Journal of Modern Optics Vol. 58, No. 17, 10 October 2011, 1538–1550 Nonlinear analysis of a photonic crystal laser Marcin Koba a,b * , Pawel Szczepan´ski a,b and Tomasz Osuch b a Institute of Microelectronics and Optoelectronics, Warsaw University of Technology, Warsaw, Poland; b National Institute of Telecommunications, Warsaw, Poland (Received 16 May 2011; final version received 25 July 2011) An approximate nonlinear analysis of light generation in two-dimensional square- and triangular-lattice photonic crystal lasers including gain saturation effects is presented for the TE modes. This model extends earlier studies which took into account only TM modes. Our approach is based on coupled mode theory. With the help of an energy theorem and a threshold field approximation an approximate formula relating the small signal gain required to obtain a given output power to the structure parameters has been obtained. It has been used to calculate laser characteristics revealing an optimum coupling strength for which laser structure achieves maximum power efficiency. Keywords: photonic crystal laser; coupled mode theory; energy theorem 1. Introduction Two-dimensional (2D) photonic crystal (PC) structures have attracted much attention from researchers due to their interesting physical properties. Since the original work by Yablonovitch [1], they have been extensively studied theoretically and experimentally. Among many other applications, they have been found to be inter- esting light sources, exhibiting, for example, surface emission, small divergence angle of output beam [2], and the possibility of tailoring both the polarization and beam pattern by proper design [3,4]. Theoretical analyses of 2D photonic crystal laser operation are mainly based on the 2D plane wave expansion method (PWEM) [3,5,6] and the finite difference time domain (FDTD) [7,8] method. These methods provide results which are found to be in good agreement with experiments but both are not very convenient for optimization and design of real devices. The former (PWEM) applies to infinite structures, and the latter (FDTD) is sufficient only for few periods of the crystal (requiring enormous computer resources in order to model real laser structures). Further improvement of 2D PC lasers requires their optimization. Therefore, it is important to develop simple and convenient analytical and semi-analytical methods. Several analyses based on the coupled mode theory have been reported [9–12]. In particular, a 2D coupled wave theory for square-lattice 2D photonic crystal lasers with TM and TE polarization has been presented in [9,10] and [11], respectively. It is worth noting here that coupled mode equations for the TE modes should include higher order waves due to a different coupling mechanism [10,13]. The threshold gain, resonance frequencies and field distribution of the modes have been determined. Especially, it has been found that the lasing mode can be selected by manipulating the hole-filling factor, the boundary conditions or end reflectors. However, more realistic models describing laser operation above the threshold should take gain satu- ration effects into account. A model for nonlinear operation (i.e. above the threshold) of a photonic laser was developed in [14] based on a semi-classical approach. In that work a multi-scaled method was used to formulate approxi- mate master equations for single mode operation. It is worth noting that this model is general and valid for one-dimensional (1D), 2D as well as three-dimensional (3D) photonic laser structures operating above the threshold and provides a sophisticated description for single mode operation but is still not very convenient to support the design procedure of real lasers. Recently, we presented an approximate method for above-threshold analysis of 2D square- and triangular- lattice photonic crystal lasers [12,15]. This model has been developed for TM modes. It is based on coupled wave equations, extended to take gain saturation effects into account. An energy theorem and a threshold field approximation allow us derive the *Corresponding author. Email: m.koba@elka.pw.edu.pl ISSN 0950–0340 print/ISSN 1362–3044 online ß 2011 Taylor & Francis http://dx.doi.org/10.1080/09500340.2011.608909 http://www.tandfonline.com