## Dual-pump parametric amplification in dispersion engineered photonic crystal waveguides |

Optics Express, Vol. 21, Issue 9, pp. 10440-10453 (2013)

http://dx.doi.org/10.1364/OE.21.010440

Acrobat PDF (2737 KB)

### Abstract

This paper describes a numerical simulation of narrow band parametric amplification in dispersion engineered photonic crystal waveguides. The waveguides we analyze exhibit group velocity dispersion functions which cross zero twice thereby enabling many interesting pumping schemes. We analyze the case of two pulsed pumps each placed near one of the zero dispersion wavelengths. These configurations are compared to conventional single pump schemes. The two pumps may induce phase matching conditions in the same spectral location enabling to control the gain spectrum. This is used to study the gain and fidelity of 40*Gbps* NRZ data signals.

© 2013 OSA

## 1. Introduction

1. L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express **14**, 9444–9450 (2006) [CrossRef] [PubMed] .

4. M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using cmos-compatible process,” Opt. Express **19**, 22208–22218 (2011) [CrossRef] [PubMed] .

5. N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E **64**, 056604 (2001) [CrossRef] .

7. M. Santagiustina, C. G. Someda, G. Vadala, S. Combrié, and A. D. Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express **18**, 21024–21029 (2010) [CrossRef] [PubMed] .

8. B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. OFaolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express **18**, 7770–7781 (2010) [CrossRef] [PubMed] .

9. I. Cestier, A. Willinger, V. Eckhouse, G. Eisenstein, S. Combrié, P. Colman, G. Lehoucq, and A. D. Rossi, “Time domain switching / demultiplexing using four wave mixing in gainp photonic crystal waveguides,” Opt. Express **19**, 6093–6099 (2011) [CrossRef] [PubMed] .

10. I. Cestier, S. Combrié, S. Xavier, G. Lehoucq, A. D. Rossi, and G. Eisenstein, “Chip-scale parametric amplifier with 11db gain at 1550nm based on a slow-light gainp photonic crystal waveguide,” Opt. Lett. **37**, 3996–3998 (2012) [CrossRef] [PubMed] .

*nm*. The 1.3

*mm*long waveguide core is a defect line of removed holes, while the dispersion properties are determined by an asymmetric shift of the two innermost rows [11

11. P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” Opt. Express **20**, 13108–13114 (2012) [CrossRef] [PubMed] .

12. S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” Photonics Journal **4**, 224–233 (2012) [CrossRef] .

7. M. Santagiustina, C. G. Someda, G. Vadala, S. Combrié, and A. D. Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express **18**, 21024–21029 (2010) [CrossRef] [PubMed] .

12. S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” Photonics Journal **4**, 224–233 (2012) [CrossRef] .

*β*

_{2}> 0). Further analysis (which incorporated the effect of loss dispersion) [13

13. S. Roy, A. Willinger, S. Combrié, A. D. Rossi, G. Eisenstein, and M. Santagiustina, “Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides,” Opt. Lett. **37**, 2919–2921 (2012) [CrossRef] [PubMed] .

*T*[12

12. S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” Photonics Journal **4**, 224–233 (2012) [CrossRef] .

*β*(

*ω*) function. The effect on NB-OPA generated by a pulsed pump was recently explored [14

14. A. Willinger, S. Roy, M. Santagiustina, S. Combrié, A. D. Rossi, I. Cestier, and G. Eisenstein, “Parametric gain in dispersion engineered photonic crystal waveguides,” Opt. Express **21**, 4995–5004 (2013) [CrossRef] [PubMed] .

*T*was shown to lead to a widening of the distance between the two ZDWs, to an increase in the SPM nonlinearity near the short ZDW, and also to a reduction of the FWM nonlinearity in neighboring wavelengths. The characteristics of the NB-OPA change as

*T*grows such that for a given pump wavelength, the signal-pump detuning range increases, the gain spectrum narrows and the maximum attainable gain is lowered.

6. A. S. Y. Hseih, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of kerr and raman nonlinearities on single-pump optical parametric amplifiers,” in Proceedings of the 33rd European Conference and Ehxibition of Optical Communication (Berlin, Germany, 2007) 1–2.

