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The aim of this paper is to investigate the existence of optimal solutions for control problems involving nonlinear stochastic Schrödinger equations perturbed by a multiplicative fractional Brownian motion. Finite-dimensional approximations and a linearization method are employed and lead to ε-optimal solutions for the considered problems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive investigation on Kerr nonlinearity in a three-level semiconductor quantum well (SQW) superlattice and validates the existence of large Kerr nonlinearity of the order of 1 0 4 W − 1 m − 1 in the vicinity of an electromagnetically induced transparency (EIT) window. The Kerr nonlinearity is found to vary with the relative phase of the applied optical fields, and by selecting suitable relative phases, an enhanced Kerr nonlinearity can be obtained. The results may find significant applications in optoelectronic and photonic devices. [ABSTRACT FROM AUTHOR]

Optics of negative index material is known for its unconventional results. In the perspective of nonlinear optics, it has a revolutionary impact. We, thus, investigate the effect of Kerr nonlinearity on the characteristics of a representative isotropic, frequency independent negative index material by defining an intensity-dependent effective permittivity and compare it to that in positive index material. Using the intensity-dependent permittivity, responses of essential characteristic features like phase and group velocities are studied and found to exhibit unconventional behavior with incident field intensity in the negative index material. At a threshold intensity, i.e., at an intensity at which effective permittivity vanishes, the material shows features of epsilon near zero and/or near zero index materials i.e., a diverging phase velocity with zero group velocity. The study shows the prospect of altering or tailoring characteristic features of a negative index material by tuning the field intensity of the propagating wave or pulse in the material. [ABSTRACT FROM AUTHOR]

We demonstrate that higher-order vortex solitons (with larger vortex charges m) in the nonlinear Schrödinger equation with cubic (defocusing Kerr) nonlinearity can be stabilized by the action of a flat-bottom potential. Such a model can also support the common fundamental (vorticityless) solitons, including the Gaussian-like and flat-top solitons. The effective radii of the fundamental and vortex solitons can be modified by tuning the radius of the flat-bottom part of the potential. We display the contours and phases of vortex solitons with vorticity numbers up to m = 12 . Interestingly, the central holes of vortex solitons increase with the increase of vortex charges, and the central portions of these higher-order vortices become flat. We investigate the existence and stability of both the fundamental and vortex solitons, for different values of the relevant model parameters: the radius of the flat bottom, initial beam power, propagation constant, and the strength of nonlinearity. We also consider the propagation of perturbed initial beams, as well as the propagation in longitudinally modulated flat-bottom potentials. Such a modulated propagation allows for an easy soliton management. We find that the fundamental solitons are completely stable, while the higher-order vortex solitons are prone to the modulation instability, degenerating into m simple vortices that fly away from the inside to the outside of solitons. Eventually, an initial higher-order vortex beam turns into a fundamental (chargeless) soliton. [ABSTRACT FROM AUTHOR]

We investigate theoretically an optomechanical system composed of an optical mode and a mechanical mode interacting through first-order coupling and second-order coupling in the presence of a Kerr nonlinear medium. We study how the nonlinearities (second-order optomechanical coupling and Kerr nonlinearity) alter the optical output spectrum, optical quadrature squeezing and optomechanical entanglement. It is shown that the intensity of the output optical spectrum decreases drastically with an increase in second-order optomechanical coupling while it increases significantly with an increase in Kerr nonlinear parameter. More interestingly, by choosing suitable second-order optomechanical coupling and detuning of the optical cavity field, one can achieve strong squeezing of the cavity light field. Further, these nonlinearities play an important role in creating robust optomechanical entanglement between optical and mechanical modes. Hence, the presence of various nonlinearities in the system can be a good platform for achieving the squeezing of light and robust optomechanical entanglement which can be used in realizing better quantum optomechanical devices. [ABSTRACT FROM AUTHOR]

