ldos-opt · Shaker et al. reproduction

Slow enlarge sin-slow-s2 |x|≤4.5 success

Dipole at (0,0) in a vacuum slot |x| < 0.5 λ0 (0.5 μm of free space on each side if λ0 = 1 μm). Design occupies 0.5 ≤ |x| ≤ 4.5 λ0 and |y| ≤ 1 λ0. Density is optimized in the first quadrant and mirrored through x = 0 and y = 0. Material ε ∈ [1, 4].

sin-slow-s2 · shifted β=∞ · updated

LDOS / vacuum
1.605e+04
best 1.605e+04 · target ≥ 500
Q
1.205e+05
best 1.205e+05 · target ≥ 50,000
Iteration
100
200 factorizations
Re ω*/ω0
1.021
wall 92.73 s
Length-scale P
0.5755
λ = 3 · erode/dilate

Verified rebuild: LDOS/vac=1.6e+04, Q_eig=1.21e+05, Q_FWHM=8.04e+04, P=0.575, fabricable=False. Gap |ε−1|≤0.00e+00, sym x/y 4.88e-15/6.66e-15.

permittivity
ε(x,y), source as red/white dot. Red band is the frozen vacuum strip when present.
field
|E|² at the evaluation frequency
fragile band
Fragile band ρ_dilate − ρ_erode. Speckle lights up; a clean interface is a thin outline.
history
LDOS enhancement, Q, and length-scale penalty vs Maxwell-matrix factorizations