15. D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express **13**, 6234–6249 (2005) [CrossRef] [PubMed] .

15. D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express **13**, 6234–6249 (2005) [CrossRef] [PubMed] .

17. A. Willinger, E. Shumakher, and G. Eisenstein, “On the roles of polarization and raman-assisted phase matching in narrowband fiber parametric amplifiers,” J. Lightwave Technol. **26**, 2260–2268 (2008) [CrossRef] .

18. A. Gershikov, E. Shumakher, A. Willinger, and G. Eisenstein, “Fiber parametric oscillator for the 2 *μ*m wavelength range based on narrowband optical parametric amplification,” Opt. Lett. **35**, 3198–3200 (2010) [CrossRef] [PubMed] .

*λ*) and red-pump (with longer wavelength

_{p,b}*λ*), can be launched into the waveguide in different configurations producing either larger gain or a wider gain spectrum, thus supporting high bit-rate signals. Since FWM of two strong waves [19] produces idler waves by itself, a configuration may also be found where the two pumps are launched (without a signal to be amplified) and produce idler waves that are built up in phased-matched wavelength regions.

_{p,r}20. A. Willinger and G. Eisenstein, “Split step fourier transform: A comparison between single and multiple envelope formalisms,” J. Lightwave Technol. **30**, 2988–2994 (2012) [CrossRef] .

7. M. Santagiustina, C. G. Someda, G. Vadala, S. Combrié, and A. D. Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express **18**, 21024–21029 (2010) [CrossRef] [PubMed] .

**4**, 224–233 (2012) [CrossRef] .

14. A. Willinger, S. Roy, M. Santagiustina, S. Combrié, A. D. Rossi, I. Cestier, and G. Eisenstein, “Parametric gain in dispersion engineered photonic crystal waveguides,” Opt. Express **21**, 4995–5004 (2013) [CrossRef] [PubMed] .

21. O. Sinkin, R. Holzlohner, J. Zweck, and C. Menyuk, “Optimization of the split-step fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. **21**, 61–68 (2003) [CrossRef] .

22. P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. **15**, 1076–1078 (1990) [CrossRef] [PubMed] .

**4**, 224–233 (2012) [CrossRef] .

*Gbps*NRZ data signal using two CW pumps.

## 2. FWM induced by two pumps

*ω*and

_{p,b}*ω*(referred to hereon as the blue-pump and red-pump, respectively) are transformed into two photons at the signal and idler frequencies

_{p,r}*ω*and

_{s}*ω*, respectively, such that

_{i}*ω*+

_{p,b}*ω*=

_{p,r}*ω*+

_{s}*ω*. The optical spectrum is schematically described in Fig. 2(a). Momentum conservation requires that the two pumps and their mixing products be phased matched, namely Δ

_{i}*k*=

*β*+

_{s}*β*−

_{i}*β*−

_{p,b}*β*should approach zero. In optical fibers having conventional dispersion profiles (characterized by a single ZDW), phase matching can be obtained for all four waves, while the simultaneous degenerate FWM process of three waves is suppressed because of a phase miss-match.

_{p,r}*ω*and two more photons at the appropriate idler frequencies

_{s}*ω*and

_{i,b}*ω*, such that 2

_{i,r}*ω*=

_{p,b}*ω*+

_{s}*ω*and 2

_{i,b}*ω*=

_{p,r}*ω*+

_{s}*ω*. Phase matching requires that Δ

_{i,r}*k*=

_{b}*β*+

_{s}*β*− 2

_{i,b}*β*and Δ

_{p,b}*k*=

_{r}*β*+

_{s}*β*− 2

_{i,r}*β*approach zero. While this seems improbable to maintain in conventional optical fibers, the complex dispersion function of the engineered PhC waveguides allows it and different corresponding scenarios are discussed in the following sections.

