WO1999052015A1 - Conversion de la frequence du signal photonique au moyen d'une structure a bande interdite photonique - Google Patents

Conversion de la frequence du signal photonique au moyen d'une structure a bande interdite photonique Download PDF

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Publication number
WO1999052015A1
WO1999052015A1 PCT/US1998/006378 US9806378W WO9952015A1 WO 1999052015 A1 WO1999052015 A1 WO 1999052015A1 US 9806378 W US9806378 W US 9806378W WO 9952015 A1 WO9952015 A1 WO 9952015A1
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frequency
photonic signal
layers
signal
index
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PCT/US1998/006378
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English (en)
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Michael Scalora
Mark J. Bloemer
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Michael Scalora
Bloemer Mark J
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Priority to PCT/US1998/006378 priority Critical patent/WO1999052015A1/fr
Priority to JP2000542693A priority patent/JP2002510809A/ja
Priority to CA002327170A priority patent/CA2327170A1/fr
Priority to US09/382,690 priority patent/US6304366B1/en
Publication of WO1999052015A1 publication Critical patent/WO1999052015A1/fr
Priority to US09/742,295 priority patent/US6744552B2/en

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B82—NANOTECHNOLOGY
    • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y20/00—Nanooptics, e.g. quantum optics or photonic crystals
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
    • G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
    • G02B6/122—Basic optical elements, e.g. light-guiding paths
    • G02B6/1225—Basic optical elements, e.g. light-guiding paths comprising photonic band-gap structures or photonic lattices
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/355—Non-linear optics characterised by the materials used
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/353—Frequency conversion, i.e. wherein a light beam is generated with frequency components different from those of the incident light beams
    • G02F1/3534—Three-wave interaction, e.g. sum-difference frequency generation
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/353—Frequency conversion, i.e. wherein a light beam is generated with frequency components different from those of the incident light beams
    • G02F1/3544—Particular phase matching techniques
    • G02F1/3548—Quasi phase matching [QPM], e.g. using a periodic domain inverted structure
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/37—Non-linear optics for second-harmonic generation
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/39—Non-linear optics for parametric generation or amplification of light, infrared or ultraviolet waves
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F2202/00—Materials and properties
    • G02F2202/32—Photonic crystals
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
    • H01S3/30—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range using scattering effects, e.g. stimulated Brillouin or Raman effects

Definitions

  • This invention relates to the generation of photonic signals at frequencies other than the input signal.
  • it relates to second or higher harmonic generation, sum, and difference frequency conversion, Raman processes and generic parametric amplification near the photonic band edge.
  • PBG photonic band gap
  • non-linear materials include potassium dihydrogen phosphate (KDP), ⁇ -barium borate (BBO), lithium triborate (LBO), lithium niobate (LiNbO 3 ), and the like.
  • KDP potassium dihydrogen phosphate
  • BBO ⁇ -barium borate
  • LBO lithium triborate
  • LiNbO 3 lithium niobate
  • lithium niobate is conventionally used for second harmonic (SH) generation because its nonlinear ⁇ (2) coefficient is larger than most other materials.
  • the effective magnitude of ⁇ (2) can be enhanced further by a process called polling.
  • polling a process called polling.
  • a certain length of LiNbO 3 material ordinarily a few millimeters to a few centimeters, is subdivided in sections each on the order of a few microns in thickness. Then, a strong, static electric field is applied to the material such that the direction of the electric field is reversed in each successive section.
  • the field leaves a permanent impression behind, similar to the impression that visible light leaves on a photographic plate, which causes the sign of the ⁇ (2) to reverse in a predetermined way in each successive section throughout the length of the material.
  • a technique that is also referred to as quasi- phase-matching (QPM) SH generation from a similar length of material that is not quasi-phase-matched can be orders of magnitude smaller than the phase-matched case.
  • the reason for this kind of material processing can be explained as follows.
  • SH generation a field at twice the original frequency is generated.
  • the index of refraction of any material also depends on frequency.
  • the indices of refraction may differ by as much as 10% or more; this means that the speed of light in the material may differ by that amount, causing the two waves, the fundamental and the SH, to get out of phase.
  • the waves tend -4-
  • QPM devices utilized in frequency conversion are typically on the order of a 1-2 centimeters (cm) in length. What is needed is a device that performs frequency conversion of a light source that is compact in size, has sufficient conversion efficiency, and can be manufactured by conventional techniques.
  • the present invention provides a new device and method to produce photonic signals at frequencies other than the frequency of the incident pump beam or pulse.
