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Optics Communications

Calculation of transverse effects in optical bistability using fast Fourier transform techniques

J. V. Moloney, Milivoj R. Belić, H. M. Gibbs

Published May 1, 1982• 48 citations
Publisher
DOI
10.1016/0030-4018(82)90417-5

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 29, 2013•8 citations
Bistable operation of an initially detuned Fabry-Perot etalon with a spatially varying transverse input is studied numerically. Non-linear medium propagation effects are accounted for explicitly. Fast Fourier transforms are used to treat beam diffraction, providing a computationally efficient numerical algorithm. Steady state bistable loops are computed for a Fresnel number close to unity, under both self-focusing and defocusing conditions. Beam diffraction causes earlier switch-on in the defocusing case.
Optical structures to implement the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms for discretely sampled data sets are considered. In particular, the decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts (the subtraction being performed after one has been appropriately phase shifted), so facilitating a simple and robust hardware implementation based on waveguided hybrid devices as employed in coherent optical detection modules. Further, a comparison is made to the optical structures proposed for the optical implementation of the quantum Fourier transform and they are shown to be very similar.