Abstract

We predict narrowband parametric amplification in dispersion-tailored photonic crystal waveguides made of gallium indium phosphide. We use a full-vectorial model including the dispersive nature both of the nonlinear response and of the propagation losses. An analytical formula for the gain is also derived.

© 2012 Optical Society of America

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References

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2012 (1)

S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, IEEE Photon. J. 4, 224 (2012).
[CrossRef]

2011 (5)

2010 (5)

2009 (2)

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K. Moravvej-Farshi, Opt. Express 17, 18340 (2009).
[CrossRef]

2008 (4)

2006 (2)

2005 (1)

2003 (1)

Beggs, D. M.

Blit, R.

Borel, P. I.

Cestier, I.

Coen, S.

Colman, P.

S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, IEEE Photon. J. 4, 224 (2012).
[CrossRef]

P. Colman, I. Cestier, A. Willinger, S. Combrié, G. Lehoucq, G. Eisenstein, and A. De Rossi, Opt. Lett. 36, 2629 (2011).
[CrossRef]

I. Cestier, A. Willinger, P. Colman, S. Combrié, G. Lehoucq, A. De Rossi, and G. Eisenstein, Opt. Lett. 36, 3936 (2011).
[CrossRef]

V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, P. Colman, A. De Rossi, M. Santagiustina, C. G. Someda, and G. Vadalà, Opt. Lett. 35, 1440 (2010).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photon. 4, 862 (2010).
[CrossRef]

P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” arXiv:1202.6498 (2012).

Combrié, S.

Corcoran, B.

Dahan, D.

De Rossi, A.

Ebnali-Heidari, M.

Eckhouse, V.

Eggleton, B. J.

Eisenstein, G.

Fage-Pedersen, J.

Frandsen, L. H.

Gomez-Iglesias, A.

Grillet, C.

Harvey, J. D.

Hughes, S.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Hugonin, J. P.

Husko, C.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photon. 4, 862 (2010).
[CrossRef]

Knight, J. C.

Krauss, T. F.

Kuipers, L.

Lalanne, P.

Lavrinenko, A. V.

Lefevre, Y.

I. H. Rey, Y. Lefevre, S. A. Schulz, N. Vermeulen, and T. F. Krauss, Phys. Rev. B 84, 035306 (2011).
[CrossRef]

Lehoucq, G.

Leonhardt, R.

Li, J.

Marhic, M. E.

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators, and Related Devices (Cambridge University, 2008), Chap. 3.5.

Martinelli, M.

Mazoyer, S.

Melloni, A.

Monat, C.

Moravvej-Farshi, M. K.

Morichetti, F.

O’Faolain, L.

Patterson, M.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Pelusi, M. D.

Rey, I. H.

J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, Opt. Express 19, 4458 (2011).
[CrossRef]

I. H. Rey, Y. Lefevre, S. A. Schulz, N. Vermeulen, and T. F. Krauss, Phys. Rev. B 84, 035306 (2011).
[CrossRef]

Roy, S.

S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, IEEE Photon. J. 4, 224 (2012).
[CrossRef]

Russell, P. St. J.

Sagnes, I.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photon. 4, 862 (2010).
[CrossRef]

Santagiustina, M.

Schenato, L.

Schulz, S.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Schulz, S. A.

Shumakher, E.

Someda, C. G.

Spasenovic, M.

Vadalà, G.

Vermeulen, N.

I. H. Rey, Y. Lefevre, S. A. Schulz, N. Vermeulen, and T. F. Krauss, Phys. Rev. B 84, 035306 (2011).
[CrossRef]

Wadsworth, W. J.

White, T. P.

Willinger, A.

Wong, C. W.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photon. 4, 862 (2010).
[CrossRef]

Wong, G. K. L.

IEEE Photon. J. (1)

S. Roy, M. Santagiustina, P. Colman, S. Combrié, and A. De Rossi, IEEE Photon. J. 4, 224 (2012).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Nat. Photon. (1)

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photon. 4, 862 (2010).
[CrossRef]

Opt. Express (9)

Opt. Lett. (5)

Phys. Rev. B (2)

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

I. H. Rey, Y. Lefevre, S. A. Schulz, N. Vermeulen, and T. F. Krauss, Phys. Rev. B 84, 035306 (2011).
[CrossRef]

Other (4)

J. B. Khurgin and R. S. Tucker, eds., Slow Light: Science and Applications (CRC, 2009).

http://ab-initio.mit.edu/photons/ .

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators, and Related Devices (Cambridge University, 2008), Chap. 3.5.

P. Colman, S. Combrié, G. Lehoucq, and A. De Rossi, “Control of dispersion in photonic crystal waveguides using group symmetry theory,” arXiv:1202.6498 (2012).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Experimentally measured losses (dots) versus the measured group index and the loss fitting function Loss(ng) (magenta solid curve), (b) the group index as a function of the wavelength, from MPB simulations (solid blue curve) and from the measurements (red triangles).

Fig. 2.
Fig. 2.

Parametric gain as a function of the pump wavelength and of the pump signal detuning (P0=1W, L=1.3mm).

Fig. 3.
Fig. 3.

Comparison of the parametric gain as a function of the pump signal detuning (P0=1.0W, L=1.3mm). Dash-dotted curve, no losses (αm=0, Δα=0); solid curve, dispersive losses (αm0, Δα0); dashed curve, constant losses (αm0, Δα=0).

Equations (2)

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dAidz=[αi2+2ιγip|Ap|2]Ai+ιγFiAp2Aj*exp(ιΔβz),i,j=1,2;ji.
G1(L)=|A1(z=L)/A1(z=0)|2=exp(αmL)|W¯(y0)|2×|[Wk,m(y0)CWk,m(y0)]Mk,m(yL)+[CMk,m(y0)Mk,m(y0)]Wk,m(yL)|2.

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