Related papers: A variational mode solver for optical waveguides b…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Directional couplers are essential components in integrated photonics. Given their widespread use, accurate characterization of directional couplers is crucial for ensuring optimal performance. However, it is challenging due to the coupling…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
In this work, we introduce a Variational Multi-Scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are approximated from the eigenpairs of associated elliptic operator. The abstract method is…
Four-wave mixing has extensively been investigated for various applications such as communications, spectroscopy, metrology, quantum computing and bio-imaging. However, there is a clear desire to implement these functionalities in a small…
Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex…
Guided waves modes in a slab waveguide formed from the isotropic dielectric layer embedded by hyperbolic materials are investigated. Optical axis is normal to the slab plane. The dispersion relations for TE and TM waves are found. The…
Monitoring polarization dynamics in multimode fibers is critical for a range of applications, spanning from optical communication to sensing. Although the modal behavior of multimode fibers is well understood through interferometry and…
In this work, we study two-dimensional diffusion-wave equations with variable exponent, modeling mechanical diffusive wave propagation in viscoelastic media with spatially varying properties. We first transform the diffusion-wave model into…
Photonic crystals with a finite size can support surface modes when appropriately terminated. We calculate the dispersion curves of surface modes for different terminations using the plane wave expansion method. These non-radiative surface…
Waveguide characterization of dielectric materials is a convenient and broadband approach for measuring dielectric constant. In conventional microwave measurements, material samples are usually mechanically shaped to fit the waveguide…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
The quasi-one-dimensional rhombic array of the waveguides is considered. System of equations describing coupled waves in the waveguide in the linear limit is solved exactly. The electric field distribution was found both for the…
Common techniques for measuring refractive indices, such as ellipsometry and goniometry, are ineffective for van der Waals crystal flakes because of their high anisotropy and small, micron-scale, lateral size. To address this, we employ…
We present ModMap, a natively multiview and multimodal framework for 3D anomaly detection and segmentation. Unlike existing methods that process views independently, our method draws inspiration from the crossmodal feature mapping paradigm…
In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations…
Electroelastic waves in piezoelectric media are widely used in sensing and filtering applications. Despite extensive research, computing the guided wave dispersion remains challenging. This paper presents semi-analytical approaches based on…
We demonstrate that the spatial profiles of both propagating and evanescent Bloch-modes in a periodic structure can be extracted from a single measurement of electric field at the specified optical wavelength. We develop a systematic…