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18 June 2004 Split-step non-paraxial beam propagation method
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A new method for solving the wave equation is presented, which, being non-paraxial, is applicable to wide-angle beam propagation. It shows very good stability characteristics in the sense that relatively larger step-sizes can be used. It is both faster and easier to implement. The method is based on symmetrized splitting of operators, one representing the propagation through a uniform medium and the other, the effect of the refractive index variation of the guiding structure. The method can be implemented in the FD-BPM, FFT-BPM and collocation schemes. The method is stable for a step size of 1 micron in a graded index waveguide with accuracy better than 0.001 in the field overlap integral for 1000-micron propagation. At a tilt angle of 50°, the method shows an error less than 0.001 with 0.25-micron step. In the benchmark test, the present method shows a relative power of ~0.96 in a 100 micron long waveguide with 1000 propagation steps and 800 sample points, while FD-BPM with Pade(2,2) approximation gives a relative power of 0.95 with 1000 sample points and 2048 propagation steps. Thus, the method requires fewer points, is easier to implement, faster, more accurate and highly stable.
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Anurag Sharma and Arti Agrawal "Split-step non-paraxial beam propagation method", Proc. SPIE 5349, Physics and Simulation of Optoelectronic Devices XII, (18 June 2004);


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