On Aug 6, 2008, at 7:02 PM, Chen wrote: > 1. In the Meep Manual, Steven suggested that we should monitor the > power going > through the linear system, then change the current amplitude to get > the > expected power. However, there are two kinds of power, which are the > time > instant power and time-average power. Which power should I monitor? > If I use > time-average power, I have to use the complex-valued fields, which are > problematic for nonlinear systems.
Normally you would want time-average power for this application. You don't need complex fields for this. You could just average the power over one period, after all. Or you could use the Fourier transform (if you are careful about normalization). > 2. How can I get a nonlinear transmission curves? I think we can not > obtain > them as in the linear system by Fourier transform, because the > amplitude of > the Gaussian pulse is different in different frequencies. Therefore, > we should > use plane wave with same power, and do many simulations for different > frequencies. Is that right? In this case, should the plane wave be > on in all > the simulated time? Are there other methods or similar ctl files to > simulate > the nonlinear transmission curves? Yes, you have to do multiple simulations, one for each frequency. One way is to use a CW source at each frequency and wait for the system to reach steady-state. Another is to use a very narrow-band Gaussian source and wait until the middle of the pulse. We often prefer to use semi-analytical methods for this, such as coupled-mode theory, based on perturbative methods. If you are careful, these can be practically exact -- perturbative methods can be very accurate here because the nonlinear change in the refractive index is very small in most practical materials. This is true even if the overall phenomenon that results from the nonlinearity is quite dramatic (e.g. optical bistability). Steven _______________________________________________ meep-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
