Simultaneous second- and third-harmonic generation in one-dimensional photonic crystals
JOSA B, Vol. 16, Issue 9, pp. 1370-1376 (1999)
http://dx.doi.org/10.1364/JOSAB.16.001370
Acrobat PDF (179 KB)
Abstract
By use of the envelope-function approach, the equation governing propagation of the TE plane wave in a one-dimensional periodic structure is reduced to a set of coupled-mode dynamical equations for slowly varying amplitudes. We applied this method to layered media possessing both χ<sup>(2)</sup> and χ<sup>(3)</sup> nonlinearities, to study the possibility of simultaneous second- and third-harmonic generation. The phenomenon is based on the geometry of the structure and is observed in a wide class of photonic crystals of different natures, provided that the thickness and refractive indices of alternating dielectric layers are appropriately chosen. By imposing various initial distributions of the energy among the individual modes, we studied the evolution of the intensities. We found that the presence of two channels for the energy transfer from the fundamental mode prevents concentration of the total energy in either of the higher modes. In all the cases considered the energy exchange among the modes is observed. We present a particular solution for the energy transfer from the fundamental and the third harmonic to the second harmonic, obtained when the cubic nonlinearity is negligible.
© 1999 Optical Society of America
OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.3970) Nonlinear optics : Microparticle nonlinear optics
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
Citation
Vladimir V. Konotop and Vladimir Kuzmiak, "Simultaneous second- and third-harmonic generation in one-dimensional photonic crystals," J. Opt. Soc. Am. B 16, 1370-1376 (1999)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-9-1370
Sort: Year | Journal | Reset
References
- H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379 (1979); H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985); F. Deylon, Y. F. Lévy, and B. Souillard, “Nonperturbative bistability in nonlinear media,” Phys. Rev. Lett. PRLTAO 57, 2010–2013 (1980); L. Kahn, N. S. Almeida, and D. L. Mills, “Nonlinear optical response of superlattices. Multistability and soliton trains,” Phys. Rev. B PRBMDO 37, 8072–8081 (1988); V. M. Agranovich, S. A. Kiselev, and D. L. Mills, “Optical multistability in nonlinear superlattices with very thin layers,” Phys. Rev. B PRBMDO 44, 10917–10920 (1991).
- B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
- M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrafast pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994); A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors,” Phys. Rev. Lett. 74, 5020–5023 (1995); M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, “The photonic band edge optical diode,” J. Appl. Phys. JAPIAU 76, 2023–2026 (1994); M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E PLEEE8 76, R1078–R1081 (1996).
- W. Chen and D. L. Mills, “Gap solitons in nonlinear periodic structures,” Phys. Rev. Lett. 58, 160–163 (1987); D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures,” Phys. Rev. B 36, 947–952 (1987).
- C. M. de Sterke and J. E. Sipe, “Envelope-function approach for the electrodynamics of nonlinear periodic structures,” Phys. Rev. A 38, 5149–5165 (1988); “Extensions and generalizations of an envelope-function approach for the electrodynamics of nonlinear periodic structures,” Phys. Rev. A 39, 5163–5178 (1989).
- S. Lee and S.-T. Ho, “Optical switching scheme based on the transmission of coupled gap solitons in nonlinear periodic media,” Opt. Lett. 18, 962 (1993); V. V. Konotop, “Vector gap solitons,” Phys. Rev. A 51, R3422–R3425 (1995); V. V. Konotop and G. P. Tsironis, “Dynamics of coupled gap solitons,” Phys. Rev. E PLEEE8 53, 5393–5398 (1996); C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E PLEEE8 53, 1969–1989 (1996).
- N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–485 (1970).
- J. P. van Ziel and M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs—Al_{0.3}Ga_{0.7}As structures,” Appl. Phys. Lett. 28, 437–439 (1976).
- J. Martorell and R. Corbalan, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319–323 (1994); J. Trull, R. Vilaseca, J. Martorell, and R. Corbalan, “Second harmonic generation in local modes of a truncated periodic structure,” Opt. Lett. 20, 1746–1748 (1995).
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
- M. J. Steel and C. M. de Sterke, “Second-harmonic generation in second-harmonic fiber Bragg gratings,” Appl. Opt. 35, 3211–3222 (1996); “Bragg-assisted parametric amplification of short optical pulses,” Opt. Lett. 21, 420–422 (1996); M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulse second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A PLRAAN 56, 3166–3174 (1997).
- V. Pruneri, G. Bonfrate, P. G. Kazansky, C. Simonneau, P. Vidakovic, and J. A. Levenson, “Efficient frequency doubling of 1.5 μm femtosecond laser pulses in quasi-phase-matched optical fibers,” Appl. Phys. Lett. 72, 1007–1009 (1998).
- V. Pruneri, G. Bonfrate, P. G. Kazansky, G. J. Richardson, N. G. Broderick, J. P. Sandro, C. Simonneau, P. Vidakovich, and J. A. Levenson, “Greater than 20%-efficient frequency doubling of 1532-nm nanosecond pulses in quasi-phase-matched germanosilicate optical fibers,” Opt. Lett. 24, 208–210 (1999).
- G. I. Stegeman, D. J. Hagan, and L. Torner, “χ^{(2)} cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” J. Opt. Quantum Electron. 28, 1691–1740 (1996).
- X. Gu, M. Makarov, Y. Ding, J. B. Khurgin, and W. P. Risk, “Backward second-harmonic and third-harmonic generation in periodically poled potassium titanyl phosphate waveguide,” Opt. Lett. 24, 127–129 (1999).
- R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16, 1732–1734 (1991).
- B. A. Saleh and T. M. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
- V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
« Previous Article | Next Article »
OSA is a member of CrossRef.