  • the photonic band gap (PBG) device comprises a plurality of first and second material layers. The first and second material layers are arranged such that the PBG device exhibits a photonic band gap structure. The photonic band gap structure exhibits a transmission band edge corresponding to the pump signal frequency. A second photonic signal at a second frequency is generated by an interaction of the input photonic signal with the arrangement of layers. The second photonic signal is an harmonic of the pump signal and can be either transmitted through the device or reflected out the input region of the PBG device.
  • the first and second layers are arranged in a periodically alternating manner.
  • the PBG device can further comprise one or more periodicity defects in order to produce other harmonics of the pump signal.
  • a method for the frequency conversion of a pump pulse comprises selecting a desired frequency for the pump signal to produce a second signal at a desired harmonic frequency.
  • a PBG structure is provided, wherein the arrangement of layers comprising the PBG structure is similar to the structure described above.
  • the method further comprises inputting -5-
  • the desired pump signal into the PBG structure in order to produce an ouput signal at a desired harmonic of the pump signal frequency.
  • the generated signals can be in the form of either a continuous wave (cw) signal, if the pump beam is a cw signal, or a pulsed signal, if the pump beam is pulsed.
  • the frequency conversion process for the PBG device is orders of magnitude more efficient than any other ordinary QPM device of comparable size. This conversion efficiency can be achieved with the utilization of a photonic band gap (PBG) structure.
  • An incident pump beam or pulse is applied to the PBG device near the photonic band edge transmission resonance, in close proximity to the photonic band gap.
  • the output signal (of different frequency or wavelength) that is generated in the PBG device is also tuned at a transmission resonance.
  • a frequency conversion device of compact size can be designed to perform a wide range of applications including harmonic generation and parametric oscillation by using a model of a one-dimensional structure.
  • These PBG devices can also be fabricated by straightforward techniques to satisfy current technology needs.
  • FIG. 1A is a schematic representation of one embodiment of the present invention, a quarter-wave frequency conversion device with a uniform PBG structure. -6-
  • FIG. IB is a diagram of the characteristic index of refraction profile of the uniform PBG structure shown in FIG. 1A.
  • FIG.2 is a schematic diagram of one embodiment of the present invention, a mixed quarter-half-wave PBG device.
  • FIG. 3 shows a characteristic transmission profile for a PBG device for third harmonic generation according to the present invention.
  • FIG. 4 shows group index versus normalized, dimensionless frequency profile according to the present invention.
  • FIG.5 shows one embodiment of the present invention, a PBG device with a periodicity defect region.
  • FIG. 6 is a diagram of the characteristic index of refraction profile of the PBG structure shown in FIG. 5.
  • FIG. 7 shows a transmission versus normalized, dimensionless frequency for a 20-period, half-quarter-wave stack.
  • FIG. 8 shows maximum energy output versus index of refraction.
  • FIG. 9 shows the pump field eigenmode distribution inside a PBG structure of the present invention, at the instant that the peak of the pulse reaches the PBG structure.
  • FIG. 10 shows a second-harmonic eigenmode for the case of FIG. 9.
  • FIG. 11 shows comparison between the SH energy output from the PBG
  • FIG. 12 shows spontaneously generated SH pulses.
  • FIG. 13 shows SH conversion efficiency versus incident pulse peak field strength.
  • FIG. 14 is a flowchart illustrating a method of generating frequency conversion according to the present invention. -7-
  • the present invention provides a frequency conversion device that utilizes a photonic band gap (PBG) structure.
  • PBG photonic band gap
  • the enhancement mechanism demonstrated in these PBG structures in the linear regime leads to frequency up- (or down-) conversion rates nearly three orders of magnitude better than conversion rates achieved with ordinary phase matched materials, or in conventional fiber grating geometries.
  • the geometrical properties and the periodicity of the PBG structure can act to significantly modify the density of electromagnetic field modes near the band edge, thus facilitating the emission of the second harmonic (SH) signal at a much-enhanced rate. More importantly perhaps, this means that current fabrication issues that arise in ordinary quasi-phase-matched structures can be avoided altogether by utilizing current technology for deposition of semiconductor or dielectric thin films and combinations thereof.
  • the present invention is described in terms of this example environment.
  • ⁇ (1) is the medium susceptibility for low incident fields
  • ⁇ ⁇ ) is the jth nonlinear coefficient whose magnitude decreases rapidly as (j) increases
  • E is the applied field. Therefore, contributions from the jth term become significant if the field strength is gradually increased.
  • the ⁇ (i) can be two to four orders of magnitude greater than each successive ⁇ ⁇ +1) coefficient, depending on the material.
  • all the coefficients with odd or even (j) greater than one may vanish, depending on the characteristics of the material at the molecular level. For example, all the even coefficients vanish if the molecule has a geometrical center of symmetry, as in a gas.
