Nonlinear Kerr Medium Research Articles

A Low-Dispersion Time Differencing Scheme for Maxwell’s Equations

A novel low-dispersion time differencing scheme for the integration of Maxwell’s equations is developed. The method employs a staggered temporal grid with a time difference operator that controls the magnitude of dispersion errors. It is tested within the physical domains employing fourth-order finite difference approximations but can be combined with grids using any order of accuracy, including the spectral grids. Stability analysis demonstrates that the proposed method achieves third- and fourth-order accuracies for amplitude and phase errors, respectively, outperforming the second-order phase error produced by the finite-difference time-domain methods based on the Yee scheme. The order of accuracy accomplished by the method and its zone of stability are comparable to the third-order Runge–Kutta scheme with the advantage of being three times more efficient. The proposed method is proven to be effective and stable when employed within the perfectly matched layers and nonlinear Kerr media. Its performance and ability to reduce the dispersion errors are demonstrated by comparing the solutions computed by the method with those obtained from the Yee and other high-order schemes.

Anisotropic nonlinear Kerr media: Z-scan characterization and interaction with hybridly polarized beams.

The interaction of intense laser with matter gives rise to a variety of novel nonlinear optical effects, reflects the nonlinear optical property of a material, and modulates the light propagation behavior. Herein, we investigate anisotropic Kerr nonlinearities induced by both scalar and vectorial optical fields. Firstly, we present the anisotropic third-order nonlinear refraction indexes related to left-hand and right-hand components, which depend on the ellipticity, the dichroism coefficient, the anisotropy coefficient, as well as the crystal orientation angle. Secondly, we develop the elliptically polarized light Z-scan technique for characterizing third-order nonlinear susceptibility tensor in anisotropic nonlinear Kerr media, which is demonstrated experimentally. Lastly, with the known nonlinear optical parameters, we numerically study both the vectorial self-diffraction behaviors and spin angular momentum (SAM) characteristics of hybridly polarized beams induced by an anisotropic Kerr nonlinearity. It is shown that the anisotropic Kerr nonlinearity offers a new approach to manipulate the polarization-structured light field, which has potential applications in SAM manipulation, three-dimensional crystal orientation, and polarization-sensitive detection and sensing.

Dynamical Properties of Intensity Dependent Two-Mode Raman Coupled Model in a Kerr Medium

The present paper describes the dynamics of a single two-level atom interacting with intensity dependent quantized bimodal field via Raman type process in an ideal cavity filled with a non-linear Kerr medium. The cavity modes interact with the atom as well as the Kerr medium. A unitary transformation method that is used to solve the time-dependent problem also gives the Eigen solutions of the interaction Hamiltonian. We study the atomic population dynamics and investigate the effects of intensity dependent coupling, Kerr medium and detuning parameters on the domain of the non-classical features of the atom field state. The intensity dependent coupling is introduced by the Hermitian operator valued functions of the number operator $$ f\left({\widehat{n}}_i\right)\kern0.36em \left(i=1,2\right) $$ . We find that the intensity dependent coupling considered by the function $$ f\left({n}_i\right)=\frac{1}{\sqrt{n_i}} $$ introduces and ameliorates the non-classical features in the presence of Kerr medium.

On the theory of adiabatic field dynamics in the Kerr medium with distributed gain and dispersion.

A general theory is presented for the adiabatic field evolution in a nonlinear Kerr medium with distributed amplification and varying dispersion. Analytical expression is derived linking parameters of the adiabaticity, gain distribution, and dispersion profile. As a particular example, an optical pulse compressor based on the adiabatic dynamics is examined.

A Quantum-Controlled NOT Gate Based on Four-Wave Mixing in a Cavity for Polarization Photonic Qubits

The possibility of effectively creating quantum gates based on polarization photon qubits using a Kerr nonlinear medium in a cavity is studied. It is shown how a quantum C-NOT gate can be produced with such qubits through four-wave mixing. A theory of this gate’s operation is constructed using an input–output formalism, and conditions of parametric matching are obtained for effective gate operation.

Instabilities and solitons in systems with spatio-temporal dispersions and non paraxial approximations

We consider the evolution of light beams in nonlinear Kerr media wherein the beam propagation is governed by the coupled non-paraxial (2+1) dimensional nonlinear Schrödinger equation. In the advent of system failing to obey the slowly varying envelope approximation, the usual paraxial approximation cannot be adopted. Our model equation could potentially serve as a governing model for nano-waveguides and on-chip silicon photonic devices. Using the trial solution method, we derive the different combinations of soliton solutions such as bright–bright, dark–dark, and bright–dark soliton and briefly discuss the characteristics of the soliton. Following the initial discussion on the soliton solution, we extend the study to investigate the modulational instability of the system of equations. We examine the role of the dispersion/diffraction in the instability spectra and demonstrate the different characteristics of the instability bands as a function of system parameters.