_{p,r}*=*

_{p}*ω*−

_{p,b}*ω*generate two idlers at lower and higher frequencies

_{p,r}*ω*and

_{i,r}*ω*, which are detuned by the same amount ΔΩ

_{i,b}*from each pump respectively. Phase matching condition is not optimal for the four waves together, yet the selection of the blue and red pump wavelengths with respect to the complex dispersion profiles ensures that phase matching is satisfied for two groups of degenerate FWM processes. The most dominant parametric process involves the two pumps and the idler at*

_{p}*ω*; nevertheless, phase matching is also satisfied between this idler at

_{i,b}*ω*, the red pump at

_{ib}*ω*and an idler of higher order which is doubly detuned at

_{p,r}*ω*− 2ΔΩ

_{p,r}*. The blue pump transfers energy to the idler at*

_{p}*ω*and to the red pump which transfers in turn transfers energy to the same idler and to another high-order idler.

_{i,b}## 3. Simulation conditions

20. A. Willinger and G. Eisenstein, “Split step fourier transform: A comparison between single and multiple envelope formalisms,” J. Lightwave Technol. **30**, 2988–2994 (2012) [CrossRef] .

*m*envelope is given by where the summation includes all the mixing terms for any combination of waves {

^{th}*a*,

*b*,

*c*} such that their carrier frequencies comply with and their propagation coefficients set the phase mismatch Δ

*k*=

_{abcm}*β*+

_{a}*β*−

_{b}*β*−

_{c}*β*. These conditions are satisfied by many combinations as seen in the exemplary spectrum shown in Fig. 3(a), where several idlers are maintained between the signal and the pumps. When using the M-SSFT algorithm, we account not only for the two pumps, the signal and the idler at

_{m}*ω̃*=

_{i}*ω*+

_{p,b}*ω*−

_{p,r}*ω*, but also for all idlers whose carrier frequencies comply with Eq. (2) together with either pump, the signal or other idlers. All idlers other than the one at

_{s}*ω̃*, are termed hereon high-order idlers (not to be confused with high-order nonlinearity which is not addressed in this work). The output spectrum in Fig. 3(a) shows that it is not possible to predict which of the high-order idlers can be neglected and hence they are all accounted for as long as they are within the waveguide transmission band.

_{i}13. S. Roy, A. Willinger, S. Combrié, A. D. Rossi, G. Eisenstein, and M. Santagiustina, “Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides,” Opt. Lett. **37**, 2919–2921 (2012) [CrossRef] [PubMed] .

14. A. Willinger, S. Roy, M. Santagiustina, S. Combrié, A. D. Rossi, I. Cestier, and G. Eisenstein, “Parametric gain in dispersion engineered photonic crystal waveguides,” Opt. Express **21**, 4995–5004 (2013) [CrossRef] [PubMed] .

*F*(defined by the sampling frequency), two neighboring waves cannot be detuned from each other by less than

_{s}*F*(otherwise the use of M-SSFT is not valid [20

_{s}20. A. Willinger and G. Eisenstein, “Split step fourier transform: A comparison between single and multiple envelope formalisms,” J. Lightwave Technol. **30**, 2988–2994 (2012) [CrossRef] .

*a*,

*b*,

*c*,

*m*} including many high-order idlers that might be separated by less than

*F*from neighboring signal, pump or idler waves. The spectrum in Fig. 3(a) represents a specific choice of wavelengths for the signal and two pumps, such that there is a finite number of FWM products {

_{s}*a*,

*b*,

*c*,

*m*} and all possible waves are not separated by less than the chosen

*F*. This is possible when the detuning of the signal from the closest pump complies with where

_{s}*q*is a rational number, and

*p*,

*m*and

*n*are integers such that

*n*>

*m*≥ 0 and

*p*≥ 0. With this selection of carrier frequencies, the detuning between two neighboring channels is This channel separation is maintained as long as 2

*πnF*≤ Ω

_{s}*.*

_{p}**21**, 4995–5004 (2013) [CrossRef] [PubMed] .

