Achieving Wide Band Gaps and a Band Edge Laser Using Face-Centered Cubic Lattice by Holography

Abstract

Complete band gaps (CBGs) is an important research topic in the study of photonic crustals (PCs). In 1990, K.M.Ho et al. demonstrated theoretically that a diamond structure possesses CBGs [1], since then, great interests were attracted in fabricating three-dimensional (3D) PCs in order to obtain CBGs. Several methods were reported, and CBGs were achieved in the range of microwave or sub-microwave. Theoretical analysis shows that although CBGs can be obtained by diamond structure, a strict condition has to be satisfied, i.e., the modulation of refractive index of the material used should be larger than 2.0 [2, 3]. So, many scientists paid their attention to find the materials with high the refractive index. Some of them tried to fill the templates with high refractive index materials to increase the modulation of the refractive index [4-6], and CBGs were obtained. However, the achieved CBGs in 3D PCs were mostly in microwave and infrared regions [5, 7-9]. Holography is a cheap, rapid, convenient, and effective technique for fabricating 3D structures. In 1997, holographic technique was introduced to fabricate the face centered cubic (fcc) structure [10]. Campbell et al. fabricated fcc structure in terms of holographic lithography [11]. Several authors reported their works in this topic [2, 3, 7, 12]. Toader and John also showed theoretically a five-beam “umbrella” configuration for synthesis of a diamond photonic crystal [13]. Because both the value and modulation of the refractive index of the holographic recording materials are commonly low so that the PCs made directly by holography would not have CBGs. For example, the epoxy photoresist is generally used in holographic lithography [11, 14-16] , but, its refractive index is n=1.6 which is a little bit too low. They may, however, be used as templates for the production of inverse replica structures by, for example, filling the void with high refractive index and burning out or dissolving the photoresist [11], and a good work was done by D.C.Meisel [17] etc. But, to find the materials with large refractive index is not easy, and the special techniques needed are very complicated and expensive. It limits the applications of PCs, especially for industrial productions. Although band gaps can be broadened by means of multi-structures [18], CBGs in visible range had not yet been achieved, especially by using the materials with low refractive index. Therefore, it is a big challenge to fabricate 3D PCs possessing CBGs in visible range by using