## Mid-infrared optical parametric oscillators based on uniform GaP waveguides |

Optics Express, Vol. 18, Issue 19, pp. 20370-20383 (2010)

http://dx.doi.org/10.1364/OE.18.020370

Acrobat PDF (2478 KB)

### Abstract

Integrated chip-scale optical systems are an attractive platform for the implementation of non-linear optical interactions as they promise compact robust devices that operate reliably with lower power consumption compared to analogs based on bulk nonlinear crystals. The use of guided modes to facilitate nonlinear parametric interactions between optical fields, as opposed to bulk beams, has certain implications on optical parametric oscillations, the most important of which are additional methods for achieving phase synchronism and reduced threshold power due to the tight confinement associated with the guided modes. This work presents a theoretical investigation on the use of polarization dependent mode dispersion in guided wave structures as a means to achieve non-linear parametric oscillations from continuous wave sources with outputs in the mid-infrared region of the spectrum. An Al_{2}O_{3}/GaP/Al_{2}O_{3} waveguide system is investigated and shown to produce parametric oscillations at 3µm to 5µm from 1µm to 2µm input waves utilizing 0.14µm to 0.30µm GaP cores. The threshold power is shown to be 320 × less than that obtainable using more traditional quasi-phase matched bulk crystals over the same wavelength range.

© 2010 OSA

## 1. Introduction

6. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. **21**(17), 1336–1338 (1996). [CrossRef] [PubMed]

7. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. **8**(3), 506–520 (2002). [CrossRef]

10. S. Zlatanovic, J. S. Park, S. Moro, J. M. Chavez Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nature Photonics Advance Online Publication, DOI 10:1038/nphoton.2010.117 (2010).

12. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature **391**(6666), 463–466 (1998). [CrossRef]

14. L. Scaccabarozzi, M. M. Fejer, Y. Huo, S. Fan, X. Yu, and J. S. Harris, “Enhanced second-harmonic generation in AlGaAs/AlxOy tightly confining waveguides and resonant cavities,” Opt. Lett. **31**(24), 3626–3628 (2006). [CrossRef] [PubMed]

*TM*-like and

*TE*-like guided modes to achieve both the phase matching condition and the strong field overlap required for efficient parametric amplification without the necessity, or growth complexity, of periodic domain inversion.

15. V. Tassev, D. Bliss, C. Lynch, C. Yapp, W. Goodhue, and K. Termkoa, “Low pressure-temperature-gas flow HVPE growth of GaP for nonlinear optical frequency conversion devices,” J. Cryst. Growth **312**(8), 1146–1149 (2010). [CrossRef]

_{2}O

_{3}/GaP/Al

_{2}O

_{3}waveguides and bulk orientation-patterned GaP QPM structures show that the OPO threshold is 320 × lower in the thin-film waveguide case. We discuss an alternative OPO strategy for the future: the use of a silicon-based waveguide having a composite Si/GaP/Si core.

## 2. Phase matching in guided wave OPOs

*λ*is converted into signal and idler waves,

_{p}*λ*and

_{s}*λ*. In general, the wave with the longer wavelength is called the idler wave, and wave with the shorter wavelength is called the signal wave. Energy conservation requires that

_{i}*n*,

_{p}*n*, and

_{s}*n*are refractive indices for the pump, signal, and idler waves respectively. It is often convenient to introduce a unitless parameter

_{i}*a*=

*λ*/

_{p}*λ*(0 <

_{i}*a*≤ ½) and express the phase synchronism condition (2) through the refractive indices at the wavelengths

19. D. E. Thompson and P. D. Coleman, “Step-tunable far infrared radiation by phase matched mixing in planar-dielectric waveguides,” IEEE Trans. Microw. Theory Tech. **22**(12), 995–1000 (1974). [CrossRef]

*TM*(transverse magnetic) mode of a planar waveguide has lower index compared to a same-order

*TE*(transverse electric) mode. Another approach is to use higher order modes for the pump wave and lower order modes for signal and idler. Modes of the same symmetry (all even, for instance) are preferable in order to avoid vanishing mode overlapping integrals. A possible configuration is a

*TM*

_{2}(third-order) pump and

*TE*

_{0}(fundamental) signal-and-idler. However, this requires selective launching of the third-order pump, and the overlap of the three modes is relatively small.

