distances (S) greater than approximately ±8 μηι from the center, representing approximately the transition from MMI theory (|S| < 8 μηι) to a directional coupler as defined by coupled mode theory (|S| > 8 μηι). This transitional position will change according waveguide design and material selection as well known by a practitioner of the art. The difference between Δβ_ΤΕ and Δβ_ΤΜ is also seen to be have a Gaussian-like shape with similar values for each the horizontal and vertical scanning offset, scaling from low values of -0.8 rad/mm at large offsets of 12 μπι, to values peaking at -2.5 rad/mm for the centrally positioned laser track at S = 0 and above the above the core waveguide for the horizontal and vertical offset distances, respectively.

The results presented in FIG. 11 and FIG. 12 were obtained for a single refractive index modification track formed in an SMF for a fixed set of laser and focusing parameters. An example embodiment provides that the values of Δβ_Ανο and Δβ_ΤΕ - Δβ_ΤΜ can be preferentially tuned with the laser parameters (e.g., power, polarization, pulse repetition rate, wavelength, scan speed), as expected by a practitioner of the art. The the amount of light coupled into and out of each of the MMI modes can also be independently tuned by the methods presented in the embodiments contained in FIG. 2 and FIG. 3. An example embodiment provides the radiation- formed MMI devices can be equally applied to other waveguide shapes and materials including for example single mode and multimode waveguides in fibers and planar lightwave circuits.

Example 5 In another example embodiment, a MMI waveguide can be formed in a section of a SMF to form a wavelength filter. Using the same laser exposure conditions as in Example 2, a uniform refractive index modification track 3 was formed parallel to the pre-existing core waveguide 1 of an SMF (as seen in FIG. 3(b)) at an offset distance (S) of 5 μηι FIG. 13 shows the unpolarized spectra of two such devices with MMI modification track lengths of 4.5 mm (Li) and 10 mm (L₂). The MMI device with a length of 4.5 mm produced a 251 nm broad passband centered at 1330 nm and a 235 nm reject-band centered at 1550 nm. The longer (10 mm) MMI device produced four passbands (1220 nm, 1310 nm, and 1450 nm, 1650 nm) and three reject-band (1255 nm, 1380 nm, and 1530 nm) over the same 1200 nm 1700 nm spectrum. The rapid wavelength oscillations (1320 nm to 1550 nm) in the L = 10 mm long device (solid line) are a result of cladding mode losses generated by a 1555 nm

Bragg grating waveguide embedded outside the MMI device and can be avoided to provide a more smooth filter profile. The extinction ratio between the pass- and reject-bands in these examples reaches up to 8 dB, which is limited here by the laser-induced birefringence. Laser exposure methods well known by a practitioner of the art may be employed here to reduce birefringence preferentially and provide higher contrast MMI filters with low polarization dependence.

Example 6 In another example embodiment, a birefringent MMI waveguide section was laser-written into a section of an SMF with an MMI waveguide length designed to form an in-line optical fiber polarizer (Point C if FIG. 7(b)). Using the same laser exposure conditions as in Example 2, except for a reduced scan speed of 0.15 mm/s, a 8.74 mm long uniform refractive index modification track 3 in the cladding region 2 of an SMF positioned parallel to and at an offset distance (S) of 5 μηι away from the center of the pre-existing core waveguide 1 as shown in FIG. 3(b). These conditions provided equal power balancing at -1400 nm wavelength. The normalized optical transmission spectra of TE and TM polarized light through this MMI device are presented in FIG. 14. The strong modulation on -50 nm period arises from a strong modal dispersion when accumulated over this long 8.74 mm length. There are several wavelengths at which the birefringent dependent differences in Δβ_ΤΕ and Δβ_ΤΜ have evolved to closely align the TE and TM modes in opposing bar and cross positions which occurs when ^ν^π , with u+v = odd. The polarization extinction ratio for these cases is strongest (24 dB) at 1403 nm where an extinction ratio greater than 20 dB over a bandwidth of 3 nm is recorded. The polarization extinction ratio can be tuned by controlling the amount of light coupled into (a_p,_q) and out (a_¾r) of each of the MMI modes, for example, as provided by the various embodiments presented in FIG. 2 and FIG. 3. The bandwidth of the polarizers can be tuned broader or narrower by various means, for example, by decreasing or increasing, respectively, the MMI waveguide length, or by increasing or decreasing, respectively, the

