Advanced Mathematical Methods for Scientists and Engineers

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.

Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits

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.

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

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.

/pdf/optical-solitons-in-pt-periodic-potentials-gr30h4uehw.pdf

Optical solitons in PT periodic potentials

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.

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

We describe the dynamics of a bound state of an attractive δ-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 wave function 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.

http://iopscience.iop.org/article/10.1209/0295-5075/86/20007/pdf

Quantum particle displacement by a moving localized potential trap

The fundamental dispersion limit for an optical communication based the On-Off-Keying format is calculated. It is shown both analytically and with numerical simulations that an OOK optical sequence, which passes through a spectrally narrow non-compensated dispersive channel cannot exceed the limit β 2 B2L < π - 1 , where β 2 , L and B are the dispersion coefficient, the fiber's length and the bit rate, respectively. To the best of our knowledge, this is the first time that such a fundamental limit was formulated. In the literature, only approximation evaluations were developed yielding much smaller limiting values. Since this fundamental limit is a manifestation of the Schrodinger equation, a correspondingly similar limit emerges in Quantum Mechanics and in the optical Paraxial Approximation.

Fundamental dispersion limit for spectrally bounded On-Off-Keying communication channels and its implications to Quantum Mechanics and the Paraxial Approximation

The dynamics of an initially sharp-boundary wave packet in the presence of an arbitrary potential barrier is investigated. It is shown that the penetration through the barrier is universal in the sense that it depends only on the values of the wave function and its derivatives at the boundary. The dependence on the derivatives vanishes at long distances from the barrier, where the dynamics is governed solely by the initial value of the wave function at the boundary.

Universal potential-barrier penetration by initially confined wave packets

A simple, affordable method for imaging through biological tissue is investigated. The method consists of (1) imaging with a wavelength that has a relatively small scattering coefficient (1310 nm in this case) and (2) collimated illumination together with (3) focal plane detection to enhance the detection of the ballistic photons relative to the diffusive light. We demonstrate ballistic detection of an object immersed in a 1-cm-thick cuvette filled with 4% Intralipid, which is equivalent to ∼1 to 2 cm of skin tissue. With the same technology, a ballistic image of a 1-mm-wide object in 10-mm-thick chicken breast is also presented. © 2015 Society of Photo-Optical

Ballistic imaging of biological media with collimated illumination and focal plane detection

There is therefore provided, in accordance with an embodiment of the present invention, a method for processing an amplitude modulated (AM) optical beam amplitude modulated with a modulation pattern having an extinction ratio (ER), said AM beam having a carrier frequency and a carrier frequency amplitude, the method comprising: estimating an absolute amplitude extremum for the AM beam that is either an absolute amplitude maximum or an absolute amplitude minimum, to which recurrent amplitude extrema of the AM beam are approximately equal; estimating a corresponding phase to which the phase of the AM beam is substantially equal whenever the amplitude of the AM beam is substantially equal to the amplitude extremum; and adjusting at least one of the magnitude and phase of the carrier amplitude of the AM beam responsive to the amplitude extremum and its corresponding phase to increase the extinction ratio of the modulation pattern. The optical processing is carried out in a Brillouin Fiber grating formed by stimulated Brillouin scattering (SBS).

Er'el Granot

Papers

Quantum particle displacement by a moving localized potential trap

Fundamental dispersion limit for spectrally bounded On-Off-Keying communication channels and its implications to Quantum Mechanics and the Paraxial Approximation

Universal potential-barrier penetration by initially confined wave packets

Ballistic imaging of biological media with collimated illumination and focal plane detection

Method and apparatus for generating optical signals