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We study scalar perturbations of topological solitons, smooth horizonless solutions in five-dimensional Einstein-Maxwell theory that correspond to coherent states of gravity via the dynamics of extra compact dimensions. First, we compute…
A theoretical approach aimed at the quantum statistical mechanics of a molecular ensemble coupled to a lossless cavity mode is presented. A canonical ensemble is considered and an approximate formula is devised for the Helmholtz free energy…
Wavefront errors are a common artifact in laser light generation and imaging. They can be described as an aberration from the spherical wavefront of an ideal Gaussian beam by combinations of higher-order Hermite- or Laguerre-Gaussian terms.…
Multimode fibers provide a promising platform for realizing high-power laser amplifiers with suppressed nonlinearities and instabilities. The potential degradation of optical beam quality has been a major concern for highly multimode fiber…
This thesis is devoted to the study of hyperbolic differential operators on globally hyperbolic manifolds, linear gauge theories and their quantisation. In the first part, we treat the Cauchy problem for symmetric hyperbolic systems and…
We present a theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…
We investigate the lasing action in coupled multi-row nanopillar waveguides of periodic or fractal structure using the finite difference time domain (FDTD) method, coupled to the laser rate equations. Such devices exhibit band splitting…
Thermal effects are already important in currently operating interferometric gravitational wave detectors. Planned upgrades of these detectors involve increasing optical power to combat quantum shot noise. We consider the ramifications of…
In this letter, we demonstrate a technique of making an ultrastable laser referenced to a multi-cavity, corresponding to a lower thermal noise limit due to the larger equivalent beam size. The multi-cavity consists of several pairs of…
This paper is devoted to logarithmic Hardy-Littlewood-Sobolev inequalities in the two-dimensional Euclidean space, in presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter,…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
We present a fast direct solver for the simulation of electromagnetic scattering from an arbitrarily-shaped, large, empty cavity embedded in an infinite perfectly conducting half space. The governing Maxwell equations are reformulated as a…
Cavity point-to-set correlations are real-space tools to detect the roughening of the free-energy landscape that accompanies the dynamical slowdown of glass-forming liquids. Measuring these correlations in model glass formers remains,…
Nonlinear interactions between phonon modes govern the behavior of vibrationally highly excited solids and molecules. Here, we demonstrate theoretically that optical cavities can be used to control the redistribution of energy from a highly…
We propose a geometry-specific, mode-selective quantization scheme in coupled field-emitter systems which makes it easy to include material and geometrical properties, intrinsic losses as well as the positions of an arbitrary number of…
Optical cavities can support many transverse and longitudinal modes. A paraxial scalar theory predicts that the resonance frequencies of these modes cluster in different orders. A non-paraxial vector theory predicts that the frequency…
In this work, we investigate the steady-states of a fiber lasers mode-locked with a nonlinear amplifying loop-mirror that has an inherent amplitude noise-suppression mechanism. Due to the interaction of the sinusoidal transmission function…
Parameter regulations of narrow-linewidth fiber lasers in frequency domain has drawn considerable interests for widespread applications in the light quantum computing, precise coherent detection, and generation of micro-waves. All-optical…