*q*value and a sampling frequency

*F*; (3) tune over a range of signal wavelengths for which a dual-pump scheme that includes the selected blue-pump is valid; (4) for each signal wavelength and blue-pump we set the red-pump according to Eq. (3), such that

_{s}*q*value and a sampling frequency

*F*, the range of possible signal wavelengths is limited by the channel separation condition:

_{s}*ω*≤

_{p,r}*ω*− 2

_{p,b}*πnF*. These limitations are the basis for the simulations performed in sections 4–6, with different values of

_{s}*q*.

**30**, 2988–2994 (2012) [CrossRef] .

*n*increases, and also when the signal detuning decreases. Nevertheless, we maintain the use of the M-SSFT algorithm to ensure that the dispersion in nonlinear parameters is properly included. This dispersion cannot be accounted for with the conventional SSFT algorithms [19, 21

21. O. Sinkin, R. Holzlohner, J. Zweck, and C. Menyuk, “Optimization of the split-step fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. **21**, 61–68 (2003) [CrossRef] .

## 4. Two pumps beating with amplified idlers

18. A. Gershikov, E. Shumakher, A. Willinger, and G. Eisenstein, “Fiber parametric oscillator for the 2 *μ*m wavelength range based on narrowband optical parametric amplification,” Opt. Lett. **35**, 3198–3200 (2010) [CrossRef] [PubMed] .

23. G. K. L. Wong, S. G. Murdoch, R. Leonhardt, J. D. Harvey, and V. Marie, “High-conversion-efficiency widely-tunable all-fiber optical parametric oscillator,” Opt. Express **15**, 2947–2952 (2007) [CrossRef] [PubMed] .

*nm*are smaller than those at 1575

*nm*and this also contributes to the asymmetry. For two identical 100

*ps*pump pulses with profiles taken from experiments, each having a peak power of 750

*mW*, the FWM is sufficiently efficient to yield an output idler pulse with a peak power of 133

*mW*, about 9% of the total input power. The two pump pulses get distorted upon propagation due to a combination of linear dispersion, SPM and XPM. This distortion is similar to what is observed in optical fibers when high power pulses propagate in the normal dispersion regime [19]. The idler pulse width (about 25

*ps*at half-power) is shorter than that of the input pulses, as in the case of NB-OPA with a single pump [14

**21**, 4995–5004 (2013) [CrossRef] [PubMed] .

*q*= 1, such that for every pair of desired idler and blue-pump frequencies, given by

*ω*and

_{i}*ω*respectively, the red-pump frequency is set by

_{p,b}*ω*= 2

_{p,r}*ω*−

_{p,b}*ω*. As mentioned before, we must account also for the evolution of the idler envelopes that are formed along the waveguide, growing or diminishing according to the overall phase matching condition for each one. With two strong pump waves that are detuned from each other by Ω

_{i}*, there could be idler waves forming as far as 2Ω*

_{p}*or 3Ω*

_{p}*away (up to the limits of high losses as in Fig. 1(b)), and the interaction between all them affects the total output power. Thus our simulations use five and six envelopes that are detuned by Ω*

_{p}*from each other, each represented by a vector of less than 200 samples (with the exact numbers varying between iterations).*

_{p}*W*), as a function of the desired idler wavelength. Each figure represents a different

*T*value, and the different curves in each figure represent different blue pump wavelengths. Conversion efficiencies of up to −5

*dB*can be obtained for an idler wavelength that ranges between 1533

*nm*and 1539

*nm*, where in waveguides with larger

*T*, the optimum conversion efficiency shifts to shorter wavelengths, and for a given blue-pump wavelength, the possible idler wavelength span is narrowed (similar to single pump NB-OPA [14

**21**, 4995–5004 (2013) [CrossRef] [PubMed] .

**21**, 4995–5004 (2013) [CrossRef] [PubMed] .

*λ̃*

_{1}and

*λ̃*

_{2}are the short and long ZDWs, respectively. The conversion ratio curves are plotted versus the normalized idler detuning Δ

*, and for different blue-pump detuning Δ*

_{i}*in Fig. 5(b), 5(d) and 5(f). The maximum conversion is obtained for similar combinations of Δ*

_{p,b}*and Δ*

_{i}*for all*

_{p,b}*T*values, yet the spectra are narrower as

*T*grows.

