Nonlinear Kerr Medium Research Articles

The nonlinear propagation of cylindrical vector beams in an optical fiber

We simulate the evolution of cylindrical vector beams (CVBs) in a Kerr nonlinear medium by the full-vector finite-element beam propagation method (VFE-BPM). This beams show poor transverse stability which contrasts with the strong transverse stability of fundamental modes. The approximate analytic theory has been used to qualitative analyze the variations of the numerically calculated instability growth rates. We present a reasonable concentric circle model to avoid the influence of triangular grids during simulation.

Phase sensitive, all-optical and self-integrated multi-logic AND, OR, XOR, and NOT gates

The design and simulation of all-optical and self-integrated primary logical AND, OR, XOR and NOT gates based on phase sensitivity of spatial optical solitons have been reported. By tuning the phase of incident solitons into a bulky nonlinear Kerr medium and interaction between the phase tuned solitons, the self-integrated logical gates are achieved simultaneously in a 50 μm long distance by one setup. These are the advantages in the application and design of integrated circuits. In addition, the proposed logical gates can be cascaded and the logical AND and XOR gates can simultaneously have two outputs. The simplicity of constructing, simultaneous functions with one setup, the possibility of integrating, high sensitivity and fabrication ease are the advantages of the proposed logical gates and may be a good candidate for the future of integrated photonic computational circuits.

Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction* *Supported by the National Natural Science Foundation of China (Grant Nos. 11705145, 11947301, 11434013, and 11425522), the Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2017KCT-12 and 2017ZDJC-32), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2018JQ1003).

We study the properties of breather interactions in nonlinear Kerr media with self-steepening and spacetime correction and with either self-focusing or self-defocusing nonlinearity, and present a new family of exact breather solutions via the Darboux transformation with a special-designed quadratic spectral parameter. In contrast to the previous results of the nonlinear Schrödinger equation (NLSE) hierarchy, we show that the relative phase of colliding breathers has a significant effect on the collision manifestation. In particular, only the out-of-phase interactions can generate small amplitude waves at the collision center, which are analogous to the NLSE super-regular breathers. Our results will deepen our understanding of the properties of breather interactions and they will offer the possibility of experimental observations of super-regular breather dynamics in systems with self-steepening and spacetime correction.

Self-phase modulation and superfluidity in twisted fluids of light

We study superfluidity of laser pulses with a finite duration, propagating in a nonlinear Kerr medium. For such pulses, self-phase modulation (SPM) is also present. Usually, superfluidity is assumed independent of SPM, because the elementary excitations of the photon fluid are observed in the transverse plane, while SPM takes place along the propagation direction. But, as shown here, for sufficiently short pulses and sufficiently long propagation distances, SPM can eventually modify the Landau criterium for the occurrence of superfluidity due to the associated frequency shifts, which modify the threshold for superfluid behaviour. Instead of plane wave or Gaussian beams, we consider twisted laser beams, with a finite amount of orbital angular momentum (OAM), because they provide the necessary transverse velocity for the photon fluid.

Fano resonance and amplification in a quadratically coupled optomechanical system with a Kerr medium

We discuss the Fano resonance and amplification in a quadratically coupled optomechanical system with a nonlinear Kerr medium. We find that effective cavity detuning and the strength of the Kerr nonlinearity lead to the appearance of the Fano resonance in the output probe field at room temperature, respectively. We show that the Kerr nonlinearity causes the asymmetric line shape to appear in the intensities of the output Stokes field and the second-order upper sideband generation. We also show that the Kerr nonlinearity can amplify the intensities of the output Stokes field and the second-order upper sideband generation, and the amplification factor is related to the strength of the Kerr nonlinearity. The findings of this study have potential applications in optical switching and frequency conversion.

Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms

We study the interaction of a three two-level atoms (3-2LA) with a one-mode op?tical coherent field in coherent state in the presence of non-linear Kerr medium. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, 3-2LA and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the 3-2LA and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and en?tanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of theoptical coherent field.

Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms

We study the interaction of a three two-level atoms (3-2LA) with a one-mode op?tical coherent field in coherent state in the presence of non-linear Kerr medium. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, 3-2LA and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the 3-2LA and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and en?tanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of theoptical coherent field.

The use of non-dispersive soliton-like fiber optic vortices to increase the efficiency of RoF systems

In this article, the propagation of soliton-like vortex beams in the optical segment of a Radio-over-Fiber system is discussed. The approach is based on the solution of the nonlinear Schrödinger equation for the Kerr nonlinear medium like optical fiber. A numerical solution of the nonlinear Schrödinger equation for vortex solitons was obtained; the propagation of soliton-like vortices along an optical fiber is simulated. Besides, a phase-amplitude filter that generates optical signals with a given state of the orbital angular momentum and conservation of polarization during propagation through the optical fiber was modeled. The amplitude-phase filter was designated based on the spinor representation of Maxwell’s equations.