*a*= ½,

*λ*=

_{i}*λ*= 2

_{s}*λ*), or for a reciprocal process – second harmonic generation – has been studied earlier [20]. With well-defined wavelengths such as

_{p}*λ*and 2

_{p}*λ*, it is easy to find the waveguide configuration that leads to the phase synchronism. In that case one would plot the effective indices for the

_{p}*TM*-polarized mode at wavelength

*λ*and for the

_{p}*TE*-polarized mode at 2

*λ*, both as a function of the guiding film thickness. The intersection of these dispersion curves defines the film thickness at which synchronism is achieved.

_{p}*a*≠ ½ (that is,

*λ*≠

_{i}*λ*), requires some additional arithmetic. It is not evident

_{s}*a priori*that the phase synchronism for guided modes is possible when the idler and signal wavelengths are substantially different.

*TM*-polarized, and, in general, at least one of the signal/idler waves must be

*TE*-polarized. Having in mind the particular nonlinearity tensor in GaP [21

21. J. Seres, “Dispersion of second-order nonlinear optical coefficients,” Appl. Phys. B **73**(7), 705–709 (2001). [CrossRef]

*TE*-polarized. Thus, the phase synchronism condition (3) is rewritten in terms of effective indices of

*TE*- and

*TM*-polarized guided modes

*t*as an independent variable. Also, it is presumed that functional dependence

*Q*=

*TE*or

*TM*, implicitly includes material dispersion through wavelength-dependent indices

*n*(

_{g}*λ*),

*n*(

_{s}*λ*), and

*n*(

_{c}*λ*) of the guiding core, substrate, and cladding respectively. In case of a thin-film waveguide, the effective indices are found by numerically solving the equation [22]where

*M*= 0, 1, 2, … is the mode order, and numerical value for

*Q*is 0 for

*TE*-polarized mode and 1 for the

*TM*case. In absence of material dispersion, the ratio

*t*/

*λ*defines the effective indices

*λ*, select the parameter

_{p}*a*in the range 0 <

*a*≤ ½, which then uniquely defines the idler and signal wavelengths

*t*to satisfy (4) assuming that the effective indices are defined according to (5). By allowing the parameter

*a*to vary in a certain range, one would find the values of film thickness needed to provide phase synchronism for optical parametric oscillations at various wavelengths. The data on

*λ*(

_{i}*a*,

*λ*),

_{p}*λ*(

_{s}*a*,

*λ*), and

_{p}*t*(

*a*,

*λ*) can then be used to plot important dependences such as the wavelengths of the idler and signal

_{p}*λ*(

_{i}*t*,

*λ*) and

_{p}*λ*(

_{s}*t*,

*λ*), versus film thickness

_{p}*t*for given values of the pump wavelength

*λ*.

_{p}*d,*is needed for the estimation of the pump power at the threshold of optical parametric oscillation. An accurate quantitative analysis of how the finite width would affect the phase synchronization and the overlap of the modal fields will be the subject of future studies. In this paper, the width of the waveguides

*d*is considered to be large enough so that all the essential waveguide characteristics are well approximated by the equations for a thin-film planar structure. Symmetric and asymmetric waveguides are schematically shown in Fig. 1 .

*λ*expressed in micrometers. This formula is presumed to be valid for 0.8μm <

*λ*< 10.0μm.

*n*–

_{g}*n*≈1.3), as well as the difference between the effective indices for

_{s}*TE*- and

*TM*-polarized waves (

*n*–

_{o}*n*≈0.008), so, the substrate index was chosen to be [23]

_{e}*λ*< 5.5μm. The upper cladding index was either equal to that of substrate

*n*=

_{c}*n*, or set be

_{s}*n*= 1 depending on the waveguide configuration under consideration.

