Physical Optics#

Scalar physical-optics field models and propagation algorithms.

class ScalarField(data: BEArrayT, dx: float, wavelength: float, dy: float | None = None, refractive_index: float = 1.0)[source]#

Bases: Generic[BEArrayT]

A sampled two-dimensional complex scalar optical field.

The last array dimension is the x-axis and the first is the y-axis. All spatial quantities, including dx, dy, and wavelength, must use the same unit.

Parameters:

  • data – Two-dimensional NumPy array or PyTorch tensor containing the sampled complex amplitude. Real arrays are promoted to complex without changing their device or floating-point precision.

  • dx – Sample spacing along x.

  • wavelength – Vacuum wavelength in the same unit as dx.

  • dy – Sample spacing along y. Defaults to dx.

  • refractive_index – Homogeneous-medium refractive index. Defaults to 1.

Raises:

  • TypeError – If data does not belong to the active backend.

  • ValueError – If the field or physical parameters are invalid.

coordinates() → tuple[BEArrayT, BEArrayT][source]#

Return centered one-dimensional x and y coordinate arrays.

property intensity: BEArrayT#

Return sampled intensity, abs(data) ** 2.

property power: ScalarOrArrayT#

Return the sampled intensity integral over the field plane.

propagate(distance: float | ScalarOrArrayT, evanescent: Literal['discard', 'decay'] = 'discard') → ScalarField[BEArrayT][source]#

Propagate the field through a homogeneous medium.

Parameters:

  • distance – Signed propagation distance in the field’s spatial unit.

  • evanescent – "discard" filters evanescent content even at zero distance. "decay" preserves the complete field at zero, up to FFT roundoff. See angular_spectrum() for distance-gradient behavior.

Returns:

Propagated field on the same sampling grid.

Return type:

ScalarField

property shape: tuple[int, int]#

Return the field shape as (ny, nx).

angular_spectrum(field: ScalarField[BEArrayT], distance: float | ScalarOrArrayT, evanescent: EvanescentPolicy = 'discard') → ScalarField[BEArrayT][source]#

Propagate a scalar field with the angular spectrum method.

The input and output use the same rectangular sampling grid. Consequently, the usual discrete-Fourier periodic-boundary assumption applies; callers should provide enough zero padding to prevent wraparound for expanding fields.

Parameters:

  • field – Input scalar field.

  • distance – Signed propagation distance. It must use the same unit as the field spacing and wavelength. A backend scalar is accepted so that PyTorch can differentiate with respect to distance, including at zero for propagating components.

  • evanescent – Handling of spatial frequencies above the propagating cutoff. "discard" removes them at every distance, including zero, so zero-distance propagation is an identity only for fields without evanescent content. "decay" attenuates them exponentially with abs(distance) and preserves the complete field at zero, up to FFT roundoff. With evanescent content, this absolute-value decay has no two-sided distance derivative at zero; PyTorch uses a zero subgradient for the absolute-value factor there.

Returns:

Propagated field on the original sampling grid.

Return type:

ScalarField

Raises:

  • TypeError – If distance is not scalar.

  • ValueError – If the distance or evanescent policy is invalid.

gaussian_field(shape: tuple[int, int], dx: float, wavelength: float, waist_radius: float, dy: float | None = None, refractive_index: float = 1.0, amplitude: complex | ScalarOrArrayT = 1.0) → ScalarField[source]#

Create a fundamental Gaussian beam sampled at its waist.

waist_radius is the conventional 1/e field-amplitude radius, or equivalently the 1/e-squared intensity radius.

Parameters:

  • shape – Number of samples as (ny, nx).

  • dx – Sample spacing along x.

  • wavelength – Vacuum wavelength.

  • waist_radius – Gaussian beam waist radius.

  • dy – Sample spacing along y. Defaults to dx.

  • refractive_index – Homogeneous-medium refractive index. Defaults to 1.

  • amplitude – On-axis complex-field amplitude. Defaults to 1.

Returns:

Gaussian field at its waist plane.

Return type:

ScalarField