Simulation of bandgap of an arbitrary crystal structure

Hey,

I have simulated some of the crystal structures using Holographic lithography technique in Matlab. Now if I want to simulate the band structure of the same which software do I need? (In my case the basis is of arbitrary shape)

Thanks in advance

I have actually done this exact thing. In my PhD dissertation, I simulated the holographic lithography process and then fed those simulated structures into electromagnetic simulations. You can download my dissertation here:

http://purl.fcla.edu/fcla/etd/CFE0001159

For dielectric photonic crystals, I suggest using a new numerical technique that I recently developed called the Slice Absorption Method (SAM). It is specially formulated to model devices with high volumetric complexity and I have shown it to be faster than finite-difference frequency-domain (FDFD) and rigorous coupled-wave analysis (RCWA) for this class of structures. See

R. Rumpf, "Rigorous Electromagnetic Analysis of Volumetrically Complex Media Using the Slice Absorption Method," J. Opt. Soc. Am. A 24(10), pp. 3123-3134 (2007).

For photonic band diagrams, I suggest the plane wave expansion method (PWEM). The PWEM can handle photonic crystals of arbitrary shape. The transfer matrix method (TMM) is also popular, particularly for metallic photonic crystals. It is also possible to modify SAM to do the same, in which case, I suspect it would be the fastest and most efficient technique.

One word of caution. Almost all photonic crystals formed by holographic lithography are "chirped" in the vertical direction due to optical absorption in the exposure process. This makes the structures non-periodic in the z-direction so the concept of photonic bands makes less sense.

In my dissertation, I completely describe FDFD, FDTD, PWEM, RCWA, and all of the method I used to model the holographic lithography process. For example, the fast marching method (FMM) is a great technique for modeling the lithographic developing process.

Hope this helps!
-Tip