Monday, November 13, 2006

Meep Introduction - AbInitio

Meep Introduction - AbInitio: "Units in Meep

You may have noticed the lack of annoying constants like ε0, μ0, c, and 4π — that's because Meep uses 'dimensionless' units where all these constants are unity (you can tell it was written by theorists). As a practical matter, almost everything you might want to compute (transmission spectra, frequencies, etcetera) is expressed as a ratio anyway, so the units end up cancelling.

In particular, because Maxwell's equations are scale invariant (multiplying the sizes of everything by 10 just divides the corresponding solution frequencies by 10), it is convenient in electromagnetic problems to choose scale-invariant units. That means that we pick some characteristic lengthscale in the system, a, and use that as our unit of distance.

Moreover, since c = 1 in Meep units, a (or a / c) is our unit of time as well. In particular, the frequency ω in Meep (corresponding to a time dependence e − iωt) is always specified in units of 2πc / a, which is equivalent to specifying ω as 1 / T: the inverse of the optical period T in units of a / c. This, in turn, is equivalent to specifying ω as a / λ where λ is the vacuum wavelength. (A similar scheme is used in MPB.)

For example, suppose we are describing some nanophotonic structure at infrared frequencies,"