Showing papers by "Er'el Granot published in 2019"
TL;DR: Results are reported for a 2D nonlinearizable model whose P-symmetric symmetry remains unbroken for arbitrarily large values of the gain-loss coefficient and an extended 2D model with the imaginary part of potential ~xy in the Cartesian coordinates.
Abstract: The real spectrum of bound states produced by $${\bf{P}}{\bf{T}}$$
-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. The breakup essentially impedes the use of $${\bf{P}}{\bf{T}}$$
-symmetric systems for various applications. On the other hand, it is known that the $${\bf{P}}{\bf{T}}$$
symmetry can be made unbreakable in a one-dimensional (1D) model with self-defocusing nonlinearity whose strength grows fast enough from the center to periphery. The model is nonlinearizable, i.e., it does not have a linear spectrum, while the (unbreakable) $${\bf{P}}{\bf{T}}$$
symmetry in it is defined by spectra of continuous families of nonlinear self-trapped states (solitons). Here we report results for a 2D nonlinearizable model whose $${\bf{P}}{\bf{T}}$$
symmetry remains unbroken for arbitrarily large values of the gain-loss coefficient. Further, we introduce an extended 2D model with the imaginary part of potential ~xy in the Cartesian coordinates. The latter model is not a $${\bf{P}}{\bf{T}}$$
-symmetric one, but it also supports continuous families of self-trapped states, thus suggesting an extension of the concept of the $${\bf{P}}{\bf{T}}$$
symmetry. For both models, universal analytical forms are found for nonlinearizable tails of the 2D modes, and full exact solutions are produced for particular solitons, including ones with the unbreakable $${\bf{P}}{\bf{T}}$$
symmetry, while generic soliton families are found in a numerical form. The $${\bf{P}}{\bf{T}}$$
-symmetric system gives rise to generic families of stable single- and double-peak 2D solitons (including higher-order radial states of the single-peak solitons), as well as families of stable vortex solitons with m = 1, 2, and 3. In the model with imaginary potential ~xy, families of single- and multi-peak solitons and vortices are stable if the imaginary potential is subject to spatial confinement. In an elliptically deformed version of the latter model, an exact solution is found for vortex solitons with m = 1.
15 citations
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TL;DR: In this article, a 2D nonlinearizable model with PT symmetry remains unbreakable for arbitrarily large values of the gain-loss coeffcient was introduced, which is not a PT-symmetric one, but it also supports continuous families of self-trapped states.
Abstract: The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the PT-symmetry can be made unbreakable in a one-dimensional (1D) model with self-defocusing nonlinearity whose strength grows fast enough from the center to periphery. The model is nonlinearizable, i.e., it does not have a linear spectrum, while the (unbreakable) PT symmetry in it is defined by spectra of continuous families of nonlinear self-trapped states (solitons). Here we report results for a 2D nonlinearizable model whose PT symmetry remains unbroken for arbitrarily large values of the gain-loss coeffcient. Further, we introduce an extended 2D model with the imaginary part of potential ~ xy in the Cartesian coordinates. The latter model is not a PT-symmetric one, but it also supports continuous families of self-trapped states, thus suggesting an extension of the concept of the PT symmetry. For both models, universal analytical forms are found for nonlinearizable tails of the 2D modes, and full exact solutions are produced for particular solitons, including ones with the unbreakable PT symmetry, while generic soliton families are found in a numerical form. The PT-symmetric system gives rise to generic families of stable single- and double-peak 2D solitons (including higher-order radial states of the single-peak solitons), as well as families of stable vortex solitons with winding numbers m = 1, 2, and 3. In the model with imaginary potential ~ xy, families of single-and multi-peak solitons and vortices are stable if the imaginary potential is subject to spatial confinement. In an elliptically deformed version of the latter model, an exact solution is found for vortex solitons with m = 1.
7 citations
TL;DR: It is shown that by utilizing the similarity between ASR and SG pulses and applying analytical continuation, chirped ASR pulses can be rewritten in a form that does have an analytical expression in both time and spectral domains.
Abstract: Analytical smooth rectangular (ASR) pulses have shown to be useful in optical communications. ASR pulses can be cascaded, and therefore they can be very useful in non-return-to-zero communication protocols. Moreover, unlike super-Gaussian (SG) pulses, the propagation of ASR pulses in dispersive media can be expressed in analytical forms (in both time and frequency domains). However, the propagation of chirped ASR as well as chirped SG pulses, which are common in direct-modulation channels, cannot be expressed analytically. It is shown that by utilizing the similarity between ASR and SG pulses and applying analytical continuation, chirped ASR pulses can be rewritten in a form that does have an analytical expression in both time and spectral domains.
