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

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.

/pdf/inverse-square-law-in-spectrally-bounded-quantum-dynamics-q3q2z368nh.pdf

Inverse Square Law in Spectrally Bounded Quantum Dynamics

We present a comparison between the well-known spectral optical coherence tomography (SOCT) technology and the fast-Fourier-transform-based (FFT-based) impulse-response reconstruction method (FIRRM), which we developed—both in the transmission configuration. It is shown that, since the transmission configuration requires relatively long interferometers, the SOCT measurements are less stable than those of the FIRRM, as seen in the impulse-response reconstruction of the two methods. The FIRRM results show much better agreement with theoretical predictions.

Comparison between spectral optical coherence tomography and the FFT-based impulse-response reconstruction method in the transmission configuration

The maximum bit rate of a slab waveguide is ultimately determined by the waveguide dispersion. We show that while the maximum bit rate in a waveguide is inversely proportional to the waveguide's width, the bit rate per unit width (i.e., spatial capacity (SC)) decreases, and in the limit of a zero-width waveguide it converges to ~ ω/√(λL) (where L is the length and ω and λ are the beam frequency and wavelength respectively). This result, which is independent of the waveguide's refractive indices, is qualitatively equivalent to the transmission rate per unit of width in free space. We also show that in a three-dimensional waveguide (e.g., fibres), unlike free space, the SC vanishes in the same limit.

https://iopscience.iop.org/article/10.1088/1464-4258/4/6/302/pdf

Limitations to bit rate and spatial capacity of an optical data transmission channel

The Kramers-Kronig technique is used to reconstruct the impulse-response of a diffusive media with picosecond resolution. We demonstrate the ability to image an object within clothing at a distance of 3m from the detection system.

Kramers-Kronig imaging of diffuse media and embedded objects

The tunneling through an opaque barrier with a strong oscillating component is investigated. It is shown, that in the strong perturbations regime (in contrast to the weak one), higher perturbations rate does not necessarily improve the activation. In fact, in this regime two rival factors play a role, and as a consequence, this tunneling system behaves like a sensitive frequency-shifter device: for most incident particles’ energies activation occurs and the particles are energetically elevated , while for specific energies activation is depressed and the transmission is very low. This effect is unique to the strong perturbation regime, and it is totally absent in the weak perturbation case. Moreover, it cannot be deduced even in the adiabatic regime. It is conjectured that this mechanism can be used as a frequency-dependent transistor, in which the device’s transmission is governed by the external field frequency.

Er'el Granot

Papers

Inverse Square Law in Spectrally Bounded Quantum Dynamics

Comparison between spectral optical coherence tomography and the FFT-based impulse-response reconstruction method in the transmission configuration

Limitations to bit rate and spatial capacity of an optical data transmission channel

Kramers-Kronig imaging of diffuse media and embedded objects

01 12 16 7 v 1 2 7 D ec 2 00 1 Selected elevation in quantum tunneling