Abstract
In this paper we discuss the conditions to obtain the enhancement of second harmonic generation in a two-dimensional circular photonic crystal AlGaAs cavity. The photonic crystal circular cavity offers the possibility of having high-Q resonance modes with respect to those obtained with other types of photonic crystal lattices. The crystallographic cut of the AlGaAs provides a strong nonlinear coupling between a transverse-magnetic (TM) polarized resonant mode at the fundamental wavelength and a transverse-electric (TE) polarized resonant mode at second harmonic wavelength. The double resonance condition leads to a strong improvement of the second harmonic generation process. A preliminary linear analysis has been performed by using the finite-difference time-domain method, which includes the dispersive response of the material, modeled using the well-known one-pole pair Lorentzian function.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benisty H., Weisbuch C., Labilloy D., Rattier M., Smith C.J.M., Krauss T.F., De La Rue R.M., Houdré R., Oesterle U., Jouanin C. and Cassagne D. (1999). Optical and confinement properties of two-dimensional photonic crystals. IEEE J. Lightwave Technol. 17(11): 2063–2077
Bourgeade A. and Freysz E. (2000). Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations. J. Opt. Soc. Am. B 17(2): 226–234
Boyd R.W. (2003). Nonlinear Optics. Academic Press, San Diego, CA
Centini M., Sibilia C., Scalora M., D’Aguanno G., Bertolotti M., Bloemer M.J., Bowden C.M. and Nefedov I. (1999). Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions. Phys. Rev. E 60(4): 4891–4898
Cowan A.R. and Young J.F. (2002). Mode matching for second-harmonic generation in photonic crystal waveguides. Phys. Rev. B 65(8): 085106
Dolgova T.V., Maidykovski A.I., Martemyanov M.G., Fedyanin A.A., Aktsipetrov O.A., Marowsky G., Yakovlev V.A. and Mattei G. (2002). Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals. Appl. Phys. Lett. 81(15): 2725–2727
D’Orazio, A., de Ceglia, D., De Sario, M., Petruzzelli, V., Prudenzano, F.: Second order nonlinear interactions in periodic waveguides. ICTON 2004, IEEE Conference Proceedings, 126-130 (2004)
D’Orazio A., de Ceglia D., De Sario M., Petruzzelli V. and Prudenzano F. (2005). FDTD analysis of second harmonic generation in a quasi-one dimensional photonic band gap waveguide. Recent Res. Devel. Optics 5: 103–116
Dumeige Y., Raineri F., Levenson J.A. and Letartre X. (2003). Second-harmonic generation in one-dimensional photonic edge waveguides. Phys. Rev. E 68: 66617
Horiuchi N., Segawa Y., Nozokido T., Mizumo K. and Miyazaki H. (2004). Isotropic photonic band gap in a circular photonic crystal. Optics Letters 29(10): 1084–1086
Joannopoulos J.D., Meade R.D. and Winn J.N. (1995). Photonic Crystals: Molding the Flow of Light. Princeton Univ. Press, Princeton, NJ
John S. (1987). Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58(23): 2486–2489
Johnson S.G. and Joannopoulos J.D. (2002). Photonic Crystals—The Road from Theory to Practice. Kluwer, Boston, MA
Liscidini, M., Andreani, L.C.: Second harmonic generation in doubly resonant planar microcavities. Icton 2004, IEEE Conference Proceedings, 346–349 (2004)
Liscidini M. and Andreani L.C. (2006). Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors. Phys. Rev. E 73: 016613
Martorell J. and Corbalán R. (1994). Enhancement of second-harmonic generation in a periodic structure with a defect. Opt. Commun. 108: 319–323
Mingaleev S.F. and Kivshar Y.S. (2001). Self-trapping and stable localized modes in nonlinear photonic crystals. Phys. Rev. Lett. 86(24): 5474–5477
Mondia J.P., Jiang W., Cowan A.R., Young J.F. and Driel H.M. (2003). Enhanced second-harmonic generation from planar photonic crystals. Opt. Lett. 28(24): 2500–2502
Raineri F., Dumeige Y., Letartre X. and Levenson J.A. (2002). Nonlinear decoupled FDTD code: phase-matching in 2D defective crystal. Electron. Lett. 38(25): 1704–1706
Reinke C.M., Jafarpour A., Momeni B., Soltani M., Khorasani S., Adibi A., Xu Y. and Lee R.K. (2006). Nonlinear finite-difference time-domain method for the simulation of anisotropic, \chi(2), and \chi(3) optical effects. J. Lightwave Technol. 24(1): 624–634
Ren F.F., Li R., Cheng C., Wang H.T., Qiu J.R., Si J.H. and Hirao K. (2004). Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes. Phys. Rev. B 70: 245109
Sakoda K. (2001). Optical Properties of Photonic Crystals. Springer-Verlag, Berlin, Germany
Scalora M., Bloemer M.J., Manka A.S., Dowling J.P., Bowden C.M., Viswanathan R. and Haus J.W. (1997). Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures. Phys. Rev. A 56(4): 3166–3174
Shi B., Jiang Z.M., Zhou X.F. and Wang X. (2002). A two-dimensional nonlinear photonic crystal for strong second harmonic generation. J. Appl. Phys. 91(10): 6769–6771
Shi B., Jiang Z.M. and Wang X. (2001). Defective photonic crystals with greatly enhanced second-harmonic generation. Opt. Lett. 26(15): 1194–1196
Taflove A. (2000). Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Norwood MA
Trull J., Vilaseca R., Martorell J. and Corbalán R. (1995). Second-harmonic generation in local modes of a truncated periodic structure. Opt. Lett. 20(17): 1746–1748
Xiao S. and Qiu M. (2005). High-Q microcavities realized in a circular photonic crystal slab. Photonics and Nanostructures, Fundamentals and Applications 3: 134–138
Yablonovitch E. (1987). Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58(20): 2059–2062
Yariv A. and Yeh P. (1984). Optical Waves in Crystals—Propagation and Control of Laser Radiation. Wiley-Interscience, New York, NY
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Antonucci, D., de Ceglia, D., D’Orazio, A. et al. Enhancement of the SHG efficiency in a doubly resonant 2D-photonic crystal microcavity. Opt Quant Electron 39, 353–360 (2007). https://doi.org/10.1007/s11082-007-9086-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11082-007-9086-4