*nm*and the red pump was set so that the desired idler will be generated at either 1538.9

*nm*or 1537.4

*nm*(when power conversion are expected to be high and low respectively according to Fig. 5(a)). Figures 6(a) and 6(b) show, for either blue-pump, red-pump and short wavelength idler respectively, the ratio between the pulse power and the total input power (1.5

*W*) as a function of waveguide length.

*L*= (

_{NL}*γP*)

_{p}^{−1}, corresponding to a 750

*mW*pump and a

*γ*of

_{SPM}*mm*. This fits well with the evolution of the idler power in both presented cases. Its power increases as more photons are converted from the strong pumps, however when phase matching is not satisfied, as in Fig. 6(b), power is cycled back to the pumps after a distance

*L*.

_{NL}*mm*when the idler reaches the same power as the blue-pump. The blue-pump is strongly coupled to the red-pump and to the idler and consequently, its envelope profile is distorted due to both linear dispersion and the nonlinear processes, as can be seen in the insets in Fig. 6(a).

## 5. Amplification by two pumps

*mW*and 750

*mW*respectively. An exemplary spectrum of the waves in this configuration was already presented in Fig. 3(a) featuring the pumps and signal spectra together with the spectra of the numerous idlers generated by multiple FWM interactions.

*T*values with and each curve representing a different choice of blue-pump wavelength and a

*q*value. More configurations of dual-pump schemes can be chosen with different

*q*values, yielding different optimum efficiencies at different signal wavelengths. The gain curves in these cases are formed with the maximum signal-pump detuning (similar to the detuning range with a single pump in [14

**21**, 4995–5004 (2013) [CrossRef] [PubMed] .

*T*is the same, as the gain spectra narrow when

*T*increases.

*nm*wide. Thus according to Eq. (5), given a choice of

*q*and pump wavelength

*λ*, the wavelength of the appropriate red-pump

_{p,b}*λ*, shifts by a small amount as well (assuming that

_{p,r}*λ*as function of

_{p,r}*λ*for different dual-pump schemes.

_{s}## 6. Amplification of high bit-rate data streams

*mW*pump to the dual-pump schemes in which each pump is 375

*mW*(equal total input power). In each of these scenarios, the signal is comprised of a 40

*Gbps*NRZ data stream made up of 1024 pulses having a peak power of 0.5

*mW*, while the pumps are CW. We chose the PhC waveguide with

*q*value), and the wavelengths of the single pump amplifiers. Since the spectral width of the signal is comparable to the narrow band gain bandwidth, it is necessary to characterize the amplifier by an average gain. Each point in Fig. 8 represents such an average gain value which is the ratio of the output pulse train energy (determined by the gain spectrum and the spectral content of the 40

*Gbps*signal) and the energy of the input signal.

*ps*pulse does not experience the maximum possible gain that is attainable from the 750

*mW*pump power. This is attributed to the 40

*Gbps*signal bandwidth being wider than the parametric gain spectrum. We examine the eye opening of each output signal, compare it to the eye opening value of the input signal (an ideal reference signal) and calculate the eye opening ratio, shown in Fig. 9(a) as a function of signal carrier wavelength. Each value in Fig. 9(a) matches an appropriate gain value in Fig. 8 for the same carrier wavelength and same single or dual-pump OPA. It is clear that as the signal wavelength is shifted to where maximum gain is obtained, the eye diagram closes since short sections of the data stream are not fully amplified. In the case of a single pump OPA, a larger eye opening is obtained for pump positioned close to the short ZDW as compared with those positioned close to the long ZDW. This happens since the longer wavelength pump is positioned deep in the normal dispersion region, where phase matching (and hence gain) occurs in a narrower region compared with the phase matching region due to the shorter wavelength pump.