MMI waveguide birefringence. Such birefringence may be controlled by various means, such as by addition of laser- formed stressing bars (US Pat. No 7,689,087, Fernandes et al., Opt. Express 20 (22), pp. 24103-24114 (2012)) or by alignment of nanograting (Mills et al., Appl. Phys. Lett. 81 (2), p.196 (2002)) according to the polarization orientation of the femtosecond writing laser with respect to laser- formed modification track, or by inherent birefringence in the waveguide structure or material. It is also provides that an additional waveguide could be positioned at the output of the MMI waveguide section, as represented in FIG. 4(d), to collect the MMI light with polarization that is cross self-imaged and otherwise rejected by the SMF core waveguide, thereby forming a polarization splitter.

Example 7

In another example embodiment, a balanced 3 dB MMI coupler has been formed by designing the MMI length (L) to stop at Point A in FIG. 7(b). Using the same laser exposure conditions as in Example 2, a 0.099 mm long uniform refractive index modification track 3 was formed parallel to the pre-existing core waveguide 1 of an SMF at an offset distance (S) of 6 μηι. The refractive index track was extended with a 30 mm radius S-bend to guide the light into an isolated spur waveguide positioned 40 μηι away and parallel with the preexisting core waveguide which thus formed an additional output port (Port 3) as represented schematically in FIG. 4(c). The optical transmission spectra for unpolarized light for the through-port SMF core waveguide (solid line; Port 2) and cross-port femtosecond laser- formed waveguide (Port 3; dashed line) are shown from 1350 nm to 1700 nm wavelength in FIG. 15. Vertical and horizontal dotted lines demark a representative example of a balanced 3 dB MMI coupler providing 38% transmission into each output port (after accounting for losses) at 1486.5 nm wavelength. This balanced output extended over a bandwidth of 57 nm for a balanced power coupling within 5% into each of Ports 2 and 3. Because of dispersion in the modes and in the coupling coefficients of the MMI device, this splitting ratio (Port 3: Port 2) is seen to vary with wavelength from 45: 17 splitting at 1370 nm to 25:65 splitting at 1650 nm wavelength in FIG. 15. It is provided that the coupling ratio at any wavelength can be tuned flexibly by controlling the length and separation of the MMI devices as well as the values of the laser radiation exposure parameters. For example, shorter MMI waveguide lengths (L) may be applied advantageously for providing broader band spectral responses as well as for minimizing any polarization dependence in the case of birefringent MMI waveguide devices. For this case, a shorter MMI beat length (L„) (i.e. larger MMI beat frequency) is expected by decreasing the offset distance (S) as shown in FIG. 12.

Example 8

In another example embodiment, a birefringent MMI waveguide section was laser-written into a section of an SMF and connected via an S-bend to a laser- written waveguide as shown in FIG. 4(c), to form a polarization selective tap (PST). Using the same laser exposure conditions as in Example 2, a 7.519 mm long uniform refractive index modification track 3 was formed parallel to the pre-existing core waveguide 1 of an SMF at an offset distance (S) of 6 μηι. As in Example 7, the refractive index track was extended with a 30 mm radius S- bend to guide the light into an isolated spur waveguide positioned 40 μηι away from the preexisting core waveguide which thus formed an additional output port (Port 3) as represented schematically in FIG. 4(c). The MMI waveguide length was designed to be at Point C (at L = 8.4 mm) in FIG. 9(b), but was reduced to a shorter length of 7.519 mm to compensate for the additional MMI mode beating expected along the beginning part of the S-bend where the two waveguides are separating slowly with distance.

Linearly polarized TE and TM modes were independently launched into the input port (Port 1) and collected from the output ports (Port 2 and Port 3). FIG 16 shows the spectra of the TE and TM coupling ratios defined here as: p ^{Ppo T}* j (Equation 6) rpORTI + r PORTS I where PPORT2 and PPORT3 are the powers measured in Port 2 and Port 3, respectively. The spectra of coupling ratios for the TE and TM polarization modes reveal several wavelengths (1355 nm, 1443 nm, and 1550 nm) where the birefringence in the MMI beam frequency, ΔβχΕ - ΔβχΜ, has evolved to align the TE and TM modes in opposing bar and cross positions and thus offer a strong polarization tapping of up to 50% over a large 25 nm bandwidth. The percentage of such polarization tapping can be tuned by controlling the amount of light coupled in (α_ΡΛ) and out (a_¾r) of each of the MMI modes, for example, by employing the various embodiments presented in FIG. 2 and FIG. 3, or by controlling the length and separation of the MMI devices or by controlling the the values of the laser radiation exposure parameters. Extending this example to a polarization splitter is expected when the coupling into the MMI modes are balanced (a_VA = a_v) for each polarization to provide up to 100% polarization tapping in the lossless case.

