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Photonic crystal fibers are used in fiber amplifiers and lasers because of the flexibility in the design of mode area and dispersion. However, these quantities depend strongly on the wavelength. The wavelength dependence of gain,…
One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for…
Controlling the flow of energy in a random medium is a research frontier with a wide range of applications. As recently demonstrated, the effect of disorder on the transmission of optical beams, may be partially compensated by wavefront…
We propose some modification of Maxwell's equations describing mediums which electric and magnetic properties are changed essentially after interaction with outer electromagnetic field. We show for such mediums that electromagnetic waves…
We consider a degenerate abstract wave equation with a time-dependent propagation speed. We investigate the influence of a strong dissipation, namely a friction term that depends on a power of the elastic operator. We discover a threshold…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
Previously we considered the effect of experimental parameters on optimized transmission through opaque media using spatial light modulator (SLM)-based wavefront shaping. In this study we consider the opposite geometry, in which we optimize…
Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the…
Classical Doppler Effect of light propagation can be calculated by making any one of the two assumptions a) Light propagates at the speed c with respect to the source or b) Light propagates at the speed c with respect to the receptor. We…
Transmission lines are essential components in various signal and power distribution systems. In addition to their main use as connecting elements, transmission lines can also be employed as continuous sensors for the measurement and…
A new mechanism of Bragg reflection is identified, one that, remarkably, occurs in a uniform medium and relies on resonant tuning of the medium's parameters. Due to uniformity, reflection ensues over a broad wavelength range, much like a…
We investigate fast collisions between pulsed optical beams in a linear medium with weak cubic loss that arises due to nondegenerate two-photon absorption. We introduce a perturbation method with two small parameters and use it to obtain…
A systematic study of the effects of polarization mode dispersion on broad-band and narrow-band, single pump, fiber parametric amplifiers is realized through numerical solutions of the equations governing the interaction. The nonlinear…
The article is devoted to the investigation of the nonlinear effects in a system of the coupled longitudinal-torsional parametric vibrations of a rotating rod. Constructed and investigated mathematical model, based on which we calculated…
We investigate light propagation through materials with periodically modulated gain/loss profile in both transverse and longitudinal directions, i.e. in material with two-dimensional modulation in space. We predict effects of…
Linear parametric amplification is a key operation in information processing. Our interest here is quantum-limited parametric amplification, $i.e.$, amplification of quantum signals while adding the minimum amount of noise allowed by…
Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to…
Evolution of the main signal in a Lorentz dispersive medium is considered. The signal propagating in the medium is excited by a sine-modulated pulse signal, with its envelope described by a hyperbolic tangent function. Both uniform and…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
We consider the propagation of solitons in media with an imprinted transverse periodic or parabolic refractive index modulation when the modulation depth slightly fluctuates along the propagation direction. We find that, under suitable…