## 7. Conclusion

**30**, 2988–2994 (2012) [CrossRef] .

*dB*is achieved when launching two 750

*mW*pumps. This could be used for a PhC based optical oscillator, similar to those implemented in optical fibers [18

18. A. Gershikov, E. Shumakher, A. Willinger, and G. Eisenstein, “Fiber parametric oscillator for the 2 *μ*m wavelength range based on narrowband optical parametric amplification,” Opt. Lett. **35**, 3198–3200 (2010) [CrossRef] [PubMed] .

*T*that controls the propagation parameters of the engineered PhC waveguide. As with the case of a single pump (shown in [14

**21**, 4995–5004 (2013) [CrossRef] [PubMed] .

*T*we narrow the effective range of signal wavelengths for which parametric gain is attainable for a given dual-pump scheme.

*W*1 waveguides (where the dispersion is only anomalous) and over fibers which exhibit but one ZDW.

## Acknowledgments

## References

1. | L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express |

2. | J. W. Li, T. P. O’Faolain, L. Gomez-Iglesias, A. Krauss, and T. F, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express |

3. | Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. |

4. | M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using cmos-compatible process,” Opt. Express |

5. | N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E |

6. | A. S. Y. Hseih, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of kerr and raman nonlinearities on single-pump optical parametric amplifiers,” in Proceedings of the 33rd European Conference and Ehxibition of Optical Communication (Berlin, Germany, 2007) 1–2. |

7. | M. Santagiustina, C. G. Someda, G. Vadala, S. Combrié, and A. D. Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express |

8. | B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. OFaolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express |

9. | I. Cestier, A. Willinger, V. Eckhouse, G. Eisenstein, S. Combrié, P. Colman, G. Lehoucq, and A. D. Rossi, “Time domain switching / demultiplexing using four wave mixing in gainp photonic crystal waveguides,” Opt. Express |

10. | I. Cestier, S. Combrié, S. Xavier, G. Lehoucq, A. D. Rossi, and G. Eisenstein, “Chip-scale parametric amplifier with 11db gain at 1550nm based on a slow-light gainp photonic crystal waveguide,” Opt. Lett. |

11. | P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” Opt. Express |

12. | S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” Photonics Journal |

13. | S. Roy, A. Willinger, S. Combrié, A. D. Rossi, G. Eisenstein, and M. Santagiustina, “Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides,” Opt. Lett. |

14. | A. Willinger, S. Roy, M. Santagiustina, S. Combrié, A. D. Rossi, I. Cestier, and G. Eisenstein, “Parametric gain in dispersion engineered photonic crystal waveguides,” Opt. Express |

15. | D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express |

16. | E. Shumakher, A. Willinger, R. Blit, D. Dahan, and G. Eisenstein, “Large tunable delay with low distortion of 10 gbit/s data in a slow light system based onnarrow band fiber parametric amplification,” Opt. Express |

17. | A. Willinger, E. Shumakher, and G. Eisenstein, “On the roles of polarization and raman-assisted phase matching in narrowband fiber parametric amplifiers,” J. Lightwave Technol. |

18. | A. Gershikov, E. Shumakher, A. Willinger, and G. Eisenstein, “Fiber parametric oscillator for the 2 |

19. | G. Agrawal, |

20. | A. Willinger and G. Eisenstein, “Split step fourier transform: A comparison between single and multiple envelope formalisms,” J. Lightwave Technol. |

21. | O. Sinkin, R. Holzlohner, J. Zweck, and C. Menyuk, “Optimization of the split-step fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. |

22. | P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. |

23. | G. K. L. Wong, S. G. Murdoch, R. Leonhardt, J. D. Harvey, and V. Marie, “High-conversion-efficiency widely-tunable all-fiber optical parametric oscillator,” Opt. Express |

**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(050.5298) Diffraction and gratings : Photonic crystals

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: February 12, 2013

Revised Manuscript: April 5, 2013

Manuscript Accepted: April 8, 2013

Published: April 22, 2013

**Citation**

A. Willinger, S. Roy, M. Santagiustina, S. Combrié, A. De Rossi, I. Cestier, and G. Eisenstein, "Dual-pump parametric amplification in dispersion engineered photonic crystal waveguides," Opt. Express **21**, 10440-10453 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10440

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### References

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