All-optical modulators hold significant prospects for future information processing technologies for they are able to process optical signals without the electro-optical convertor which limits the achievable modulation bandwidth. However, owing to the hardly-controlled optical backscattering in the commonly-used device geometries and the weak optical nonlinearities of the conventional material systems, constructing an all-optical modulator with a large bandwidth and a deep modulation depth in an integration manner is still challenging. Here, we propose an approach to achieving an on-chip ultrafast all-optical modulator with ultra-high modulation efficiency and a small footprint by using photonic topological insulators (PTIs) made of metallic quantum wells (MQWs). Since PTIs have attracted significant attention because of their unidirectional propagating edge states, which mitigate optical backscattering caused by structural imperfections or defects. Meanwhile, MQWs have shown a large Kerr nonlinearity, facilitating the development of minimally sized nonlinear optical devices including all-optical modulators. The proposed photonic topological modulator shows a remarkable modulation depth of 15 dB with a substantial modulation bandwidth above THz in a tiny footprint of only 4 × 10 µm2, which manifests itself as one of the most compact optical modulators compared with the reported ones possessing a bandwidth above 100 GHz. Such a high-performance optical modulator could enable new functionalities in future optical communication and information processing systems.

Background. Generation of a wave with a double reversed wavefront in multimode waveguides increases the efficiency of six-wave radiation converters and expands the possibilities of its use in adaptive optics problems and the conversion of complex spatially inhomogeneous waves. Aim. The quality of double wavefront reversal during six-wave interaction in a waveguide with infinitely conducting surfaces with Kerr nonlinearity is analyzed for the ratio of the wave numbers of the pump waves equal to 2 and 0,5, and the condition that one of the pump waves excites the zero mode of the waveguide, and the amplitude distribution of the other pump wave excites the edges of the waveguide are described by a Gaussian function. Methods. The influence of pump wave parameters on the half-width and contrast of the amplitude modulus of the object wave was studied using numerical methods. A wave from a point source located on the front face of the waveguide was used as a signal wave. Results. The dependences of the half-width and contrast of the amplitude modulus of the object wave on the ratio between the width of the waveguide and the width of the Gaussian pump wave are obtained. Conclusion. It is shown that the maximum change in the characteristics of a wave with a double reversed wavefront is observed when the width of the Gaussian pump waves changes in the range from 0,3 to 2 half-widths of the waveguide.

We introduce a system of fractional nonlinear Schrödinger equations (FNLSEs) which model the copropagation of optical waves carried by different wavelengths or mutually orthogonal circular polarizations in fiber‐laser cavities with the effective fractional group‐velocity dispersion (FGVD), which were recently made available to the experiment. In the FNLSE system, the FGVD terms are represented by the Riesz derivative, with the respective Lévy index (LI). The FNLSEs, which include the self‐phase‐modulation (SPM) nonlinearity, are coupled by the cross‐phase‐modulation (XPM) terms, and separated by a group‐velocity (GV) mismatch (rapidity). By means of systematic simulations, we analyze collisions and bound states of solitons in the XPM‐coupled system, varying the LI and GV mismatch. Outcomes of collisions between the solitons include rebound, conversion of the colliding single‐component solitons into a pair of two‐component ones, merger of the solitons into a breather, their mutual passage leading to excitation of intrinsic vibrations, and the elastic interaction. Families of stable two‐component soliton bound states are constructed too, featuring a rapidity which is intermediate between those of the two components. [ABSTRACT FROM AUTHOR]

The study examines the linear absorption and third-order nonlinear dispersion properties of a dielectric slab doped with asymmetric InAs/GaAs double-quantum-dot molecules interacting with a low-intensity laser field. Unlike other studies, this research utilizes a gate voltage to induce tunneling-induced transparency to enhance Kerr nonlinearity. The study presents the optimal conditions for achieving Kerr nonlinearity enhancement and demonstrates that interdot electron tunneling increases the group index, leading to subluminal light propagation. Furthermore, the study shows that a dielectric slab with high electric permittivity is the most effective choice for achieving absorption-free, large Kerr nonlinearity. [ABSTRACT FROM AUTHOR]

