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 40Gbps NRZ data signals.

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  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. Express14, 9444–9450 (2006).
    [CrossRef] [PubMed]
  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. Express16, 6227–6232 (2008).
    [CrossRef] [PubMed]
  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.34, 1072–1074 (2009).
    [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. Express19, 22208–22218 (2011).
    [CrossRef] [PubMed]
  5. N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
    [CrossRef]
  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. Express18, 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. Express18, 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. Express19, 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]
  11. P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” Opt. Express20, 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 Journal4, 224–233 (2012).
    [CrossRef]
  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. Express21, 4995–5004 (2013).
    [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. Express13, 6234–6249 (2005).
    [CrossRef] [PubMed]
  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. Express14, 8540–8545 (2006).
    [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 μm wavelength range based on narrowband optical parametric amplification,” Opt. Lett.35, 3198–3200 (2010).
    [CrossRef] [PubMed]
  19. G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).
  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]
  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]
  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. Express15, 2947–2952 (2007).
    [CrossRef] [PubMed]

2013 (1)

2012 (5)

2011 (2)

2010 (3)

2009 (1)

2008 (2)

2007 (1)

2006 (2)

2005 (1)

2003 (1)

2001 (1)

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
[CrossRef]

1990 (1)

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

Baba, T.

Bhat, N. A. R.

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
[CrossRef]

Blit, R.

Borel, P. I.

Cestier, I.

Chernikov, S. V.

Coen, S.

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.

Colman, P.

Combrié, S.

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. Express21, 4995–5004 (2013).
[CrossRef] [PubMed]

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 Journal4, 224–233 (2012).
[CrossRef]

P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” Opt. Express20, 13108–13114 (2012).
[CrossRef] [PubMed]

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]

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]

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. Express19, 6093–6099 (2011).
[CrossRef] [PubMed]

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. Express18, 21024–21029 (2010).
[CrossRef] [PubMed]

Corcoran, B.

Dahan, D.

De Rossi, A.

P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” Opt. Express20, 13108–13114 (2012).
[CrossRef] [PubMed]

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 Journal4, 224–233 (2012).
[CrossRef]

Eckhouse, V.

Eggleton, B. J.

Eisenstein, G.

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. Express21, 4995–5004 (2013).
[CrossRef] [PubMed]

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]

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]

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]

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. Express19, 6093–6099 (2011).
[CrossRef] [PubMed]

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

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]

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. Express14, 8540–8545 (2006).
[CrossRef] [PubMed]

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. Express13, 6234–6249 (2005).
[CrossRef] [PubMed]

F, T.

Fage-Pedersen, J.

Frandsen, L. H.

Gershikov, A.

Gomez-Iglesias, L.

Grillet, C.

Hama, Y.

Hamachi, Y.

Harvey, J. D.

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. Express15, 2947–2952 (2007).
[CrossRef] [PubMed]

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.

Holzlohner, R.

Hseih, A. S. Y.

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.

Ishikura, N.

Krauss, A.

Krauss, T. F.

Kubo, S.

Lavrinenko, A. V.

Lehoucq, G.

Leonhardt, R.

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. Express15, 2947–2952 (2007).
[CrossRef] [PubMed]

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.

Li, J. W.

Mamyshev, P. V.

Marie, V.

Menyuk, C.

Monat, C.

Moss, D. J.

Murdoch, S. G.

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. Express15, 2947–2952 (2007).
[CrossRef] [PubMed]

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.

O’Faolain, T. P.

OFaolain, L.

Pelusi, M.

Rossi, A. D.

Roy, S.

Santagiustina, M.

Shinkawa, M.

Shumakher, E.

Sinkin, O.

Sipe, J. E.

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
[CrossRef]

Someda, C. G.

Suzuki, K.

Vadala, G.

Vanholsbeeck, F.

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.

White, T. P.

Willinger, A.

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. Express21, 4995–5004 (2013).
[CrossRef] [PubMed]

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]

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]

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. Express19, 6093–6099 (2011).
[CrossRef] [PubMed]

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

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]

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. Express14, 8540–8545 (2006).
[CrossRef] [PubMed]

Wong, G. K. L.

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. Express15, 2947–2952 (2007).
[CrossRef] [PubMed]

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.

Xavier, S.

Zweck, J.

J. Lightwave Technol. (3)

Opt. Express (11)

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. Express21, 4995–5004 (2013).
[CrossRef] [PubMed]

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. Express18, 7770–7781 (2010).
[CrossRef] [PubMed]

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. Express18, 21024–21029 (2010).
[CrossRef] [PubMed]

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. Express19, 6093–6099 (2011).
[CrossRef] [PubMed]

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. Express19, 22208–22218 (2011).
[CrossRef] [PubMed]

P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” Opt. Express20, 13108–13114 (2012).
[CrossRef] [PubMed]

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. Express13, 6234–6249 (2005).
[CrossRef] [PubMed]

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. Express14, 8540–8545 (2006).
[CrossRef] [PubMed]

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. Express14, 9444–9450 (2006).
[CrossRef] [PubMed]

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. Express15, 2947–2952 (2007).
[CrossRef] [PubMed]

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. Express16, 6227–6232 (2008).
[CrossRef] [PubMed]

Opt. Lett. (5)

Photonics Journal (1)

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 Journal4, 224–233 (2012).
[CrossRef]

Phys. Rev. E (1)

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
[CrossRef]

Other (2)

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.

