← Back to Lab

Cylinder Dispersion

Guided-mode dispersion ω(qz) of an infinite cylinder in a homogeneous host. Roots are found from det M(qa, ka, ε₁, εh, m) = 0 with exact complex-argument Bessel functions.

Parameters

—
EELS parameters
outside the cylinder

Model. Tangential E, H matching at r = a gives a 4×4 system. Guided modes satisfy det M = 0 inside the window kh < q < kmat. A small Im(ε₁) regularizes the search.

References

  • C. F. Bohren & D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), §8 — infinite cylinder expansion.
  • Abramowitz & Stegun, §9.1.11 — integer-order Ym series used to compute complex-argument Bessel functions in the browser.
  • Internal port of Álvaro Rodríguez Echarri's MATLAB cylinders library (matrix giveM, dispersion root solver).