Showing papers by "Er'el Granot published in 2016"

Affordable dispersion mitigation with an analog electrical filter.

Abstract: A new method for dispersion mitigation is presented for low-cost and simple networks. The method does not require dispersion-compensating fibers, special optical filters, coherent detection, or external modulation. It can work in a direct modulation scheme and with a standard optical detector. The disadvantage of this method is the requirement to operate in the weak modulation regime of the signal. In this regime, the dispersive channel can be regarded as linear in the power domain, and not only in the field domain, so that the effects of dispersion can be reduced with a proper electronic filter. Since electronic filters are usually considerably cheaper than coherent optical solutions, this solution can be implemented in low-cost networks, where dispersion is a more severe problem than noise. We show that by adding the filter to a low-noise on-off keying (OOK) system it is possible to transmit data at bit rates of 50 Gb/s to distances at least sixfold larger than its OOK limit (6 km in this case), i.e., 40 km and beyond.

Study of a simple model for the transition between the ballistic and the diffusive regimes in diffusive media

Abstract: A Monte Carlo simulation was utilized to investigate a simple model for the transition between the ballistic and the diffusive regimes in diffusive media. The simulation focuses on the propagation of visible and near-infrared light in biological tissues. This research has mainly two findings: (1) the transition can be described, as was found experimentally, with good accuracy by only two terms (ballistic and diffusive). (2) The model can be utilized for cases where the absorption coefficient is not negligible compared to the scattering coefficient by adding a power-law prefactor to the diffusive term.

Analytical solutions for beams passing apertures with sharp boundaries

Abstract: An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, in terms of the exact analytical solution.

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.

State orthogonality, boson bunching parameter and bosonic enhancement factor

Abstract: It is emphasized that the bunching parameter β ≡ 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 β = 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 β (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.

Generic propagation of sharp boundaries electromagnetic signals in any linear dispersive medium

Abstract: A generic formalism for the propagation of a pulse with sharp boundaries in any linear medium is derived. It is shown that such a pulse experiences generic deformations. For any given linear medium, the pulse deformation is expressed as a generic differential operator, which characterizes the medium and which operates on the pulse at the singular points (the sharp boundaries). The theory is then applied to a Fabry–Perot etalon and to dispersive media with second order dispersion, third order dispersion, and a combination of both. Simple approximate expressions are also derived for a relatively short, i.e., low dispersive, medium and compared with exact numerical solutions.

Dynamic Resonant Tunneling

Abstract: The physics of dynamic resonant tunneling is investigated. First, the resonant tunneling effect through an opaque barrier via a delta-function well is illustrated. Then, it is shown that, even in the adiabatic regime, where the dynamics can be governed by an analytic solution, the particle can be activated to higher energies. If the well varies quickly enough that the particle cannot escape from the well during the energetic elevation, the activation can be enhanced, as was anticipated by Azbel. However, and this is the main result of this work, the quasi-bound state of the well can even “reduce” the activation. In fact, because the resonant energy of the well matches twice the incoming particle’s energy, and if the contribution to the wave function from both parts destruc‐ tively interferes, then the particle cannot dwell in the well and activation is suppressed. This effect can be utilized in frequency-controlled transistors, and it is even speculated that it may explain the reason that humans can distinguish between tens of thousands of different odors with merely few hundreds of odor receptors. Lastly, the short time dynamics of a very fast perturbative well is also discussed.

Analytical Solutions for Beams Passing Apertures with Sharp Boundaries

Abstract: An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.