arXiv subjects

Jyoti Prasad Deka

Publications and source records attributed to Jyoti Prasad Deka.

7 recordsLinked to original sources

arXiv2024

Temporal Dynamics beyond the Exceptional Point in the Ikeda Map with Balanced Gain and Loss

We investigate the temporal dynamics of the Ikeda Map with Balanced Gain and Loss and in the presence of feedback loops with saturation nonlinearity. From the bifurcation analysis, we find that the temporal evolution of optical power undergoes period quadrupling at the exceptional point (EP) of the system and beyond that, chaotic dynamics emerge in the system and this has been further corroborated from the Largest Lyapunov Exponent (LLE) of the model. For a closer inspection, we analyzed the parameter basin of the system, which further leads to our inference that the Ikeda Map with Balanced Gain and Loss exhibits the emergence of chaotic dynamics beyond the exceptional point (EP). Furthermore, we find that the temporal dynamics beyond the EP regime leads to the onset of Extreme Events (EE) in this system via attractor merging crisis.

eess.SP↗

arXiv2023

Anti-Phase Synchronization of Chaos in PT-Symmetric Nonlinear Oscillators

We investigate the temporal dynamics of the PT-Symmetric nonlinear oscillators in the presence of Duffing nonlinearity for two forms of oscillator configuration. In the former, we consider two oscillator coupled to each other. One oscillator is amplified and the other is attenuated. From the bifurcation analysis, we find that the temporal evolution of oscillators exhibit the transition from quasiperiodic to chaotic dynamics. This has been corroborated by the maximal Lyapunov exponent of the system. Furthermore, on investigating the correlation of the time-series using the Pearson's correlation coefficient, it is found that the chaotic system is anti-phase synchronized, whereas the quasiperiodic is not synchronized in any form. The parametric regime where this transition has been observed is from the Unbroken PT regime to the Broken PT regime. Similarly, in the latter configuration with two amplified oscillators coupled to two attenuated oscillators, a similar transition has been observed. But in the neighbourhood of the Exceptional Point (EP) of the system, the system is shown to exhibit in-phase synchronized dynamics as is evident from the correlation analysis.

nlin.AO↗

arXiv2019

Multifaceted nonlinear dynamics in $\mathcal{PT}$-symmetric coupled Liénard oscillators

We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Liénard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of Jacobian and evaluate the stability threshold thereafter. In the first order nonlinear damping model, we discover that the temporal evolution of both gain and lossy oscillators attains a complete convergence towards the stable stationary state leading to the emergence of oscillation and amplitude deaths. Also, the system displays a remarkable manifestation of transient chaos in the lossy oscillator while the gain counterpart exhibits blow-up dynamics for certain choice of initial conditions and control parameters. Employing an external driving force on the loss oscillator, we find that the blow-up dynamics can be controlled and a pure aperiodic state is achievable. On the other hand, the second order nonlinear damping model yields a completely different dynamics on contrary to the first order where the former reveals a conventional quasi-periodic route to chaos upon decreasing the natural frequency of both gain and loss oscillators. An electronic circuit scheme for the experimental realization of the proposed system has also been put forward.

nlin.CD↗

arXiv2018

Chaotic Dynamics and Optical Power Saturation in Parity-Time (PT) Symmetric Double Ring Resonator

We report emergence of saturation and chaotic spiking of optical power in a double ring resonator with balanced loss and gain, obeying the so-called parity-time symmetry. We have modeled the system using a discrete-time iterative equation known as the Ikeda Map. In the linear regime, evolution of optical power in the system shows power saturation behavior below the PT threshold and exponential blow-up above the PT threshold. We found that in the unbroken PT regime, optical power saturation occurs owing to the existence of stable stationary states, which lies on the surface of 4-dimensional hypersphere. Inclusion of Kerr nonlinearity into our model leads to the emergence of a stable, chaotic and divergent region in the parameter basin for period-1 cycle. A closer inspection into the system shows us that the largest Lyapunov exponent blows up in the divergent region. It is found that the existence of high non-negative largest Lyapunov exponent causes chaotic spiking of optical power in the resonators.

physics.optics↗

arXiv2018

Highly Amplified Light Transmission in Parity-Time Symmetric Multilayered Structure

We propose a parity-time symmetric dielectric-nanofilm-dielectric multilayered structure that could facilitate highly amplified transmission of optical power in the infrared spectrum. We have theoretically studied our model using the transfer matrix formalism. The reflection and the transmission coefficients of the S-matrix are evaluated. The theoretical results are validated by FDTD numerical simulation. We have shown how the thickness of the layers and the gain/loss coefficient of the active layers could generate spectral singularities in the S-matrix and how these singularities could be exploited to achieve amplified transmission of a single wavelength through the structure.

physics.optics↗

arXiv2016

Perturbative Dynamics of Stationary States in Nonlinear Parity-Time Symmetric Coupler

We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a nonlinear coupler, the PT threshold governs the existence of stationary points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. Moreover, we found that instabilities in initial conditions can lead to aperiodic oscillations as well as exponential growth and decay of optical power. At the PT threshold, we observed the existence of a stable attractor under the influence of fluctuating gain/loss coefficient. Phase plane analysis has shown us the presence of a toroidal chaotic attractor. The chaotic dynamics can be controlled by a judicious choice of the waveguide parameters.

nlin.CD↗

arXiv2015

Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective

We report a study on a closed-form nonlinear parity-time symmetric optical quadrimer waveguides system with a specific coupling scheme. The system yields power saturation behavior in the modes, which may be attributed to the inherent attractor in the system. A detailed analysis has been provided to confirm the attractor aspect of the system. This work also addresses a crucial issue regarding choice of initial conditions while carrying out numerical simulation for such systems.

physics.optics↗