arXiv subjects

Ali Dorostkar

Publications and source records attributed to Ali Dorostkar.

6 recordsLinked to original sources

arXiv2023

A Theoretical Framework for Electromechanically Reinforced Brillouin Scattering in Integrated Photonic Waveguides

Current theoretical demonstration of the Stimulated Brillouin scattering (SBS) in waveguides composed of centrosymmetric materials does not capture physics of the phenomenon in waveguides composed of non-centrosymmetric materials. The SBS in the latter problem, entails mutual coupling of the electric and acoustic waves due to piezoelectricity, and ends up to a different power conversion equation than that in a centrosymmetric material. In this study, we theoretically investigate Brillouin scattering in chip-scale waveguides with non-centrosymmetric material when excited by an Inter-Digital-Transducer. We explain how Brillouin scattering is formulated in the presence of externally injected acoustic waves. Also we demonstrate the effect of this external signal on reinforcing Stimulated Brillouin scattering. As a case study we study SBS in a gallium arsenide nonowire. It is shown that the Stokes amplification due to electromechanically reinforced SBS in this waveguide can grow several orders of magnitude higher than the values reported for the SBS in a silicon nanowire; This enables reducing the waveguide length required for a given Stokes amplification from centimeters to few hundred micrometers.

physics.optics↗

arXiv2023

On optimization and solution of roots of a function using Taylor's expansion and fractional derivatives

A method is given for finding roots of a one-variable function using Taylor's expansion of that function and fractional derivative calculated at a suitable tangent point without using Newton's method, but is regarded as a variant of Halley and Newton's one. Several examples regarding polynomials are stated as well. Then, the given method is generalized to functions of several variables belonging to an $n$-dimensional space and one example is given for optimization and solution of a nonlinear system of equations by both our method and Gradient Descent one. A comparison of our method is made with Gradient descent one for a system of the functions of three variables. Our given method seems to be much more rapidly than the Newton's one since by finding a suitable point on the function's curve, the number of iterations is to be much less than Newton's iterative steps. We also find order of fractional derivative, which corresponds to equation's found root and compare tangent lines drawn at the root by both fractional and classical derivatives. The methods given in this paper can be used for optimization of function via fractional derivatives of order $β$.

math.OC↗

arXiv2023

The Role of Fractional Dimension in Study Physics: A Two-Channel Representation with Geometric Memory

In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between these integer dimensions. The concept of fractional dimensional space arises from the idea that the space between integer dimensions is filled, which occurs through the application of a fractional derivative operator (the local part) that rotates the integer dimension to encompass all spaces between two integers. It examines how fractional dimensional frameworks can enhance our understanding of classical mechanics, particularly regarding the duality of memory versus no-memory behavior, or local versus non-local dynamics. In the lens of fractional dimension, motion in classical physics can be analyzed through two distinct solutions. When the fractional dimensional trajectory takes values of 1 or 2 corresponding to the first and second integer derivatives, it represents linear and accelerated systems, respectively, yielding trivial solutions via differentiation. However, if the fractional dimensional trajectory evolves as a linear function of time in fractional dimensional space or follows a nonlinear path, surprisingly it results in a non-trivial solution for linear and accelerated systems, respectively. This approach offers a broader framework for describing motion, extending to memory (non-local) effect beyond traditional local integer-order differentiation . Moreover, we propose that the coupling of space and time, commonly referred to as space-time, is better understood as space-dimension-time within this framework, where the dimension serves as an interconnecting platform.

physics.gen-ph↗

arXiv2022

Fourier Series in Fractional Dimensional Space

In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;α)$. We call it fractional Fourier series of the order $α$. Extending the basis functions of the linear space into fractional one, by rotation transformation, we define a real and complex Fourier series and obtain their coefficients. It is also shown that the fractional derivative of a periodic function can be realized through (fractional) Fourier series with modified coefficients.

math.GM↗

arXiv2019

Complementary Fractional Dimensional Order of Nyquist Sinc Sequences for Time Division Multiplexing

High speed data transmission is enabled by time and wavelength division multiplexing. Here is introduced fractional dimension order of Nyquist pulses sequences for orthogonal time division multiplexing. Firstly, with a representation of the Nyquist sinc sequence by a cosine Fourier series, in one side it is introduced the complementary Nyquist sinc sequences as a better option for data transmission. On the other side, a possibility of optical time delay by an electrical phase shifter for optical time division multiplexing is theoretically demonstrated. In continue, the fractional dimensional order of signal is defined to open a new window for data transmission. Moving of function in fractional dimension can be realized as a new freedom for a signal processing. In other words, dimension itself is a dimension. In this regard, dimensional transformation is introduced to give a mapping of the function in dimensional domain or variations of function in fractional dimension. This mapping gives more information about signal in different point of view like Fourier transformation. Then, the complementary fractional dimensional order of Nyquist sinc sequences is defined to reach higher data rate. It has not a unique solution, however; the best set of solutions for data transmission must be taken in to accounted. Furthermore, the trajectory of fractional dimension can be found by a numerical iterative algorithm which will be explained in the appendix.

eess.SP↗

arXiv2018

Faster than Nyquist Transmission by Non-Orthogonal Time Division Multiplexing of Nyquist Sinc Sequences

One possibility to break down the capacity limit in optical transmission systems are higher spectral efficiencies, enabled by Faster-than-Nyquist signaling. Here we present the utilization of non-orthogonal time division multiplexing of sinc pulse sequences for this purpose. The mathematical expression, with a representation of the Nyquist sinc sequence by a cosine Fourier series and simulation results show that non-orthogonal time-division multiplexing increases the transmittable symbol rate by up to 25%.

eess.SP↗