  • a strong external optical field at frequency ⁇ is capable of generating light at frequency 2 ⁇ , 3 ⁇ , 4 ⁇ , and so on.
  • light at frequencies ( ⁇ ] + ⁇ 2 ) and ( ⁇ ,- ⁇ 2 ) i.e., sum and difference frequencies
  • a ⁇ (2) medium which means that the first order nonlinear coefficient dominates the dynamics, is capable of SH generation, and sum and difference frequency conversion;
  • a ⁇ ( ) medium is capable of third harmonic generation, and so on.
  • nonlinear frequency conversion For example, a type of nonlinear frequency conversion that is typically sought in nonlinear media is SH generation. However, the present description is also applicable for nonlinear frequency conversion to higher or lower frequencies, such as third harmonic generation, and so on.
  • Conventional nonlinear materials used for frequency conversion processes such as LiNbO 3 , are processed in such a way that the nonlinear contribution to the index of refraction alternates sign every few tens of microns.
  • the linear index of refraction of the LiNbO 3 host material is not modified in any way (i.e., it is spatially uniform).
  • the method of forming a device designed to perform frequency conversion, according to the present invention is completely different: a spatial modulation is imparted to the linear part of the refractive index.
  • the linear index of refraction of the structure alternates between a high and a low value. This is accomplished by alternating at least two materials, such as GaAs
  • PBG photonic band gap
  • the physical processes that are exploited in the present invention are different from conventional frequency conversion techniques in that photonic band edge effects are utilized.
  • Photonic band edge effects cause strong overlap of the pump and SH signals, significant reduction of the respective propagation velocities, and therefore, increased interaction times.
  • some of the advantages of the present invention include: (1) the structure can be 100 to 1000 time shorter than typical QPM structures, with comparable conversion efficiencies; (2) ordinary semiconductor materials can be used in forming the PBG structure, leading to a reduction of production costs; and (3) the PBG device is compatible with integrated circuit environments due to its size and composition. -10-
  • a photonic band gap structure comprises a plurality of layers, as shown in FIG. 1 A, where the plurality of layers alternates between a low and a high index of refraction.
  • PBG structure 102 comprises a stack of alternating layers 108 and 110 of refractive materials having predetermined indices of refraction n, and n 2 (for low incident pump powers), and predetermined thicknesses a and b, respectively.
  • the first type of layer 108 can be chosen such that it is a high index layer n,.
  • the second type of layer 110 can be chosen to be a low index layer n 2 .
  • the widths of the layers can be chosen such that they are both a fraction of the size of the incident pump wavelength.
  • This pattern can be repeated for N periods 122, where a period is equal to one set of alternating layers 112.
  • This type of structure is also referred to as a quarter-wave structure.
  • other arrangements of alternating layers can also be made, depending on the particular frequency conversion application. Adjusting the width of the layers causes a shift of the location of the band gap to a different frequency. This property is a beneficial one, which adds flexibility when the options of input and output laser frequencies are being considered.
  • FIG. IB is a diagram of a characteristic index of refraction square- wave pattern profile of PBG structure 102 for N periods.
  • Diagram 150 plots the index of refraction (n) 152 of a uniform PBG structure as a function of distance (z) 154, which is limited by the number of periods 156 in the device.
  • Diagram 150 illustrates the periodic nature of the abrupt refractive index changes occurring in the material. -11-
  • PBG structure 200 is formed in such a way that a single period comprises two layers: a quarter- wave layer 202 and a half- wave layer 204, to form a periodic, mixed quarter-half-wave structure.
  • This particular choice causes the first and second order band edges to be approximately a factor of two apart from each other, as indicated in FIG.4, described in detail below.
  • both the pump and SH fields are tuned to their respective photonic band edges.
  • This coincidence of the band edges leads to strong overlap of the fields, significant reduction of the wave velocities by several orders of magnitude below the speed of light in either medium, and increased interaction times. See, e.g., "Pulsed second harmonic generation in one-dimensional, periodic structures", Phys. Rev. A, October 1997, by Scalora et al. (incorporated by reference herein in its entirety).
  • the types of structures discussed above result in a PBG structure in which a range of frequencies about some reference frequency cannot propagate inside a PBG device.
  • the structure may be transparent to other frequencies away from the band gap. For example, a representative photonic band -12-
  • FIG.3 shows a characteristic transmission profile for structure 301.
  • higher order gaps may also appear to create a series of gaps. Usually, however, the higher order gaps are ignored.
  • FIG. 3 both the first order band gap 302 and second order band gap 304 are depicted.
  • the maximum possible transmission is 1. Therefore, it is the absence of those frequencies from the transmitted spectrum that gives rise to the name "band gap” , in analogy to the electronic band gap of semiconductors where electrons having a specific range of energies cannot propagate inside a semiconductor crystal.