Transforming higher order bright and dark solitons to the first order solitons in Kerr medium: A review

A higher order soliton is a soliton where the initial energy is higher than the fundamental one by a specific coefficient. The value of the coefficient is square of an integer number. The intensity profile of higher order soliton (spatial or temporal) is not constant but varies periodically during propagation. The period of their evolution, called soliton-period. However, when the coefficient is not the square of an integer, the complicated intensity profile by propagation occurs. In this work, it is demonstrated and discussed the reason why higher order soliton is made, and how it modifies a factor in Nonlinear Schrödinger Equation (NLS), in positive and negative third order nonlinear (Kerr) medium. In this modified NLS equation, the exact analytical fundamental soliton solution which doesn’t show the soliton-period is obtained. Followed by numerical simulation by MATLAB, with Split-Step method, and comparison between modified initial beam-width which produces fundamental soliton and nonmodified initial beam-width that gives the other order of solitons for bright and dark solitons.

New features of non-linear time-dependent two-level atoms

Abstract In this paper, two-level atoms interacting with a single-mode radiation field alongside important properties are presented. The model presented discusses multi-photon process and it has also a nonlinear Kerr-medium and Stark-shift. In addition, the coupling parameter is discussed in a time-dependent fashion. The results show that Stark-shift, time-dependent coupling parameter, and nonlinear Kerr-medium play significant roles regarding the evolution of the von-Neumann entropy and the system's geometric phases. We've used accessible parameters to examine these observations, and some new results are obtained. Remarkably, the geometric phase shows high sensitivity to any change of the considered parameters.

Dark solitons for a (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients in a diffractive nonlinear Kerr medium with anomalous dispersion

Kerr media are applied in the photonic lattices and optical fibers, while optical fiber communication becomes one of the main pillars of modern communication. In this letter, we study a (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation with distributed coefficients for the spatiotemporal optical solitons or light bullets in a diffractive nonlinear Kerr medium with anomalous dispersion. The N-dark soliton solutions in terms of the Gramian is obtained via the Kadomtsev–Petviashvili hierarchy reduction, where N is a positive integer. Via the graphic analysis, we observe the interaction of the two dark solitons. Effects from the diffraction/dispersion coefficient [Formula: see text] and gain coefficient [Formula: see text] are also discussed on the amplitudes and oscillations of the two dark solitons, as well as on the interaction of the two dark parabolic shape solitons.

Optical bistable switch based on the nonlinear Kerr effect of chalcogenide glass in a rectangular defect of a photonic crystal

An optical bistable switch based on a photonic crystal resonator using the nonlinear effect of a chalcogenide glass in a rectangular defect cavity is proposed and investigated numerically. The influences of the designed cavity and refractive index of the Kerr nonlinear medium on the transmission of the resonator are analyzed precisely through finite-difference time-domain simulation. The simulation results show that our compact structure possesses excellent switching characteristics by tuning the incident electric intensity. The properties of the optical bistability are investigated at the resonance wavelength with three different detuning parameters. In addition, the results show that this switch has a wide operating wavelength regime and fast operation speed of 90 Gb/s. Considering numerous characteristics, such a high-speed switch can find application for all-optical devices.

Theoretical analysis of the stretched optical pulse ripple and novel chirped pulse retrieving algorithm.

Amplitude and phase ripples of an ultrafast chirped pulse complex envelope are considered. The formula that establishes the relation between the pulse complex envelope and its spectrum amplitude was theoretically derived for both cases of the ripple. Based on current results, a linearly chirped pulse can be retrieved using only a spectrum analyzer and Kerr nonlinear medium.

Propagation dynamics of cosh-Airy beams in Kerr nonlinear media

We investigate propagation dynamics of cosh- and cosine-Airy beams in Kerr nonlinear media. The cosh-Airy and cosine-Airy beam can be considered as a superposition of two Airy beams with different decay factors and different propagation trajectories, respectively. It is shown that the solitons shedding from cosh-Airy and cosine-Airy beams and their interaction in both in-phase and out-of-phase cases are strongly dependent on the modulation parameter associated with the cosh function. The interaction between two cosine-Airy beams can exhibit attraction or repulsion under proper interval and initial angle condition in both in-phase and out-of-phase cases.

