Mirrorless Lasing in Liquid Crystalline Photonic Bandgap Materials
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Mirrorless Lasing in Liquid Crystalline Photonic Bandgap Materials Wenyi Cao, Antonio Muñoz , Peter Palffy-Muhoray* and Bahman Taheri Liquid Crystal Institute, Kent State University, Kent, OH, 44242, USA 1 Departamento de Fisica, Universidad Autonoma Metropolitana, Mexico 1
ABSTRACT Liquid crystals (LC) are promising photonic bandgap (PBG) materials. Certain LC phases have spatially modulated ground states and effectively form self-assembled PBG structures. These structures can also be made permanent by photopolymerization. Typically, LCs respond readily to applied fields, enabling modulation and switching of the bandgap. Since classical light propagation is forbidden, fluorescent emission in the band gap can lead to population inversion and stimulated emission at the band edges. Mirrorless lasing experiments provide an effective probe of the bandgap. We discuss the underlying physics, and present the results of mirrorless lasing in a variety of cholesteric LC materials, including recent results of photon counting statistics and 3-D lasing in the cholesteric blue phase. INTRODUCTION According to Floquet’s theorem [1], in certain regions of parameter space, there are no stable solutions to certain second order ordinary differential equations with periodic coefficients. The generality of the theorem allows the analogy between electrons in semiconductors and photons in a periodic structure. If the dielectric constant is periodic in space, a photonic band gap (PBG) exists where classical light propagation is forbidden. The detailed physics underlying PBG processes is not yet completely understood, but PGB materials offer great potential towards new device applications. A wide variety of methods have been developed for the production of man-made PBG structures. These make use of techniques ranging from deposition, sedimentation, photoand holographic lithography, etching, to two photon polymerization, and electrochemical patterning [2]. The materials formed may be periodic in 1-, 2- or 3-D. Our main interest is in liquid crystalline PBG materials. Liquid crystals are soft materials, and they respond readily even to modest fields. In order to realize switchable PBD materials, it has been proposed that liquid crystals be used to fill cavities in periodic structures [3]. However, since the ground states of certain liquid crystalline phases are inhomogenous and spatially periodic, these materials spontaneously form PBG structures via self-assembly. Therefore they are the focus of our interest. HELICAL CHOLESTERIC LIQUID CRYSTALS: 1-D PHOTONIC BAND GAP MATERIALS Cholesteric liquid crystals consist of chiral rod-like molecules, with anisotropic molecular polarizabilities. In the helical cholesteric phase, the molecules are oriented, on
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