  • the properties of the structures are such that a series of transmission resonances are obtained.
  • the number of such resonances is equal to the number of periods that make up the structure.
  • the bandwidth of said resonances is a sensitive function of the total number of periods, the indices n x and n 2 , and their difference ⁇ n-
  • a PBG structure can be formed where nonlinear gain, or the production of SH signal, is maximized.
  • the equations that describe the propagation of electromagnetic waves in PBG structures can be solved. The results of the calculations show that if a pulse of light interacts with a nonlinear ⁇ (2) medium to produce a SH signal, then the SH energy output from the PBG structure is approximately three orders of magnitude greater than the energy output of a simple bulk nonlinear medium of approximately the same length.
  • One embodiment of the present invention is a PBG structure that comprises 20 periods (or 40 layers) of alternating layers of GaAs and AlAs.
  • the PBG structure can also comprise different sets of materials, for example, air and GaAs, glass and AlAs, a combination of other dielectric -13-
  • the PBG structure may also be created in an optical fiber, in the form of a fiber grating. This illustrates that this frequency conversion capability is not specific to any one material, and that some flexibility exists according to the specific needs of a particular application. Accordingly, the structure of the present invention should not be limited solely to the embodiments described herein.
  • a pulse of light of about one picosecond or more in duration can be tuned to the frequency corresponding to the maximum of the first transmission resonance away from the low frequency band edge.
  • FIG. 4 which plots group index as a function of normalized frequency.
  • the total energy of a signal produced at twice the frequency of a pump i.e., at the SH frequency
  • the signal generated at the second harmonic frequency is tuned to the second transmission resonance of the low frequency band edge of the second order gap, as shown in FIG. 4.
  • a PBG structure comprises a quarter-wave periodic structure with a "defect" layer one half wavelength thick at the center of the structure.
  • Device 502 comprises at least two stacks (or regions) 504 and 506 of alternating layers of refractive materials similar to those described above in connection with FIG. 1A.
  • a periodicity defect region 508 is interposed (or placed) between stacks 504 and 506, with each stack having an equal number of alternating layers of refractive material.
  • Defect region 508 is also a refractive material that can have an index of refraction (n) that is equivalent to either n, or n 2 , and with the same ⁇ (2) nonlinear coefficient.
  • the thickness of periodicity defect region 508 can be one half or one wavelength in thickness.
  • other thicknesses for periodicity defect region 508 can also be utilized.
  • defects in this context, simply means a break in the periodicity of the structure.
  • This defect layer breaks the periodicity in such a way that it generates a transmission resonance in the middle of every gap, as shown in FIG. 6.
  • the distance between the center of the first and second order gap is exactly a factor of three. Therefore, tuning the pump signal to the center of the first order gap will enhance the generation of light at the third harmonic.
  • a pump signal wavelength of approximately 1550 nm such as found in conventional communications laser diodes
  • a third harmonic signal will be output from the PBG device at a wavelength of approximately 516 nanometers (nm). Therefore, by selecting the proper set of parameters, such as material type, material parameters, and the exact geometrical properties of the materials (i.e., layer thickness), a person of skill in the art can arrive at a device with the desired properties.
  • Another embodiment of the present invention is a PBG device comprising a plurality of periodicity "defects.” In other words, several defects of varying -15-
  • thicknesses can be placed in a PBG device.
  • the placement of these multiple defects between stacks of alternating layers forms an a-periodic structure, that also exhibits a photonic band gap structure.
  • This a-periodic structure can be utilized to perform any of the frequency conversion techniques described herein, as would be apparent to one of skill in the art based on the present description.
  • conversion efficiencies can be even higher for structures with an increased number of periods. For example, by increasing the structure length by 50% (from 20 to 30 periods), the energy output can increase by a factor of 5.
  • the transmission resonance bandwidth decreases as UN 2 , where N is the number of periods, so that the pulse duration needs to be increased in order to ensure large pump enhancement inside the structure; and (2) a material breakdown may occur because of excessive electric-field buildup, or enhancement, inside the PBG structure.
  • Typical nonlinear index changes in GaAs or AlAs layers can be of order ⁇ n NL ⁇ 10 "3 . This implies that nonlinear index shifts can be larger than the linear index modulation depth. Consequently, the location of the gap on the frequency axis can shift dramatically to higher or lower frequencies, and its bandwidth can increase or decrease significantly, depending on the sign of the nonlinearity.
  • the frequency bandwidth of an ultrashort pulse of only a few hundred optical cycles in duration can be smaller (depending on the wavelength) than the bandwidth of the PBG's first transmission resonance peak, where the group velocity is a minimum.
  • ultrashort pulse propagation can be nondispersive.
  • the nonlinear index change remains orders of magnitude smaller than the index modulation depth, which for PBG structures can be of order unity or larger.
  • the stability of the band structure in the frequency domain is also important in parametric optical up- and down-conversion, and harmonic generation.
  • This result highlights the fact that a new generation of compact and efficient high gain optical amplifiers and optical parametric oscillators based on photonic band-edge effects can be achieved according to the present invention.
  • the enhancement of gain in these PBG structures is understood by recalling that the density of accessible field modes in the vicinity of dielectric boundaries is modified by the boundary. This means that if a linear or nonlinear gain medium is introduced with in a PBG structure, the stimulated and spontaneous emission rates are modified according to Fermi's golden rule (see below). In QPM structures, a minimization of the phase difference between the waves is desirable in order to avoid a phase mismatch in the continuous wave case.
  • phase difference is typically achieved by poling the active material, which is uniform in its composition and contains no linear index discontinuities. Accordingly, the nonlinear coefficient only alternates sign in the longitudinal direction every few tens of micrometers ( ⁇ m).
  • the unusually strong confinement of both the pump and the SH signal that occurs near the photonic band edges is relied on.
  • the density of electromagnetic field modes is large, the group velocity is low, the field amplitude may be enhanced over bulk values by one order of magnitude or more, and strong pump and SH mode overlap occurs.
  • the material is not poled in the usual manner; it is the geometrical properties of the structure that cause strong mode overlap, co- propagation, and larger interaction times, the combination of which is ultimately responsible for the enhanced gain of these PBG structures.
  • the invention can be implemented in group III-V or
  • III-V or II-VI materials as well as with dielectric materials.
  • dielectric materials for purposes of explanation, the above examples are described in GaAs/AlAs material systems, but it will be understood by those skilled in the art that the invention described herein can also be implemented with other III-V or II-VI systems.
  • the PBG structures of the present invention can be utilized to perform a variety of frequency conversion techniques.
  • a mixed quarter- half-wave structure can be utilized to perform SH generation of a variety of coherent light sources, including tunable solid state lasers, gas lasers and semiconductor diode lasers.
  • a PBG structure can be placed at the output facet of a conventional AlGaAs diode laser that emits a laser beam at a wavelength of approximately 810 nm.
  • Diode lasers of various output wavelengths are commercially available from a number of commercial vendors, including Spectra Diode Labs, Inc. and Coherent Inc., both of California.
  • SH generation optical cavity arrangements e.g., external cavity and intra-cavity designs
  • Typical optical layouts for harmonic generation are well known. See e.g. , W. Koechner, “Solid-State Laser Engineering,” Springer- Verlag, 2 nd Ed. (1988), especially Chapter 10, which is incorporated by reference herein.
  • Known anti-reflection coatings can also be utilized to reduce spurious reflections, as would be apparent to one of skill in the art.
  • the PBG structures of the present invention can also be utilized in parametric oscillation techniques where, for example, output wavelengths greater than the pump pulse wavelengths can be generated. Based on the known methods of optical parametric oscillation, such as those described in the Koechner reference, it would be apparent to one of skill in the art to design a parametric device utilizing the PBG structure of the present invention to achieve frequency conversion at lower frequencies (i.e., longer wavelengths).
  • optical fiber gratings can be designed similar to the types of PBG structures described above.
  • Optical fiber gratings are also periodic structures.
  • the index of refraction for a fiber grating can achieve an index modulation depth
  • a fiber grating can be created on an optical fiber by well-known fabrication techniques. For example, see the fiber grating applications and fabrication techniques described in "Continuously tunable single-mode erbium fiber laser," by G. Ball and W. Morey, Optics Letters, Vol. 17, No. 6, p.420 (1992) and “Spatially-multiplexed fiber-optic bragg grating strain and temperature-sensor system based on interferometric wavelength shift," by Y. Rao, et al. , Electronics Letters, Vol. 31, No. 12, p. 1009 (1995), which are both incorporated by reference in their entirety.
  • fiber grating fabrication can be accomplished by placing an optical "mask" over a photo-sensitive fiber core and then by illuminating the mask- fiber assembly with a high intensity ultraviolet light beam, such as an Excimer laser.
  • a high intensity ultraviolet light beam such as an Excimer laser.
  • the resulting grating referred to as a fiber grating, displays much the same properties of a high index contrast semiconductor PBG structure, especially with respect to band gaps and transmission resonances.
  • a mask can be designed to create a grating that imparts either a band-edge effect or a transmission resonance similar to the one shown above in FIG. 5. Based on the present description, it would be apparent to one of skill in the art to design a fiber grating capable of frequency conversion.
  • a fiber grating device designed according to the parameters discussed above can be coupled to the output of a laser diode to produce a compact source capable of output emissions in the blue wavelength range.
  • a model can be utilized to allow one of ordinary skill in the art to design a PBG structure to perform optical frequency conversion for a desired application.
  • shown here is an analysis describing the dynamics associated with ultrashort pulses (about 1 ps or less) in one-dimensional systems.
  • This model extends the analysis of SH generation and enhancement to arbitrarily deep PBG gratings in the pulsed regime by directly integrating Maxwell's equations in the time domain.
  • ⁇ (2) 0.1 pm/V (roughly 3 x 10 "9 cm/statvolt in Gaussian units) is chosen and it is assumed that the nonlinear material is distributed uniformly throughout the PBG structure.
  • FIG. 7 indicates that this choice of parameters causes the location of the second- order gap to be removed from the first-order gap by approximately a factor of 2.
  • a factor of 3 separates the first- and second-order band edges. Utilizing these two edges is more suitable for third-harmonic generation.
  • the nonlinear polarization can be expanded in powers of the electromagnetic field strength as follows:
  • the SH signal is initially zero everywhere.
  • the direction of propagation of the spontaneously generated SH field and the exact nature of the quasi-standing wave inside the structure are dynamically determined by (a) the nature of the initial and boundary conditions, (b) pump-frequency tuning with respect to the band edge, and (c) the distribution of nonlinear dipoles inside the structure. This nonlinear dipole distribution can significantly affect the results.
  • SH generation is a phase- sensitive process. The field and its phase at any point inside the structure are a superposition of all fields originating everywhere else inside the structure. Thus, the phase is important element that should be included in the integration of the equations of motion.
  • dipole distribution is important to the extent that it is modified in the layers where the fields happen to be localized. For example, near the low-frequency band edges, the fields are localized in the high-index layers. Modifying the nonlinear medium distribution in the low-index layers will have little effect, although some mode overlap between layers always occurs. -22-
  • Equation (8) describes the rate of change of the SH field, whereas equation (7) describes the pump (or fundamental) signal.
  • the spatial coordinate z has been conveniently scaled in units of ⁇ 0 ; the time is then expressed in units of the corresponding optical period.
  • a frequency conversion device can either transmit or reflect the output harmonic signal.
  • the SH frequency is found well away from the second-order band edge: it is tuned in the middle of the pass band, as indicated in FIG. 7. In order -24-
  • the band structure and its features are strongly influenced by (a) the number of periods, (b) layer thickness, and (c) material dispersion. For example, increasing (or decreasing) the number of layers sharpens the band edges, and increases (or decreases) the number of transmission resonances between gaps, causing an effective shift of each resonance. Changing layer thickness away from the quarter- or half-wave conditions (in units of ⁇ 0 ) can also cause frequency shifts in the location of the band gaps and transmission resonances. A structure with the desired properties can be realized when these frequency shifts are coupled with material dispersion.
  • the higher-index value corresponds to
  • SH generation just inside the second-order gap, where its suppression is expected. For intermediate values of the index, SH generation also occurs at frequencies where the density of modes is a maximum.
  • the degree of dispersion assumed is typical of the degree of dispersion found in both dielectric or semiconductor materials, 5 - 10% in this case.
  • the maximum group index is also a sensitive function of ⁇ n, the index modulation depth, and the number of periods.
  • the maximum value of the group index for this mixed half- quarter- wave structure is similar in magnitude to that of a quarter- wave, 20-period -25-
  • n 2 ( ⁇ ) 1.42857
  • n 2 (2 ⁇ ) 1.519. Note also that the magnitude of this function is largest near the high-and low-frequency band edges.
  • a high pump index implies that a dramatic increase in the field intensities inside the structure occurs at that frequency. This is important, since SH gain is nonlinear in the field, as Eq. (8) suggests.
  • the enhancement is reduced due to the broad frequency content of the pulse.
  • SH generation is not at a maximum when the SH signal is tuned at the density of the mode maximum, because the fields do not have the right phase for this to occur.
  • the phase of the transmitted, plane-wave field undergoes a ⁇ phase shift across the gap, and a phase shift of 2 ⁇ between consecutive resonances on the same side of any gap. Therefore, the number of periods chosen can have an impact on the overall phase of the SH field inside the structure. For short pulses, the circumstances are much more complicated, because of their broadband frequency makeup.
  • Fig. 8 shows the calculated SH energy output for a 1 ps pulse, as a function of n 2 (2 ⁇ ), i.e., dispersion. The maximum energy output occurs when -26-
  • n 2 (2 ⁇ ) 1.519, which corresponds to the second transmission or group index maximum.
