ldos-opt · Shaker et al. reproduction

E homotopy n=1.45/1.55 finished

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 ∈ [2.1025, 2.4025].

phc-E-d05 · shifted β=∞ · updated

LDOS / vacuum
1.174
best 1.331 · target ≥ 500
Q
47.95
best 52.14 · target ≥ 50,000
Iteration
940
1640 factorizations
Re ω*/ω0
1
wall 566.3 s
Length-scale P
0.4677
λ = 3 · erode/dilate

Verified rebuild: LDOS/vac=1.17, Q_eig=47.9, P=0.468, fabricable=False. Gap |ε−1|≤0.00e+00, sym x/y 4.44e-16/4.44e-16.

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