_{c}*TM*

_{0}mode at the pump wavelength

*λ*= 1.5μm, which represents the left hand side of Eq. (4). For comparison, the effective index for the

_{p}*TE*

_{0}mode is shown by long-dash black line, and, as seen, it is always larger than the index of

*TM*

_{0}mode. The right hand side of Eq. (4) is a linear combination of the effective indices of the

*TE*

_{0}modes at wavelengths

*λ*=

_{i}*λ*/

_{p}*a*and

*λ*=

_{s}*λ*/(1 –

_{p}*a*) respectively, and is shown in Fig. 2 as a function of various values of

*a*as green dot-, dot-dash, and short-dash lines. The intersection of these lines with the solid black line indicates that the phase matching condition (4) is satisfied. For each value of

*a*(and, respectively, a given value of idler wavelength

*λ*=

_{i}*λ*/

_{p}*a*) there are two intersection points at around

*t*≈0.07μm and between 0.2μm and 0.3μm in Fig. 2. The larger of these two values of the film thickness is preferable as it is expected to provide larger value of the mode-overlap integral suggesting greater parametric conversion efficiency.

*a*values is limited. Setting the longest wavelength of the idler wave to be

*λ*= 5.5μm, the smallest

_{i}*a*is found to be

*a*=

*λ*/

_{p}*λ*≈0.273. Allowing the parameter

_{i}*a*to vary from 0.273 to 0.5, the associated values of idler wavelength,

*λ*=

_{i}*λ*/

_{p}*a*, and signal wavelength,

*λ*=

_{s}*λ*/(1 –

_{p}*a*), can be plotted as a function of film thickness,

*t*(

*a*), which will allow for phase matching. Results of these calculations are shown in Fig. 3 for pump wavelengths of 1.0µm, 1.5µm and 2.0µm with signal and idler wavelengths shown in blue and red respectively.

*TE*or

*TM*. This means that, aside from material properties, there is no fundamental limit on how long the idler wavelength can be. In contrast, in an asymmetric structure, the idler mode will experience cutoff if its wavelength becomes too long. This was not shown in Fig. 4 because the longest wavelength in calculations was set to be at 5.5μm and this long wave cutoff is predicted to be at about 7.1μm (for 0.23μm thick film and transparent claddings with index of 1.7). Although not particularly relevant in the case presented here, cutoff will become important when the index contrast in an asymmetric waveguide is small and/or the idler wavelength is long.

*TE*-like and

*TM*-like modes vanishes and thus the polarization mode dispersion can no longer be used for the purpose of facilitating the phase synchronism. A detailed study of the effects of finite width of the waveguide on the phase matching condition is beyond the scope of this paper.

## 3. Threshold condition for OPO

*d*is the second order nonlinearity tensor,

_{ijk}*ε*

_{0}is the vacuum permittivity, and

*E*and

_{j}*E*are the time dependent components of the vector of the electric field strength. Here, the tensor terms are expressed in meters per Volt. For a given symmetry of a crystal and given direction of propagation, similar relations hold between the complex amplitudes of polarization and the electric field strength for the pump, signal, and idler waves:

_{k}*d*in (8) depends on the propagation direction and polarizations of the pump, signal, and idler waves. In QPM crystals the relative phase between oscillations of electric field in a wave and corresponding nonlinear polarization produced by the other waves is step-like adjusted at interfaces between the domains. Compared to a case of a perfect phase matching in a uniform crystal, this leads to a reduced effective nonlinearity:

_{eff}_{3}, the use of QPM is justified as it allows for selecting the propagation direction and polarizations of waves to maximize

*d*, so that the reduced value of

_{eff}*d*=

_{QPM}*η*is still larger than the effective nonlinearity of the waves propagating in the direction of phase synchronism defined by the birefringence.

