Meaning of phase in Meep

[harnessa]

I am curious about how well I can trust the relative phase of a field in Meep.

Here is an outline of my simulation: I am working in 2D and am propagating a plane wave through the air gap between two sides of a metal coated silicon wafer (Gaussian source wavelength: 0.6 microns, gap width >10 microns, Al coating: 0.25 microns thick, cSi wafer: 2 microns thick). I want to calculate the amplitude and phase change at the bottom of the wafer (downstream of the source) that is caused by the presence of the wafer. I run one simulation with the wafer and save the DFT_fields from the bottom of the wafer (I'll call these wafer_fields). I run a second simulation with all materials removed (vacuum simulation) and save the DFT_fields at the same location at the bottom of the wafer (I'll call these vacuum_fields). Both simulations are run for the same amount of time (occasionally they differ by 1 timestep).

The amplitude and phase change is calculated as: wafer_fields / vacuum_fields - 1. Dividing by vacuum_fields normalizes the amplitude and subtracts the phase that would occur due to propagation only.

My question is: can that relative phase change be trusted? Is this the correct way to get the phase change? This approach works when compared to the analytic solution of a plane wave propagating through a gap in a PEC screen, but will this approach still hold when using a cSi wafer? Am I missing something or being overly skeptic?

Thanks,

[stevengj]

It sounds fine. (I'm not entirely clear on your geometry, however. Note that the "input and output" media should probably be the same between your first and second simulations — in your wafer simulation, is the light entering and exiting from vacuum, or from a semi-infinite Si medium?)

Also, note that you don't need (or necessarily want) to run for the same amount of time in the two simulations — you just need to run long enough for the DFT (the Fourier transform) to converge, i.e. until the time-domain fields have decayed away. (Depending on the structure, you might need to run for longer, e.g. if there is a resonance that takes a long time to decay.)

[harnessa]

Below is a figure of the geometry. The red dotted line is the location of the source (and propagating with positive X, i.e., 'down') . The black dotted line is where I am most interested in the field. Light enters and exits from vacuum.

Yes, I run until the time-domain fields have decayed away in the wafer simulation. Originally I did the same for the vacuum simulation, but was concerned about a time difference in the phase, so I ran for the same amount of time as the wafer simulation. There was not a meaningful difference between the too.

Thanks

[oskooi]

For reference, another way to set up this calculation is demonstrated in Tutorial/Focusing Properties of a Metasurface Lens. This example involves computing the transmittance and relative phase (using mode decomposition) of the zeroth diffraction order of a unit cell of a metalens as a function of its duty cycle. Note that the get_eigenmode_coefficients function can be passed a DiffractedPlanewave object (rather than the band number which mainly applies to guided modes) for specifying the diffraction order in 3d.

[harnessa]

Could that approach still be used if the geometry was a one-sided edge? (i.e., the wafer on the right side is removed)

[oskooi]

Yes. More generally, in the context of coupling from one mode to another, you can take the ratio of the two complex mode coefficients which is defined as the scattering (S) parameter. The phase of the S-parameter (itself a complex quantity) is equivalent to the relative phase of the two modes at the two monitors.