Nonreciprocal devices, allowing to manipulate one‐way signals, are crucial to quantum information processing and quantum networks. Here a nonlinear cavity‐magnon system is proposed, consisting of a microwave cavity coupled to one or two yttrium–iron–garnet (YIG) spheres supporting magnons with Kerr nonlinearity, to investigate nonreciprocal unconventional photon blockade. The nonreciprocity originates from the direction‐dependent Kerr effect, distinctly different from previous proposals with spinning cavities and dissipative couplings. For a single sphere case, nonreciprocal unconventional photon blockade can be realized by manipulating the nonreciprocal destructive interference between two active paths, via varying the Kerr coefficient from positive to negative, or vice versa. By optimizing the system parameters, the perfect and well‐tuned nonreciprocal unconventional photon blockade can be predicted. For the case of two spheres with opposite Kerr effects, only reciprocal unconventional photon blockade can be observed when two cavity‐magnon coupling strengths Kerr strengths are symmetric. However, when coupling strengths or Kerr strengths become asymmetric, nonreciprocal unconventional photon blockade appears. This implies that two‐sphere nonlinear cavity‐magnon systems can be used to switch the transition between reciprocal and nonreciprocal unconventional photon blockades. This study offers a potential platform for investigating the nonreciprocal photon blockade effect in nonlinear cavity magnonics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the absorption tunability of a silver plasmonic grating incorporating Kerr-type nonlinear graphene-oxide (GO) nanoslits and Ge2Sb2Te5 (GST225) phase-change material at telecom wavelengths. The linear absorption spectra reveal that the amorphous GST225 grating exhibits two distinct absorption peaks, while half-crystallization leads to a single pronounced peak, and full crystallization results in a redshifted peak with a slightly decreased value. These findings confirm that the crystalline degree of GST225 significantly modulates the absorption characteristics. Upon exposure to a nanosecond Gaussian pulse laser irradiation with appropriate fluences, the electric field confinement within the nanoslits intensifies, particularly at the center of the pulse, leading to a pronounced absorption adjustment due to Kerr nonlinearity. Temporal examination at the L-band wavelength of 1591.5 nm reveals a U-shaped absorption response for both amorphous and crystalline GST225, with a pronounced dip at the pulse’s peak. In the half-crystallized state, the weak linear absorption can be substantially enhanced at both the leading and trailing edges of the pulse, with a dip at the center, illustrating the Kerr nonlinearity within the GO nanoslits. The dynamic behavior of absorption under different laser fluences underscores the potential of this system for high-contrast optical switching. Our results offer insights into the development of reconfigurable optical switches utilizing nonlinear Kerr effects, paving the way for advancements in tunable optical communication technologies.

Background. The need to implement controlled coupling between qubits, which are the logical elements of quantum devices such as quantum computers and quantum networks, requires, along with the use of traditional methods, the development of new, more effective ways to organize the interaction of qubits with the microwave fields of resonators used to generate and control the entanglement of qubits. As one of these methods, a method based on the influence of frequency-regulated radio frequency signals on a superconducting Josephson qubit connected by a large Josephson junction to a free qubit has been proposed. Aim. The influence of the Kerr medium of the resonator, in which one of the two qubits is placed, on their entanglement induced by the coherent or thermal frequency-regulated radio frequency field of the resonator is considered. Methods. To analyze the dynamics of the system under consideration, the solution of the quantum Liouville equation for the full density matrix is studied. An exact solution o this equation is found in the case of initial separable and entangled states of qubits. The exact solution of the evolution equation is used to calculate the criterion of qubit-qubit entanglement – cconcurrence. Numerical modeling of the concurrence was carried out for various states of qubits, coherent and thermal fields of the resonator, as well as various values of the intensity of the resonator field and the Kerr nonlinearity parameter. Results. It is shown that for separable initial states of qubits, the inclusion of Kerr nonlinearity reduces the maximum degree of entanglement of qubits. For an entangled initial state of qubits, the possibility of creating long-lived entangled states in the presence of Kerr nonlinearity is shown. Conclusion. The type of initial states of qubits and the range of values of the intensities of the resonator fields and the Kerr nonlinearity parameters have been established, for which the most effective control and operation of the evolution of qubits, as well as the degree of their entanglement, in the physical system under consideration, is possible.

We found the exact solution for a model consisting of two dipole-coupled qubits, one of which is an isolated, and the other interacts with the thermal mode of a cavity with the Kerr medium. The results showed that Kerr nonlinearity may greatly enhance the degree of entanglement induced by a thermal field both for separable and entangled initial states of qubits. We also showed the possibility of the disappearance of the sudden death of entanglement for a model with a Kerr nonlinearity. [ABSTRACT FROM AUTHOR]