_{QPM}d_{eff}*L*is the length of the nonlinear crystal, and

*δ*and

_{s}*δ*are the loss factors for the signal and idler waves as a function of the round trip losses in the resonator. These losses include possible absorption and scattering at the signal/idler wavelengths in the nonlinear crystal

_{i}*α*, non-perfect reflection by resonator mirrors

_{s,i}*R*

_{1}

*and*

_{s,i}*R*

_{2}

*, and non-perfect transmission through internal components of the resonator*

_{s,i}*P*/

_{th}*A*in the pump beam, the threshold condition (10) can be written as follows

*A*has the dimension of area and can be considered as a normalized area defined by the overlap of the three waves. Reduced

_{norm}*E*,

_{p}*E*, and

_{s}*E*field overlap would result in a larger normalized area, which effectively accounts for a weaker nonlinear interaction of the waves. This normalized area, rather than the pump beam cross section, appears in the formula (11) for the threshold power of the OPO as

_{i}*w*,

_{p}*w*, and

_{s}*w*respectively:

_{i}*w*=

_{p}*w*=

_{s}*w*, Eq. (16) gives

_{i}*b*close to

*ξ*is the numerical constant on the order of unity, for Gaussian beams found to be

*ξ*≈2.84 [25

25. G. D. Boyd and D. A. Kleiman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. **39**(8), 3597–3639 (1968). [CrossRef]

*L*= 25mm,

*λ*= 1.5μm,

_{p}*λ*= 2.25μm,

_{s}*λ*= 4.5μm,

_{i}*n*≈

_{p}*n*≈

_{s}*n*≈3.0, and

_{i}*ξ*= 2.84, we then find

*A*≈5⋅10

_{norm}^{3}μm

^{2}.

*A*≈(

_{w}*λ*/

*n*)

^{2}. Using the longest wavelength in the above numerical example,

*λ*= 4.5μm and

_{i}*n*≈3.0, one finds

*A*≈2.25 μm

_{w}^{2}, so that

*A*/

_{norm}*A*≈2.2⋅10

_{w}^{3}. This implies that the threshold power in a waveguide device can be thousands of times smaller than that in the case of bulk beams. Even though a non-perfect overlap of the pump, signal, and idler guided modes can reduce the nonlinear interaction, the expected decrease of the required pump power is still substantial. This brings the threshold power down to the tens or hundreds milliwatt level, quite suitable for chip-scale integrated optoelectronic devices and systems.

27. W. Denzer, G. Hancock, A. Hutchinson, M. Munday, R. Peverall, and G. A. D. Ritchie, “Mid-infrared generation and spectroscopy with a PPLN ridge waveguide,” Appl. Phys. B **86**(3), 437–441 (2007). [CrossRef]

30. S. M. Spillane, M. Fiorentino, and R. G. Beausoleil, “Spontaneous parametric down conversion in a nanophotonic waveguide,” Opt. Express **15**(14), 8770–8780 (2007). [CrossRef] [PubMed]

*d*, similar to the case of bulk beams, is reduced, which is accounted for by the factor

_{eff}*E*(

*x*,

*y*) can be factorized and presented in a form

*E*(

*x*)

*F*(

*y*). Then one can also factorize the expression for the normalized area

*F*(

*y*) and thus rather accurately predict OPO threshold power in wide waveguides. For the purpose of order-of-magnitude estimations, we accept further simplification assuming that all the field distributions in the lateral direction

*F*(

*y*) are approximated by a model function cos(

*πy*/

*d*) for |

*y*| <

*d*/2 and zero everywhere else, where

*d*is the waveguide width. The integration in (22) then leads to

*d*is used in a bulk QPM OPO and in a waveguide-based OPO, and assuming that the length of the nonlinear medium is the same in both cases, while taking the resonator loss factors to be identical for both configurations, the ratio of threshold powers for a guided wave device

_{eff}*W*parameter in (23) is not an effective extent of the modal fields in the

_{x}*x*-direction, but rather a normalization factor that takes into account both the extent of the modal fields and fields’ overlap within the nonlinear part of the waveguide’s cross section. In particular, all modal fields may be strongly confined, but, if the overlap integral vanishes, or, if the nonlinear material occupies only a tiny fraction of the waveguide’s core, the

*W*parameter would diverge. The fact that only the core or, maybe, only a part of the core in a composite waveguide is nonlinear is already accounted for in (20) – (22) as long as the overlap of the

_{x}*E*,

_{p}*E*, and

_{s}*E*fields is calculated within the nonlinear part of the waveguide’s cross section. The overlap of pump, signal, and idler waves in a bulk crystal and in a waveguide is schematically illustrated in Fig. 5 .

