Homogeneous medium; independent flux budget; guided channels

← Verification · Cylinders · Point dipole
Reference
homogeneous medium; independent flux budget; guided channels
Kind
analytic / method: a closed form, limit or conservation law: independent of any code
Calculated
rate channels
Agreement
1e-8 / 1e-5 / 1e-6
A dipole in and around a cylinder of n = 1.5 in n = 1.5 at 600 nm: the rates of free space A cylinder of the medium's own index changes nothing: every rate is the free-space one, 1, for any position and orientation, inside the cylinder (r < 100 nm) or out; the test also checks escape = 1, no guided or absorbed power and the quantum yield 0.4 passed through. Floored at 1e-17 for the logarithmic axis.
05010015020025030010⁻¹⁷10⁻¹⁶10⁻¹⁵distance from the axis [nm]|Γ / Γ₀ − 1|
electric dipole, max over orientations, PyStratify magnetic dipole, max over orientations, PyStratify
Hover to read values.
  • largest |Γ / Γ₀ − 1|: 1.11×10⁻¹⁶
An electric dipole outside a coated cylinder (n = 1.5 core, absorbing n = 0.2 + 3i coating, 50/100 nm), 600 nm: the total against its channels A electric dipole outside a cylinder of n = 1.5 (50 nm) under 50 nm of an absorbing n = 0.2 + 3i coating, 600 nm. The total rate comes from the Green's function at the source; the channels separately, from the power escaping to infinity, the power carried by guided modes and the power absorbed in the coating, so their sum is an independent budget.
15020025030035040010⁻¹11010²distance from the axis [nm]Γ / Γ₀
radial, total (PyStratify) azimuthal, total (PyStratify) axial, total (PyStratify) radial, escape + guided + absorbed azimuthal, escape + guided + absorbed axial, escape + guided + absorbed
Hover to read values.
  • largest relative difference: 3.21×10⁻¹²
  • PyStratify the lines, the reference the circles
A magnetic dipole outside a coated cylinder (n = 1.5 core, absorbing n = 0.2 + 3i coating, 50/100 nm), 600 nm: the total against its channels A magnetic dipole outside a cylinder of n = 1.5 (50 nm) under 50 nm of an absorbing n = 0.2 + 3i coating, 600 nm. The total rate comes from the Green's function at the source; the channels separately, from the power escaping to infinity, the power carried by guided modes and the power absorbed in the coating, so their sum is an independent budget.
15020025030035040010⁻¹110distance from the axis [nm]Γ / Γ₀
radial, total (PyStratify) azimuthal, total (PyStratify) axial, total (PyStratify) radial, escape + guided + absorbed azimuthal, escape + guided + absorbed axial, escape + guided + absorbed
Hover to read values.
  • largest relative difference: 4.31×10⁻¹¹
  • PyStratify the lines, the reference the circles
A dipole inside a lossless guide (n = 1.5, radius 100 nm) in air, 600 nm: the total against escape + guided An electric dipole inside the guide, averaged over orientations: a point source (unlike a line source) sends a finite share of its power into the guided mode, here about a tenth of the free rate; the total from the Green's function must equal what escapes plus what is guided, since nothing absorbs.
02040608000.20.40.60.8distance from the axis [nm]Γ / Γ₀
total, PyStratify escape guided escape + guided
Hover to read values.
  • largest relative difference: 4.35×10⁻¹²
  • PyStratify the lines, the reference the circles

Run it yourself: unified_checks.py · test_unified.py · figures.py · UNIFIED_CHECKS.md on GitHub, PyStratify 97e52a9