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

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Figures (9)

Fig. 1
Fig. 1

Dispersion of the propagation parameters of the engineered PhC waveguides: (a) group index and GVD, (b) losses and SPM nonlinearity. The different curves represent different values of the ratio T a: 0.1, 0.125 and 0.15.

Fig. 2
Fig. 2

Schematic description of FWM with two pumps (blue and red arrows) and a signal wave (black arrow) in (a) a dispersion shifted fiber, and (b) a dispersion engineered PhC. Exemplary spectra of the dispersion coefficient β2 are shown in black curves for each waveguide type. The idlers in (b) match the pump with which they are phased matched.

Fig. 3
Fig. 3

(a) Input (blue curve) and output (black curve) spectra with two pumps at λp,b and λp,r, a signal at λs and many high-order idlers, where the simulation sampling frequency is Fs. (b) FWM maps for the parametric gain coefficient (taken from [14]) describing where parametric gain is obtained for T a values of 0.1, 0.125 and 0.15. The choice of the two pumps in (a) matches the FWM map of T a = 0.125 (green curve with dashed lines) so that each of the pumps generates NB-OPA in the region of the signal wave.

Fig. 4
Fig. 4

Example of (a) input and Output spectra and (b) output envelope profiles of two strong pumps with FWM idlers in the engineered PhC waveguides ( T a = 0.15). In (a) the input (dash) spectrum belongs to two strong pumps that produce two idler waves at shorter and longer wavelengths that are added to the output (black) spectrum. In (b) the identical input profiles (shown in the inset) of both pumps get distorted while the short wavelength idler is produced with a narrower envelope.

Fig. 5
Fig. 5

Conversion ratio of the output short-wavelength idler pulse to the input pumps power in waveguides having different T a. The ratios are plotted against an absolute or normalized wavelength scales: (a,b) T a = 0.1, (c,d) T a = 0.125, (e,f) T a = 0.15. The different curves are plotted against desired idler wavelength, and each curve represent different blue-pump wavelength choice. As T grows, the conversion efficiency spectra become narrower.

Fig. 6
Fig. 6

The evolution of the blue-pump (blue dots) red-pump (red dots) and short-wavelength idler (black dots) along the waveguide. The vertical axis describes the ratio between the pulse power and the total input power (1.5W). The blue-pump was set to 1545nm and the red pump was set so that the desired idler will be generated at (a) 1538.9nm (with optimal phase matching) and (b) 1537.4nm (with phase miss-match). The insets show the envelope of the blue-pump at selected points along the waveguide.

Fig. 7
Fig. 7

Gain spectra for different dual-pump schemes (with 100ps pulses) in engineered PhC waveguides with (a) T a = 0.1, (b) T a = 0.125 and (c) T a = 0.15. The blue-pump wavelength λp,b and the q values are stated in the legends. (d) Calculated red-pump wavelength λp,r for a few dual-pump schemes taken from (a), (b) and (c) in regions where the gain is larger than 3dB. λp,r changes by no more than 1nm and can be considered fixed. Here the legend is formatted as λp,b, q @ T a.

Fig. 8
Fig. 8

Curves of the average signal gain as a function of the NRZ signal carrier wavelength for the two OPA types: a dual-pump scheme with 375mW each (green curve) and a single pump with 750mW (blue and red curves). The calculations are for an engineered PhC waveguide with T a = 0.15. The insets depict the eye diagrams for output signals around 1529.7nm at different OPA configurations.

Fig. 9
Fig. 9

(a) Eye opening ratio of the signal as a function of signal wavelength for the two OPA types: a dual-pump scheme with 375mW each (green curves) and a single pump with 750mW (blue and red curves). The calculations are done for simulations performed in an engineered PhC waveguide with T a = 0.15. (b) Curves of the eye opening ratio matching the average signal gain. These curves show that signal output is cleaner after the dual-pump OPA given the same gain level as a single pump OPA, for gain above 5dB.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

{ a , b , c } γ a , b , c , m A a A b A c * exp ( j Δ k a b c d z ) ,
ω a + ω b = ω c + ω m ,
ω s ω p , b = q Ω p ( p + m n ) ( ω p , b ω p , r ) ,
Δ ω min = { Ω p n , m > 0 Ω p , m = 0 , n = 1 .
ω p , r = ( 1 + q ) ω p , b ω s q .
Δ p , b = λ p , b λ ˜ 1 λ ˜ 2 λ ˜ 1 , Δ i = λ i λ p , b λ ˜ 2 λ ˜ 1 ,
Δ λ p , r 1 q Δ λ s .

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