The plasmonic nanostructures optical properties, both linear and nonlinear, offer valuable insights for designing nanoscale all-optical devices with rapid response times. This study proposes a novel plasmonic structure, which includes graphene, for developing a wedge hybrid plasmonic waveguide for Kerr nonlinear applications. The behavior of this structure was simulated using the finite element method, and the results indicate that increasing the chemical potential in graphene from μ = 0.1 to 0.45 eV causes the Kerr nonlinear figure of merit curve to move upwards. The wedge-shaped hybrid plasmonic waveguide, which includes graphene, produces comparable results to the conventional wedge-shaped hybrid plasmonic waveguide. With the appropriate values of the graphene sheet Fermi level (i.e. μ = 0.45 eV), the maximum nonlinear coefficient of 2.68 × 107 W−1km−1, Kerr nonlinear figure of merit FoM = 0.029, and minimum effective mode area of Aeff = 0.052 μm2 can be achieved. Thus, changing the chemical potential in graphene can be utilized to manipulate the Kerr nonlinear performance of plasmonic waveguides. [ABSTRACT FROM AUTHOR]

We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase space. We use the Strichartz estimates in a known combination with energy estimates to show the new well-posedness results for quasilinear Maxwell equations. [ABSTRACT FROM AUTHOR]

The existence and stability of moving Bragg grating solitons are systematically investigated in a dual-core system, where one core is uniform and has Kerr nonlinearity, and the other is linear with Bragg grating and dispersive reflectivity. It is found that moving soliton solutions exist throughout the upper and lower bandgaps, whereas no soliton solutions exist in the central bandgap. Similar to the quiescent solitons in the system, it is found that when dispersive reflectivity is nonzero, for certain values of parameters, sidelobes appear in the solitons' profiles. The stability of the moving solitons is characterized using systematic numerical stability analysis. Additionally, the impact and interplay of dispersive reflectivity, soliton velocity, and group velocity on the stability border are analyzed. [ABSTRACT FROM AUTHOR]

We have analyzed the photon blockade effect in a double-cavity optomechanical system. We have explained the conventional and unconventional photon blockade effects in both weak and strong Kerr-nonlinear regimes. Through the analytical solution of the non-Hermitian Hamiltonian and the numerical solution of the master equation, the second-order correlation function of the cavity field has been calculated. We can control photon blockade effects under a small value of external pump amplitude. In this theoretical simulation, both numerical and analytical results are agreed well. The photon blockade effect is visualized by using a different contour plot. In this study, we achieve the optimal conditions for red detuning and blue detuning. We can control the rate of transmission and minimal points to locate g 2 0 . This proposal may be used to generate a single photon source with sub-Poissonian distribution and can also be useful for quantum information processing in quantum communication technology. [ABSTRACT FROM AUTHOR]

A new technique is presented for computing very useful propagation parameters like effective core area and effective index of refraction of mono-mode dispersion shifted and dispersion flattened fibers both in the presence and in the absence of Kerr nonlinearity. The technique involves application of accurate but simple expressions for modal fields developed by Chebyshev formalism. The study of the influence of Kerr nonlinearity on the aforementioned parameters, however, requires the application of the method of iteration. For the purpose of such investigation, in linear as well as nonlinear region, we take some typically used dispersion shifted and dispersion flattened fibers and we show that the results found by our simple formalism are in excellent agreement with those obtained by using complex finite element method. Further, the necessary evaluation by our simple method needs very less computations. Thus, our formalism generates ample opportunity for applications in many areas in the field of nonlinear optics. [ABSTRACT FROM AUTHOR]

We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart for Dirac operators of the Keller estimates for the Schrödinger operator, which are equivalent to some Gagliardo-Nirenberg-Sobolev interpolation inequalities. Domain, self-adjointness, optimality and critical values of the norms are addressed, while the optimal potential is given by a Dirac equation with a Kerr nonlinearity. A new critical bound appears, which is the smallest value of the norm of the potential for which eigenvalues may reach the bottom of the gap in the essential spectrum. The Keller estimate is then extended to a Lieb-Thirring inequality for the eigenvalues in the gap. Most of our result are established in the Birman-Schwinger reformulation. [ABSTRACT FROM AUTHOR]

This article experimentally demonstrates the generation of mode-locked (ML) pulses, which can operate either at 1568 nm or 1608 nm in an Erbium/Ytterbium co-doped fiber laser cavity (EYDF). The wavelength switching was achieved by adjusting the cavity loss. Depending on the cavity length and losses, the laser could operate in either mode-locked (ML) or Q-switched (QS) regimes. We explored the characteristics of the QS and ML pulses, based on the pump power, cavity length and loss. The laser produced stable QS pulses with a repetition rate of 22.73 kHz and a width of 12.2 μs at a pump power of 3.1 W at 1608 nm, for a 30 m long cavity. The laser produced 520 ns ML pulses at 1568 nm with a repetition rate of 877 kHz, average output power of 2.15 mW, and energy of 2.45 nJ with an additional single-mode fiber (SMF) length 200 m at the same pump power. The laser could switch to 1608 nm wavelength when the cavity losses were adjusted.

