ldos-opt · Shaker et al. reproduction

E homotopy n=1.00/2.00 running

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-E-d50 · shifted β=∞ · updated

LDOS / vacuum

0.8193

best 0.8272 · target ≥ 500

7.697

best 7.815 · target ≥ 50,000

Iteration

300

600 factorizations

Re ω*/ω0

wall 1.229e+03 s

Length-scale P

0.02705

λ = 3 · erode/dilate

Shifted log-LDOS at Re ω*. Fig. 6 bars (LDOS/vac≥500, Q≥50000) are reference only — this geometry is an open slot.

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