  • Evidence of the curvature of the band structure near the band edge is rather weak away from the second transmission resonance.
  • Pulses whose spectral widths are larger than the band-edge transmission resonance tend to couple poorly with the structure. This situation leads to dispersive propagation, and to only slightly enhanced field intensities inside the PBG structure.
  • a pulse whose frequency band-width is smaller than the band-edge resonance bandwidth has fewer frequency components, experiences little or no dispersion, and allows the field to build up inside the structure by about one order of magnitude or more with respect to its free space or bulk values, where the field amplitude is in general proportional to E free / «.
  • FIG. 9 plots the pump-field intensity inside the structure, at the instant the peak of the 1-ps pulse reaches the structure.
  • the maximum field intensity is amplified by more than one order of magnitude (compared to its peak value outside the structure) by linear interference effects of backward- and forward- traveling components.
  • FIG. 10, represents the SH field intensity quasistanding-wave pattern at the same instant in time as FIG. 9. Both eigenmodes overlap to a large extent inside the high index layers, and the fields propagate in this configuration for the entire duration of the pump pulse. This mode overlap, combined with the -27-
  • Fig.1 1 shows the total-energy output (forward and backward included) as a function of incident pulse width, expressed in optical cycles, for a 20-period, 12- ⁇ m-thick device (solid line), and a 12- ⁇ m bulk sample coated with anti- reflection layers at both ends to minimize pump reflections (dotted line).
  • Low input field intensities are considered that yield conversion efficiencies on the order of 10 '12 , although this trend persists as long as pump depletion is not significant.
  • the abscissa is plotted on a logarithmic scale.
  • FIG. 11 shows that the total-energy output (and therefore power output) becomes about 500 times greater for the PBG sample than for index-matched bulk material when an input pulse width approaches 300 optical cycles, or about 1 ps.
  • the results indicate that at these length scales the energy output for the bulk sample increases linearly with incident pulse width.
  • this figure clearly demonstrates that suitable output energies can be obtained from the PBG devices of the present invention when continuous wave input pulses are applied.
  • FIG. 12 shows the SH field propagating away from the structure. While the pump was incident from the left, note that the structure radiates significantly in both directions, and that the SH pulses generated have the same width as incident pump pulses. It would be difficult to predict this overall behavior a priori, especially in the absence of analytical results in this regime. Further, tuning the pump away from the band edge, tuning to the high- -28-
  • FIG. 13 is a plot of the conversion efficiency vs. peak field intensity in Gaussian units, for a pulse of 1 ps duration, where IEP of 10 9 in these units corresponds to roughly 10 GW/cm 2 in free space.
  • the free-space value of the energy flow is to be distinguished from energy flow inside the structure.
  • efficiency is defined as the ratio between the final total SH energy and the total initial pump energy. This ratio is also representative of the ratio between the corresponding peak field intensities, respectively.
  • FIG. 13 indicates that for this simple PBG structure only 12 ⁇ m in length, a conversion efficiency of order 10 "2 can be achieved with pump intensity of 10 GW/cm 2 , yielding a SH signal intensity of approximately 10 GW/cm 2 .
  • any small deviation in the actual ⁇ (2) value, tuning with respect to the band edge, and input pulse width can significantly affect comparison with experimental results.
  • the model presented above is of great value in order to determine the overall behavior of a PBG structure, and it can be used in the determination of ⁇ (2) . Therefore, exercising reasonable care in the design process of a PBG device based on the present invention can produce a very efficient SH generator, provided absorption at the SH wavelength is minimized. Note that a similar model can also be used to design an efficient third harmonic generator, and the like.
  • tuning the pump at the first resonance of the first-order, high- frequency band edge causes the SH signal to be tuned at the second resonance of the second-order high-frequency band edge, in analogy to what was accomplished above for the low-frequency band edge.
  • the high frequency band edge example can increase up to about a factor of two for a 1 ps pulse, compared to the low-frequency band-edge conversion efficiency.
  • Tuning the pump at the high-frequency band edge causes a shift of the pump field localization in the low index layer. This shift increases the field eigenmode intensity in that layer.
  • the width of the active layer increases by about 30%>, from 0.5 ⁇ 0 to 0.65 ⁇ 0 . This combination can account for the increase in overall nonlinear gain for a device length of approximately 12 ⁇ m in length.
  • the input photonic signal has an input photonic signal frequency and an input photonic signal bandwith.
  • step 1402 the frequency of -31-
  • the input photonic signal is selected so as to correspond to a second signal at a desired harmonic frequency.
  • the type of input signal e.g., continuous wave or pulsed operation
  • the device comprises an arrangement of material layers that exhibits a photonic bandgap structure.
