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I maybe do not quite understand what you are asking. Do you want to calculate the propagation constant of a waveguide mode? If so, is there a reason you want to do this with FDTD? I would suggest looking at a frequency-domain tool like the finite element method (FEM) or finite-difference frequency-domain (FDFD). A frequency-domain code can very easily solve an eigen-value problem where the eigen-values are your propagation constants. What type of waveguides are you interested?
I will keep this e-mail short incase I do not understand what you are interested in.
Calculating the propagation constant (beta) of a guided mode using FDTD works backwards from what you may be thinking. Instead of FDTD giving you beta, you will give FDTD the beta quantity and it will compute the modes that result. Essentially, you will iterate this method until the mode you are interested in falls onto the frequency you are interested in. The algorithm works like this:
1. Pick a beta
2. Run 2D FDTD with d/dz=i*beta
3. FFT the time response
4. Look for peaks in the FFT. These are your modes
5. The beta you assumed is the beta of the mode you just calculated.
6. Adjust your beta and rerun FDTD until the frequency of the mode is the frequency you are interested in.
Here are two references:
Min Qui, "Analysis of Guided Modes in Photonic Crystal Fibers Using the Finite-Difference Time-Domain Method," Microwave and Optical Technology Letters 30(5), pp. 327-330 (2001).
T. Ando, "Eigenmode Analysis of Optical Waveguides by a Yee-Mesh-Based Imaginary-Distance Propagation Method for an Arbitrary Dielectric Interface," J. Lightwave Technol. 20(8), pp. 1627-1634 (2002).
I maybe do not quite understand what you are asking. Do you want to calculate the propagation constant of a waveguide mode? If so, is there a reason you want to do this with FDTD? I would suggest looking at a frequency-domain tool like the finite element method (FEM) or finite-difference frequency-domain (FDFD). A frequency-domain code can very easily solve an eigen-value problem where the eigen-values are your propagation constants. What type of waveguides are you interested?
I will keep this e-mail short incase I do not understand what you are interested in.
solving an eigen-value problem with FEM is easier and harder. It is harder in the sense that FEM requires more upfront work formulating the equations you type into the computer to build the matrices. It is easier in the sense that once you have the matrices, you can simply solve for the eigen-values (propagation constants) and eigen-vectors (the mode profiles) and the answers fall right out.
What type of waveguide are you analyzing? If you are just starting out, can I recommend a frequency-domain finite-difference method?
For a good ebook on numerical modeling, try this...
solving an eigen-value problem with FEM is easier and harder. It is harder in the sense that FEM requires more upfront work formulating the equations you type into the computer to build the matrices. It is easier in the sense that once you have the matrices, you can simply solve for the eigen-values (propagation constants) and eigen-vectors (the mode profiles) and the answers fall right out.
What type of waveguide are you analyzing? If you are just starting out, can I recommend a frequency-domain finite-difference method?
For a good ebook on numerical modeling, try this...
Does Optiwave FDTD have a way to distinguish degenerate modes? That is, can it separate distinct modes that happen to have the same propagation constant?
Unfortunately, I have not written this form of FDTD. You may look for codes that go along with Taflove's book on FDTD, but I do not know if you will find it there. If not, you have three options: (1) you can purchase an off-the-shelf software; (2) you can pay somebody to write the code for you and provide you the code; or (3) be satisfied with a different modeling approach like FDM or EM where codes are available online. I suspect in these tough economic times, there would be plenty of individuals willing to write the code for you.
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