ldos-opt · Shaker et al. reproduction

E homotopy n=1.30/1.70 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 ∈ [1.69, 2.89].

phc-E-d20 · shifted β=∞ · updated

LDOS / vacuum
0.7848
best 2.492 · target ≥ 500
Q
136
best 189.6 · target ≥ 50,000
Iteration
700
1400 factorizations
Re ω*/ω0
0.9886
wall 640 s
Length-scale P
0.2072
λ = 3 · erode/dilate

Verified rebuild: LDOS/vac=0.785, Q_eig=136, P=0.207, fabricable=False. Gap |ε−1|≤0.00e+00, sym x/y 1.78e-15/1.11e-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