ldos-opt · Shaker et al. reproduction

B per-penalty a=0.45 s4 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| ≤ 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].

phc-B-s4-a45 · shifted β=∞ · updated

LDOS / vacuum
1.370e+05
best 1.370e+05 · target ≥ 500
Q
1.056e+06
best 1.056e+06 · target ≥ 50,000
Iteration
100
200 factorizations
Re ω*/ω0
1.021
wall 99.14 s
Length-scale P
0.5854
λ = 3 · erode/dilate

Verified rebuild: LDOS/vac=1.37e+05, Q_eig=1.06e+06, Q_FWHM=7.04e+05, P=0.585, fabricable=False. Gap |ε−1|≤0.00e+00, sym x/y 8.44e-15/7.99e-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