  • the specific type of arrangement depends upon factors that include, but are not limited to: (1) the absorption and transmission properties of the materials selected; (2) the indices of refraction of the materials forming the structure, which affects such parameters as the index discontinuity; (3) the thicknesses of the material layers; and (4) the number of periods of alternating layers.
  • the combination of parameters results in a PBG structure that preferably exhibits a transmission band edge corresponding to the input photonic signal frequency.
  • the input photonic signal is delivered into the device in order to generate a second photonic signal at an harmonic frequency of the pump signal.
  • An interaction of the input photonic signal with the arrangement of layers generates the second photonic signal at a second frequency, where the second frequency is different than the first frequency. It will be apparent to one of skill in the art to use this method to perform such frequency conversion techniques as, for example, harmonic generation and optical parametric oscillation.

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Abstract

L'invention concerne un nouveau générateur d'une seconde harmonique utilisant une structure périodique, de bande interdite photonique (PBG), hybride demi-onde quart d'onde. La production d'énergie et le rendement de conversion sont quasiment trois ordres supérieurs à des dispositifs en milieu ambiant à concordance de phase aux longueurs comparables. On obtient des résultats semblables pour une structure périodique à semi-conducteur GaAs/A1As. Ces résultats sont utilisés immédiatement dans des lasers de conversion de fréquence, pour la génération d'une harmonique supérieure ou inférieure, et pour des lasers de type Ramam. Les résonance Stokes ou anti-Stokes peuvent être améliorées ou supprimées à proximité du bord de bande. En général, les logiques mises en oeuvre nécessitent que les champs soient fortement confinés, assurant ainsi des durées d'interaction plus longues, des longueurs de gain améliorées et efficaces et des rendements de conversion améliorés. Il est à noter qu'on peut aboutir à une génération d'une seconde harmonique sensiblement plus forte uniquement grâce à un puissant confinement de la pompe.
PCT/US1998/006378 1998-04-02 1998-04-02 Conversion de la frequence du signal photonique au moyen d'une structure a bande interdite photonique WO1999052015A1 (fr)

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JP2000542693A JP2002510809A (ja) 1998-04-02 1998-04-02 フォトニックバンドギャップ構造を用いたフォトニック信号の周波数変換
CA002327170A CA2327170A1 (fr) 1998-04-02 1998-04-02 Conversion de la frequence du signal photonique au moyen d'une structure a bande interdite photonique
US09/382,690 US6304366B1 (en) 1998-04-02 1999-08-25 Photonic signal frequency conversion using a photonic band gap structure
US09/742,295 US6744552B2 (en) 1998-04-02 2000-12-22 Photonic signal frequency up and down-conversion using a photonic band gap structure

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WO2001046725A1 (fr) * 1999-12-23 2001-06-28 Aguanno Giuseppe D Commande de la reflectivite et de la transmissivite d'un signal photonique a l'aide d'une structure photonique a largeur de bande interdite
EP1255158A1 (fr) * 2001-05-01 2002-11-06 PIRELLI CAVI E SISTEMI S.p.A. Dispositif pour la conversion de longueur d'onde
US6867902B2 (en) 2001-05-01 2005-03-15 Pirelli Cavi E Sistemi S.P.A. Parametric device for wavelength conversion
US7324267B2 (en) 2002-06-28 2008-01-29 Pirelli & C. S.P.A. Four-wave-mixing based optical wavelength converter device

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JP2007148463A (ja) * 2002-09-20 2007-06-14 Rikogaku Shinkokai フォトニック結晶
JP2007286635A (ja) * 2002-09-20 2007-11-01 Rikogaku Shinkokai フォトニック結晶
JP2004279604A (ja) * 2003-03-13 2004-10-07 Fuji Xerox Co Ltd 波長変換装置
JP5527570B2 (ja) * 2007-09-07 2014-06-18 国立大学法人 香川大学 テラヘルツ光源

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2001046725A1 (fr) * 1999-12-23 2001-06-28 Aguanno Giuseppe D Commande de la reflectivite et de la transmissivite d'un signal photonique a l'aide d'une structure photonique a largeur de bande interdite
US6414780B1 (en) 1999-12-23 2002-07-02 D'aguanno Giuseppe Photonic signal reflectivity and transmissivity control using a photonic band gap structure
EP1255158A1 (fr) * 2001-05-01 2002-11-06 PIRELLI CAVI E SISTEMI S.p.A. Dispositif pour la conversion de longueur d'onde
US6867902B2 (en) 2001-05-01 2005-03-15 Pirelli Cavi E Sistemi S.P.A. Parametric device for wavelength conversion
US7324267B2 (en) 2002-06-28 2008-01-29 Pirelli & C. S.P.A. Four-wave-mixing based optical wavelength converter device

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