Er'el Granot

Bio: Er'el Granot is an academic researcher from Ariel University. The author has contributed to research in topics: Dispersion (optics) & Brillouin scattering. The author has an hindex of 15, co-authored 132 publications receiving 801 citations. Previous affiliations of Er'el Granot include Israel Atomic Energy Commission & Tel Aviv University.

Quantum particle displacement by a moving localized potential trap

Abstract: We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the initially confined wavefunction remains confined to the moving potential. However, it is shown that besides the probability to remain confined to the moving barrier and the probability to remain in the initial position, there is also a certain probability for the particle to move at double speed. A quasi-classical interpretation for this effect is suggested. The temporal and spectral dynamics of each one of the scenarios is investigated.

State Orthogonality, Boson Bunching Parameter and Bosonic Enhancement Factor

Abstract: It is emphasized that the bunching parameter $\beta=P_B/P_D$ , i.e. the ratio between the probability to measure two bosons and two distinguishable particles at the same state, is a constant of motion and depends only on the overlap between the initial wavefunctions. This ratio is equal to $\beta=2/(1+I^2)$ , where $I$ is the overlap integral between the initial wavefunctions. That is, only when the initial wavefunctions are orthogonal this ratio is equal to 2, however, this bunching ratio can be reduced to 1, when the two wavefunctions are identical. This simple equation explains the experimental evidences of a beam splitter. A straightforward conclusion is that by measuring the local bunching parameter $\beta$ (at any point in space and time) it is possible to evaluate a global parameter$ I$ (the overlap between the initial wavefunctions). The bunching parameter is then generalized to arbitrary number of particles, and in an analogy to the two-particles scenario, the well-known bosonic enhancement appears only when all states are orthogonal.

Nonlocal Inverse Square Law in Quantum Dynamics

Abstract: Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

Efficient phase spectrum reconstruction with the discrete multiply subtractive anchoring algorithm

Abstract: We apply the multiply subtractive anchoring method for efficient phase spectrum retrieval, which is based on the fast Fourier transform and Lagrange polynomials. Because the polynomials eventually diverge, choosing the optimum anchoring points is crucial. It is demonstrated that, if more than two anchoring points are chosen, the algorithm’s performance can easily deteriorate.

PAM-N—Fundamental Limits in Chromatic Dispersive-Uncompensated Channels

Abstract: The fundamental chromatic dispersion limit for an optical communication N-level pulse amplitude modulation (PAM-N) format without any dispersion compensating module is calculated. The main result of this analysis shows that in a non-dispersion-compensated channel, the product β2B2L (where β2, L, and B are the dispersion coefficient, fiber length, and the Baud rate, respectively) is bounded by a number, which depends only on the number of levels N. In particular, β2B2L < 0.318, β2B2L < 0.212, and β2B2L < 0.14 for N values of 2, 4, and 8, respectively. Moreover, an analytical expression for a noisy channel’s power penalty was formulated. This analytic expression shows high agreement with numerical simulations. To the best of our knowledge, this is the first time that such a fundamental limit has been formulated for PAM-N systems.

Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits

Abstract: We review recent progress in inducing and harnessing stimulated Brillouin scattering (SBS) in integrated photonic circuits. Exciting SBS in a chip-scale device is challenging due to the stringent requirements on materials and device geometry. We discuss these requirements, which include material parameters, such as optical refractive index and acoustic velocity, and device properties, such as acousto-optic confinement. Recent work on SBS in nano-photonic waveguides and micro-resonators is presented, with special attention paid to photonic integration of applications such as narrow-linewidth lasers, slow- and fast-light, microwave signal processing, Brillouin dynamic gratings, and nonreciprocal devices.

Ultrasound-mediated biophotonic imaging: A review of acousto-optical tomography and photo-acoustic tomography

Abstract: This article reviews two types of ultrasound-mediated biophotonic imaging–acousto-optical tomography (AOT, also called ultrasound-modulated optical tomography) and photo-acoustic tomography (PAT, also called opto-acoustic or thermo-acoustic tomography)–both of which are based on non-ionizing optical and ultrasonic waves. The goal of these technologies is to combine the contrast advantage of the optical properties and the resolution advantage of ultrasound. In these two technologies, the imaging contrast is based primarily on the optical properties of biological tissues, and the imaging resolution is based primarily on the ultrasonic waves that either are provided externally or produced internally, within the biological tissues. In fact, ultrasonic mediation overcomes both the resolution disadvantage of pure optical imaging in thick tissues and the contrast and speckle disadvantages of pure ultrasonic imaging. In our discussion of AOT, the relationship between modulation depth and acoustic amplitude is clarified. Potential clinical applications of ultrasound-mediated biophotonic imaging include early cancer detection, functional imaging, and molecular imaging.

Optical solitons in PT periodic potentials

Abstract: We investigate the effect of nonlinearity in novel parity-time (PT) symmetric potentials. We show that new types of nonlinear self-trapped modes can exist in optical PT synthetic lattices.

Optical nonlinearities in fibers: review, recent examples, and systems applications

Abstract: Optical nonlinearities give rise to many ubiquitous effects in optical fibers. These effects are interesting in themselves and can be detrimental in optical communications, but they also have many useful applications, especially for the implementation of all-optical functionalities in optical networks. In the present paper, we briefly review the different kinds of optical nonlinearities encountered in fibers, pointing out the essential material and fiber parameters that determine them. We describe the effects produced by each kind of nonlinearity, emphasizing their variations for different values of essential parameters. Throughout the paper, we refer to recent systems applications in which these effects have been dealt with or exploited.