Third-order Nonlinear Medium Research Articles

Generation of multiple ultrashort temporal solitons in a third-order nonlinear composite medium with self-focusing and self-defocusing nonlinearities

Generation of multiple ultrashort temporal solitons in a third-order nonlinear composite medium with self-focusing and self-defocusing nonlinearities

A FETD scheme and analysis for photonic crystal waveguides comprising third-order nonlinear and linear materials

In this paper, we design a time-domain finite element (FETD) algorithm for solving Maxwell’s equations in third-order nonlinear media. The Cardano’s method is used to solve the nonlinear constitutive equation. At the same time, we also establish the continuous stability of the third-order nonlinear model and the numerical stability of the FETD scheme. In order to reduce the wave reflection from the truncated domain boundary, the anisotropic perfectly matched layer model is developed and solved. Extensive numerical simulations are carried out and they demonstrate that bistable transmission switches depending on the incident wave’s intensity can be obtained if a number of rods made of Kerr-type nonlinear materials are inserted around the bend of the linear bent photonic crystal waveguides.

Optical bistability and absorption characteristic of an optomechanical system embedded with double quantum dot and nonlinear medium

This paper theoretically studies a hybrid optomechanical system embedded with two coupled quantum dots and a third-order Kerr nonlinear medium inside the cavity. The optical bistability and absorption spectrum are analyzed for the proposed system. From the Hamiltonian which describes the proposed system, a set of quantum Langevin equations are derived. Using these equations of motion, the steady-state mean field analysis is done which gives the phenomena of optical bistability. The performance of the optical switch is also analyzed in terms of gain and switching ratio. Further, the absorption spectrum of the system is derived and analyzed from the fluctuation dynamics. The optical bistability has the potential to design tunable all-optical switches. The absorption spectra display peculiar characteristics of negative absorption (transparency dip). The transparency dips are found to be strongly dependent on the frequency of the mechanical resonator. The results of our investigation reveal that the proposed system can be used as an optical switch and has numerous other applications in quantum communication systems.

Normal mode splitting and four-wave mixing in Kerr-nonlinear optical system containing coupled double quantum dot

We theoretically investigate the four wave mixing (FWM) and normal mode splitting (NMS) in coupled double quantum dots cavity system in the presence of a third-order Kerr nonlinear medium. The FWM generated in the system has narrow spectral width and this can be tuned by nonlinear medium strength, the coupling strength between two coupled quantum dots and pump strength. Further, we study NMS that can also be tuned by various physical parameters and show that energy exchange between different modes is possible. The proposed model have potential applications in the field of quantum information processing.

Controlled conversion of transverse symmetries in a four-wave mixing process

Precise light manipulation in optical media has been important for developing new communication protocols, particle tracking and control, environmental sensing and quantum computing, to cite a few applications. Here, we explore the nonlinear light-matter interactions of Hermite-Gaussian (HG) beams with a rubidium vapor. We analytically and numerically predict the possibility of generating a nearly pure optical HG mode as a result of the four-wave mixing of two different HG modes. In contrast, four-wave mixing of other linear solutions of the paraxial wave equation in a third-order nonlinear medium results in the up-converted beam consisting of a superposition of multiple modes. In addition, we identify a large family of solutions of the paraxial wave equation, including cylindrical and elliptical modes, that can be generated in the process of the four-wave mixing by precisely adjusting the weights of the input HG beams. This study may find applications in the development of new classical and quantum optical sources, with more spatial versatility.

Optical response in a double quantum dot in an optomechanical system

In this work, we theoretically investigate the optical response in a hybrid optomechanical system comprising two coupled quantum dots (QDs) embedded in a photonic crystal optomechanical cavity with a third-order Kerr nonlinear medium. The microcavity is created by the sequence of distributed Bragg reflectors (DBR). InAs QDs and GaAs photonic crystal cavities have been easily integrated using well-known techniques. We show that the optical bistability, can be used to fabricate all-optical switches and can be tuned by the optomechanical coupling strength, nonlinear medium strength, and other parameters. The results of our study reveals that the proposed model can be used as an optical switch which is essential for various quantum practical applications.

