Unusual transmission through usual one-dimensional photonic crystal in the presence of evanescent wave Yun-tuan Fang a, * , Zhong-cheng Liang b a Department of Physics, Zhenjiang Watercraft College, Zhenjiang 212003, China b College of Optoelectronic Engineering, Center of Optofluidic Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China article info Article history: Received 19 August 2009 Received in revised form 8 January 2010 Accepted 10 January 2010 abstract Basing on the condition that the incident angle is larger than the total internal reflection angle, we pres- ent a systematic study of transmission properties of one-dimensional photonic crystal with all dielectric materials by the transfer matrix method and the Bloch’s theorem. Due to the existence of the evanescent field within the structure, the transmission bands consist of some discrete symmetry peaks. For light with these peak frequencies, the structure is either transparent or opaque depending on the number of the structure periods. The unusual transmission properties are attributed to the field distribution and Bloch wave vector. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Photonic crystals (PCs) have both fundamental interest and po- tential applications because of their unique ability to control and manipulate light [1–7]. A band diagram describes properties of an infinite periodic structure. Usually, PCs are composed of dielec- tric layers. But one-dimensional (1D) PCs composed of alternating layers of metal and dielectric materials [8–10] have some promis- ing features, e.g. a 100% transmission of the evanescent waves is achieved by means of surface plasmon excitation [11,12]. However, Refs. [11,12] did not consider the effect of the loss of metal on the transmission of M-D PCs. If the loss of metal is considered, the ideal performance of the M-D PCs may be hardly obtained in real appli- cation. In this paper, we study the transmission properties of 1D PCs composed of alternating layers of two dielectric materials. Un- like previous studies that all the waves in dielectric layers are propagating mode, our study in this paper is based on the case that the electromagnetic wave is made evanescent within one of two dielectric materials through a proper incidence condition. Thus some unusual transmissions will be found, which unlike not only the transparent band of the M-D PCs, but also conventional pass bands of 1D PC. For example, for a special frequency, the structure considered here can be made total transparent (100% transmis- sion), or be made almost opaque just through adding one period into its structure or cutting off one period from its structure. Due to its total dielectric structure, the effect of loss of the materials can be neglected. 2. Structure and Bloch mode The schematic of 1D PC is shown in Fig. 1. The air-dielectric multilayer stack (AD) N is placed between two prisms (the grey layer D is dielectric and the white layer A is the air ðn A ¼ 1Þ). The prisms on the top and bottom of the PC are used to couple light into and out of the PC, respectively. When the light is incident nor- mally on the top surface of the top prism, it will enter into the PC with an incidence angle h. As we have known, as light propagates from optically denser medium to optically thinner medium, there is a total reflection angle called h 0 here. Without loss of generality, the refractive index for both the prisms and the layer D is firstly as- sumed to be n D ¼ 3:23. According to the geometrical optics and Fig. 1, the incidence angles from the layers D to layers A are all h. If h > h 0 ¼ arcsinð1=3:23Þ¼ 0:3184 rad, all the electromagnetic wave within layers A is evanescent mode, while if h < h 0 , the elec- tromagnetic wave in all layers is propagating mode. As is well known, an evanescent wave cannot propagate through a single dielectric layer. However, evanescent waves in metallodielectric photonic crystal can propagate through evanescent coupling of surface plasmons between interfaces of metal/dielectric layers [11,12]. This transmission mechanism can be looked as a cou- pled-plasmon-resonant-waveguide (CPRW). The CPRW is a special case of the coupled-resonator optical waveguide (CROW) proposed by Yariv et al. [13]. The field in this case decays exponentially both in dielectric and in metal, but is amplified at each metal–dielectric interface. For our current structure, on the condition of h > h 0 , the electromagnetic waves within layers A are all evanescent. Thus each layer D may be looked as a resonator cavity. If there is a coupling of evanescent wave between two layers D, the whole 0030-4018/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.01.014 * Corresponding author. E-mail address: fang_yt1965@sina.com (Y.-t. Fang). Optics Communications 283 (2010) 2102–2108 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/optcom