Related papers: A variational mode solver for optical waveguides b…
In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain…
Achieving precise control of light intensity in 3D volumes is highly in demand in many applications in optics. Various wavefront shaping techniques have been utilized to reconstruct a target amplitude profile within a 3D space. However,…
In this work a new generalization of the theory of coupled modes for non-periodic structured waveguide is presented. Based on a set of eigen waves of a homogeneous periodic waveguide, a new basis of vector functions is introduced that takes…
In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The…
Fibre modal noise occurs in high spectral resolution, high signal-to-noise applications. It imposes fundamental limits on the photometric accuracy of state-of-the-art fibre-spectrograph systems. In order to maximize the performance of…
We present a semi-analytical framework for computing the coupling of radiative and guided waves in slowly varying (nearly uniform or nearly periodic) surfaces, which is especially relevant to the exploitation of nonlocal effects in…
Two-dimensional van der Waals (vdW) crystals can sustain various types of polaritons with strong electromagnetic confinements, making them highly attractive for the nanoscale photonic and optoelectronic applications. While extensive…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
Multimodal learning leverages complementary information derived from different modalities, thereby enhancing performance in medical image segmentation. However, prevailing multimodal learning methods heavily rely on extensive well-annotated…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
The conformal mapping approach is a well established technique for solving the Euler equations for potential flows with one spatial dimension. In this work, we extend this framework to problems with a weakly transversal dependence and, by…
In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an application, a (2+1)-dimensional variable-coefficient…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
We investigate optical (transverse gradient) forces between two high-index dielectric planar waveguides immersed in low-index dielectric fluid media. Complimentary to previous studies, we extend optical forces calculations, in order to take…
The concept of photonic modes is the cornerstone in optics and photonics, which can describe the propagation of the light. The Maxwell's equations play the role in calculating the mode field based on the structure information, while this…
In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the…
At a fixed frequency, a general wave field in an open optical waveguide is a sum of finite number of guided modes and an integral of radiation modes. Most studies on open lossless dielectric waveguides are concerned with regular guided…
A method is proposed to obtain full-domain spatial modes based on Proper Orthogonal Decomposition (POD) of Particle Image Velocimetry (PIV) measurements performed at different (overlapping) spatial locations. This situation occurs when…
In this paper we study the problem of wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem,…
A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes…