Nonlinear Kerr Medium Research Articles

Influence of Kerr nonlinearity on propagation characteristics of twisted Gaussian Schell-model beams.

The analytical propagation formulae of twisted Gaussian Schell-model (TGSM) beams through nonlinear Kerr media are derived. It is found that a TGSM beam is less sensitive to Kerr nonlinearity than a Gaussian Schell-model (GSM) beam. Furthermore, the propagation characteristics of TGSM beams with stronger twist and worse spatial coherence are less affected by Kerr nonlinearity. The self-focusing effect enhances the beam twist, but degrades the beam spatial coherence. In the atmosphere (one kind of self-focusing media), a TGSM beam has greater resistance to self-focusing effects and atmospheric turbulence effects than a GSM beam or an ideal Gaussian beam.

Solution of coupled nonlinear Schrödinger equations in focusing-defocusing medium by modified perturbation theory

The interaction of bright solitons of different orders and two different wavelengths propagating in the medium focusing for one wavelength and defocusing for the other is considered. The system of nonlinear Schrödinger equations is solved by means of perturbation theory. Application of an additional postulate to adjust both widths of the solitons and to modify the amplitude by a factor determined by the overlap integral greatly improves the accuracy of the description. The good accuracy of description is confirmed by numerical calculations. Full Text: PDF ReferencesY. Kivshar, G. P. Agrawal, Optical Solitons. From Fibers to Photonic Crystals, (Amsterdam, Academic Press 2003). CrossRef F. Abdullaev, S. Darmanyan, P. Khabibullaev, Optical Solitons, (Springer-Verlag, Berlin, 1993) CrossRef G.I.A Stegema, D.N. Christodoulides, M. Segev, IEEE J. Selected Topics Quantum Electron. 6, (2000), 1419 CrossRef J. Yang, "Nonlinear Waves in Integrable and Nonintegrable Systems", (SIAM, Philadelphia 2010). CrossRef Y. Kivshar, B. Malomed, "Dynamics of solitons in nearly integrable systems", Rev. Mod. Phys. 61, 763 (1989). CrossRef P.G. Kevrekidis, D.J. Frantzeskakis, "Solitons in coupled nonlinear Schrödinger models: A survey of recent developments", Reviews in Physics 1 (2016), 140 CrossRef R. de la Fuente, A. Barthelemy, "Spatial soliton-induced guiding by cross-phase modulation", IEEE J. Quantum Electron. 28, 547 (1992). CrossRef H. T. Tran, R. A. Sammut, "Families of multiwavelength spatial solitons in nonlinear Kerr media", Phys. Rev. A 52, 3170 (1995). CrossRef S. Leble, B. Reichel, "Coupled nonlinear Schrödinger equations in optic fibers theory", Eur. Phys. J. Special Topics 173, 5 (2009). CrossRef M. Vijayajayanthi, T.Kanna, M. Lakshmanan, "Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing, defocusing and mixed type nonlinearities", Eur. Phys. J. Special Topics 173, 57 (2009). CrossRef S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electromagnetic waves ", Sov. Phys. JETP 38 (1973), 248 DirectLink J. Yang, Phys. Rev. E 65, 036606 (2002). CrossRef T.Kanna, M. Lakshmanan, "Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations", Phys. Rev. Lett. 86, 5043 (2001). CrossRef M. Jakubowski, K. Steiglitz, R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media", Phys. Rev. E 58, 6752 (1998). CrossRef P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, "Supermode spatial optical solitons in liquid crystals with competing nonlinearities", Phys. Rev. A 95 (2017). CrossRef P. S. Jung, M. A. Karpierz, M. Trippenbach, D. N. Christodoulides, and W. Krolikowski, "Supermode spatial solitons via competing nonlocal nonlinearities", Photonics Lett. Pol. 10 (2018). CrossRef A. Ramaniuk, M. Trippenbach, P.S. Jung, D.N. Christodoulides, W.Krolikowski, G. Assanto, "Scalar and vector supermode solitons owing to competing nonlocal nonlinearities", Opt. Express 29, 8015 (2021) CrossRef

Soliton‐mode proliferation induced by cross‐phase modulation of harmonic waves by a dark‐soliton crystal in optical media

AbstractThe generation of high‐intensity optical fields from harmonic‐wave photons, interacting with dark solitons via a cross‐phase modulation coupling, both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time‐entangled dark‐soliton patterns, forming a periodic waveguide along the path of the harmonic‐wave probe. It is shown that an increase of the strength of cross‐phase modulation coupling respective to the self‐phase modulation coupling, favors soliton‐mode proliferation in the bound‐state spectrum of the trapped harmonic‐wave probe. The induced soliton modes, which display structures of periodic soliton lattices, are not just rich in numbers, they also form a great diversity of population of soliton crystals with a high degree of degeneracy.

