Related papers: Resonant state expansion applied to three-dimensio…
The single-mode approximation of the resonant state expansion has proven to give accurate first-order approximations of resonance shifts and linewidth changes when modifying the material properties inside open optical resonators. Here, we…
The increase of resolution by the use of microspheres is related to the use of evanescent waves, satisfying complex Snell law where the trigonometric functions of the incident and refracted angles are complex trigonometric functions,…
We study the possible expansion of the electromagnetic field scattered by a strictly convex metallic nanoparticle with dispersive material parameters placed in a homogeneous medium in a low-frequency regime as a sum of modes oscillating at…
In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this…
A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional (2-D) open structures. In contrast with the bounded case which have only discrete spectrum (real in the…
Parametric radiative transfer equation (RTE) occurs in multi-query applications such as uncertainty quantification, inverse problems, and sensitivity analysis, which require solving RTE multiple times for a range of parameters.…
This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width $h\ll1$. The model is representative among many 3D subwavelength hole…
Single-molecule tip-enhanced Raman spectroscopy (TERS) under ultra-high vacuum (UHV) and cryogenic conditions enables exploration of the relations between the adsorption geometry, electronic state, and vibrational fingerprints of individual…
We predict a resonant enhancement of the nonlinear optical response of an interacting Rydberg gas under conditions of electromagnetically induced transparency. The enhancement originates from a two-photon process which resonantly couples…
Two schemes of amplification of two-mode squeezed light in the continuous variable EPR-state are considered. They are based on the integrals of motion, which allow conserving quantum correlations whereas the power of each mode may increase.…
We present a finite element method (FEM) solver for computation of optical resonance modes in VCSELs. We perform a convergence study and demonstrate that high accuracies for 3D setups can be attained on standard computers. We also…
We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a…
We consider solutions to the Lam\'e system in two dimensions. By using systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation), we establish a rigorous asymptotic expansion for the…
The synergistic formation of ``zero'' (exponentially small or thermally activated) resistance states (ESRS) in high mobility two-dimensional electron systems (2DES) in a static magnetic field B and exposed to strong microwave radiation has…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
Text-to-image generation powered by Diffusion Transformers (DiTs) has made remarkable strides, yet remote sensing (RS) synthesis lags behind due to two barriers: the absence of a domain-specialized DiT prior and the prohibitive cost of…
The extended state observer (ESO) plays an important role in the design of feedback control for nonlinear systems. However, its high-gain nature creates a challenge in engineering practice in cases where the output measurement is corrupted…
In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter.…
We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}_2$ [1] to position-orientation space $\mathbb{M}_2 \cong \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance and…
We argue and numerically substantiate that the real-space entanglement spectrum (RSES) of composite fermion quantum Hall states is given by the spectrum of a local boundary perturbation of a $(1+1)$d conformal field theory (CFT), which…