In an example embodiment, there is provided a multi-port MMI device consisting of more than one waveguide, comprising isolated or weakly coupled (e.g. directional coupler) preexisting waveguides, or strongly coupled pre-existing waveguides (e.g. pre-existing MMI), formed from the pre-existing optical waveguide(s), the modified optical waveguide

including: a core waveguide; and/or a surrounding volume, wherein at least one of the core waveguide(s) and the surrounding volume, from a respective pre-existing core waveguide or pre-existing surrounding volume, has permanent refractive index changes from external radiation of a controlled shape that are patterned along an axial length of the core waveguide to add or shape at least one mode of the MMI waveguide.

In the above case, a second, third, etc. waveguide may be added to one (or more) pre-existing waveguide(s) to form a multiport (NxM) MMI waveguide device by laser modification in various modalities (in one or more waveguides or surrounding zones). In example embodiments which refer to irradiating, this can further include multiple sweeps with the with external radiation with overwriting, and/or side by side, and/or angled overlays, to generate a plurality of patterns. In an example embodiment, a pre-existing core waveguide is birefringent. In an example embodiment, at least one of the refractive index changes is birefringent or induces a birefringence in the resulting MMI waveguide.

Methods of the example embodiments can enable MMI based couplers, and wavelength filters to be formed in a single step process.

Certain adaptations and modifications of the described embodiments can be made. Therefore, the above discussed embodiments are considered to be illustrative and not restrictive.

Example embodiments described as methods would similarly apply to systems, as applicable, and vice- versa.

Variations may be made to some example embodiments, which may include combinations and sub-combinations of any of the above. The various embodiments presented above are merely examples and are in no way meant to limit the scope of this disclosure. Variations of the innovations described herein will be apparent to persons of ordinary skill in the art, such variations being within the intended scope of the present disclosure. In particular, features from one or more of the above-described embodiments may be selected to create alternative embodiments comprised of a sub-combination of features which may not be explicitly described above. In addition, features from one or more of the above-described embodiments may be selected and combined to create alternative embodiments comprised of a combination of features which may not be explicitly described above. Features suitable for such combinations and sub-combinations would be readily apparent to persons skilled in the art upon review of the present disclosure as a whole. The subject matter described herein intends to cover and embrace all suitable changes in technology.

Claims

WHAT IS CLAIMED IS:

1. A method of modifying an optical waveguide, wherein the optical waveguide includes a core waveguide and a surrounding volume, the method comprising:

irradiating at least one of the core waveguide and the surrounding volume with external radiation in a preferentially shaped beam with an intensity to create permanent refractive index changes of a controlled shape that are patterned along an axial length of the core waveguide to add or shape at least one mode of the optical waveguide,

wherein the irradiated optical waveguide forms a Multimode Interference (MMI) waveguide.

2. The method of claim 1, wherein the permanent refractive index changes are made without affecting a surface of the surrounding volume.

3. The method of claim 1, wherein the surrounding volume comprises a cladding.

4. The method of claim 1, wherein the core waveguide comprises a pre-existing

Multimode Interference (MMI) waveguide.

5. The method of claim 1, wherein the core waveguide comprises a pre-existing single mode waveguide.

6. The method of claim 1, wherein the irradiated optical waveguide further comprises an MMI coupler due to the controlled shape and pattern.

7. The method of claim 6, wherein the MMI coupler comprises at least one of a plurality of input port waveguides and a plurality of output port waveguides.

8. The method of claim 1, wherein the irradiated optical waveguide further comprises an MMI wavelength filter due to the controlled shape and pattern.

9. The method of claim 1, wherein the controlled shape and pattern are used to adiabatically redistribute the light amongst the modes of the optical waveguide.

10. The method of claim 1, wherein the controlled shape and pattern are used to include a plurality of refractive index modifications in the optical waveguide.

11. The method of claim 1, wherein the external radiation comprises at least one of an electron beam device, ion beam devices, x-ray device, laser, ultraviolet laser, C0₂ laser, femtosecond pulsed laser, and picosecond pulsed laser.

