International Journal of Modern Communication Technologies & Research (IJMCTR) ISSN: 2321-0850, Volume-2, Issue-4, April 2014 15 www.erpublication.org Abstract — In this paper, transmittivity of photonic crystal-based bandpass filter is numerically simulated for both normal and oblique incidence of electromagnetic wave considering the effect of optical gain factor. Results are compared with that obtained for normal incidence, and both positive and negative gain (loss) factors are considered. Conventional SiO2-air system is taken for simulation purpose, and it has also shown that slight tuning of structural parameters makes a large shift of passband position from the desired spectrum, both for unpolarized and polarized conditions. The extent of shift is large when layer dimensions are smaller. Results are important for optical communication applications at 1.55 μm. Index Terms— One-dimensional photonic crystal, Transmittivity, Optical gain factor, Polarized incidence I. INTRODUCTION One-dimensional photonic crystal is a special periodic arrangement of dielectric/ semiconducting/ metallic /combination of materials [1-3] which exhibits the novel property of photonic bandgap [4]. By virtue of this property, selected wavelength bands of the incident electromagnetic wave on photonic crystal is restricted to propagate, whereas other spectra are allowed to free [5]; thus demonstrated the property of optical filter, passband of which depends on the structural parameters and material composition [6], and tuning of incident angles can also modify the filter performance [7]. This novel structure can be used for photonic integrated circuit [8], optical transmitter [9], optical receiver [10], photonic crystal fiber [11-12], quantum information processing applications [13]. Conventional optical fiber is now-a-days replaced by photonic crystal fiber due to very low attenuation and dispersion [14], thus providing excellent efficiency for high-speed communication [15]. Work on 1D photonic crystal has attracted several researchers due to its potential advantage for communication point-of-view, and also due to ease of fabrication processes, thanks to the rapid advancement of microelectronics technology. Mekis etc. [16] obtained high transmission in presence of sharp bends in photonic crystal-based optical waveguides. Chen [17] demonstrated optical filter by making air-gap in otherwise solid photonic crystal structure. Szczepański [18] proposed distributed feedback laser using photonic crystal, whereas Hansyrd [19] made parametric Manuscript received April 03, 2014 Rajashree Khan, Department of Electronics & Communication Engineering, RCC Institute of Information Technology, Kolkata, INDIA, Arpan Deyasi, Department of Electronics & Communication Engineering, RCC Institute of Information Technology, Kolkata, INDIA, amplifiers in optical range. In this paper, transmittance of one-dimensional conventional photonic crystal using SiO 2 -air is calculated incorporating the effect of optical gain factor for filter applications. Dimensions of periodic layers are varied to observe the effect on pass bandwidth, and incidence angles are also tuned for studying the effect of different polarization conditions. Structural parameters are tuned to observe the shift the passband position from the desired zone. Results are important for 1550 nm based optical communication applications. II. MATHEMATICAL MODELING Consider the smallest unit of 1D photonic crystal structure where forward and backward propagating waves are given by- 2 12 1 21 2 b r a t a   (1) 1 21 2 12 1 a r b t b   (2) where r ij and t ij are reflectivity and transmittivity in passing from layer i to layer j. Fig 1: Schematic picture of forward and backward waves in smallest unit of 1D photonic crystal For p-polarized incident wave at angle θ 1 , interface reflectivities are given by         1 2 2 1 1 2 2 1 21 12 cos cos cos cos     n n n n r r      (3) For s-polarized incident wave at angle θ 1 , interface reflectivities are given by         2 2 1 1 2 2 1 1 21 12 cos cos cos cos     n n n n r r      (4) From the wave equations, transfer matrix corresponding to the interface can be obtained as          1 1 1 12 , 21 12 , 21 2 , 1 r r t M T (5) Considering the phase factor of the field propagating through uniform medium, propagation matrix is given as           ] exp[ 0 0 ] exp[ 2 , 1 2 , 1 2 , 1 2 , 1 2 , 1 d jk d jk P (6) where d i is the propagation length in i th layer, and k i is the wavevector in that layer. Thus, transfer matrix for the Effect of Optical Gain Factor on Transmittivity of SiO 2 -Air 1D Photonic Crystal under Polarized and Normal Incidence Rajashree Khan, Arpan Deyasi