Related papers: Minimum Dielectric-Resonator Mode Volumes
In many cosmological models, including the $\Lambda$CDM concordance model, there exist a theoretical upper bounds on the size of collapsing structures. The most common formulations in the literature refer to a turnaround radius in spherical…
We present a design for an optical dielectric bowtie cavity which features deep sub-wavelength confinement of light. The cavity is derived via simplification of a complex geometry identified through inverse design by topology optimization,…
Recent advances in the design and fabrication of on-chip optical microresonators has greatly expanded their applications in photonics, enabling metrology, communications, and on-chip lasers. Designs for these applications require fine…
A composite model of the standard model particles was recently derived using the Dirac Lagrangian on a spacetime where time does not advance along the worldlines of fundamental dust particles, called an 'internal spacetime'. The aim of…
On geometrically finite hyperbolic manifolds $\Gamma\backslash H^{d}$, including those with non-maximal rank cusps, we give upper bounds on the number $N(R)$ of resonances of the Laplacian in disks of size $R$ as $R\to \infty$. In…
We apply a systematic inverse design approach to discover foundry-compliant, multilayer grating couplers that can efficiently couple a number of independent waves from free space to on-chip propagating modes. For visible- and near-infrared…
Subwavelength resonance is a vital acoustic phenomenon in contrasting media. The narrow bandgap width of single-layer resonator has prompted the exploration of multi-layer metamaterials as an effective alternative, which consist of…
We develop a unified framework for identifying bounds to maximum resonant nonlinear optical susceptibilities, and for "inverse designing" quantum-well structures that can approach such bounds. In special cases (e.g. second-harmonic…
We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…
Small form-factor, narrowband, and highly directive antennas are of critical importance in a variety of applications spanning wireless communications, remote sensing, Raman spectroscopy, and single photon emission enhancement. Surprisingly,…
We demonstrate, for the first time, an all-dielectric metamaterial resonator in the mid-wave infrared based on high-index tellurium cubic inclusions. Dielectric resonators are desirable compared to conventional metallo-dielectric…
On a class of asymptotically conical manifolds, we prove two types of low frequency estimates for the resolvent of the Laplace-Beltrami operator. The first result is a uniform $ L^2 \rightarrow L^2 $ bound for $ \langle r \rangle^{-1} (-…
We deal with the inverse problem of reconstructing acoustic material properties or/and external sources for the time-domain acoustic wave model. The traditional measurements consist of repeated active (or passive) interrogations, as the…
Modal volumes at the nano-scale, much smaller than the "diffraction-limit", with appreciable quality factors, are calculated for a dielectric cavity embedded in a space between metal plates. The modal field is bounded between the metal…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
We establish a method for giving lower bounds for the fundamental tone of elliptic operators in divergence form in terms of the divergence of vector fields. We then apply this method to the $L_{r}$ operator associated to immersed…
Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the…
The problem of finding the optimal current distribution supported by small radiators yielding the minimum quality (Q) factor is a fundamental problem in electromagnetism. Q factor bounds constrain the maximum operational bandwidth of…
Two-dimensional (2-D) boundary integral equation analysis of a notched circular microdisk resonator is presented. Results obtained provide accurate description of optical modes, free from the staircasing and discretization errors of other…
We study complex structure deformations of special Lagrangian cycles associated to fractional D-branes at $\mathbb{Z}_2$ singularities in Type II/$\Omega \mathcal{R}$ orientifold models. By means of solving hypersurface constraints, we show…