Nonlinear optical response in coupled quantum wells optomechanical microcavity

We investigate the optical properties of a hybrid solid-state optomechanical microcavity containing two coupled quantum wells interacting with the cavity mode in the presence of a third-order nonlinear medium and a mechanically compliant distributed Bragg reflector (MC-DBR). The MC-DBR interacts with the cavity mode via the nonlinear radiation pressure effect. The steady state mean-field analysis shows the existence of optical bistability, which can be utilized to design all optical tunable switch. The coupling between the two quantum wells, the interaction between the excitons and the optical mode, the Kerr nonlinearity, and the optomechanical interaction can be tuned to operate the optical switch at lower input laser power. The fluctuation dynamics demonstrate the presence of optomechanically induced transparency (OMIT) and optomechanically induced absorption (OMIA). We find that both OMIT and OMIA can be manipulated efficiently by optomechanical coupling strength and the quantum well tunneling rate.

Optical Kerr nonlinearity in quantum-well microcavities: From polariton to dipolariton

In this paper, we investigate the nonlinear optical properties and photon correlations in a cavity containing quantum wells and interacting with a third-order nonlinear medium. More precisely, we study the interaction of the photonic Kerr nonlinearity with polariton and dipolariton quasiparticles in thermal environments. The optical bistability, the intensity spectrum, and the squeezing spectrum of the transmitted radiation are analyzed. It is shown that the regime of the bistability is reached in the dipolariton cavity faster than attained by the polariton system. Furthermore, the increase of the coupling with the wells reduces the squeezing. More interestingly, it turns out that the additional interactions arising in the dipolariton cavity, between direct and indirect excitons, slow down the variation of the squeezing. As a consequence, dipolaritons offer a greater margin of squeezed light than polaritons, and also than the ${\ensuremath{\chi}}^{(3)}$ medium in the absence of quantum wells. Moreover, the dipolariton system is found to be much more robust against the bath temperature in the weak-coupling regime.

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.

All-reflective self-referenced spectral interferometry for single-shot measurement of few-cycle femtosecond pulses in a broadband spectral range

An all-reflective self-referenced spectral interferometry based on the transient grating (TG) effect is proposed for single-shot measuring of the amplitude and phase of ultrashort pulses in a broadband spectral range. Except for a thin third-order nonlinear medium, which was used to generate the TG signal, no transmitted optics were used in the proposed device, and few-cycle pulses in a broad spectral range from deep UV to mid-IR can be characterized. With a homemade compact and alignment-free device, a 5.0 fs pulse at 800 nm corresponding to about two cycles and a 14.3 fs pulse at 1800 nm corresponding to less than three cycles were successfully characterized.

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.

Third-harmonic pulse generation in one-dimensional photonic crystal structures

Enhanced third-harmonic generation in a one-dimensional photonic crystal doped with third-order nonlinear medium was numerically investigated using the multiple-scale method and the split-step Fourier transform. The optimal fundamental frequency for third-harmonic wave generation was determined from the transmission spectrum. The third-harmonic pulse intensities grow, depending on the structure thickness and the fundamental-frequency detuning parameter, which determines the band-edge phase matching condition. Furthermore, the total energy output of third-harmonic pulses, depending on the fundamental-frequency pulse width, may be more than 1000 times the energy produced by a phase-matched bulk medium. A narrow pulse with bandwidth less than the band-edge transmission peak enables high conversion efficiency. The maximum conversion efficiency of the forward component may be 12 to 13 orders of magnitude greater than that of the backward component.

Metallic slit arrays filled with third-order nonlinear media: Optical Kerr effect and third-harmonic generation

We acknowledge support from the Spanish Ministry of Science and Innovation under Projects No. MAT2008-06609-C02 and No. CSD2007-046-Nanolight.es

Nonlinear chirp effect introduced by Kerr medium as optical switches in ultrafast time-resolved measurements

We report the study on the nonlinear chirp effect introduced by third-order nonlinear media used as Kerr gates in time- and spectrum-resolved measurements. In our experiment, white-light continuum generated by a femtosecond laser was used as the source pulse to examine the chirping introduced by a variety of Kerr media of various thicknesses as the optical gates, and the results were compared with that gated by a 1 mm beta-barium borate noncollinear optical parametric amplifier (NOPA). Remarkable nonlinear chirp was observed in the experiments when Kerr media compared with that measured by NOPA. The results indicate that the chirping introduced by Kerr media is significant and cannot be neglected, especially when the Kerr gate is employed in broadband femtosecond time-resolved ultraviolet-visible spectrum measurements.