Multispectral Switching Using Fano Resonance and Plasmon-Induced Transparency in a Plasmonic Waveguide-Coupled Resonator System

Quantum interference effects, namely Fano resonance producing asymmetric resonant excitation and plasmon-induced transparency (PIT), are demonstrated in a plasmonic waveguide-coupled resonator device incorporated with a third-order Kerr nonlinear medium. Occurrence of both Fano and induced transparency peaks is modulated by alteration of the nonlinear permittivity through an external control beam and the phenomenon is further utilized to investigate optical switching in the plasmonic device. Simultaneous switching at multiple wavelengths is explored using Fano and PIT effect and the multispectral optical switching at four or more wavelengths is employed for proposed realization of trinary logic operations.

Stark and Kerr Effects on the Dynamics of Moving N-Level Atomic System

We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) for N-level atomic system interacting with a coherent field in the presence of Kerr (linear and non-linear medium) and Stark effects. It is observed that the Stark and Kerr effects play a prominent role during the time evolution of the quantum system. The evolving quantum Fisher information (QFI) is noted as time grows under the non-linear Kerr medium contrary to the QE for higher dimensional systems. The effect of non-linear Kerr medium is greater on the QE as we increase the value of Kerr parameter. However, QFI and QE maintain their periodic nature under atomic motion. On the other hand, linear Kerr medium has no prominent effects on the dynamics of N-level atomic system. Furthermore, it has been observed that QFI and QE decay soon under the influence of Stark effect. In short, the N-level atomic system is found prone to the change of the Kerr medium and Stark effect for higher dimensional systems.

Control not quantum gate on the states of photon orbital angular momentum

The possibility of effectively creating quantum gates based on orbital angular momentum photon qubits using a Kerr nonlinear medium in a cavity is studied. It is shown how a quantum C-NOT gate can be produced with such qubits through four-wave mixing process. A theory of this gate operation is constructed using an input–output formalism. Parametric matching conditions are obtained for effective gate operation.

Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits a global collective behavior characterized by a dramatic narrowing and amplification in the strongly non-linear regime. The theoretical analysis based on the Vlasov formalism and the method of the characteristics applied to a reduced hydrodynamic model reveal that such a strong amplitude-incoherent pulse originates in the existence of a concurrent shock-collapse singularity (CSCS): The envelope of the intensity of the random wave exhibits a collapse singularity, while the momentum exhibits a shock singularity. The dynamic behavior of the system after the shock-collapse singularity is characterized through the analysis of the phase-space dynamics.

Nonlinearity modulation based multiple Fano resonance and multi-spectral switching in a nanoplasmonic waveguide-coupled cavity system

Dual and multiple asymmetric Fano resonance are theoretically explored in a subwavelength plasmonic cavity-coupled waveguide system incorporated with a third order Kerr nonlinear medium. The degree of asymmetry and the number of multiple resonances are controlled by an external pump beam which modulates the Kerr permittivity thereby dictating the resonant behavior. Electromagnetically induced transparency in plasmonic systems, referred to as plasmon induced transparency, is a special case of Fano resonance and plays a key role for the occurrence of multiple Fano excitations. Plasmon induced transparency appears as induced reflectance dips when analyzed in reflection mode. Though geometrical dependency of dual and multiple Fano effect is demonstrated, the main interest and importance is focused on the generation and manipulation of multiple Fano resonances by intensity modulation of the pump beam and its application in multispectral switching and quality factor tuning at a fixed operating frequency.

Optical vortex trapping and annihilation by means of nonlinear Bessel beams in nonlinear absorbing media

In nonlinear Kerr media at intensities such that multiphoton absorption is significant, a vortex of topological charge m in the center of a high-order nonlinear Bessel beam (NBB) can be stable and subsist endlessly. We show that the m-charged NBB is not only stable but is formed spontaneously from any other n-charged NBB and N "foreign" vortices of total charge s randomly nested in the beam cross section if n + s = m. All nested vortices merge in the center of the original NBB, which undergoes a mode conversion to the NBB that preserves the topological charge and the inward-directed power current that sustains the diffraction-free and attenuation-free propagation in the medium with nonlinear absorption. We foresee different applications such as the creation of stable, multiply charged vortices without tight alignment requirements but by spontaneous vortex combination, mixing waves or particles that the vortices can guide, fast annihilation of vortex dipoles, and cleaning of speckled beams by massive annihilation of vortices.