We present investigation of Petermann I and II spot sizes in the presence of Kerr nonlinearity. Our study is based on the simple power series formulation for fundamental modal field of single-mode-graded index fiber developed by Chebyshev formalism. Based on the said power series expression in the absence of nonlinearity, analytical expressions of the said spot sizes can be prescribed. Using the analytical expressions of the said spot sizes in the absence of nonlinearity, we apply iterative technique in order to predict the said propagation characteristics in presence of Kerr nonlinearity. In this context, we choose some typical single-mode step and parabolic index fibers. We show that the our results agree excellently with the exact results which can be obtained by using rigorous finite-element technique. This leads to verification of accuracy of our simple technique. Moreover, evaluation of the concerned parameters by our formalism involves little computation. Thus, our method provides an accurate but simple alternative to the existing rigorous methods in this context. Accordingly, this novel and simple formalism will prove user friendly to the system engineers in the field non linear optics. [ABSTRACT FROM AUTHOR]

In past years, optical lattices have been demonstrated as an excellent platform for making, understanding, and controlling quantum matters at nonlinear and fundamental quantum levels. Shrinking experimental observations include matter-wave gap solitons created in ultracold quantum degenerate gases, such as Bose–Einstein condensates with repulsive interaction. In this paper, we theoretically and numerically study the formation of one-dimensional gap soliton molecules and clusters in ultracold coherent atom ensembles under electromagnetically induced transparency conditions and trapped by an optical lattice. In numerics, both linear stability analysis and direct perturbed simulations are combined to identify the stability and instability of the localized gap modes, stressing the wide stability region within the first finite gap. The results predicted here may be confirmed in ultracold atom experiments, providing detailed insight into the higher-order localized gap modes of ultracold bosonic atoms under the quantum coherent effect called electromagnetically induced transparency. [ABSTRACT FROM AUTHOR]

This paper reports simple but accurate analytical expressions of group delay and modal dispersion parameters for single-mode graded index fibers over a wide range of V numbers. The formulation employs power series expression for the fundamental modal field of graded index fiber derived by Chebyshev formalism. Choosing some typical step, parabolic and triangular index fibers as examples in our present study, we use the prescribed formulations to estimate group delay and modal dispersion parameters of those fibers both in presence and absence of Kerr nonlinearity. Iterative technique is applied for prediction of concerned propagation parameters in presence of Kerr nonlinearity. Our results show excellent agreement with the numerical exact ones both in absence and presence of Kerr nonlinearity. The exact results in case of Kerr nonlinearity are obtained using cumbersome finite element method. The execution of our accurate formalism involves little computation and is thus user friendly for technologists and researchers working in the field of nonlinear optical engineering. [ABSTRACT FROM AUTHOR]

The single‐ and two‐photon blockade effects in an optical cavity with a nonlinear Kerr medium, which is coupled with a three‐level atom, forming a Δ‐type transition configuration and closed‐loop coupling are investigated by introducing two driving fields in the atom‐cavity system. It is found that single‐ and two‐photon blockades can be remarkably enhanced by the Kerr nonlinearity, however, the parameter regimes governing two blockades are distinctly different. It is demonstrated that a large Kerr nonlinearity makes more contribution to the single‐photon blockade, as compared to the two‐photon blockade effect. Furthermore, by varying the atom‐cavity coupling strength, single‐ and two‐photon blockades can alternatingly occur. Additionally, the region where two‐photon blockade occurs is widened at the cost of increased Kerr nonlinearity and atom‐cavity coupling. This work provides an alternative way to manipulate the few‐photon states and has potential applications in generating single‐photon or two‐photon sources. [ABSTRACT FROM AUTHOR]

