Search

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]

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]

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.

• 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]

We propose a scheme to generate photon–phonon entanglement and spin squeezing in a hybrid system which is composed of the nitrogen–vacancy (NV) centers, nanomechanical resonator (NMR), and optical cavity. The triplet ground states of the NV centers which have been embedded in the middle of the clamped–clamped NMR are dressed by two strong microwave fields. Kerr nonlinearity is established by an applied microwave field and the vibrational modes of NMR coupling to the dressed-state transitions. The quantum correlations of the applied microwave field, vibrational mode, and NV centers are realized based on the parametric down-conversion-like and beam-splitter-like interactions in the hybrid system, which generate the photon–phonon entanglement and spin squeezing. In this nonlinear processes, the dynamically mediated strain of NMR, as a nonlinear switch, plays the central role in the establishment of such quantum correlations. Our scheme can be applied to quantum nondemolition measurement, quantum sensing, and quantum metrology. • Photon–phonon entanglement and spin squeezing are established based on parametric down-conversion-like and beam-splitter-like interactions. • In the existed schemes based on NV centers, the triplet ground states were just dressed partially, and simplified to the two-level system. In our scheme, we study in the dressed picture and found quantum correlations. • Our scheme can be applied to quantum nondemolition measurement, quantum sensing, and quantum metrology. [ABSTRACT FROM AUTHOR]

It has been shown that magnon–photon coupling, which has received a great attention in connection with quantum information science, can experimentally be demonstrated in cavity QED. Here we study the quantum entanglement in a lossy optomagnonical microcavity in the presence of photon and magnon Kerr nonlinearities. The system contains two optical modes of the cavity which couple to two ferromagnetic YIG spheres, with the losses of two optical fields and the magnonic modes. We then numerically obtain the entanglement between optical modes as photon–photon entanglement, magnonic modes as magnon–magnon entanglement, and one of the optical modes and the magnon modes as photon–magnon entanglement. Afterward, we examine the roles of photon–magnon coupling strength, dissipation, Kerr nonlinearities and thermal noise in the degree of entanglement between bipartite subsystems. The numerical results show that the increment of photon–magnon coupling and Kerr nonlinear susceptibility increase the maximum values of bipartite entanglements. Moreover, the maximum survival temperature of bipartite entanglements can appropriately be tuned by Kerr nonlinearity of magnon. Furthermore, the entanglement between subsystems can be observed at cryogenic temperatures. • An optomagnonical system with two YIG spheres is described in a lossy cavity. • Entanglement between photon–photon, magnon–magnon, and photon–magnon pairs is studied. • The effects of photon–magnon coupling, dissipation, and thermal noise are examined. • The maximum survival temperature can be controlled by magnonic Kerr nonlinearity. • The degree of entanglement between subsystems can be seen at cryogenic temperatures. [ABSTRACT FROM AUTHOR]