Hi Dr. Johnson and other MEEP/FDTD knowledgeables, I was thinking about why MEEP should allow only a real dielectric constant. In the monochromatic case it would make sense to evaluate the dielectric function at the frequency-of-interest \omega_0 and plug that into Maxwell's equations, simplify, and solve but in the most general case, a complex value would be required.
The magnitude of \eps(\omega_0) is absolute permittivity while the phase shows how much time the D field lags the E field by which is constrained to one time-period because the system is a forced oscillator). Please correct me if I am wrong here. Getting MEEP to support this would then entail a modification to the D-field data structure to store the values of the field for all previous time-steps that fall within the interval corresponding to the phase. Is this correct? How does the representation of the dielectric function in a Kramers-Kronig compatible manner ensure that we don't need so much memory? In MEEP's "sum-of-Lorentzians" model, each Lorentzian ensures that the K-K relations are satisfied. Also, they arise from damped harmonic oscillator equations so we can "get away with" storing polarizations for just two time steps in the past. So would a memory-efficient way to trick MEEP into performing a monochromatic simulation be fitting a fictitious Lorentzian to pass through our \eps(\omega_0) point? Would this obviate the need to specially implement the complex \eps constant case? Of course this would be done only if it is difficult to fit the real material function to a weighted sum of Lorentzians as is the case with transition metals like Au, Ag etc. Please correct me if I am wrong here. _______________________________________________ meep-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