We study transverse magnetic (vector valued) wave packets in the time dependent Kerr nonlinear Maxwell's equations at the interface of two inhomogeneous dielectrics with an instantaneous material response. The resulting model is quasilinear. The problem is solved on each side of the interface and the fields are coupled via natural interface conditions. The wave packet is localized at the interface and propagates in the tangential direction. For a slowly modulated envelope approximation the nonlinear Schr\o"dinger equation is formally derived as an amplitude equation for the envelope. We rigorously justify the approximation in a Sobolev space norm on the corresponding asymptotically large time intervals. The well-posedness result for the quasilinear Maxwell problem builds on the local theory of [R. Schnaubelt and M. Spitz, Commun. Math. Sci., 20 (2022), pp. 2265--2313] and extends this to asymptotically large time intervals for small data using an involved bootstrapping argument. [ABSTRACT FROM AUTHOR]

The waveguide properties of the parabolic graded-index slab in the Kerr nonlinear medium are described theoretically. The proposed model includes the dielectric function consisting of two parts with different optical properties. The optical properties of a nonlinear medium are characterized by the dielectric function depending on the electric field intensity (the Kerr nonlinearity). The optical properties of the slab are characterized by the dielectric function depending on the distance with parabolic profile. The exact solution to the wave equation with such a dielectric function is found in explicit analytical form. The found solution describes the transverse electric guided wave modes symmetrically localized near the slab and propagating along it. The effect of the change in the waveguide parameters on the electric field distribution in the guided wave is analyzed. The dependence of the order up to which waveguide modes can be excited on the waveguide system parameters is obtained. The smallest possible plate thickness required for mode excitation is found. The calculations of the power flow show the redistribution of the guided wave energy between the slab and the nonlinear medium with an increase in the mode order. [ABSTRACT FROM AUTHOR]

The existence and stability of moving Bragg grating solitons are systematically investigated in a dual-core system, where one core is uniform and has Kerr nonlinearity, and the other is linear with Bragg grating and dispersive reflectivity. It is found that moving soliton solutions exist throughout the upper and lower bandgaps, whereas no soliton solutions exist in the central bandgap. Similar to the quiescent solitons in the system, it is found that when dispersive reflectivity is nonzero, for certain values of parameters, sidelobes appear in the solitons’ profiles. The stability of the moving solitons is characterized using systematic numerical stability analysis. Additionally, the impact and interplay of dispersive reflectivity, soliton velocity, and group velocity on the stability border are analyzed.

Optical nonlinear neuron, as an essential implementation method for optical interconnection, could greatly promote the development of optical neuron networks, which appears to be a promising alternative to electronic neural networks that are limited by computing speed and the end of Moore's law. However, restricted by weak nonlinearities, the modulation performance of optical nonlinear neuron networks is much lower compared to their electronic counterparts. Therefore, an effectual all‐optical nonlinear neuron is proposed by combining a double‐ring resonator with field‐enhancement and metallic quantum wells (MQWs) with a large Kerr nonlinear response. Based on the large and ultrafast Kerr nonlinearity provided by MQWs, the device can achieve a modulation extinction ratio of 18.78 dB and a transition rate of 13 GW cm−2 per 3 dB. The work may provide a new route for integrated, ultrafast, and high‐efficient optical nonlinear neurons for on‐chip neuron networks. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically analyze optically-induced transparency and absorption properties of a weak probe field in a two-mode coupled micro-cavity system and explore the tunable asymmetric Fano line shape of the transmission rates of the probe field. Both the modes in our system consist of an optical Kerr medium, one of them being passive while the other mode can be either active or passive. The forward transmission and backward reflection profile of the probe field are investigated for both passive–passive and passive–active cavity systems by varying different system parameters such as probe field detuning, photon tunneling strength, gain-to-loss ratio, etc. The results of this study have the potential to be applied in construction of quantum telecommunication and photonic devices. [ABSTRACT FROM AUTHOR]

The paper focuses on the problem of transverse electric wave propagation in a plane-shielded waveguide filled with a nonhomogeneous and nonlinear (Kerr) medium. The nonlinear part of the permittivity is characterized by the Kerr law in the focusing regime, while its linear part is a constant that is perturbed by a small continuous function. Such perturbation can be considered to be an attempt to take into account the inevitable presence of impurities in the medium, causing slight deviations in the dielectric permittivity. In the paper, the existence of solutions to the considered problem is proved, including solutions with and without linear counterparts. Some numerical results are presented as well. [ABSTRACT FROM AUTHOR]