4 citations
TL;DR: In this paper, the authors present a handbook of analytical expressions for pulse propagations in a dispersive medium, which can simulate real-physical pulses with great accuracy, including the dynamics of smooth rectangular pulses, physical Nyquist-Sinc pulses, and slowly rising but sharply decaying ones.
Abstract: Ultrashort pulses are severely distorted even by low dispersive media. While the mathematical analysis of dispersion is well known, the technical literature focuses on pulses, Gaussian and Airy pulses, which keep their shape. However, the cases where the shape of the pulse is unaffected by dispersion is the exception rather than the norm. It is the objective of this paper to present a variety of pulse profiles, which have analytical expressions but can simulate real-physical pulses with great accuracy. In particular, the dynamics of smooth rectangular pulses, physical Nyquist-Sinc pulses, and slowly rising but sharply decaying ones (and vice versa) are presented. Besides the usage of this paper as a handbook of analytical expressions for pulse propagations in a dispersive medium, there are several new findings. The main findings are the analytical expressions for the propagation of chirped rectangular pulses, which converge to extremely short pulses; an analytical approximation for the propagation of super-Gaussian pulses; the propagation of the Nyquist-Sinc Pulse with smooth spectral boundaries; and an analytical expression for a physical realization of an attenuation compensating Airy pulse.
4 citations
20 Jan 2019
TL;DR: In this article, the authors present a handbook of analytical expressions for pulse propagations in a dispersive medium, which can simulate real-physical pulses with great accuracy, including the dynamics of smooth rectangular pulses, physical Nyquist-Sinc pulses, and slowly rising but sharply decaying ones.
Abstract: Ultrashort pulses are severely distorted even by low dispersive media. While the mathematical analysis of dispersion is well known, the technical literature focuses on pulses, Gaussian and Airy pulses, which keep their shape. However, the cases where the shape of the pulse is unaffected by dispersion is the exception rather than the norm. It is the objective of this paper to present a variety of pulse profiles, which have analytical expressions but can simulate real-physical pulses with great accuracy. In particular, the dynamics of smooth rectangular pulses, physical Nyquist-Sinc pulses, and slowly rising but sharply decaying ones (and vice versa) are presented. Besides the usage of this paper as a handbook of analytical expressions for pulse propagations in a dispersive medium, there are several new findings. The main findings are the analytical expressions for the propagation of chirped rectangular pulses, which converge to extremely short pulses; an analytical approximation for the propagation of super-Gaussian pulses; the propagation of the Nyquist-Sinc Pulse with smooth spectral boundaries; and an analytical expression for a physical realization of an attenuation compensating Airy pulse.
3 citations
TL;DR: In this article, a simple method for calculating diffraction effects in a beam passing an aperture is presented, which follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities.
Abstract: We present a simple method for calculation of diffraction effects in a beam passing an aperture. It follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities. It is thus shown that in the near-field region, i.e., at short propagation distances, most results depend on values of the beam's field at the aperture's boundaries, making it possible to derive diffraction effects in the form of a simple contour integral over the boundaries. For a uniform, i.e., plane-wave incident beam, the contour integral predicts the diffraction effects exactly. Comparisons of the analytical method and full numerical solutions demonstrate highly accurate agreement between them.
2 citations
TL;DR: In this paper, the authors suggest the implementation of a dispersion module to substantially reduce the MZM-induced nonlinearity in low-cost direct-detection links, which is possible only because linear dispersion mitigation filters can be implemented post detection.
Abstract: External modulation, such as with a Mach–Zehnder modulator (MZM), is commonly used in optical communications to reduce nonlinear signal distortions. However, in addition to the signal distortion due to chromatic dispersion, the MZM itself is another source of nonlinear distortion. Despite the fact that dispersion is a linear distortion that develops in the field domain, in low-cost direct-detection links, the detector destroys the system’s linearity. Therefore, in these channels, dispersion is another source of nonlinearity. We suggest the implementation of a dispersion module to substantially reduce the MZM-induced nonlinearity. This technique is possible only because linear dispersion mitigation filters can be implemented post detection. We show experimentally that chromatic dispersion can indeed substantially reduce the channel’s nonlinear distortion, in good agreement with theoretical predictions.
1 citations
TL;DR: In this paper, the Nyquist theorem is used to replace the wave function with a discrete series of numbers, and the Schrodinger dynamics can be formalized as a universal set of ordinary differential Equations, with universal coupling between them.
Abstract: The object of the paper is to formulate Quantum (Schrodinger) dynamics of spectrally bounded wavefunction. The Nyquist theorem is used to replace the wavefunction with a discrete series of numbers. Consequently, in this case, Schrodinger dynamics can be formalized as a universal set of ordinary differential Equations, with universal coupling between them, which are related to Euler’s formula. It is shown that the coefficient (m, n) is inversely proportional to the distance between the points n and m. As far as we know, this is the first time that this inverse square law was formulated.