symop.modes.transfer.quadratic_dispersion

Quadratic dispersion transfer function.

This module defines a pure quadratic spectral-phase transfer.

The transfer applies a frequency-dependent phase around a reference frequency \(\omega_\mathrm{ref}\):

\[H(\omega) = \exp\left( -i\frac{\beta_2}{2}(\omega-\omega_\mathrm{ref})^2 \right).\]

This changes the temporal shape of an envelope through quadratic dispersion while leaving the spectral intensity \(|Z(\omega)|^2\) unchanged.

Notes

This transfer is kept in the generic transfer layer rather than the Gaussian-closed transfer layer. A quadratic spectral phase generally produces chirped Gaussian envelopes, so closed-form support would require an extended Gaussian family that explicitly represents chirp.

Classes

QuadraticDispersion(beta2[, w_ref])

Pure quadratic spectral phase around \(\omega_\mathrm{ref}\).

class QuadraticDispersion(beta2: float, w_ref: float = 0.0) → None

Bases: TransferBase

Pure quadratic spectral phase around \(\omega_\mathrm{ref}\).

The transfer is

\[H(\omega) = \exp\left( -i\frac{\beta_2}{2}(\omega-\omega_\mathrm{ref})^2 \right).\]

Parameters:

• beta2 (float) – Quadratic dispersion coefficient \(\beta_2\).

• w_ref (float) – Reference angular frequency \(\omega_\mathrm{ref}\).

_abc_impl = <_abc._abc_data object>

_signature_tag: ClassVar[str] = 'quad_dispersion'

beta2: float

w_ref: float = 0.0