Self-focusing of multiple interacting Laguerre-Gauss beams in Kerr media

Using a variational approach, we obtain the self-focusing critical power for a single and for any number of interacting Laguerre-Gauss beams propagating in a Kerr nonlinear optical medium. As is known, the critical power for freely propagating higher-order modes is always greater than that of the fundamental Gaussian mode. Here, we generalize that result for an arbitrary incoherent superposition of Laguerre-Gauss beams, adding interactions between them. This leads to a vast and rich spectrum of self-focusing phenomena, which is absent in the single-beam case. Specifically, we find that interactions between different modes may increase or decrease the required critical power relative to the sum of individual powers. In particular, high-orbital angular momentum modes can be focused with less power in the presence of low-orbital angular momentum beams than when propagating alone. The decrease in required critical power can be made arbitrarily large by choosing the appropriate combinations of modes. Besides, in the presence of interactions, an equilibrium configuration of stationary spot-size for all modes in a superposition may not even exist, a fundamental difference to the single-beam case in which a critical power for self-focusing always exists.

A Model Describing the Propagation of a Femtosecond Pulse in a Kerr Nonlinear Medium

We consider a model of nonlinear interaction of femtosecond pulses with a Kerr nonlinear medium, allowing for first and second order dispersion, nonlinear response dispersion, and mixed time and space derivatives. The invariants are constructed by a transformation of the generalized nonlinear Schrodinger equation that involves changing to new functions and reduces the original equation to a form without the nonlinear response derivatives and the mixed derivatives. Appropriate conservation laws are established for the transformed equation. The invariants derived in this article lead to conservative difference schemes and allow control of computer simulation results.

Quantum Fisher Information and Entanglement of Moving Two Two-Level Atoms under the Influence of Environmental Effects

We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) of a two moving two-level atomic systems interacting with a coherent and thermal field in the presence of intrinsic decoherence (ID) and Kerr (non-linear medium) and Stark effects. The state of the entire system interacting with coherent and thermal fields is evaluated numerically under the influence of ID and Kerr (nonlinear) and Stark effects. QFI and von Neumann entropy (VNE) decrease in the presence of ID when the atomic motion is neglected. QFI and QE show an opposite response during its time evolution in the presence of a thermal environment. QFI is found to be more susceptible to ID as compared to QE in the presence of a thermal environment. The decay of QE is further damped at greater time-scales, which confirms the fact that ID heavily influences the system’s dynamics in a thermal environment. However, a periodic behavior of entanglement is observed due to atomic motion, which becomes modest under environmental effects. It is found that a non-linear Kerr medium has a prominent effect on the VNE but not on the QFI. Furthermore, it has been observed that QFI and QE decay soon under the influence of the Stark effect in the absence of atomic motion. The periodic response of QFI and VNE is observed for both the non-linear Kerr medium and the Stark effect in the presence of atomic motion. It is observed that the Stark, Kerr, ID, and thermal environment have significant effects during the time evolution of the quantum system.

Entanglement Dynamics of Three and Four Level Atomic System under Stark Effect and Kerr-Like Medium

We investigated numerically the dynamics of quantum Fisher information (QFI) and entanglement for three- and four-level atomic systems interacting with a coherent field under the effect of Stark shift and Kerr medium. It was observed that the Stark shift and Kerr-like medium play a prominent role during the time evolution of the quantum systems. The non-linear Kerr medium has a stronger effect on the dynamics of QFI as compared to the quantum entanglement (QE). QFI is heavily suppressed by increasing the value of Kerr parameter. This behavior was found comparable in the cases of three- and four-level atomic systems coupled with a non-linear Kerr medium. However, QFI and quantum entanglement (QE) maintain their periodic nature under atomic motion. On the other hand, the local maximum value of QFI and von Neumann entropy (VNE) decrease gradually under the Stark effect. Moreover, no prominent difference in the behavior of QFI and QE was observed for three- and four-level atoms while increasing the value of Stark parameter. However, three- and four-level atomic systems were found equally prone to the non-linear Kerr medium and Stark effect. Furthermore, three- and four-level atomic systems were found fully prone to the Kerr-like medium and Stark effect.

Study of the combined effects of a Kerr nonlinearity and a two-level atom upon a single nonstationary cavity mode

We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium and a two-level atom. We obtain approximate expressions for the time-evolution operator valid at short times and/or low average photon number. We have found an interplay between the effect of the nonlinear Kerr medium, which is to decrease the growth of photon generation from the vacuum state, and that of the two-level atom, which is to increase the photon generation. We explore an ample range of Hamiltonian parameters going from the resonant to the dispersive regimes.

Effect of Stark- and Kerr-like medium on the entanglement dynamics of two three-level atomic systems

We study time evolution of quantum Fisher information (QFI) and entanglement for two three-level atomic systems influenced by Stark effect and Kerr-like medium. It is seen that Stark and Kerr media play dominant role during the time evolution of the quantum system. Dynamics of QFI is heavily influenced under the effect of linear Kerr medium as compared to the entanglement. However, the effect of nonlinear Kerr medium is more prominent on the entanglement. Similarly, Stark effect strongly influences the entanglement of two three-level atomic systems. Furthermore, the entanglement evolves with time as we increase the Stark effect. Finally, the quantum system is found highly sensitive to these environmental influences.