Quasistatic

Backend lightsmith-quasistatic (method quasistatic, module lightsmith.backends.quasistatic). It uses the dipole (Rayleigh–Gans) approximation for particles much smaller than the wavelength. auto never picks it; request it with method="quasistatic".

Method

The polarisability is computed with the relative permittivity ε_p / n_m² (Bohren & Huffman, chapter 5):

• Sphere: α = 4πa³(ε − 1)/(ε + 2).
• Layered sphere: the recursive effective permittivity of Bohren & Huffman eq. 5.36.
• Spheroid: Gans theory with closed-form depolarisation factors.

From the polarisability:

• C_abs = k Im(e·α·e)
• C_sca = k⁴|α·e|²/(6π)

With any correction switched on, C_ext comes from the optical theorem instead. Orientation averages are the mean over the three principal axes. The far field is that of the induced dipole.

Options

options["quasistatic"] or options["lightsmith-quasistatic"].

Option	Default	Meaning
corrections	"none"	One of: "none" (static dipole); "radiative" (adds radiative damping); "mlwa" (modified long-wavelength approximation: dynamic depolarisation plus radiative damping); "mie_dipole" (the Mie dipole term exact to O(x⁴) plus damping, homogeneous spheres only)

The solver runs on the CPU in float64. There are no gradients.

Validation

All tests are in tests/test_quasistatic.py. They cover 400–800 nm in water, with the native Mie solver as the reference.

Test	Reference	Tolerance
test_dielectric_5nm_sphere_matches_mie (every correction mode)	Mie	C_ext, C_sca, C_abs < 1 %
test_metal_5nm_sphere_matches_mie: Drude sphere	Mie	mie_dipole C_ext < 1 %; error ordering mie_dipole < mlwa < none
test_coated_sphere_matches_mie: 3 nm core with a 2 nm shell	Mie	C_ext < 1 %
test_depolarization_factors	numerical quadrature	1e-12
test_far_field_integrates_to_csca	∫ dC/dΩ = C_sca	1e-12
test_energy_balance_with_radiative_damping: lossless spheroid, mlwa	C_abs = 0	< 1e-12 C_ext

Limits

• One particle only.
• Shapes: spheres, layered spheres and spheroids; cylinders are refused. mie_dipole accepts plain spheres only.
• No near field and no substrate. The far field cannot be combined with orientation_average.
• Warns when the size parameter x = 2π n_m a_max / λ_min exceeds 0.3. At that size, use Mie or DDA instead.