Re: Software to plot transmittance of Bragg reflector?

On Wed, 17 Jan 2007, Paul Ciszek wrote:

We would like to design a distributed Bragg reflector with certain
properties. Sure, there are formulas for bandwidth and central
frequency, but then there are all these side peaks and whatnot. Is
there an inexpensive software package that will plot the transmittance
and reflectance of a structure with many, many layers? We would like
to be able to tweak the design and look at the predicted result.

I don't know of any available package (I haven't looked), but depending on what you want to do, it might not be too hard to even do yourself, or, depending on what you call inexpensive, pay somebody to do it (to some, 20K is inexpensive, while to others, anything above $40 is expensive, sp YMMV).

If you can approximate the problem as a stack of infinite uniform layers with plane wave illumination (not necessarily at normal incidence), then it isn't too hard - a task that should take an advanced undergrad or beginning graduate student about 2-3 days if starting from scratch. Basically, one can write down the effect of one interface as a matrix relating the left-hand incident and reflected amplitudes and the right-hand incident and reflected amplitudes. Next, one can write the effects of propagation through a layer as a matrix, which will just be phase changes (unless there is absorption). The effect of the total system is just the product of each of these matrices, easily done on something like matlab or octave. Perhaps such software is out there already. Collins's EM book has a good coverage of such matrix methods.

If you have a sinusoidal modulation of refractive index, then the basic theory is all in a paper by Gaylord and Moharam, Proc IEEE, 1985. (Beware: there are typos! I had to redo the derivations before I could get working code.) This is far more effort to code, but feasible, given a respectable linear alebra package (eg, matlab or octave). It might be worthwhile searching to see if anybody implementing Garlord and Moharam's algorithm (or any of the later improved versions) has released their code to the public.

If you're dealing with Bragg reflectors in optical fibres outside the weakly-guiding limit, then it might get hard, since you won't be able to pretend you have an infinite planar structure or incident plane waves.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
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