Amplitude-squared and amplitude-cubed squeezing in stimulated Raman and in spontaneous Raman scattering

Coherent light coupled to a third-order nonlinear medium is responsible for spontaneous and for stimulated Raman processes. The analytical solutions up to second order in coupling constants of various field modes for spontaneous Raman and for stimulated Raman processes are utilized to obtain the amplitude-squared and amplitude-cubed squeezing of the input coherent light. The amplitude-squared and amplitude-cubed squeezing are completely ruled out for all modes for spontaneous Raman processes. For stimulated Raman processes, we observe that the squeezing for amplitude-squared and amplitude-cubed are possible for pump and for vibrational phonon modes. It is found that the percentage of higher ordered amplitude squeezing decreases with the increase of the orders. The squeezing in Stokes and in anti-Stokes modes are ruled out even for stimulated Raman processes.

Toward single-shot measurement of a broadband ultrafast continuum

We discuss the problem of measuring the intensity and phase of a broadband continuum in a single shot, considering three possible methods, and perform preliminary measurements using one of them. Our measurements use transient-grating cross-correlation frequency-resolved optical gating (TG XFROG) with a third-order nonlinear medium, which currently can phase match over 300 nm simultaneously. We demonstrate this technique for a continuum generated in bulk fused silica that is 12.5 mm thick. Due to limited reference-pulse energy, we do not achieve a true single-shot measurement, instead averaging over approximately five shots. The retrieved trace and spectrum contain fine structure, and the retrieved temporal phase is mainly quadratic.

Electrically and optically controlled cross-polarized wave conversion

Light wave propagation in third-order nonlinear media with applied external electric field is investigated. Interplay between the nonlinear electro-optic and all-optical effects is examined theoretically. Energy exchange between the orthogonal light polarizations, the cross polarization conversion, results. The assisting external field acts as either the effect-enhancing or functionality-controlling parameter. Various materials such as silica glass, silicon, other bulk and quantum well semiconductors, organic materials, and particle-doped nanostructures are referred to as possible candidates for device implementations. Numerical estimates of achievable parameters in a selected suitable material are discussed.

Quantum statistical properties of the radiation field in spontaneous Raman and stimulated Raman processes

The initially prepared coherent state coupled to a third-order nonlinear medium is responsible for stimulated Raman and spontaneous Raman processes. By exploiting the analytical solutions of field operators for various modes, we investigate the quantum statistical properties for pure and two modes of the input coherent light responsible for stimulated Raman and spontaneous Raman processes. For spontaneous Raman processes the photons are unbunched for the pure and two-mode cases. By a suitable choice of phase, we obtain the bunching and antibunching of photons for stimulated Raman processes.

A semi-classical approach to two-frequency solitons in a three-level cascade atomic system

A semi-classical theory of two intense optical fields interacting with a third-order non-linear medium composed of a three-level cascade atomic system is presented. It is predicted that non-linear atom-field interactions allow the formation of two-frequency bright, dark and grey spatial solitons. We demonstrate through numerical simulations and analytic stability analysis that the bright and grey solitons are stable.

Theory of pump–probe propagation in third-and higher-order, nonlinear optical media

A theory to treat the propagation of an intense pump pulse and a weak probe pulse in nonlinear media is presented. We give a general formalism applicable to the pump–probe propagation in a variety of nonlinear optical media. Based on this formalism, we obtain first an analytic, closed-form solution of pump–probe propagation in a third-order nonlinear medium, including linear absorption, nonlinear refraction, and two-photon absorption. The effects of velocity mismatch are also considered in our results. The general formalism leads further to analytic results for pump–probe propagation in a medium with both third- and fifth-order nonlinearity.