fdtdx.compute_eps_spectrum_from_coefficients

fdtdx.compute_eps_spectrum_from_coefficients#

fdtdx.compute_eps_spectrum_from_coefficients(c1, c2, c3, inv_eps_inf, omegas, dt, weights=None, c4=None)[source]#

Spatially-averaged complex permittivity spectrum for a block of cells.

For each angular frequency in omegas, evaluates the per-cell complex permittivity \(\varepsilon(\omega) = \varepsilon_\infty + \chi(\omega)\) where \(\chi\) is reconstructed from the ADE recurrence coefficients, and averages over the spatial axes (uniformly or with supplied weights).

This is the broadband generalization of the single-frequency effective_inv_permittivity() used for carrier-frequency impedance matching — callers that need a frequency-dependent impedance (e.g. for a convolution-based broadband source correction) use this to build the \(\varepsilon(\omega)\) spectrum that feeds compute_impedance_corrected_temporal_profile().

Parameters:

  • c1 (Array | ndarray) – ADE coefficient array of shape (num_poles, num_components, *spatial) as stored on ArrayContainer, with num_components in (1, 3) (the material-component axis; size 3 for per-axis anisotropic dispersion). Anisotropic components are averaged, mirroring the inv_eps_inf reduction.

  • c2 (Array | ndarray) – ADE coefficient array, same shape as c1.

  • c3 (Array | ndarray) – ADE coefficient array, same shape as c1.

  • inv_eps_inf (Array | ndarray) – Per-cell inverse of the high-frequency permittivity, shape (num_components, *spatial) with num_components in (1, 3, 9). For anisotropic tensors (9 components) only the diagonal entries are used.

  • omegas (ndarray) – 1D array of angular frequencies (rad/s) to evaluate at.

  • dt (float) – Simulation time step (seconds) used to derive the coefficients.

  • weights (ndarray | None) – Optional spatial weights with the same shape as the trailing axes of c1. If None, uniform averaging.

Return type:

ndarray

Returns:

Complex numpy array of shape (len(omegas),) — the volume-averaged \(\varepsilon(\omega)\) at each requested frequency.