A transmission eigenvalue problem for nonlinear Maxwell's equations that describes propagation of monochromatic transverse electric waves in a dielectric film having cubic inhomogeneous permittivity sandwiched between two half-spaces with constant permittivities is considered. It is proved that even if the nonlinearity coefficient is small, there exist guided waves with as well as without linear counterparts. The found theoretical results predict existence of a new type of nonlinear guided waves. The paper suggest an original mathematical approach that allows one to determine asymptotic distribution of the eigenvalues and zeros of the eigenfunctions. Numerical results are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper focus on new optical soliton solutions of a nonlinear Schrödinger equation with self-frequency shift , and kerr nonlinearity terms. We utilize the extended version of modified tanh expansion technique associated with new Riccati solutions. We extract optical soliton solutions such as dark and bright optical solitons, breathers type, periodic and hybrid type optical soliton solutions. We display all the solutions with help of Mathematica in 2D and 3D graphs. [ABSTRACT FROM AUTHOR]

We look for travelling wave fields E (x , y , z , t) = U (x , y) cos (k z + ω t) + U ~ (x , y) sin (k z + ω t) , (x , y , z) ∈ R 3 , t ∈ R satisfying Maxwell's equations in a nonlinear medium which is not necessarily cylindrically symmetric. The nonlinearity of the medium enters Maxwell's equations by postulating a nonlinear material law D = ε E + χ (x , y , ⟨ | E | 2 ⟩) E between the electric field E, its time averaged intensity ⟨ | E | 2 ⟩ and the electric displacement field D. We derive a new semilinear elliptic problem for the profiles U , U ~ : R 2 → R 3 L u - V (x , y) u = f (x , y , u) with u = U U ~ , for (x , y) ∈ R 2 , where f (x , y , u) = ω 2 χ (x , y , | u | 2) u . Solving this equation we can obtain exact travelling wave solutions of the underlying nonlinear Maxwell equations. We are able to deal with super quadratic and subcritical focusing effects, e.g. in the Kerr-like materials with the nonlinear susceptibility of the form χ (x , y , ⟨ | E 2 | ⟩ E) = χ (3) (x , y) ⟨ | E | 2 ⟩ E . A variational approach is presented for the semilinear problem. The energy functional associated with the equation is strongly indefinite, since L contains an infinite dimensional kernel. The methods developed in this paper may be applicable to other strongly indefinite elliptic problems and other nonlinear phenomena. [ABSTRACT FROM AUTHOR]

We study the full discretization of a general class of first- and second-order quasilinear wave-type problems with the implicit midpoint rule and a linearized variant thereof. Based on a proof by induction, we prove wellposedness and a rigorous error estimate for both schemes, combining energy techniques, inverse estimates and a linearized fixed-point iteration for the analysis of the nonlinear scheme. To confirm the relevance of the general framework, we derive novel error estimates for the full discretization of two prominent examples from nonlinear physics: the Westervelt equation and the Maxwell equations with Kerr nonlinearity. [ABSTRACT FROM AUTHOR]

In past years, optical lattices have been demonstrated as an excellent platform for making, understanding, and controlling quantum matters at nonlinear and fundamental quantum levels. Shrinking experimental observations include matter-wave gap solitons created in ultracold quantum degenerate gases, such as Bose–Einstein condensates with repulsive interaction. In this paper, we theoretically and numerically study the formation of one-dimensional gap soliton molecules and clusters in ultracold coherent atom ensembles under electromagnetically induced transparency conditions and trapped by an optical lattice. In numerics, both linear stability analysis and direct perturbed simulations are combined to identify the stability and instability of the localized gap modes, stressing the wide stability region within the first finite gap. The results predicted here may be confirmed in ultracold atom experiments, providing detailed insight into the higher-order localized gap modes of ultracold bosonic atoms under the quantum coherent effect called electromagnetically induced transparency.

A scheme for optical nonreciprocity is proposed via dual-mode Raman process in thermal atoms. We investigate a far-detuned nonlinear Raman process, with the assistance of the Doppler effect to achieve chiral optical nonlinearity. The resulting Kerr nonlinear absorption is subject to a direction-dependent Doppler shifts seen by the thermal atoms. Moreover, the inter-channel Raman interference could significantly enhance Kerr nonlinear absorption for probe field, leading to the enhancement of the optical nonreciprocity. Simulation results show that the isolation ratio could reach 41 dB and the insertion loss is about 0.16 dB, with bandwidth up to 2π ×48 MHz. Furthermore, the sensitivity of the system is investigated under different strengths of the control and Raman fields.

