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In this work, we demonstrate a discrete dispersion scan scheme using a low number of flat windows to vary the dispersion of laser pulses in discrete steps. Monte Carlo simulations indicate that the pulse duration can be retrieved accurately…
The Fractional Fourier Transform (FRFT) has been playing a unique and increasingly important role in signal and image processing. In this letter, we investigate the property of frequency shift in two-dimensional FRFT (2D-FRFT) domain. It is…
The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in a previous paper by the authors for scalar valued functions, or zero-forms, and represents a new…
Multi-plane light conversion allows to perform arbitrary transformations on a finite set of spatial modes with no theoretical restriction to the quality of the transformation. Even though the number of shaped modes is in general small, the…
A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…
In this paper, we introduce and analyze multidimensional vector-valued Laplace transform of functions with values in sequentially complete locally convex spaces. A great number of our results seem to be new even for the functions with…
Observing and studying the evolution of rare non-repetitive natural phenomena such as optical rogue waves or dynamic chemical processes in living cells is a crucial necessity for developing science and technologies relating to them. One…
Perfectly Matched Layer (PML) is a widely adopted non-reflecting boundary treatment for wave simulations. Reducing numerical reflections from a discretized PML has been a long lasting challenge. This paper presents a new discrete PML for…
The most recent theoretical and experimental results in the field of diffractive scattering are reviewed. A parallel between the two current theoretical approaches to diffraction, the DIS picture in the Breit frame and the dipole picture in…
By solving Maxwell equations with the ideal-metal boundary conditions in the TM case, we have fully described the transmission and diffraction properties of a single slit regardless of its width. Efficiencies of the main transformation…
We demonstrate a physics-aware transformer for feature-based data fusion from cameras with diverse resolution, color spaces, focal planes, focal lengths, and exposure. We also demonstrate a scalable solution for synthetic training data…
Periodic optical structures, such as diffraction grating and numerous photonic crystals, are one of the staples of modern nanophotonics for the manipulation of electromagnetic radiation. The array of subwavelength dielectric rods is one of…
The paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites on eleven regular space filling tessellations. First, significant contributions of different parameters, which play an…
A simple vibrational model of heat transfer in two-dimensional (2D) fluids relates the heat conductivity coefficient to the longitudinal and transverse sound velocities, specific heat, and the mean interatomic separation. This model is…
Sparse representation of 3D images is considered within the context of data reduction. The goal is to produce high quality approximations of 3D images using fewer elementary components than the number of intensity points in the 3D array.…
This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling. Focusing on two mainstream samplers -- the denoising diffusion implicit model (DDIM) and the denoising diffusion…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
Important recent advances in transmission electron microscopy instrumentation and capabilities have made it indispensable for atomic-scale materials characterization. At the same time, the availability of two-dimensional materials has…
A new technique for obtaining switched wave packets using spectrally truncated chirped laser pulses is demonstrated experimentally and numerically by one-dimensional alignment of both linear and asymmetric top molecules. Using a simple…