iteration formula
In D. Sullivan's book, he use Z transform to deduce the iteration formula for these materials respectively. But I don't know how to calculate all these materials in one system?
Anyone knows, pls tell me how to do it. Thanks!
Modeling dispersion is different than modeling nonlinear material properties so there is not one formula for both. Further, there are many different formulations you can use. Identifying the "best" one depends on what you are modeling. I suspect you will need to use at least two at the same time.
Are you wanting to incorporate the dispersion for metals or dielectrics? What frequency range are you interested?
Metals: Low frequencies (RF & microwave) the perfect electric conductor approximation works very well. For infrared and longer wavelength light, the Drude model will give you excellent results and will still be somewhat easy to implement. For visible light and shorter wavelengths, the Drude model will no longer be accurate and you will need to adopt the more general Lorentz-Drude model of higher order.
Dielectrics: For dielectrics you will need the Lorentz model. If you are away from resonance in frequency, a low order model will work fine if not just a constant permittivity/permeability.
For my FDTD work, I incorporated dispersion through the material polarization and polarization current. All techniques incorporating dispersion use intermediate variables for integration or convolution. This technique produces intermediate quantities that have physical meaning so it is perhaps more useful in a research environment. While I did not do it, this approach also makes it straight forward to incorporate nonlinear material properties. You can read what I did in my PhD dissertation. See Chap. 1, section 1.7, and all of Chap. 4. You can download my dissertation from here:
http://purl.fcla.edu/fcla/etd/CFE0001159
Sullivan's Z-transform method is good, but I seldom see it used. There are many papers providing the Lorentz parameters for metals that you can directly program into the Lorentz-Drude model for FDTD. For example, see
A. Rakic, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, pp. 5271-5283, 1998.
Hope this helps!
-Tip
Dear Rumpf,
Thank you for your reply very much! Your thesis is helpful for me! I know that we must use different iteration formula at different material regions respectively.
However, your FDTD method will use 5 field variables (E,H,D,P and J), which is memory intensive espetially for 3D calculation. Can you give a more simper iteration method?
You have mentioned that you have developed a new electromagnetic method published on JOSA. Can this method deal with material dispersion,loss and nonlinear? Is it faster than FDTD?
Hope your reply soon. Thanks!