We consider propagation of optical modes in the chain of identical spheres. Optical coupling between whispering gallery modes of individual spheres result in formation of bands supporting propagation of optical excitations along the chain. Most of these bands, however, overlap resulting in strong inter-band mixing effects, which significantly influence both dispersions and radiative losses of the respective modes. We develop a general theory of these effects for the cases of weak inter-band mixing, and discuss its results in the context of recent experiments.1 Introduction Recent proposal of coupled resonator optical waveguides and optical filters [1, 2] stimulated interest in systems of optically coupled micro-spheres. It has been known for a long time that electromagnetic modes of an individual sphere (Mie resonances) with large enough values of their angular momentum can have very long radiative life-times [3]. These, so called, whispering gallery modes (WHM) are characterized by concentration of the electromagnetic field along the surface of a sphere with an evanescent tail escaping outside. Such filed configuration makes it possible to optically couple two spheres positioned in the proximity of one another. Initial work on the optical coupling of the microspheres was concentrated on the case of just two spheres (the arrangement is known as photonic atoms or molecules), where the splitting of the modes and the formation of the coupled states was observed [4][5][6][7]. Recently, however, an interest has shifted toward linear chains of many spheres with several groups reporting observation of photonic propagating bands in such chains almost at the same time [8][9][10]. Resonances of individual spheres in such chains couple to form bands of propagating excitations, similar to conduction bands of solids. However, violation of spherical symmetry in the chains results in mixing between modes characterized by different angular momentums. Such a mixing affects significantly both band structure of the chains and their radiative properties.The admixture of WGM with different angular momentums arises already for two interacting spheres, and it has been realized early on that the inter-mode mixing is primary responsible for the radiative decay of the coupled modes [11], and may also affect positions of the resonances in a bi-spherical structure [12]. However, the manifestation of the mode mixing effects in the chains has not yet been treated theoretically. In this paper we develop a theory of propagating optical bands in the linear chain of identical spheres, and show that mode-mixing in these systems has much more profound effects than in the case of bi-spheres.
Comparative study of thin film Cholesteric Liquid Crystal (CLC) lasers made from different materials and optically pumped by external solid state laser reveals a striking dependence of lasing behaviour (ranging from single mode at the edge of the selective reflection band to multimode lasing) on the morphology and microstructure of CLC films. The materials studied belong to two groups: low molar mass liquid crystals and polymers. It is shown that the orientation of individual chiral domains and fluctuations in helical pitch contribute significantly to the type of lasing displayed by the material. Different ways of preparing CLC cells that lead to predominantly one type of lasing are discussed. The importance of variations of the helical pitch and domain orientation in producing single and multimode lasing is justified by optical simulations (4x4 matrix method) of lasing in multi-layered samples.
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