Transit-time of electromagnetic Gaussian packets traversing nonlinear periodic layered systems C. Aguilar-Galicia a , M. Palomino-Ovando a, * , F. Ramos-Mendieta b a Facultad de Ciencias Fı ´sico Matema ´ ticas, Posgrado en Fı ´sica Aplicada, Beneme ´ rita Universidad Auto ´ noma de Puebla, Apartado Postal 1152, Puebla, Puebla 72000, Mexico b Departamento de Investigacio ´n en Fı ´sica, Universidad de Sonora, Apartado Postal 5-088, Hermosillo, Sonora 83190, Mexico Received 24 April 2006; received in revised form 5 September 2006; accepted 14 September 2006 Available online 3 November 2006 Abstract We investigate the transmission of Gaussian packets of light in periodic binary multilayers with the two constituent materials having dielectric constant dependent on the electric field intensity. The transmission spectra for the linear response and for the second and third harmonics were calculated within the undepleted approximation. For the transit-time calculation we use the stationary phase method. The wave packets were constructed with the mid-frequency lying either at the lower gap edge, at the mid-gap or at the higher gap edge of the first photonic band gap of the linear contribution. In some cases the transmitted packets (of both the linear and harmonic responses) preserve the form, but not the mid-frequency values; in other cases the transmitted packets unfold producing peaks that leave the super- lattice at different times. Ó 2006 Elsevier B.V. All rights reserved. PACS: 42.70.M; 42.70.Q Keywords: AlAs/GaAs; Nonlinear optics; Photonic band gap-materials 1. Introduction Artificial materials whose dielectric constant present periodicity in one, two or three dimensions have been of special importance during the last decade [1–4]. The main reason for the increasing interest in these photonic crystals (PC’s) is that they can support forbidden frequency bands for the electromagnetic radiation – the so called photonic band gaps. Of special interest are the PC’s whose response to the electromagnetic radiation depends on the electric field intensity. The nonlinear response of one or the two components of a PC affects the bands structure of the lin- ear problem modifying positions and sizes of the corre- sponding forbidden bands [4,5]. In this paper we calculate the time that a Gaussian wave packet takes to traverse a periodic binary layered system with the two material components supporting nonlinear effects. Of current interest are the transit-time calculations because of the possible occurrence of superluminal phe- nomena – the group velocity of a wave packet in a crystal greater than the speed of light in vacuum. This is a contro- versial phenomenon and its understanding or explanation could be relevant for fundamental physics [6–10]. The first approximation for the transit-time is the phase- time [11–13]. We calculate the phase-time using the method proposed by Zohta [12]. The method allows us to deter- mine the transit-time associated to the three wave packet that traverses the nonlinear structure; these are the times for the fundamental (first harmonic) and for the second and third harmonics. As we shall see the transit-time can be interpreted in terms of the so called delay time, the difference between the time that the wave packet takes to 0925-3467/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2006.09.001 * Corresponding author. Tel.: +52 22 22 29 55 00; fax: +52 22 22 29 56 36. E-mail address: marthap@fcfm.buap.mx (M. Palomino-Ovando). www.elsevier.com/locate/optmat Optical Materials 29 (2007) 1667–1671