_{i}*λ*= 1.5μm. With waveguide thickness rounded to

_{p}*t*= 0.236μm, the signal and idler wavelengths are

*λ*≈2.25μm and

_{s}*λ*≈4.48μm. The strength of electric field for the pump, signal, and idler modes, as a function of a coordinate across the waveguide, is shown in Fig. 6 . The pump wave is a

_{i}*TM*

_{0}mode, while signal and idler are

*TE*

_{0}modes.

*TM*-polarized pump wave shows a large field discontinuity at the film boundaries so that the field maximum is reached at the interfaces rather than in the middle of the film.

*TE*-polarized modes, in general, are confined more tightly. In this example, the signal wave, even though its wavelength is somewhat longer than the pump wavelength, shows comparable penetration into the claddings, but the mode profile is smooth and the field maximum is reached in the middle of the film, so that this mode is confined somewhat better. The idler wave though, due to its much longer wavelength, shows very long wings expanding far into the claddings. Even without accurate arithmetic it is evident that the guided modes at the pump, signal, and idler wavelengths are not really strongly confined in the guiding film.

*W*≈5.5μm. Setting, rather conservatively,

_{x}*d*= 10μm (smaller values might well be acceptable as long as

*d*is still several times more than the extent of each of the modal fields in the vertical direction at the 1/

*e*level), one gets

*dW*≈38μm

_{x}^{2}. Compared to the normalized area (18) estimated for bulk beams

*A*≈5⋅10

_{norm}^{3}μm

^{2}, this waveguide configuration provides about 130 times smaller normalized area. Also, with no need for the QPM, the effective nonlinearity in the waveguide’s core is 1/

*η*=

_{QPM}*π*/2 times larger than in the bulk QPM crystal. This translates into 320 times smaller threshold pump power required for optical parametric oscillator when compared to Gaussian beams propagating in a QPM crystal.

## 4. Conclusions

*TE*and

*TM*modes, we have derived the CW perfect phase matching conditions for a three-layer uniform waveguide in which a thin film of crystalline GaP forms the second-order NLO waveguide core. For Al

_{2}O

_{3}waveguide claddings and for

*TM*

_{0}pump wavelengths in the 1μm to 2μm range, signal outputs in the 3 μm to 5 μm range are predicted for phase matched film thicknesses of 0.14 μm to 0.30 μm. We then used orientation-patterned quasi-phase-matched GaP as a standard of comparison for our waveguide, in terms of the pump power required for OPO threshold, assuming in both cases that the signal mode as well as the idler mode are resonant in a Fabry Perot cavity. Gaussian beam theory and mode overlap theory was used to show that the thin-film waveguide has a threshold 320 × lower than that of QPM GaP case. The present waveguide appears suitable for low-power mid-infrared on-chip optoelectronics networks. Looking to future improvements and alternatives to the GaP/sapphire waveguide, we believe that the uniform OPO waveguide with a Si/GaP/Si core is also capable of perfect mid-infrared phase matching. That waveguide, with its lattice-matched core, has the advantage of being readily integrateable (directly grown, easily manufactured) on a silicon-on-sapphire wafer or on the silicon-on-insulator wafer that has become the standard platform of the silicon photonics industry.

