Spectrally and Spatially Degenerate Coherent Perfect Absorbers and a Renormalization-Free Model for Casimir Forces

Abstract

This thesis deals with two separate topics. First, we design coherent perfect absorbers (CPAs) that remove the spatial-mode selectivity of conventional CPAs, and we then extend this idea to achieve both spatial and spectral degeneracy by operating at an exceptional point (EP). Second, we develop a renormalization-free scattering formulation for Casimir (van der Waals) forces in a one-dimensional model with a chain of point particles, for which we derive the continuum limit.MAD-CPA. A central insight of non-Hermitian photonics is that familiar devices possess time-reversed counterparts. Most notably, a laser becomes a coherent perfect absorber (CPA) under time-reversal. Consider a simple cavity with a partially transmitting input coupler, a highly reflecting end mirror, and a gain medium. In the forward (laser) picture, the cavity amplifies light and, above threshold, emits a coherent beam. In the time-reversed picture, the external beam is incident on the cavity, the gain medium is replaced by loss, and – when the parameters are tuned appropriately – the incident field is absorbed completely. This can be understood as an interferometric effect: perfect absorption occurs when internal dissipation is precisely balanced by external coupling so that the incident field and the steady-state intracavity field cancel at the input coupler, extinguishing the outgoing waves. However, this standard CPA is intrinsically mode-selective:perfect absorption is achieved only for a single, carefully prepared spatial wavefront(or a small set of modes). To overcome this limitation, we introduce a massively degenerate CPA (MAD-CPA). The construction time-reverses a degenerate-cavity laser: a self-imaging resonator with two lenses in a telescopic arrangement between planar mirrors (a 4f cavity) reproduces any injected transverse field on every roundtrip. In this geometry a weak absorber, placed inside the cavity and tuned to threshold, extinguishes not merely a few special modes but any supported spatial input. Even random speckle fields, consisting of superpositions of plane waves with random phases, get absorbed with high efficiency.To enable compact implementations, we replace the bulk 4f-cavity with a graded index(GRIN) glass fiber segment that approximately self-images over a designed propagation distance at a given wavelength. We quantify how intermodal dispersion and accumulated phase errors perturb the ideal degeneracy and identify parameters for which a high CPA effect persists for broad number of spatial modes. This analysis yields guidance on GRIN profile and segment length, so that the MAD-CPA mechanism remains effective despite moderate deviations from exact self-imaging.EP-MAD-CPA. While a MAD-CPA removes the spatial bottleneck of a CPA, the design remains narrowband. We achieve spectral tolerance without sacrificing spatial universality by operating at an exceptional point (EP) in a coupled-resonator architecture, yielding an EP-MAD-CPA. Two complementary realizations are presented:a two-cavity (8f) design with a central coupler, and a compact two-lens (4f) folded design with a split input mirror. For both, a closed-form reflection matrix that is independent of the transverse mode proves spatial degeneracy for arbitrary inputs.Enforcing CPA and EP simultaneously leads to a reflection spectrum where the reflectivity near resonance develops a broader quartic dip rather than a Lorentzian. Fourier-optics simulations reveal relevant design details: The internal absorber’s refraction detunes the cavity; compensating this shift is required to reach perfect absorption and recover the broadened, approximately quartic spectrum. Sensitivity analyses show that performance is only mildly affected by small errors in the input coupler but is tightly constrained by the central coupler and by sub-cavity length matching; microradian tilts and residual facet reflections lift the minimum yet preserve the characteristic broadening. Scaling to three or more coupled self-imaging cavities further flattens the line toward a Butterworth-like profile. Finally, forcing operation on the first longitudinal order yields genuinely broadband dips while retaining the EP-induced flattening. A time-domain analysis of the settling dynamics complements the results.Casimir forces from scattering. The final part of the thesis tackles a separate question: how to compute Casimir (van der Waals) forces between and inside homogeneous and inhomogeneous media without renormalization, i.e. without ambiguous subtractions of divergent local energies. We develop an alternative, renormalization-free route that formulates forces directly in terms of scattering by constructing a discrete one-dimensional model in which matter is represented by a chain of polarizable point scatterers. Transfer-matrix recursions yield closed expressions forthe force on each scatterer, and a controlled continuum limit connects the discrete formulation to a standard wave equation together with a Green-function representation for the spectral force density. The framework provides operational definitions for all quantities entering the numerics and explains the origin and scaling of local divergences in inhomogeneous susceptibility profiles. The method is predictive and practical. For homogeneous slabs the discrete force density converges rapidly and reproduces the expected continuum result inside a single block, while the net interaction between separated slabs matches established benchmarks. For inhomogeneous slabs the local force density need not converge pointwise, yet the macroscopic force on a slab across a vacuum gap does converge and can be computed with controlled accuracy. A multithreaded C++ implementation supports chains with up to millions of scatterers, enabling high-precision comparisons between discrete and continuum predictions and extensive parameter sweeps.