For linear calculations in electromagnetism, most quantities of interest are naturally expressed as dimensionless quantities, such as the ratio of the wavelength to a given lengthscale, the transmitted or reflected power as a fraction of input power, or the lifetime in units of the optical period. Matters are more complicated when one includes nonlinear effects, however, because in this case the absolute amplitude of the electric field becomes significant. We discuss how to relate Meep's units to those of experimental quantities relevant for nonlinear problems. See also Nonlinearities.
Meep supports instantaneous Kerr nonlinearities characterized by a susceptibility
However, the number usually reported for the strength of the Kerr nonlinearity is the AC Kerr coefficient
This equation itself is somewhat subtle: it is not the actual instantaneous change in refractive index at every point. Rather, it is a sort of average change in index, and in particular is the change in effective index
The relationship between
where
Warning: The optics literature uses a variety of conflicting conventions for defining the dimensionful quantities
The key to using correct magnitudes is nonlinear calculations in Meep is to realize that the units are still somewhat arbitrary: only the product
For example, suppose that
To monitor the power in a structure, we can use a variety of functions. See Python Interface. One can get the power flux directly through the flux_in_box
function. Or, one can alternatively get the intensity at a single point by calling get_field_point
and passing Sx
etc. for the component. One thing to be cautious about is that these return the power or intensity at one instant in time, and not the time-average unless you use complex-valued fields (which are problematic for nonlinear systems).
You may have been hoping for a simple formula: set the current to x to get y power. However, this is not feasible since the amount of power or field intensity you get from a current source depends on the source geometry, the dielectric structure, and so on. And a formula for the units of current is not terribly useful because usually the current source in an FDTD calculation is artifically inserted to create the field, and doesn't correspond to the current source in a physical experiment.