## Acknowledgements

## References and links

1. | I. T. Sorokina, and K. L. Vodopyanov, eds., |

2. | A. Berrou, J.-M. Melkonian, M. Raybaut, A. Godard, E. Rosencher, and M. Lefebre, “Specific architectures for optical parametric oscillators,” C. R. Phys. |

3. | M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity-ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (6–8μm) optical parametric oscillator,” Appl. Phys. B |

4. | G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. |

5. | P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. |

6. | W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. |

7. | J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. |

8. | S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. |

9. | X. Liu, R. M. Osgood, Y. A. Vlasov, W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguide,” Nature Photonics Advance Online Publication, DOI 10:1038/nphoton.2010.119 (2010). |

10. | S. Zlatanovic, J. S. Park, S. Moro, J. M. Chavez Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nature Photonics Advance Online Publication, DOI 10:1038/nphoton.2010.117 (2010). |

11. | R. W. Boyd, Nonlinear Optics, 3rd ed., (Academic Press, 2008). |

12. | A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature |

13. | E. Guillotel, M. Ravaro, F. Ghiglieno, C. Langlois, C. Ricolleau, S. Ducci, I. Favero, and G. Leo, “Parametric amplification in GaAs/AlOx waveguide,” Appl. Phys. Lett. |

14. | L. Scaccabarozzi, M. M. Fejer, Y. Huo, S. Fan, X. Yu, and J. S. Harris, “Enhanced second-harmonic generation in AlGaAs/AlxOy tightly confining waveguides and resonant cavities,” Opt. Lett. |

15. | V. Tassev, D. Bliss, C. Lynch, C. Yapp, W. Goodhue, and K. Termkoa, “Low pressure-temperature-gas flow HVPE growth of GaP for nonlinear optical frequency conversion devices,” J. Cryst. Growth |

16. | R. A. Soref, “Mid-infrared photonics in silicon and germanium,” Nature Photonics, to be published in August 2010. |

17. | R. A. Soref, “Towards silicon-based longwave integrated optoelectronics (LIO)”, SPIE Proceedings, 6898, paper 09 (2008). |

18. | S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal, and quasi-phase-matching techniques,” J. Opt. A |

19. | D. E. Thompson and P. D. Coleman, “Step-tunable far infrared radiation by phase matched mixing in planar-dielectric waveguides,” IEEE Trans. Microw. Theory Tech. |

20. | H. Ishikawa, T. Kondo, “Birefringent phase matching in thin rectangular high-index-contrast waveguides,” Applied Physics Express 2(4), Art. No. 042202 (2009). |

21. | J. Seres, “Dispersion of second-order nonlinear optical coefficients,” Appl. Phys. B |

22. | M. J. Adams, |

23. | http://refractiveindex.info |

24. | A. Yariv, and P. Yeh |

25. | G. D. Boyd and D. A. Kleiman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. |

26. | R. S. Bennink, “Optimal co-linear Gaussian beams for spontaneous parametric down-conversion,” arXiv:1003.3810v1 [quant-ph] (2010). |

27. | W. Denzer, G. Hancock, A. Hutchinson, M. Munday, R. Peverall, and G. A. D. Ritchie, “Mid-infrared generation and spectroscopy with a PPLN ridge waveguide,” Appl. Phys. B |

28. | T. Matsushita, I. Ohta, T. Kondo, “Quasi-phase-matched parametric fluorescence in a periodically inverted GaP waveguide,” Applied Physics Express 2(6), Art. No. 061101 (2009). |

29. | M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express |

30. | S. M. Spillane, M. Fiorentino, and R. G. Beausoleil, “Spontaneous parametric down conversion in a nanophotonic waveguide,” Opt. Express |

**OCIS Codes**

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(130.7405) Integrated optics : Wavelength conversion devices

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: July 12, 2010

Revised Manuscript: August 19, 2010

Manuscript Accepted: August 23, 2010

Published: September 9, 2010

**Citation**

Ivan Avrutsky, Richard Soref, and Walter Buchwald, "Mid-infrared optical parametric oscillators based on uniform GaP waveguides," Opt. Express **18**, 20370-20383 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20370