The waveguide properties of a symmetrical three-layered structure consisting of a linearly graded-index layer in nonlinear medium are described theoretically. The new form of dielectric constant combining the spatially distributed part and intensity dependent Kerr type part is proposed. The exact solutions of the nonlinear wave equation with the complex dielectric constant in the case of positive (self-focusing) and negative (defocusing) nonlinear response were found. The formation of transverse electric waveguide modes are described analytically using four new types of the nonlinear guided waves in the self-focusing and defocusing media. The discrete spectra of the effective refractive index of even and odd modes are obtained in exact analytical form. The order of even and odd modes coincides with the number of maxima in the field distribution in the across graded-index layer direction. It is shown that a mode of order not higher than the determined one can be excited in the waveguide. Restrictions for the highest order of the waveguide modes that can be excited for given values of the optical and geometrical parameters of the waveguide are found. The influence on the profile of the electric field distribution of the unperturbed dielectric constants, the nonlinearity coefficients, the wave number, the thickness of the graded-index layer is studied. [ABSTRACT FROM AUTHOR]

We investigate theoretically, the optical response for a cavity optomechanical system containing a Kerr non-linear substrate. The optomechanical cavity's moving membrane interacts linearly and quadratically with the radiation pressure of the photons. We found that the quadratic non-linear coupling and Kerr non-linearity strongly influence the system's optical multistability. Further, the transmission spectrum is observed under the influence of both non-linearities. Our theoretical results show that the width of the spectrum alters significantly by tuning the non-linearities present in the system. In addition, our results show that a peculiar positive value of quadratic optomechanical coupling is instrumental in generating Normal Mode splitting while the absence and negative value of quadratic optomechanical coupling inhibit the Normal-Mode splitting. [ABSTRACT FROM AUTHOR]

This paper focuses on electromagnetic transverse-electric wave propagation in a planar shielded waveguide filled with nonlinear medium. Instead of using the standard local Kerr (cubic) nonlinearity, we suggest a (nonlocal) modification of this law. In comparison with the standard formula, this modification does not produce infinitely many nonperturbative guided modes. In this research, we present the dispersion equation for propagation constants, eigenwaves and propagation constants via explicit formulas. The found results are compared with the ones relating to the corresponding linear problem and the nonlinear one with the classical Kerr's law. Numerical results are also presented and discussed. [ABSTRACT FROM AUTHOR]

We consider the contact of a medium in which the refractive index linearly decreases depending on the distance to a nonlinear medium, where the sign of the Kerr nonlinearity can change abruptly when the electric-field strength reaches a threshold value. It is established that surface waves of three types can propagate along such a contact, depending on the sign of the nonlinearity and the range of values of the effective refractive index. Explicit analytical expressions are obtained for the distribution of the electric-field strength in the transverse direction with respect to the contact plane, which are exact solutions of the formulated nonlinear equations. It is shown that the formation of electric-field distributions corresponding to waveguide modes with several intensity maxima is possible in the layer with a refractive-index gradient. [ABSTRACT FROM AUTHOR]

The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence o Abstract The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field. f Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.

• New exact analytical solution describing transverse profile of the surface wave is found. • The formation of the near interface optical domain with the dielectric constant different from its value in the rest nonlinear medium is described. • The depth of field penetration into the hyperbolic graded-index layer decreases and it increases into the nonlinear medium with an increase in the effective refractive index. • The depth of field penetration into the hyperbolic graded-index layer increases and it decreases into the nonlinear medium with an increase in the dielectric constant at the medium interface. • Thickness of the optical domain decreases with increase in the interface dielectric constant and it increases with increase in the effective refractive index. A new exact analytical solution describing the transverse profile of the surface wave in the case of contact with nonlinear medium with the step-wise nonlinearity and the hyperbolic index profile and describing new features of the light localization near such an interface are found. The formation of the near interface cladding layer with the dielectric constant different from its value in the rest nonlinear medium is described. It is found that light localization can be effectively controlled by the parameters of the hyperbolic profile such as the interface dielectric constant and the effective refractive index. The depth of field penetration decreases inside the hyperbolic graded-index layer and it increases in the nonlinear medium with an increase in the effective refractive index. The depth of field penetration in the hyperbolic graded-index layer increases and it decreases in the nonlinear medium with an increase in the value of the dielectric constant at the medium interface. Thickness of the formed cladding layer decreases with increase in the interface dielectric constant and it increases with increase in the effective refractive index. [ABSTRACT FROM AUTHOR]