## Third-order nonlinear influence on the specular reflectivity of two-dimensional waveguide-based photonic crystals

JOSA B, Vol. 19, Issue 9, pp. 2224-2231 (2002)

http://dx.doi.org/10.1364/JOSAB.19.002224

Acrobat PDF (517 KB)

### Abstract

Specular reflectivity spectra of plane waves incident upon two-dimensional waveguide-based photonic crystals are rigorously calculated by use of the linear and the third-order nonlinear susceptibilities of the semiconductor core layer. The Fano-like features associated with coupling to leaky photonic eigenstates that are attached to the porous slab are shifted and distorted at high intensities. Although some of this nonlinear behavior is qualitatively similar to that observed in simple Fabry–Perot cavities, there are striking differences. The main difference is that one can engineer the *Q* values and the in-plane dispersion of the microcavity modes associated with the leaky eigenstates of the photonic crystal over a wide range by varying the properties of the etched texture. Examples are given that demonstrate bistable behavior and intensity-dependent reflectivities that can vary from zero to unity. Both degenerate (single-beam) and nondegenerate (pump- and signal-beam) cases are considered.

© 2002 Optical Society of America

**OCIS Codes**

(190.1450) Nonlinear optics : Bistability

(190.3270) Nonlinear optics : Kerr effect

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(230.7400) Optical devices : Waveguides, slab

(250.5300) Optoelectronics : Photonic integrated circuits

**Citation**

M. G. Banaee, A. R. Cowan, and Jeff F. Young, "Third-order nonlinear influence on the specular reflectivity of two-dimensional waveguide-based photonic crystals," J. Opt. Soc. Am. B **19**, 2224-2231 (2002)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-9-2224

Sort: Year | Journal | Reset

### References

- J. F. Young, P. Paddon, V. Pacradouni, T. Tiedje, and S. Johnson, “Photonic lattices in semiconductor waveguides,” in Future Trends in Microelectronics, S. Luryi, J. Xu, and A. Zaslavsky, eds. (Wiley, Toronto, 1999), pp. 423–432.
- M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, “Observation of leaky slab modes in air-bridge semiconductor waveguides with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
- D. M. Atkin, P. St. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
- S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
- P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B 61, 2090–2101 (2000).
- V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
- V. Pacradouni, J. Mandeville, A. R. Cowan, P. Paddon, and J. F. Young, “Photonic bandstructure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B 62, 4204–4207 (2000).
- A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, “Resonant scattering and mode coupling in two-dimensional textured planar waveguides,” J. Opt. Soc. Am. A 18, 1160–1171 (2001).
- S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
- O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
- A. R. Cowan and J. F. Young, “Mode matching for second harmonic generation in photonic crystal waveguides,” Phys. Rev. B 65, 085106 (2002).
- E. Popov and M. Nevière, “Surface-enhanced second-harmonic generation in nonlinear corrugated dielectrics: new theoretical approaches,” J. Opt. Soc. Am. B 11, 1555–1564 (1994).
- P. Vincent, N. Paraire, M. Nevière, A. Koster, and R. Reinisch, “Gratings in nonlinear optics and optical bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
- E. Garmire, “Resonant optical nonlinearities in semiconductors,” IEEE J. Sel. Top. Quantum Electron. 6, 1094–1110 (2000).
- E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, R7683–R7686 (2000).
- G. Assanto, M. B. Marques, and G. I. Stegeman, “Grating coupling of light pulses into third-order nonlinear waveguides,” J. Opt. Soc. Am. B 8, 553–561 (1991).
- C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, and J. D. Velera, “Nonlinear distributed waveguide couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
- R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, and G. I. Stegeman, “Pulsed excitation of nonlinear distributed coupling into zinc oxide optical guides,” J. Opt. Soc. Am. B 5, 425–431 (1988).
- M. Nevière, E. Popov, and R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
- P. Tran, “Photonic band-structure calculation of material possessing Kerr nonlinearity,” Phys. Rev. B 52, 10673–10676 (1995).
- V. Lousse and J. P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
- A. Hache and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089–4091 (2000).
- S. V. Popov, Y. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics Publishing, Bristol, UK, 1995).
- A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electron and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).

## 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.