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### References

- I. T. Sorokina, and K. L. Vodopyanov, eds., Solid-State Mid-Infrared Laser Sources, (Springer, 2003).
- A. Berrou, J.-M. Melkonian, M. Raybaut, A. Godard, E. Rosencher, and M. Lefebre, “Specific architectures for optical parametric oscillators,” C. R. Phys. 8(10), 1162–1173 (2007). [CrossRef]
- M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity-ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (6–8μm) optical parametric oscillator,” Appl. Phys. B 75(2–3), 367–376 (2002). [CrossRef]
- G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74(1), 1–18 (2003). [CrossRef]
- P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31(1), 71–73 (2006). [CrossRef] [PubMed]
- W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. 21(17), 1336–1338 (1996). [CrossRef] [PubMed]
- J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002). [CrossRef]
- S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2(6), 498–513 (2008). [CrossRef]
- X. Liu, R. M. Osgood, Y. A. Vlasov, W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguide,” Nature Photonics Advance Online Publication, DOI 10:1038/nphoton.2010.119 (2010).
- S. Zlatanovic, J. S. Park, S. Moro, J. M. Chavez Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nature Photonics Advance Online Publication, DOI 10:1038/nphoton.2010.117 (2010).
- R. W. Boyd, Nonlinear Optics, 3rd ed., (Academic Press, 2008).
- A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998). [CrossRef]
- E. Guillotel, M. Ravaro, F. Ghiglieno, C. Langlois, C. Ricolleau, S. Ducci, I. Favero, and G. Leo, “Parametric amplification in GaAs/AlOx waveguide,” Appl. Phys. Lett. 94(17), 171110 (2009). [CrossRef]
- L. Scaccabarozzi, M. M. Fejer, Y. Huo, S. Fan, X. Yu, and J. S. Harris, “Enhanced second-harmonic generation in AlGaAs/AlxOy tightly confining waveguides and resonant cavities,” Opt. Lett. 31(24), 3626–3628 (2006). [CrossRef] [PubMed]
- V. Tassev, D. Bliss, C. Lynch, C. Yapp, W. Goodhue, and K. Termkoa, “Low pressure-temperature-gas flow HVPE growth of GaP for nonlinear optical frequency conversion devices,” J. Cryst. Growth 312(8), 1146–1149 (2010). [CrossRef]
- R. A. Soref, “Mid-infrared photonics in silicon and germanium,” Nature Photonics, to be published in August 2010.
- R. A. Soref, “Towards silicon-based longwave integrated optoelectronics (LIO),” SPIE Proceedings, 6898, paper 09 (2008).
- S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal, and quasi-phase-matching techniques,” J. Opt. A 6(6), 569–584 (2004).
- D. E. Thompson and P. D. Coleman, “Step-tunable far infrared radiation by phase matched mixing in planar-dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 22(12), 995–1000 (1974). [CrossRef]
- H. Ishikawa and T. Kondo, “Birefringent phase matching in thin rectangular high-index-contrast waveguides,” Appl. Phys. Express 2(4), Art. No. 042202 (2009).
- J. Seres, “Dispersion of second-order nonlinear optical coefficients,” Appl. Phys. B 73(7), 705–709 (2001). [CrossRef]
- M. J. Adams, An Introduction to Optical Waveguides, (Wiley, 1981).
- http://refractiveindex.info
- A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed., (Oxford University Press, 2006).
- G. D. Boyd and D. A. Kleiman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39(8), 3597–3639 (1968). [CrossRef]
- R. S. Bennink, “Optimal co-linear Gaussian beams for spontaneous parametric down-conversion,” arXiv:1003.3810v1 [quant-ph] (2010).
- W. Denzer, G. Hancock, A. Hutchinson, M. Munday, R. Peverall, and G. A. D. Ritchie, “Mid-infrared generation and spectroscopy with a PPLN ridge waveguide,” Appl. Phys. B 86(3), 437–441 (2007). [CrossRef]
- T. Matsushita, I. Ohta, T. Kondo, “Quasi-phase-matched parametric fluorescence in a periodically inverted GaP waveguide,” Appl. Phys. Express 2(6), Art. No. 061101 (2009).
- M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15(12), 7479–7488 (2007). [CrossRef] [PubMed]
- S. M. Spillane, M. Fiorentino, and R. G. Beausoleil, “Spontaneous parametric down conversion in a nanophotonic waveguide,” Opt. Express 15(14), 8770–8780 (2007). [CrossRef] [PubMed]

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