Mie

Exact solution for a single homogeneous or layered sphere. It is the reference for every other scattering method. There are two backends, both under method mie.

Backend	Module	Shapes	Fields	Device	Gradients
miepython	lightsmith.backends.mie	Sphere	—	CPU	—
lightsmith-mie	lightsmith.backends.mie_native	Sphere, LayeredSphere	near and far	CPU or GPU (NumPy or PyTorch)	through mie_cross_sections

Method

miepython wraps miepython (MIT), a core dependency. miepython uses the n − ik convention, so the index is conjugated before the call.

lightsmith-mie is a native Lorenz–Mie series that follows Bohren & Huffman's conventions.

• Recursions. It uses the log-derivative recursions of Yang (2003) and Peña & Pal (2009), vectorised over wavelengths. D1 comes from a downward recursion. D3 and the inner-layer ratios come from upward recursions, so no Riccati–Bessel function is formed for the cross sections.
• Coefficients. a_n and b_n are written in a form that keeps Re(a_n) accurate for tiny, weakly absorbing spheres.
• Number of orders. Wiscombe's rule for homogeneous spheres; Peña & Pal's rule for layered spheres.
• Far field. Computed from S1 and S2.
• Near field. Matches tangential E and H at every interface. It always runs in double precision.
• Incidence. Any direction, and orientation averaging, which is trivial for a sphere.
• Gradients. The functional API lightsmith.backends.mie_native.mie_cross_sections(radii_nm, eps, wavelength_nm, medium_index, n_max=None) is differentiable with PyTorch tensors, on a CPU or a GPU.

Options

options["mie"] or options["lightsmith-mie"]. miepython has no options.

Option	Default	Meaning
precision	"double"	"single" or "double" for the series. Single precision is typically about 1e-7 relative, but can degrade to about 1e-3 near zeros of ψ_n(x). Single is not faster on GPUs, because the series is memory-bound. Near fields always use double.
n_max	None	Number of multipole orders. Default: Wiscombe's or Peña & Pal's rule.
wavelength_chunk	None	Wavelengths per vectorised batch. Default: as many as fit in about 1 GiB of work arrays.

Validation

All tests are in tests/test_mie_native.py unless noted.

Test	Reference	Tolerance
test_matches_miepython: n = 1.5 + 0.02i and a gold-like Drude sphere; r = 2–1000 nm; 450–900 nm	miepython	C_ext, C_sca < 1e-6 relative; |ΔC_abs|/C_ext < 1e-6
test_hard_cases_against_mpmath: x = 0.028; x = 42 with |mx| = 126; a Drude sphere near ε ≈ 0	40-digit mpmath (Bohren & Huffman)	Q_ext, Q_sca to 1e-11
test_coated_sphere_against_mpmath: 30/42 nm core-shell, three material pairs	40-digit mpmath (Bohren & Huffman 8.1)	1e-11
test_shell_of_core_material_reproduces_sphere	55 nm homogeneous sphere	cross sections and far field < 1e-10; near field 1e-7
test_far_field_integrates_to_csca: r = 80 nm and a core-shell, oblique incidence	∫ dC/dΩ = C_sca	1e-10
test_near_field_boundary_conditions	continuity of tangential E and normal D	< 1e-4 of the field scale
test_autodiff_matches_finite_differences	central differences	1e-6 relative
test_gpu_matches_cpu (gpu)	CPU, double precision	C_ext and far field < 1e-12; near field 1e-10; single precision < 1e-3
tests/test_core.py::test_mie_rayleigh_limit (miepython): a = 2 nm	Rayleigh formula	C_abs 5e-3

Limits

• A single particle only. For clusters, use T-matrix or DDA.
• Spheres only: plain spheres for miepython, plain or layered for lightsmith-mie. Use DDA or FDTD for other shapes.
• No substrate.
• miepython refuses near and far fields, and ignores the device (it always runs on the CPU).
• lightsmith-mie warns about non-finite cross sections. If that happens, use precision="double" or a larger n_max.