Vol. 158

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Realization of All-Optical Digital Amplification in Coupled Nonlinear Photonic Crystal Waveguides

By Vakhtang Jandieri, Ramaz Khomeriki, Daniel Erni, and Weng Cho Chew
Progress In Electromagnetics Research, Vol. 158, 63-72, 2017


In this conceptual study, all-optical amplification of the light pulses in two weakly coupled nonlinear photonic crystal waveguides (PCWs) is proposed. We consider two adjacent PCWs, which consist of line defects in a 2D square lattice of periodically distributed circular rods made from dielectric material with Kerr-type nonlinearity. Dispersion diagrams of the PCW's symmetric and antisymmetric modes are analyzed using a recently developed analytical formulation. The operating frequency is properly chosen to be located at the edge of the PCW's dispersion diagram (i.e. adjacent to the photonic crystals low-energy band edge), where in the linear case no propagation modes are excited. However, in case of a nonlinear medium when the amplitude of the injected signal is above some threshold value, solitons are formed propagating inside the coupled nonlinear PCWs. The near field distributions of the propagating light pulse inside the coupled nonlinear PCWs and the output power of the received signal are numerically studied in a detail. A very good agreement between the analytic soliton solution based on the nonlinear Schrödinger equation and numerical result is obtained. Amplification coefficients are calculated for the various amplitudes of the input signals. The results vividly demonstrate the effectiveness of the weakly coupled nonlinear PCWs as an all-optical digital amplifier.


Vakhtang Jandieri, Ramaz Khomeriki, Daniel Erni, and Weng Cho Chew, "Realization of All-Optical Digital Amplification in Coupled Nonlinear Photonic Crystal Waveguides," Progress In Electromagnetics Research, Vol. 158, 63-72, 2017.


    1. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.

    2. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, 2486-2489, 1987.

    3. Khomeriki, R. and J. Leon, "All-optical amplification in metallic subwavelength linear waveguides," Phys. Rev. A, Vol. 87, 053806-053809, 2013.

    4. Jandieri, V. and R. Khomeriki, "Linear amplification of optical signal in coupled photonic crystal waveguides," IEEE Photonics Technology Letters, Vol. 27, 639-641, 2015.

    5. Malaguti, S., G. Bellanca, S. Combrie, A. de Rossi, and S. Trillo, "Temporal gap solitons and all-optical control of group delay in line-defect waveguides," Phys. Rev. Lett., Vol. 109, 163902, 2012.

    6. Cuesta-Soto, F., A. Martinez, J. Garcia, F. Ramos, P. Sanchis, J. Blasco, and J. Marti, "All-optical switching structure based on a photonic crystal directional coupler," Optics Express, Vol. 12, 161-167, 2004.

    7. Adibi, A., Y. Xu, R. Lee, A. Yariv, and A. Scherer, "Properties of the slab modes in photonic crystal optical waveguides," J. Lightwave Technology, Vol. 18, 1554-1564, 2000.

    8. Qiu, M., K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B, Vol. 64, 155113-155117, 2001.

    9. Monat, C., B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. Pelusi, D. Moss, B. Eggleton, T. White, and T. Krauss, "Slow light enhanced nonlinear optics in silicon photonic crystal waveguides," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 16, No. 1, 344-356, 2010.

    10. Blanco-Redondo, A., C. Husko, D. Eades, Y. Zhang, J. Li, T. Krauss, and B. Eggleton, "Observation of soliton compression in silicon photonic crystals," Nature Communications, Vol. 5, 2014.

    11. Geniet, F. and J. Leon, "Energy transmission in the forbidden band gap of a nonlinear chain," Phys. Rev. Lett., Vol. 89, 134102-134105, 2002.

    12. Khomeriki, R., "Nonlinear bandgap transmission in optical waveguide arrays," Phys. Rev. Lett., Vol. 92, 063905-063908, 2004.

    13. Chen, W. and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett., Vol. 58, 160-163, 1987.

    14. Martijn de Sterke, C. and J. E. Sipe, "Envelope-function approach for the electrodynamics of nonlinear periodic structures," Phys. Rev. A, Vol. 38, 5149-5165, 1988.

    15. Martijn de Sterke, C. and J. E. Sipe, "Coupled modes and the nonlinear Schrodinger equation," Phys. Rev. A, Vol. 42, 550-555, 1990.

    16. Agrawal, G. P., Nonlinear Fiber Optics, Academic Press, New York, 1989.

    17. Kivshar, Y. S. and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, San Diego, California, 2003.

    18. Akhmediev, N. N. and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, Chapman and Hall, London, 1997.

    19. Segev, M., B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett., Vol. 68, 923-926, 1992.

    20. Christodoulides, D. N. and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett., Vol. 13, 794-796, 1988.

    21. Mandelik, D., H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett., Vol. 90, 053902-053905, 2003.

    22. Khomeriki, R. and J. Leon, "Bistable light detectors nonlinear waveguide arrays," Phys. Rev. Lett., Vol. 94, 243902-243905, 2005.

    23. Khomeriki, R. and J. Leon, "Driving light pulses with light in two-level media," Phys. Rev. Lett., Vol. 99, 183601-183604, 2007.

    24. Christodoulides, D. N. and R. I. Joseph, "Slow Bragg solitons in nonlinear periodic structures," Phys. Rev. Lett., Vol. 62, 1746-1749, 1989.

    25. Millar, P., R. M. De La Rue, T. F. Krauss, J. S. Aitchison, N. G. R. Broderick, and D. J. Richardson, "Nonlinear propagation effects in an AlGaAs Bragg grating filter," Optics Lett., Vol. 24, 685-687, 1999.

    26. Aceves, A. B. and S. Wabnitz, "Self-induced transparency solitons in nonlinear refractive periodic media," Phys. Rev. A, Vol. 141, 37-42, 1989.

    27. Conti, C. and S. Trillo, "Bifurcation of gap solitons through catastrophe theory," Phys. Rev. E, Vol. 64, 036617, 2001.

    28. Krauss, T., "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys., Vol. 40, 2666-2670, 2007.

    29. Yasumoto, K., V. Jandieri, and Y. Liu, "Coupled-mode formulation of two-parallel photonic crystal waveguides," Journal of the Optical Society of America A, Vol. 30, No. 1, 96-101, 2013.

    30. Jandieri, V., K. Yasumoto, and J. Pistora, "Coupled-mode analysis of contra-directional coupling between two asymmetric photonic crystals waveguides," Journal of the Optical Society of America A, Vol. 31, No. 3, 518-523, 2014.

    31. Taniuti, T. and N. Yajima, "Perturbation method for a nonlinear wave modulation," Journal of Mathematical Physics, Vol. 10, 1369-1372, 1969.

    32. Oikawa, M. and N. Yajima, "A perturbation approach to nonlinear systems. II. Interaction of nonlinear modulated waves," Journal of the Physical Society of Japan, Vol. 37, 486-496, 1974.

    33. Taflove, A., Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Norwood, 1995.