Beam propagation method: Difference between revisions

Revision as of 05:49, 19 May 2011

Revision as of 23:19, 25 June 2011

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==Principles==

BPM is generally formulated as a solution to [[Helmholtz equation]] in a time-harmonic case,

<ref>Okamoto K. 2000 Fundamentals of Optical Waveguides (San Diego, CA: Academic)</ref>

<ref>EE290F: BPM course slides, Devang Parekh, University of Berkeley, CA</ref>

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:<math>E(x,y,z,t)=\psi(x,y,z)exp(-j\omega t)</math>.

Now the spatial dependence of this field is written according to any one [[Transverse mode|TE]] or [[Transverse mode|TM]] polarizations

:<math>\psi(x,y) = A(x,y)exp(+jk_o\nu y)

</math>,

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visualize the fields along the propagation direction, or the cross section waveguide modes.

The master equation is discretized (using various [[central difference|centralized difference]], crank[[Crank–Nicolson nicholson schememethod]] etc.) and rearranged in a causal fashion. Through iteration the field evolution is computed, along the propagation

and rearranged in a causal fashion. Through iteration the field evolution is computed, along the propagation

direction.