I used TMM to design a filter in one dimensional photonic crystal using Matlab. What other techniques I should do ?
Hi, Asama,
You can use the scattering matrix method. It's slightly different formalism but you can avoid the problem of mixing the small and large numbers in the same matrix in case of very thick absorbing layers.
The TMM usually refers to a 1D code that only models dielectric slabs. When it is generalized to handle inhomogeneities, it is more commonly called the method of lines or rigorous coupled-wave analysis. I cover all these methods in detail here:
http://emlab.utep.edu/ee5390cem.htm
As Sergey said, TMM is inherently unstable. When it is fixed, it resembles scattering matrices which have emerged as the most popular way to model multi-layer problems. I have found the enhanced transmittance matrix method to be almost 10x faster than scattering matrices, but less memory efficient. There are also R and H matrices that claim greater efficiency as well, but I not have personally worked with them. Again, check out the lectures above. Hopefully you will like them.
Hi Asama,
In my M.Sc. thesis I was working on 1D photonic crystal (PC) by using transfer matrix method (TMM). First of all, until now I haven't faced any problems and limitation about TMM. Second, about the other techniques that you can use instead of TMM, I'm not sure but I think you can use FDTD method to analyse the 1D PC.
When given the complex refractive index n, set the permeability to ur = 1.0 and then just square the complex refractive index to get complex permittivity, er = n^2. It is that easy! Good luck!
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