Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, and J. A. Levenson a) Laboratoire de Photonique et de Nanostructures (CNRS UPR 20), 196, av. Henri Ravera, 92220 Bagneux, France C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora INFM at Dipartimento di Energetica-Universita’ di Roma ‘‘La Sapienza,’’ Roma, Italy ~Received 18 September 2000; accepted for publication 20 March 2001! We demonstrate significant enhancement of second-order nonlinear interactions in a one-dimensional semiconductor Bragg mirror operating as a photonic band gap structure. The enhancement comes from a simultaneous availability of a high density of states, thanks to high field localization, and the improvement of effective coherent length near the photonic band edge. © 2001 American Institute of Physics. @DOI: 10.1063/1.1372356# The increase of nonlinear conversion efficiency has been a long-standing goal in nonlinear optics. In particular, one of the fundamental issues in second order nonlinear interactions is the realization of phase matching ~p.m.! conditions, which traditionally are achieved using birefringent crystals. More recently, quasiphase matching, which consists of modulating the quadratic susceptibility with a spatial period of the order of the coherence length, has become widely used. 1,2 The spa- tial modulation of the nonlinear optical coefficient leads to efficient nonlinear interactions by allowing the use of non- linear tensor components inaccessible in birefringent p.m. An alternative possibility afforded by the use of a periodic medium, was first mentioned in Ref. 3: by modulating the linear refractive index, the reciprocal vector of the periodic structure becomes a part of the total momentum conservation relation and allows for the realization of p.m. conditions. Thus, in contrast with the now widely used crystals for qua- siphase matched interaction, the layered structure is charac- terized by a spatial modulation of the refractive index rather than a modulation of the nonlinear susceptibility. The spatial modulation is formed such that the propagation of certain wavelengths is not allowed. Those same wavelengths are then absent in transmission, which gives rise to the term photonic band gaps ~PBGs!. The characteristic spatial scale of the variation of the refractive index in PBGs is of the order of the optical wavelength, i.e., significantly smaller than the periodic modulation of the nonlinear susceptibility used for quasiphase matched interactions. A first experiment of this kind of implementation of p.m. was reported in Ref. 4, where conditions were optimized for reflected second har- monic generation. In the analysis, the authors considered a structure of infinite length. More recently, the use of PBGs for second order nonlinear interactions has become a topic of heated discussion. 5–7 As mentioned previously, the notion of utilizing the dispersion of the periodic structure is not new. 3 However, the renewal of interest in PBGs is associated with the recent introduction of an effective dispersion relation for finite structures. 6 This makes it possible to describe the p.m. conditions in terms of an effective index of refraction. Another remarkable property of PBG structures is asso- ciated with transmission ~or reflection! resonances that ap- pear close to the band gaps. They are associated with strong field confinement and consequential enhancement of the electromagnetic field which can be understood in terms of an increase in the density of modes ~DOM! and corresponds to a slowing down of the optical wave at frequencies near the band gap edge. This enhancement is extremely promising for linear and nonlinear optical applications. Although the linear properties of three-dimensional PBGs have been extensively studied, only a few papers treat second order nonlinear inter- actions in layered structures of finite length. 5–8 In this letter we demonstrate that a large enhancement of second harmonic generation can be obtained once the two key points of the interaction have been addressed: that is, the simultaneous availability of increase the effective coherent length and a large DOM. In Ref. 9, the nonlinear interaction was described in terms of slowly varying field envelopes. An effective nonlinear coupling coefficient that takes into ac- count the spatial distribution of the interacting fields, F F ( z ) and F SH ( z ), was introduced, and given by d eff 5 1 L s E 0 L s d ~ 2 ! ~ z ! u F F ~ z ! u 2 u F SH ~ z ! u dz , ~1! where d (2) ( z ) is the spatially dependent nonlinear coefficient of the corresponding layers. L s is the total length of the structure. The suffixes F and SH apply for the fundamental and second harmonic fields, respectively. As it was shown in Ref. 6, an effective refractive index n eff can be introduced in complete analogy with propagation in a homogeneous mate- rial. n eff describes the total phase w t accumulated by the field during its propagation through the stack. That is, for a trans- mission coefficient t: w t 5 1 i log S t u t u D 5k ~ v ! L s 5 v c n eff ~ v ! L s . ~2! a! Electronic mail: ariel.levenson@rd.francetelecom.fr APPLIED PHYSICS LETTERS VOLUME 78, NUMBER 20 14 MAY 2001 3021 0003-6951/2001/78(20)/3021/3/$18.00 © 2001 American Institute of Physics Downloaded 28 May 2001 to 194.199.156.168. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp