Kerr Type Research Articles

Dynamic stability of the sandwich nano-beam system

This article explores the stochastic stability of a three nanobeam system connected by Kerr type elastic layer, subjected to the magnetic effects and compressive axial forces. While considering nano beams rotary inertia is taken into account and differential equations of nanobeams are given according to Eringen's nonlocal elasticity theory. The impact of a longitudinal magnetic field on the behavior of the nanobeam system is described using Lorentz magnetic forces. The objective of this research paper is to investigate the moment and almost sure stability of the system. It analyzes the system's stability under white noise excitation by employing the contact transformation method and perturbation approach. Notably, we consider the case where the system exhibits low damping. The study focuses on examining the system's dynamic behavior and stability characteristics under these conditions. The stochastic stability of this system is investigated through moment Lyapunov exponents and Lyapunov exponents for the first time and interesting conclusions regarding the stability region of this system were obtained by varying various system parameters. These conclusions are presented in a visual manner and discussed.

Born and inverse Born series for scattering problems with Kerr nonlinearities

We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give alternate explicit conditions for convergence of the Born series. We illustrate our results with numerical experiments.

2D Jackiw–Rebbi and trivial localized states in square interfaced binary waveguide lattices

We investigate optical analogs of two-dimensional (2D) Jackiw–Rebbi (JR) states and 2D trivial localized states in square interfaced binary waveguide lattices in the linear and nonlinear regimes of Kerr type. The 2D JR states can be formed in the square interfaced binary lattice during propagation of optical beams and turn out to be quite robust, especially in the linear and defocusing nonlinearity regime where established 2D JR state profiles are well conserved during propagation. The established profiles of nonlinear 2D JR states formed during propagation agree well with exact solutions obtained by using the Newton–Raphson method. The 2D nonlinear trivial localized states found by the successive approximation method are much broader than 2D JR states with the same peak amplitudes. The 2D JR states can also be well trapped within the central interface of the lattices even in the presence of an initial tilt of the input beam which can easily displace 2D trivial localized states in square interfaced binary waveguide lattices, 2D Dirac solitons in perfectly periodic binary waveguide lattices and other solitonic structures in the continuous media.

A simple but accurate technique for prediction of confinement and normalized group delay parameters for propagation of first higher order mode in graded index fiber

Abstract This paper deals with expressions for simple but precise analyses of fractional modal power (FMP) inside the core of optical fibers, the excitation efficiency and the normalized group delay (NGD) for the first higher order (LP11) mode in step and parabolic index fibers both with and without Kerr type non linearity. To get the analytical results, we have employed simple power series Chebyshev expansion for the LP11 mode of the above mentioned fibers. At first, the analytical expression for linear case is found out and then by applying the method of iteration the propagation parameters are estimated when there is nonlinearity of the Kerr type. Here, some typical step and parabolic profile fibers have been used for our investigation. Our findings of confinement and group delay parameters perfectly match with the precise numerical findings made by the intricate finite element method (FEM). This implies the precision of our formalism. The study of nonlinear optical transmission systems will benefit from the findings.

Modulation instability effects of the conventional Kerr type nonlinearity on the three-core oppositely directed coupler

The present design deals with a three-core system in which two channels are made of negative index material and one made of positive index material. The nonlinear Schrodinger equation is modified by adding the Kerr-type nonlinearity and coupling coefficient terms. We derive the dispersion relation for the optical coupler under investigation in the presence of added terms. Using a linear stability analysis, we examine the modulation instability characteristic gain in both the normal and anomalous group-velocity dispersion regimes. We study the system in diversified physical parameter space to unveil many possibilities. The analytical results demonstrate that, in contrast to Shafeeque et al. (2016), some novel instability bands are produced in the normal and anomalous dispersion regimes. We observe the modulational instability (MI) occurring due to Kerr-type nonlinearity. It is also evident that MI can be controlled by varying pump power and nonlinear factors. As a result, we observe new possibilities for producing and managing the MI in three-core oppositely directed couplers with the impact of opposite directionality.

Multistability in Coupled Nonlinear Metasurfaces

Multistability, namely, the property of obtaining different outputs depending on the past values of the input, is the key effect behind memory components in a variety of electronic, chemical, biological, and quantum systems. Two electromagnetic metasurfaces, with nonlinear admittances of Kerr type, are found to manifest significant multistability regarding their transmissivity. Such a feature is owed to the discontinuous variation of the response once the nature of the material changes from dielectric to plasmonic and vice versa, occurring at different levels of incoming power. The conditions for giving sizable hysteresis loops, with respect to either the input intensity or its operational wavelength, are determined. The reported results are expected to assist the modeling of nonlinear metasurfaces and open unexplored opportunities toward the efficient design of photonic memory elements.

An accurate but simple method for estimation of the influence of kerr nonlinearity on the far field pattern of LP11 mode in dispersion-shifted and dispersion-flattened fibers

Abstract In this paper, we have presented the far field pattern in presence and absence of Kerr type nonlinearity for the first higher order mode in Dispersion shifted and dispersion flattened type optical fibers. Our analytical results are based on simple power series expressions for the first higher order (LP11) mode of aforesaid fibers, which have been formulated by Chebyshev formalism. Using the analytical expressions for the linear case, method of iteration is applied in order to predict the concerned propagation parameters in presence of Kerr type nonlinearity. We have taken some typical trapezoidal index, step W and Parabolic W fibers for our study. Our results for the far field pattern have been shown to be in excellent agreement with the exact numerical results computed by rigorous finite element technique. The simplicity and accuracy of our formalism will prove helpful to the designers for setting up of efficient low dispersion optical link.

Effect of Kerr nonlinearity on signal and pump intensities in EDFA comprising single-mode step index fiber: Estimation by a simple but accurate mathematical formalism

The paper presents simple but accurate analytical expressions for the estimation of variation of signal and pump intensity with normalised radial distance in case of erbium doped fiber amplifier. Choosing two typical single-mode step index fibers in our investigation, we hereby predict the said variations relating to both pump and signal in presence as well as absence of Kerr nonlinearity. The stated formulation uses power series expression for the fundamental modal field of graded index optical fiber as derived by Chebyshev formalism. Method of iteration is applied for the prediction of concerned parameters in presence of Kerr type nonlinearity. Our results have been shown to be agreeing excellently with the numerical exact ones in absence and also in presence of Kerr nonlinearity. Exact results in case of Kerr nonlinearity are determined using the cumbersome finite element method. It is noteworthy that execution of our proposed method requires very less computation and as such it will be remarkably user friendly for researchers and technologists associated with nonlinear optical engineering.

Light localization in a linearly graded-index substrate covered by intensity dependent nonlinear self-focusing cladding

The new features of the light localization along the graded-index substrate covered by the cladding characterized by a self-focusing nonlinearity are described theoretically. In the model of nonlinearity the dielectric function in substrate depends linearly on the distance from the cover-substrate interface. The optical characteristics of Kerr type positive nonlinear response in the cover is changed abruptly with an increasing light intensity. The light intensity distribution in across interface direction described by exact solution to nonlinear wave equation is calculated and analyzed. It is found that increasing the width of the graded-index layer leads to a shift in the position of the maximum intensity. The intensity maximum appears in the graded-index substrate after the effective refractive index reaches the critical value. The thickness of nonlinear near-surface layer, which is formed after the light intensity reaches the critical value, monotonically decreases with increasing width of the graded-index layer. The possibility of realizing a multimode regime of the light propagation, which can be realized with an increasing width of the graded-index layer and it is characterized by a deep penetration of the light field into the substrate, is derived. The possibility of control the distribution of the light power between the cover and substrate by change in the effective refractive index and the width of the graded-index layer is described.

Switchable selective interactions in a Dicke model with a driven biased term.

In this work, we propose a method to investigate controllable qubit-resonator interactions in a Dicke model with driven biased term. The nonlinearity of the spectrum, which can be induced by qubit-resonator interactions, plays an important role in such controllable interactions. To gain insight into the mechanism of the nonlinearity, we perform a unitary transformation of the Hamiltonian. The results show that the nonlinearity of the transformed Hamiltonian depends on the qubit-resonator coupling strength. The general forms of the effective Hamiltonians are discussed in detail based on the frequency modulation approach. The dynamical evolution can be switched on and off by adjusting the modulation parameters. By utilizing such controllable interactions, we discuss the creation of Dicke states and the arbitrary superposition of Dicke states. We also consider the nonlinearity of the energy level for the limit of large qubit numbers. In the thermodynamics limit, the Kerr type nonlinearity is induced from "magnon"-resonator coupling, and the selective preparation of "magnon" Fock states can be studied under a "magnon" scenario.

The domain derivative for semilinear elliptic inverse obstacle problems

<p style='text-indent:20px;'>We consider the recovering of the shape of a cavity from the Cauchy datum on an accessible boundary in case of semilinear boundary value problems. Existence and a characterization of the domain derivative of solutions of semilinear elliptic equations are proven. Furthermore, the result is applied to solve an inverse obstacle problem with an iterative regularization scheme. By some numerical examples its performance in case of a Kerr type nonlinearity is illustrated.</p>

The composite planar waveguide structure consisting of the linearly graded-index layer and the nonlinear layer formed with an increasing the electric field

The new type of the composite planar waveguide characterized by unique optical properties caused by the special selection of the waveguide layers is described. The interface between linearly graded-index layer and medium characterized by a sharp appearance of self-focusing Kerr type nonlinear response is considered. The nonlinear surface wave propagating along the interface is obtained analytically as exact solution to the wave equation with dielectric function depending on across interface coordinate and electric field. The possibility of controlling the redistribution of wave energy between layers along the waveguide with an increase in the effective refractive index and the characteristic distance of the gradient medium is shown.

Efficient realization of infrared coherent radiation by the method of parametric light amplification in nonlinear photonic crystals

The process of parametric amplification of light from short laser pulses in nonlinear photonic crystals is analyzed numerically. The calculations were carried out taking into account the effects of the dispersion of the medium up to the third order and cubic nonlinearity of the Kerr type. It is shown that a change in the size of domains can significantly affect the formation of a signal wave pulse. On the basis of the results obtained, we analyzed the optimal values of the domain size at which the efficient energetic generation of the signal wave is observed.

Spatial and spectral features of the luminescence of liquid nitrogen stimulated by infrared lasers

Spectral features of cryogenic liquids, especially nitrogen, seem to be clearly investigated due to the wide application in science. On the other hand, material properties can really be different under intensive laser irradiation. During irradiation of liquid nitrogen with pulsed (pulse duration 20 ns) YaG: Nd 1064 nm laser with average power of 0.3 W we have found bright luminescence in the visible region with five narrow spectral lines. This phenomenon can be explained by the multiphoton excitation of nitrogen molecules and ions with infrared photons. Its spatial and spectral characteristics are attributed to Amplified Spontaneous Emission. The main features include super-linear dependence of the emission intensity on the intensity of the excitation radiation, limited amount of narrow spectral bands and conical geometry of the emission with the clear separation of the cones in correspondence with the spectral lines of the emission. This phenomenon manifests liquid nitrogen as the convenient substance of Kerr type for studies of various non-linear optical processes by means of nanosecond lasers instead of femtosecond lasers applied usually for these purposes.

Analysis of Kerr type nonlinear single-mode triangular index fiber directional coupler by a simple method

We present the coupling characteristics of directional coupler comprising two identical single-mode triangular index fibers both in the presence and the absence of Kerr nonlinearity. Triangular index fibers of some typical V numbers are chosen for our investigation. Our analysis is based on the simple series expression for the fundamental modal field for triangular index fiber developed by Chebyshev technique. Analytical expression of the coupling length in the absence as well as in the presence of Kerr nonlinearity is prescribed. Using the said expression of coupling length, we apply a method of iteration to evaluate the said coupling parameter in the presence of Kerr nonlinearity. We also show that our results match excellently with the exact results obtainable by rigorous finite-element technique. The execution of our formalism requires little computation. Thus our simple but accurate formalism to study the triangular index directional coupler will prove a suitable alternative to the existing rigorous methods in the field of nonlinear optics. This user-friendly method will prove beneficial to the scientists and technologists working in the field of nonlinear optics.

Localized states in the crystal characterized by the switching between self-focusing and defocusing Kerr type nonlinearities and the surface interaction

Localized states in the crystal characterized by the switching between self-focusing and defocusing Kerr type nonlinearities and the surface interaction

Particularities of the Formation of Localized States near a Planar Defect in Media with an Abruptly Changing Defocusing Nonlinear Response

Particularities of field (light beam) localization near a planar defect in media with an abrupt defocusing Kerr type nonlinearity is studied theoretically using a one-dimensional model based on a generalization of the nonlinear Schrodinger equation with a point potential modeling the interaction of excitations with a planar defect and a nonlinear summand in which coefficients of the linear and nonlinear response change abruptly depending on the field amplitude in the medium. It is shown that there exist two types of symmetric localized steady states in different energy ranges. The influence of the intensity of the interaction between excitations and the defect on the profile of localization of states and conditions of their existence are studied.

Extraction of optical solitons in birefringent fibers for Biswas-Arshed equation via extended trial equation method

Abstract This article obtains optical solitons to the Biswas-Arshed equation for birefringent fibers with higher order dispersions and in the absence of four-wave mixing terms, in a media with Kerr type nonlinearity. Optical dark, singular and bright soliton solutions are articulated by applying an imaginative integration technique, the extended trial equation scheme. Various additional traveling wave solutions are produced with this integration technique, which include rational solutions, Jacobi elliptic function solutions and periodic singular solutions. From the mathematical analysis some constraints are recognized that ensure the actuality of solitons.

Особенности формирования локализованных состояний вблизи плоского дефекта в средах со скачкообразно меняющимся дефокусирующим нелинейным откликом

A theoretical study of the features of the localization of fields (light beam) near a plane defect in media with a stepwise defocusing nonlinearity of the Kerr type is carried out. A one-dimensional model is used based on a generalization of the nonlinear Schrödinger equation with a point potential that simulates the interaction of excitations with a plane defect, and a nonlinear term in which the coefficients of the linear and nonlinear responses abruptly change in depending on the field amplitude in the medium. It is found two types of symmetric localized stationary states in different energy ranges. The influence of the intensity of the interaction of excitations with a defect on the profile of localization of states and the conditions for their existence is studied.

Effect of Surface Recombination on Diffusion Length and Active Cavity Life time

This work presents an analytical study for simulating a Fabry-Perot Bi-stable etalon (F-P cavity) filled with a dispersive optimized nonlinear optical material (Kerr type) such as semiconductors Indium Antimonite (InSb). Depending on the obtained results and because of a trade-off between the optical path length of the sample and active cavity lifetime, an optimization procedure was applied on the InSb etalon/CO laser parameters; critical switching irradiance (Ic) was applied via simulation systems of optimization procedures of optical cavity (Matlap program was used to study the optical Bi-stability of a nonlinear Fabry-Perot cavity). In order to achieve minimum switching power and faster switching time, the optimization surface recombination on the diffusion length and effective cavity lifetime was studied.
 In addition, for a specific absorption value 400 cm-1, the lifetime coefficient values were 0.33 , 0.091 , 0.0172 ns for sample thickness (D) = 500 , 60 , 20 mm, respectively. Also, for a bulk recombination time (Tl) of 200 ns, specific absorption (α) of 50 cm1, and D of 20 mm, the surface recombination speed value was 2.845 x 105 cm/sec, whereas the active lifetime, which is defined as the thickness over the surface recombination speed (sυ) (D/2sυ), was equal to 3.5ns.