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5 November 2018 Mode interactions in a three-layered slab waveguide with periodic structures
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We investigate a slab waveguide with periodic structures on the both sides of the core to study the optical mode interaction behaviors in the presence of structure periodicity. As the variation is taking place in both substrate and coating at the same time, the refractive index can be formulated as nsb(z) = ncl(z) = n0(1 + εW(z)), where W(z) = W(z +T) is a periodic function with period T, and ε is a small parameter. Considering a two-dimension mathematical problem, the Maxwell’s equations have been solved by assuming the Bloch modes in transverse direction. Particularly, the Ey component have been solved when the function W(z) is selected as a sine function. The field distributions of both straight and periodic core waveguide have been compared to get a better insight of modes generation. The waveguide mode field in a non-periodic waveguide is centered in the core layer, and exponentially decays outside the core, and the size of the mode field is only related to the lateral distance x. Introducing a variation in the refractive index by a sine function, influences the propagation of modes. The mode field distribution of the core layer remains unchanged, but the pattern field distributions in the cladding layer and the substrate have changed significantly. The TE0 and TE1 modes in the cladding and substrate are not continuous and decay gently, but periodically fluctuate along the z-axis. Changing the distribution of the mode field in the periodic structure destroys the orthogonality of the modes and leads to the interaction between a series of modes, referred as resonance.
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Aysha Bibi, Ya-Xian Fan, Jiang Nan, and Zhi-Yong Tao "Mode interactions in a three-layered slab waveguide with periodic structures", Proc. SPIE 10815, Optical Design and Testing VIII, 1081517 (5 November 2018);

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