qiu_classical_simulation.wave_optics.analysis

Quantities to analyze a lens experiment with, e.g. its beam waist along the way.

Functions:

• beam_waist –

  Return the beam waist of a field, twice the standard deviation of its intensity.

• principal_plane_position –

  Return the depth of the principal plane of the lens, from where the beam enters.

• propagation_distances –

  Return the propagation distances of the snapshots after each slice and step.

• thin_lens_reference_states –

  Return the thin lens profiles at the distances of propagation_distances.

• lens_surface –

  Return the depth of the convex lens surface at each transverse position.

beam_waist

beam_waist(state: ArrayLike, x_values: ArrayLike) -> float

Return the beam waist of a field, twice the standard deviation of its intensity.

This is the waist radius of a Gaussian beam exp(-x**2 / w**2).

Source code in packages/qiu-classical-simulation/src/qiu_classical_simulation/wave_optics/analysis.py

def beam_waist(state: npt.ArrayLike, x_values: npt.ArrayLike) -> float:
    """Return the beam waist of a field, twice the standard deviation of its intensity.

    This is the waist radius of a Gaussian beam `exp(-x**2 / w**2)`.
    """
    intensity = np.abs(np.asarray(state)) ** 2
    x = np.asarray(x_values)
    mean = np.sum(x * intensity) / np.sum(intensity)
    variance = np.sum(x**2 * intensity) / np.sum(intensity) - mean**2
    return float(2 * np.sqrt(variance))

principal_plane_position

principal_plane_position(parameters: ExperimentParameters) -> float

Return the depth of the principal plane of the lens, from where the beam enters.

It is at the vertex of the convex surface, which is the exit for the reverse order; for the forward order, it lies at t - t / n for the thickness t.

Source code in packages/qiu-classical-simulation/src/qiu_classical_simulation/wave_optics/analysis.py

def principal_plane_position(parameters: ExperimentParameters) -> float:
    """Return the depth of the principal plane of the lens, from where the beam enters.

    It is at the vertex of the convex surface, which is the exit for the reverse order;
    for the forward order, it lies at `t - t / n` for the thickness `t`.
    """
    if parameters.lens_reverse_order:
        return parameters.lens_thickness
    return parameters.lens_thickness - parameters.lens_thickness / (
        parameters.refractive_index
    )

propagation_distances

propagation_distances(parameters: ExperimentParameters) -> list[float]

Return the propagation distances of the snapshots after each slice and step.

Source code in packages/qiu-classical-simulation/src/qiu_classical_simulation/wave_optics/analysis.py

def propagation_distances(parameters: ExperimentParameters) -> list[float]:
    """Return the propagation distances of the snapshots after each slice and step."""
    return [
        parameters.lens_slice_thickness * (i + 1) for i in range(parameters.lens_slices)
    ] + [
        parameters.lens_thickness + parameters.step_size_after_lens * (j + 1)
        for j in range(parameters.num_of_steps_after_lens)
    ]

thin_lens_reference_states

thin_lens_reference_states(parameters: ExperimentParameters) -> list[NDArray[float64]]

Return the thin lens profiles at the distances of propagation_distances.

The ideal thin lens sits at the principal plane of the lens.

Source code in packages/qiu-classical-simulation/src/qiu_classical_simulation/wave_optics/analysis.py

def thin_lens_reference_states(
    parameters: ExperimentParameters,
) -> list[npt.NDArray[np.float64]]:
    """Return the thin lens profiles at the distances of `propagation_distances`.

    The ideal thin lens sits at the principal plane of the lens.
    """
    principal_plane = principal_plane_position(parameters)
    return [
        thin_lens_simulation(parameters, distance, 0)
        if distance < principal_plane
        else thin_lens_simulation(
            parameters, principal_plane, distance - principal_plane
        )
        for distance in propagation_distances(parameters)
    ]

lens_surface

lens_surface(parameters: ExperimentParameters) -> NDArray[float64]

Return the depth of the convex lens surface at each transverse position.

The depth is measured from where the beam enters, as in propagation_distances.

Source code in packages/qiu-classical-simulation/src/qiu_classical_simulation/wave_optics/analysis.py

def lens_surface(parameters: ExperimentParameters) -> npt.NDArray[np.float64]:
    """Return the depth of the convex lens surface at each transverse position.

    The depth is measured from where the beam enters, as in `propagation_distances`.
    """
    x = np.asarray(parameters.x_axis.values, dtype=np.float64)
    x = x - parameters.transverse_length / 2
    radius = parameters.radius_of_curvature
    if parameters.fresnel_approximation:
        sag = x**2 / (2 * radius)
    else:
        sag = radius - np.sqrt(radius**2 - x**2)
    return parameters.lens_thickness - sag if parameters.lens_reverse_order else sag