Tunable infrared wide band-stop plasmonic filter using T-shaped resonators

In this paper, a tunable wide band-stop plasmonic filter in infrared (IR) wavelength range is proposed. The designed filter consists of a bus Metal-Insulator-Metal (MIM) waveguide coupled with T-shaped resonators containing a Kerr nonlinear medium. Simulation results show that, the stop wavelength range in Near-Infrared (NIR) is broadened by increasing the number of T-shaped resonators. Also, the stop wavelength band is shifted to Mid-Infrared (MIR) band with increasing the insulator permittivity. In this way, the insulator region is realized by Kerr nonlinear medium which possesses incident light intensity-dependent permittivity. Therefore, the stop wavelength band can be tuned to desired range with the number of T-shaped resonators and incident light intensity. Simulation results are obtained using CST Microwave Studio software.

Electronically controlled polarization beat length in Kerr nonlinear media

The polarization beat length of propagating optical fields in nonlinear birefringent Kerr medium is investigated in the presence of an externally applied DC electric field. We show that the critical power, at which the effective polarization beat length becomes infinite, can be controlled through adjusting the externally applied electric field. The principle of operation is based on modifying the polarization instability by electronically adjusting the effective birefringence through an external electrical bias. The presented analytical expressions describe the beat length and the polarization instability as a function of the applied electric field for an arbitrary optical input state.

A time-domain finite element scheme and its analysis for nonlinear Maxwell's equations in Kerr media

The purpose of this paper is to develop and analyze a finite element method for solving the time-dependent Maxwell's equations in nonlinear Kerr media. The proposed fully-discrete scheme is proved to be conditionally stable and optimally convergent in the spatial variable and second order in time. Numerical results are presented to support our theoretical analysis and also to demonstrate the practical soliton propagation phenomena in Kerr media.

Investigation of coupled self-tapering/self-uptapering of soliton beams in nonlinear media

Coupled tapering/uptapering phenomenon of two coaxially co-propagating mutually incoherent beams of same frequency with finite loss/gain is investigated in this paper for Kerr nonlinear medium. The phenomenon is investigated, in detail, for different situations and parameters for coupling coefficient equal to 2 and 2/3.

Low-threshold bistable reflection assisted by oscillating wave interaction with Kerr nonlinear medium* *Projected supported by the Open Fund by State Key Laboratory of Advanced Optical Communication Systems and Networks (Grant No. 2017GZKF18), the National Natural Science Foundation of China (Grant Nos. 12064017, 61765008, 11764020, 11864017, 11804133, and 51567011), the Jiangxi Provincial Natural Science Foundation (Grant No. 20181BAB206034), the Fundamental Research

Owing to the enormously enhanced oscillating wave, a minute variation of the incident light intensity will give rise to a change in the dielectric constant of the Kerr nonlinear medium and lead to a bistable reflection with an ultra-low threshold intensity, which is closely related to the angle of incidence and the thickness of the Kerr nonlinear medium. The criterion for the existence of optical bistability is derived. Our bistability scheme is simple and not limited to the TM-polarization.

Quantum Fisher Information of Two-Level Atomic System under the Influence of Thermal Field, Intrinsic Decoherence, Stark Effect and Kerr-Like Medium

In this paper, we have proposed the numerical calculations to study the quantum entanglement (QE) of moving two-level atom interacting with a coherent and the thermal field influenced by intrinsic decoherence (ID), Kerr medium (non-linear) and the Stark effect. The wave function of the complete system interacting with a coherent and the thermal field is calculated numerically affected by ID, Kerr (non-linear) and Stark effects. It has been seen that the Stark, Kerr, ID and the thermal environment have a significant effect during the time evolution of the quantum system. Quantum Fisher information (QFI) and QE decrease as the value of the ID parameter is increased in the thermal field without the atomic movement. It is seen that QFI and von Neumann entropy (VNE) show an opposite and periodic response in the presence of atomic motion. The non-linear Kerr medium has a more prominent and significant effect on the QE as the value of the Kerr parameter is decreased. At smaller values of the non-linear Kerr parameter, the VNE increases, however, QFI decreases, so QFI and VNE have a monotonic connection with one another. As the value of the Kerr parameter is increased, the effect of non-linear Kerr doesn’t stay critical on both QFI and QE. However, a periodic response of QE is seen because of the atomic movement which becomes modest under natural impacts. Moreover, it has been seen that QFI and QE rot soon at the smaller values of the Stark parameter. However, as the value of the Stark parameter is increased, the QFI and QE show periodic response even when the atomic movement is absent.

