Robust constrained optimization of nonequilibrium Casimir repulsion in a biased-semiconductor cavity

Abstract

Nonequilibrium electromagnetic fluctuations offer a route to repulsive Casimir--Lifshitz forces. However, designs optimized only at nominal conditions may be fragile. We formulate repulsion in a planar PEC--vacuum--biased-GaAs--vacuum--PEC stack as a robust constrained optimization problem. The smaller of the outward pressures on the two conductors is maximized under fabrication and drive uncertainties. In the optically thick-slab limit, we prove that identical boundaries admit a symmetric optimizer, so equality of the optimal gaps emerges from the model rather than being imposed. At $300~\mathrm{K}$, with gap uncertainty of $\pm10~\mathrm{nm}$ and drive uncertainty of $\pm0.005$, the optimized design sustains a worst-case outward pressure of $2.257~\mathrm{mPa}$ and exceeds the corresponding far-field radiation-pressure plateau by $0.1812~\mathrm{mPa}$. At the nominal and active worst-case points, a full finite-slab scattering calculation agrees with the reduced model to within $1.60\times10^{-3}\%$. These results provide a design bound for cavity-enhanced nonequilibrium Casimir--Lifshitz repulsion and show how robust optimization can distinguish cavity enhancement from ordinary far-field radiation pressure.