Graphene-coated sphere plasmons; thin-film limit of a sheet

← Verification · Spheres · Plane wave
Reference
graphene-coated sphere plasmons; thin-film limit of a sheet
Kind
analytic: a closed form, limit or conservation law: independent of any code
Calculated
resonance position; second-order limit
Agreement
retardation shift; 2e-3
A graphene-coated sphere (ε = 2.1 in ε = 1.77, E_F = 0.5 eV): the dipole plasmon against the quasi-static resonance The full solution with a conducting sheet on the sphere against the quasi-static resonance condition: they meet as R → 0 and part by retardation, too little to see here (5e-5 at 5 nm, 9e-4 at 60 nm); the test asserts the shift stays within (kR)².
102030405060345678910radius [nm]λ [µm]
resonance, PyStratify (peak of |T₁|) quasi-static: ε₁ℓ + ε₂(ℓ + 1) + iσℓ(ℓ + 1)/(k₀R) = 0
Hover to read values.
  • relative shift at R = 5 nm: 5.2×10⁻⁵
  • PyStratify the lines, the reference the circles
A 1 nm film of ε = 15 + 5i on a 200 nm sphere of n = 3.5 in water: the film as a 2D sheet Sheet.from_film turns a thin film into surface conductivities with the normal (out-of-plane) term; its error falls as d² (halving d quarters it, the test's check), against the film solved as a shell of its own.
500550600650700750800850900012345λ [nm]Qext
Qext, 2D sheet (PyStratify) Qext, explicit 1 nm film
Hover to read values.
  • largest relative difference: 0.004232
  • PyStratify the lines, the reference the circles

Run it yourself: sphere_checks.py · test_sheets.py · figures.py · SPHERE_CHECKS.md on GitHub, PyStratify 97e52a9