Collision-mediated radiation due to Airy-soliton interaction in a nonlinear Kerr medium

We study the interaction of a co-propagating finite energy Airy pulse and a soliton in a Kerr medium under third order dispersion. It is observed that a strong radiation appears when selfaccelerating Airy pulse collides with a delayed soliton in time domain. We confirm both analytically and numerically that this radiation can only be initiated in the environment of third order dispersion (TOD). The radiation frequency is red or blue shifted depending on the numeric sign of TOD parameter. We adopt a simple Si-based waveguide to validate the normalised parameter that we use for the analysis. We develop a theory to explain the collision-mediated radiation and our theoretical results are found to be in good agreement with the direct numerical modelling of the generalised nonlinear Schrodinger equation (GNLSE).

Quantum X waves with orbital angular momentum in nonlinear dispersive media

We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.

Stationary wave packets in the Kerr nonlinear media with imaginary harmonic potential and linear gain

The existence of stationary wave packets in the nonlinear Kerr media with an imaginary harmonic potential and a linear gain is investigated. By employing a variational approach the existence of stable bright solitons is shown for the case of a defocusing nonlinearity. In focusing nonlinear media, the bright solitons have been shown to be unstable. The predictions of variational approach are confirmed by numerical simulations of the full modified NLS equation. The predicted stationary localized wave packets can be observed in a quasi-one-dimensional BEC with an imaginary optical potential and atoms feeding.

Double-hump solitons in fractional dimensions with a 𝒫𝒯-symmetric potential.

We investigate the properties of double-hump solitons supported by the nonlinear Schrödinger equation featuring a combination of parity-time symmetry and fractional-order diffraction effect. Two classes of nonlinear states, i.e., out-of-phase and in-phase solitons are found. Each class contains two families of solitons originating from the same linear mode in both focusing and defocusing nonlinear Kerr media. The critical phase-transition point increases monotonously with increasing Lévy index. For strong gain and loss, out-of-phase solitons in focusing media are stable in a wide parameter window and are almost completely unstable in media with a defocusing nonlinearity. The stability of in-phase solitons is opposite to that of out-of-phase solitons. In-phase solitons in defocusing media are stable in their entire existence domains provided that the gain-loss strength is below a critical value. Meanwhile, the stability region shrinks with the decrease of Lévy index. We, thus, put forward the first example of spatial solitons in fractional dimensions with a parity-time symmetry.

Controllable optical bistability and Fano line shape in a hybrid optomechanical system assisted by kerr medium: possibility of all optical switching

We theoretically analyse the optical and optomechanical nonlinearity present in a hybrid system consisting of a quantum dot(QD) coupled to an optomechanical cavity in the presence of a nonlinear Kerr medium, and show that this hybrid system can be used as an all optical switch. A high degree of control and tunability via the QD-cavity coupling strength, the Kerr and the optomechanical nonlinearity over the bistable behaviour shown by the mean intracavity optical field and the power transmission of the weak probe field can be achieved.The results obtained in this investigation has the potential to be used for designing efficient all-optical switch and high sensitive sensors for use in Telecom systems.

Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

The potential of nonharmonic systems has several applications in the field of quantum physics. The photon-added coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function, Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.

All-Optical Multiple Logic Gates Based on Spatial Optical Soliton Interactions

In this letter, all-optical logic gates with attraction and repulsive interactions of coherent spatial optical solitons have been designed in a bulky nonlinear Kerr medium. The logic gates comprise logical AND and OR gates by the attraction of two obliquely propagating inphase spatial optical solitons and logical NOR and XNOR gates based on repulsive interaction among three out of phase spatial optical solitons. The numerical results show that soliton interactions perform a high contrast power level between ON/OFF states. The proposed model is applicable to design phase-modulated logical gates too. The simplicity and ease for fabrication of the proposed logic gates would be a potential key component for the future of all-optical logical photonic devices and computational photonic circuits.

Temporal rocking in a nonlinear hybrid optomechanical system

We explore theoretically the optomechanical interaction between a light field and a mechanical mode mediated by a Kerr nonlinear medium inside a Fabry-Perot cavity. When the system is driven by a strong and fast amplitude-modulated light field, i.e., in the so-called temporal rocking region, the cavity field and the mechanical oscillator show the characteristics of multistability. The rocking breaks down the continuous phase symmetry of the cavity field to a bistable case of two equivalent states with exact π phase difference. In addition, the rocking can significantly enhance the optomechanical coupling between the light field and the mechanical oscillator, which can be used as a new handle to control the normal mode splitting of the mechanical spectrum. Moreover, the optomechanical cooling rate can be greatly modified by the rocking. With the optimized rocking parameters, the mechanical oscillator can be cooled down to its ground state more efficiently. Such a temporal rocking optomechanical system has potential applications in all-optical switching and enhancement of quantum effects.