12. The method of claim 1, wherein the irradiated optical waveguide further comprises a birefringent MMI waveguide.

13. The method of claim 12 wherein a polarization selective filter or tap is further formed in the irradiated optical waveguide.

14. The method claim 13 wherein the optical waveguide originally comprises a preexisting waveguide in which to form the polarization selective filter or tap comprises a biomedical probing waveguide, photonic bandgap (holey) waveguide, active (laser amplifier) waveguide, or sensor waveguide, or a section of telecommunications optical fiber or a waveguide section of a planar lightwave circuit or a three-dimensional circuit.

15. The method of claim 12, wherein the irradiated optical waveguide further comprises a polarization attenuator or a polarizer.

16. The method of claim 15 wherein the optical waveguide originally comprises a pre- existing waveguide in which to form the biomedical probing waveguide, photonic bandgap

(holey) waveguide, active (laser amplifier) waveguide, or sensor waveguide, or a section of telecommunications optical fiber or a waveguide section of a planar lightwave circuit or a three-dimensional circuit.

17. The method of claim 12, wherein the irradiated optical waveguide further comprises a polarization splitter.

18. The method claim 17 wherein the optical waveguide originally comprises a preexisting waveguide in which to form the polarization splitter comprises a biomedical probing waveguide, photonic bandgap (holey) waveguide, active (laser amplifier) waveguide, or sensor waveguide, or a section of telecommunications optical fiber or a waveguide section of a planar lightwave circuit or a three-dimensional circuit..

19. The method of claim 1 wherein the irradiated optical waveguide further comprises a combination of polarizers, wavelplate retarders, splitters and polarization dependant taps to produce a polarimeter.

20. The method of claim 1 wherein said irradiating further includes multiple sweeps with the with external radiation with overwriting, and/or side by side, and/or angled overlays, to generate a plurality of patterns.

21. The method of claim 1 wherein a pre-existing core waveguide is birefringent.

22. The method of claim 21, wherein at least one of the refractive index changes is birefringent or induces a birefringence in the resulting MMI waveguide.

23. A Multimode Interference (MMI) waveguide formed from a pre-existing optical waveguide, the modified optical waveguide comprising:

a core waveguide; and

a surrounding volume,

wherein at least one of the core waveguide and the surrounding volume, from a respective pre-existing core waveguide or pre-existing surrounding volume, has permanent refractive index changes from external radiation of a controlled shape that are patterned along an axial length of the core waveguide to add or shape at least one mode of the MMI waveguide,

wherein an interface between a permanent refractive index change and a pre-existing refractive index is unitary.

24. A multi-port MMI device comprising:

a plurality of core waveguides; and

a surrounding volume,

wherein at least one of the core waveguides and the surrounding volume, from a respective at least one pre-existing core waveguide or pre-existing surrounding volume, has permanent refractive index changes from external radiation of a controlled shape that are patterned along an axial length of the core waveguide,

wherein at least two of the pre-existing core waveguides comprise isolated or weakly coupled pre-existing waveguides, or strongly coupled pre-existing waveguides.

25. The multi-port MMI device of claim 24 wherein the controlled shape and pattern are used to add or shape at least one mode of the at least one pre-existing core waveguide.

26. The multi-port MMI device of claim 24 wherein the controlled shape and pattern are used to add a further waveguide or more than one further waveguide of the plurality of core waveguides to the at least one pre-existing core waveguide.

27. The multi-port MMI device of claim 24 wherein at least one pre-existing core waveguide is birefringent.

28. The multi-port MMI device of claim 24, wherein at least one of the refractive index changes is birefringent or induces a birefringence in at least one of the core waveguides.

29. A method of modifying an optical waveguide, wherein the optical waveguide includes a core waveguide and a surrounding volume, the method comprising:

irradiating at least one of the core waveguide and the surrounding volume with external radiation in a preferentially shaped beam with an intensity to create permanent refractive index changes of a controlled shape that are patterned along an axial length of the core waveguide,

wherein at least two of the pre-existing core waveguides comprise isolated or weakly coupled pre-existing waveguides, or strongly coupled pre-existing waveguides.

wherein the irradiated optical waveguide forms a multi-port Multimode Interference (MMI) device.

30. The method of claim 29 wherein at least one pre-existing core waveguide is birefringent.

31. The method of claim 29, wherein at least one of the refractive index changes is birefringent or induces a birefringence in at least one of the core waveguides.