15 October 2012 Application of the transfer matrix method to reflection gratings in positive and negative index materials
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Abstract
The transfer matrix method (TMM) has been used to analyze plane wave and beam propagation through linear photonic bandgap structures. Here, we apply TMM to determine the exact spatial behavior of TE and TM waves in periodic refractive index structures of arbitrary thickness. First, we extend the TMM approach to analyze plane wave propagation through Kerr type nonlinear media. Secondly, we analyze second harmonic fields in a 1D nonlinear photonic crystal for arbitrary angle of incidence of the fundamental plane wave. This allows us to construct the overall transfer matrix of nonlinear waves for the whole nonlinear optical structure from all the individual layer transfer matrices. We extend this method to analyze the effect of second order nonlinearity to beam propagation by applying TMM to the angular spectral components of the beam(s).
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R. Aylo, R. Aylo, H. Li, H. Li, G. Nehmetallah, G. Nehmetallah, P. P. Banerjee, P. P. Banerjee, } "Application of the transfer matrix method to reflection gratings in positive and negative index materials", Proc. SPIE 8497, Photonic Fiber and Crystal Devices: Advances in Materials and Innovations in Device Applications VI, 84970C (15 October 2012); doi: 10.1117/12.930509; https://doi.org/10.1117/12.930509
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