Role of the finite size of the pump beam for second harmonic generation in photonic crystals

Summary form only given. In recent years, photonic crystals have received increasing attention both for their linear and nonlinear properties; in this field numerical modeling plays a crucial role in guiding towards new devices and in improving the performances of existing ones. Recently, only for the linear regime, a very efficient numerical approach has been suggested, the bidirectional beam propagation method (BI-BPM). The extension of this algorithm to the nonlinear regime, not reported so far neither for second nor for third order nonlinearities, has been implemented here and used to describe the influence of the finite size of the pump beam in the efficiency of second harmonic generation (SHG) in photonic crystals.