We develop a comprehensive theoretical framework for photon propagation through a transmissive Casimir cavity operating in the unexplored wavelength-matched regime 2d, where the probe photon wavelength approaches the fundamental mode cutoff of the cavity. Beginning from the quantized electromagnetic field in bounded geometries, we derive the vacuum stress-energy tensor, the Euler--Heisenberg effective Lagrangian, and the Scharnhorst refractive-index correction, demonstrating explicitly that the perturbative expansion breaks down as 2d. We characterize this breakdown as a topological transition in the mode spectrum---a discrete change in mode count accompanied by a van~Hove singularity in the local density of states---and develop an effective field theory parametrization valid near the cutoff boundary. We then introduce quasicrystalline boundary conditions as a new theoretical tool for Casimir physics: Fibonacci gratings and Penrose tilings etched into the cavity surfaces impose aperiodic boundary conditions that produce self-similar, fractal vacuum mode spectra qualitatively distinct from those of periodic or smooth surfaces. We derive the modified local density of states, Casimir energy, and vacuum stress tensor for quasicrystalline cavities. We analyze the dynamic Casimir effect at the mode cutoff, showing that the vanishing group velocity near the cutoff frequency produces a parametric enhancement of photon creation rates by a factor (c/vg) ², potentially reducing the threshold for observable vacuum photon production by many orders of magnitude. Finally, we examine the thermodynamics of vacuum mode cycling through the cutoff boundary and derive conditions under which the Casimir interaction may exhibit non-conservative behavior, with implications for asymmetric vacuum stress and force generation in cavities with broken spatial symmetry. Target venue: Physical Review A. Author preprint deposited for archival and citation. Draft — pending author review.
Andrew Bond (Sun,) studied this question.