Use of KDP crystal as a Kerr nonlinear medium for compressing PW laser pulses down to 10 fs

Abstract The input pulse of the laser PEARL with energy of 18 J and pulse duration of about 60 fs was compressed to 10 fs after passage through a 4-mm-thick KDP crystal and reflection at two chirped mirrors with sum dispersion of −200 fs2. The experiments were performed for the В-integral values from 5 to 19 without visible damage to the optical elements, which indicates that small-scale self-focusing is not a significant issue. It was shown that, by virtue of the low dispersion of the group velocity, the KDP crystal has some advantages over silica: a larger pulse compression coefficient, especially at a small value of the В-integral (B = 5, …, 9), lower absolute values of chirped mirror dispersion, and also a possibility to control the magnitude of nonlinearity and dispersion by changing crystal orientation.

Direct and inverse problems for the nonlinear time-harmonic Maxwell equations in Kerr-type media

In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of the medium by making electromagnetic measurements on the boundary. We are interested in the case of the time-harmonic Maxwell equations.

Propagation characteristics of focused astigmatic Gaussian beams in Kerr nonlinear media

When a powerful laser beam propagates in a Kerr nonlinear medium, the Kerr effect on the beam propagation characteristics is very significant. The astigmatic laser beams are often encountered in practice. Until now, much work has been carried out on the propagation characteristics of astigmatic laser beams in linear media, but a few researches have been reported about the propagation of astigmatic laser beams through nonlinear media. To the best of our knowledge, the propagation or the transformation of astigmatic laser beams through an optical system in a Kerr nonlinear medium has not been investigated. In this paper, the propagation characteristics of focused astigmatic Gaussian beams in a nonlinear Kerr medium are studied. The Kerr effect on the beam astigmatism and the focal shift of focused astigmatic Gaussian beams are investigated in detail, and the self-focusing focal length and focus control of focused astigmatic Gaussian beams in the Kerr nonlinear medium are also studied. For the beam spreading case, the analytical formula for each of the beam width, the beam waist position, and the focal shift of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is shown that in the self-focusing medium, as the beam power increases (i.e. the self-focusing effect becomes stronger), the beam astigmatism becomes stronger, but the focal shift decreases. However, in a self-defocusing medium, as the beam power increases (i.e. the self-defocusing effect becomes stronger), the beam astigmatism becomes weaker, but the focal shift increases. On the other hand, for the beam self-focusing case, the analytical formula of the self-focusing focal length of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is found that the number of foci can be controlled by applying beam astigmatism. The results obtained in this paper are of theoretical and practical significance.

Mechanical oscillator thermometry in the nonlinear optomechanical regime

Optomechanical systems are promising platforms for controlled light-matter interactions. They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems. In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, we depart from this regime by considering an undriven optomechanical system via non-Gaussian radiation-pressure interaction. To measure the temperature of the mechanical oscillator, initially in a thermal state, we use light as a probe to coherently interact with it and create an entangled state. We show that the optical probe gets a nonlinear phase, resulting from the non-Gaussian interaction, and undergoes an incoherent phase diffusion process. To efficiently infer the temperature from the entangled light-matter state, we propose using a nonlinear Kerr medium before a homodyne detector. Remarkably, placing the Kerr medium enhances the precision to nearly saturate the ultimate quantum bound given by the quantum Fisher information. Furthermore, it also simplifies the thermometry procedure as it makes the choice of the homodyne local phase independent of the temperature, which avoids the need for adaptive sensing protocols.

All-optical computing circuits half-subtractor and comparator based on soliton interactions

The speed limitations of electronic processors have created a demand for a high bandwidth and ultra-fast computing circuits. By replacing the electric logic gates with photonic ones, a high bandwidth and fast photonic microprocessor will be achieved which will overcome the speed limitations of electronic circuits. Digital photonic logic circuits are key elements in the next generation optical computers. In this paper, all-optical logical half-subtractor and digital comparator are designed based on spatial optical solitons. These computational gates are designed simply with repulsive and attractive interactions of three inphase and out of phase spatial optical solitons in a bulky nonlinear Kerr medium. With tuning the phase input solitons and exploiting inphase and out of phase soliton interactions a high functional circuit with broad operational bandwidth, high switching speed and high contrast ratio between ON/OFF states is achieved by a simple structure.

Ultra-high quality graphene perfect absorbers for high performance switching manipulation.

