Artificially Induced Perturbations in Chirped Magneto-Optical Bragg Gratings
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Artificially Induced Perturbations in Chirped Magneto-Optical Bragg Gratings Fredrik Jonsson1∗ and Christos Flytzanis2 1 National Microelectronics Research Centre, Lee Maltings, Prospect Row, Cork, Ireland 2 Laboratoire Pierre Aigrain, Ecole Normale Superieure, F-752 31 Paris, France ∗ Corresponding author. Email: [email protected] Abstract We report on theoretical analysis of magneto-optically induced longitudinal perturbations in chirped magneto-optical Bragg gratings. The induced perturbations considered are of Lorentzian shape, with a spatial extent considerably larger than the spatial grating period but at least an order of magnitude less than the geometrical length of the grating. In the numerical simulation of the proposed device, we show on a high polarization state selectivity in the region of the perturbation, with resonance peaks of transmission for circularly polarized orthogonal components possessing a full width at half maximum as narrow as 0.18 nm, meanwhile being separated by 0.6 nm. Introduction Currently one major research direction in photonics is towards bringing photonic devices into a true nano-technological scale, with optical routing and switching ultimately performed in a sub-micrometer length scale. However, in today’s high-performance optical systems the necessary interaction lengths are still rather in the millimetre order, with typical devices of fiber Bragg gratings and waveguiding structures in silica. In this respect, for these macroscopic systems, the introduction of magneto-optically induced local perturbations along the light path imposes the interesting feature that the lifting of the polarization state degeneracy can be locally exploited in the spectrum, leaving other essential requirements such as a fixed spectral window width and position unchanged. It is the purpose of this work to show on the possibility of a high polarization state selectivity in weakly modulated gratings by introducing a magneto-optically induced perturbation of a macroscopic spatial extent. In this paper, we focus on chirped optical gratings possessing a linear magneto-optical effect. In the absence of a magnetic field, this class of gratings provide a flat window of reflection, with its boundaries determined by the extreme values taken by the spatially varying grating period. Furthermore, we consider magneto-optically induced perturbations of Lorentzian shape, with a spatial extent which is considerably larger than the spatial grating period but at least an order of magnitude less than the geometrical length of the grating. In a linear magneto-optical medium as here considered, the complex-valued envelope of the electric polarization density obeys the local constitutive relation [1] Pω = ε0 [(n2 (z) − 1)Eω + iEω × g(z)], in which n(z) is the refractive index and g(z) the magneto-optically induced gyration vector. The refractive index distribution n(z) is in the present case modulated around a bias index n0 with a bias spatial grating period of Λ, as [n2 (z) − n20 ]/n0 = ac f (z) cos [(2π/ξ)
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