Photonic membranes are the most widely used kind of 2D photonic crystals in signal processing. Nevertheless, some important aspects of electromagnetic field behavior in membrane like photonic crystals (MPCs) need detail investigation. We develop the approach close to resonant coupling modes method which unites both external and intrinsic problems, in-plane and out-of-plane geometries, and resonator properties of MPC. The resonator standing modes are excited by an external source through the special inputs and may be controlled due to the nonlinear coating. Typical photonic manifestations are studied for Si/SiO2 2D membrane resonators of rectangular. 1. Introduction Usually, membranes perform the task of separation during the process of selective transport of particles of a matter through the membrane channels. In photonics, the membranes are a kind of 2D photonic crystals which may be characterized as thin and wide systems ordered in both transversal directions and filtering radiation along the normal to surface direction. Many examples of membrane usage in photonics are discussed in the literature beginning from mechanical usage in mirrors and actuators [1–3] and up to laser applications. Photonic membranes transmit and reflect incident light uniting diffractional out-of-plane phenomena and the in-plane geometry interference phenomena caused by complicated inner structure of the membrane. The membrane peculiarities in reflected light angular distribution in grating spectra were well known long ago beginning with R. Wood’s work [4]. Recently, the photonic bandgap manifestations in the reflectivity of periodically patterned systems were investigated experimentally and theoretically in [5–8] using a novel resonant coupling wave method (RCWM) connecting photonic bands existing for in-plane geometry of incidence with both diffractional signals in reflection and transmission. In [9] sharp resonances in the optical transmission spectra at normal incidence were observed for high-quality chalcogenide photonic crystal membranes and associated with Fano coupling between free space and the membrane-guided modes. It was shown in [9] that the membrane-guided modes near the centre of the first Brillouin zone are responsible for the main spectral features. An overview of silicon-based photonic crystals is presented in [10]. Optical effects in the thin-film 2D photonic crystals were overviewed in [11]. The gratings on thin silicon membranes fabricated in [12] exhibit clearly expressed resonant behaviour of responses that gives an opportunity for narrow bandwidth
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