Wavelength-selective light absorption and the related switching operations are highly desired in optical devices. Herein, we report the approach for ultra-high quality (Q) graphene perfect optical absorption, which possesses impressive performance in switching manipulation. A record-breaking Q-factor (up to 105) is observed, suggesting one or two orders of magnitude larger than that of the conventional graphene absorbers. The ultra-low external leakage loss rate of quasi-bound states in the continuum (BIC) resonator and the ultra-low intrinsic absorption loss rate in the resonant mode volume are the main contributions for the ultra-high Q perfect absorption. By introducing a Kerr nonlinear medium, spectral relative intensity can be changed from 0 to 100% when an ultra-low pump light with the intensity of only 5 kW cm-2 is used. After a rather slight tuning of the refractive index (Δn = 5×10-4) for the resonators, the absorption contrast ratio reaches 31 dB. The switching related spectral wavelength shift sensitivity is up to 915 nm/RIU and the figure of merit (FOM) is 50 833. These features confirm the ultra-high tunability and switching manipulation. It is believed that the ultra-high Q-factor absorption offered by all-dielectric configuration provides plentiful potential applications for graphene-based devices in the all-optical switch, modulator, notch filter, etc.

Optimal estimation of gravitation with Kerr nonlinearity in an optomechanical system

We present a high precision scheme of a gravitational accelerometer which consists of an optomechanical system embedding a Kerr nonlinear medium. The quantum Cramer–Rao bound and the quantum Fisher information (QFI) are well-known tools to depict the ultimate precision limit in quantum parameter estimation. In our scheme, the analytical expression of time-dependent QFI is obtained with the absence of noise, which shows that the precision has been improved due to the existence of Kerr nonlinearity. At the light-matter decoupling time, the theoretical bound for the relative sensitivity is $$\varDelta g/g\approx 6.36\times 10^{-13}$$ .

Integrated Source of Path-Entangled Photon Pairs with Efficient Pump Self-Rejection.

We present a theoretical proposal for an integrated four-wave mixing source of narrow-band path-entangled photon pairs with efficient spatial pump self-rejection. The scheme is based on correlated loss in a system of waveguides in Kerr nonlinear media. We calculate that this setup gives the possibility for upwards of 100 dB pump rejection, without additional filtering. The effect is reached by driving the symmetric collective mode that is strongly attenuated by an engineered dissipation, while photon pairs are born in the antisymmetric mode. A similar set-up can additionally be realized for the generation of two-photon NOON states, also with pump self-rejection. We discuss the implementation of the scheme by means of the coherent diffusive photonics, and demostrate its feasibility in both glass (such as fused silica-glass and IG2) and planar semiconductor waveguide structures in indium phosphide (InP) and in silicon.

Modulated solitons, soliton and vortex clusters in purely nonlinear defocusing media

By means of standard Thomas–Fermi approximation, we present stable solutions of one- and two-dimensional (1D and 2D) multihump soliton structures, including 1D and 2D modulated solitons as well as 2D soliton clusters, supported by inhomogeneous defocusing nonlinear Kerr media. Such nonlinear settings may apply to nonlinear optics and Bose–Einstein condensates. All the 1D and 2D fundamental modes with different numbers of humps (for both modulated solitons and soliton clusters) are demonstrated to be robustly stable. Besides, the considered 2D nonlinear setting also supports a vast varieties of vortex modes—vortex soliton clusters. Such novel type of vortex soliton clusters is qualitatively different from the ordinary vortex clusters, on the account of the fact that the latter type is a single large soliton with several-vortex configurations inside it, while our predicted vortex clusters structures are composed of the arrays of unitary vortex solitons. Stability regions for all the soliton structures are identified via linear stability analysis and direct simulations.

Polarization rotation and singularity evolution of fundamental Poincaré beams through anisotropic Kerr nonlinearities

We report a theoretical investigation on polarization rotation and singularity evolution of focused fundamental Poincaré beams in free-space propagation and through isotropic and anisotropic Kerr nonlinear media. It is found that the optical nonlinearity enhances the polarization rotation of the focused beams during propagation. Furthermore, the anisotropy of optical nonlinearity causes the symmetry breaking of the polarization distribution. Further studies show that the C-point and L-line singularities of the lemon Poincaré beams do not change while propagating in free space or through the isotropic nonlinear Kerr medium. Interestingly, the anisotropic Kerr nonlinearity evokes the C-point singularity splitting, and the distortion and birth of L-line singularities. However, the total singularity index always remains the conservation within the light field, regardless of the optical nonlinearity.

Evolution of rectangular and triangular initial beam profiles in positive Kerr local medium

The hyperbolic secant (Sech) shape, as the initial beam profile, is the well-know profile that compensates the diffraction and self-focusing effect during propagation in Kerr medium, and evolves as the bright spatial soliton. The Sech beam can be confined in the Kerr medium andinduces its own waveguide. In this work, two initial beam profiles, rectangular and triangular functions, that are different than Sech profile, are considered, and the propagation of these beam profiles in third-order nonlinear (Kerr) medium is investigated. As a result, the initialbeam-width played an important role in confining the beam profiles in direction of propagation. In addition, the intensity profiles change to the Sech profile after some initial step of propagation. All the calculations and simulations have been done by the Split-Step numericalmethod with MATLAB program.