Fifth-order Nonlinear Susceptibility Research Articles

Theory of fifth-harmonic generation in cubic centrosymmetric crystals

We derive wave equations for fifth-harmonic generation in cubic centrosymmetric crystals in direct and indirect processes when an incident electric field propagates along a cubic axis. We elucidate the dependence of fifth-harmonic fields on crystal length and polarization directions of an incident field. We also devise a method to measure elements of a fifth-order nonlinear susceptibility tensor in the transparent regime by measurement of fifth-harmonic intensity from crystals of different lengths.

Triphoton correlations in six-wave mixing

The generation of nonclassical multiphoton has aroused and renewed interest in recent years. Here, we theoretically propose a new method to generate a temporal triplet correlation via a spontaneous six-wave mixing process. In the dressed-state picture at atomic ensemble, we forecast two or more different resonant dispersion modes of each generated photons. With energy conservation condition, these resonant dispersion modes compose multiple six-wave mixing processes, and the different processes could beat with each other. When we only consider the nonlinear optical response, the coincidence counts of triplets perform as a damped Rabi oscillation (three conditional two-photon correlations with four or six periods) because of the destructive interference among the possible six-wave mixing processes. The coherent time in the system is determined by the effective dephasing rate. Furthermore, we study the triphoton correlation with the fifth-order nonlinear susceptibility and the phase matchings mixing.

Fifth-order nonlinear susceptibility: Effect of third-order resonances in a classical theory

We compute the fifth-order nonlinear susceptibility in the frame of a classical model based on an anharmonic oscillator, taking into account the local field corrections. A third-harmonic resonance is evidenced, which explains the strong enhancement of some measured values of the corresponding nonlinear index and its sign changes with the wavelength. The ratio between the fifth-order nonlinear index and the fifth-order nonlinear absorption is computed and is in good agreement with experimental data measured in carbon disulfide ${\mathrm{CS}}_{2}$.

Solitons of four-wave mixing in competing cubic-quintic nonlinearity.

We experimentally investigate the soliton formation and dynamics in the nonlinear propagation of the generated signal and probe beams in four-wave mixing (FWM) process with atomic coherence in a three-level atomic system, under the competition between focusing and defocusing nonlinearities, as well as between gain and dissipation, due to the third- and fifth-order nonlinear susceptibilities with opposite signs. With multi-parameter controllability and nonlinear competition in the system, fundamental, dipole, and azimuthally-modulated vortex FWM solitons can transform mutually from one to the other. Such investigations have potential applications in optical pattern formation and control, and all-optical communication.

Nonreciprocity of a six-wave mixing light droplet by a moving electromagnetically induced grating

For the first time, we investigate the nonreciprocal generation of six-wave mixing (SWM) in an inverted-Y type four-level system with spatially uniform distribution of atoms. The nonreciprocity results from a moving electromagnetically induced grating (EIG) which is formed by two coupling beams with different frequencies. We demonstrate that the nonreciprocity can be controlled by the frequencies of the coupling fields and the powers of the dressing beams. As the distribution of atoms is uniform, the atomic density cannot affect the nonreciprocity, but it will affect the formation of the photonic band gap structure of the moving EIG. This research can be used to make optical diodes or optical isolators, because the moving EIG, the speed of which is related to the frequency difference of the two coupling beams, can break time-reversal symmetry. We also demonstrate that the nonreciprocal SWM can form a nonreciprocal light droplet when it propagates in atomic vapors with third- and fifth-order nonlinear susceptibilities.

Cubic-quintic condensate solitons in four-wave mixing

We experimentally investigate the two-dimensional condensate (optical dropletlike) soliton formation and dynamics of the generated signal and probe beams in four-wave mixing (FWM) process with atomic coherence, under competition between the third- and fifth-order nonlinear susceptibilities. With such competing nonlinearities, mutual transformations among dropletlike fundamental, dipole, and azimuthally modulated vortex FWM solitons are observed. The influence of nonlinear competition on the photonic band gap is also investigated. All the results are obtained under low powers.

Investigation of odd-order nonlinear susceptibilities in atomic vapors

We theoretically deduce the macroscopic symmetry constraints for arbitrary odd-order nonlinear susceptibilities in homogeneous media including atomic vapors for the first time. After theoretically calculating the expressions using a semiclassical method, we demonstrate that the expressions for third- and fifth-order nonlinear susceptibilities for undressed and dressed four- and six-wave mixing (FWM and SWM) in atomic vapors satisfy the macroscopic symmetry constraints. We experimentally demonstrate consistence between the macroscopic symmetry constraints and the semiclassical expressions for atomic vapors by observing polarization control of FWM and SWM processes. The experimental results are in reasonable agreement with our theoretical calculations.

Bunching-induced optical nonlinearity and instability in cold atoms [Invited

We report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(⁵) = 7.6 × 10⁻¹⁵ (m/V)⁴, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/10⁵), and enhanced atomic coherence times (> 100 μs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm² in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.

Observation of a Microscopic Cascaded Contribution to the Fifth-Order Nonlinear Susceptibility

Typically, low-order nonlinearities are much stronger than high-order nonlinearities. In this Letter, we demonstrate a procedure by which strong high-order nonlinearities can be synthesized out of low-order nonlinearities. Our procedure involves the use of the previously largely overlooked process of microscopic cascading, which results from local-field effects. We have performed an experiment that allows us to distinguish the influence of microscopic cascading from the more-well-known process of macroscopic cascading, and we find conditions under which microscopic cascading can be the dominant effect. The ability to create a large high-order nonlinear response could prove useful for applications in quantum-information science that require the detection of the simultaneous presence of N entangled photons.

Conical Third-Harmonic Generation in Normally Dispersive Media

It is shown, both theoretically and experimentally, that in normally dispersive media under tight-focusing conditions third harmonic is generated by six-wave mixing rather than via common third-order frequency tripling. Though far-field pattern of third-harmonic signal was an axially symmetric ring for a wide range of the material wave vector mismatch and laser beam focusing conditions, in some cases the generation of more complex beams has been found possible. Results of simulations of the proposed model qualitatively correspond well with experimental data for the calculated values of third- and fifth-order nonlinear susceptibilities of sodium.

Fifth-order phase-sensitive detection of ultrafast polarization beats in cascade four-level system

We study the colour-locked twin-noisy-field correlation effects in the fifth-order nonlinear susceptibility of ultrafast polarization beats in a cascade four-level system. More importantly, the fifth-order phase-sensitive heterodyne detection of ultrafast polarization beats has been exploited. The fifth-order nonlinear optical response can be controlled and modified through the colour-locked correlation of twin noisy fields. Thus, this method with the phase dispersion information is a good way to measure the real and imaginary parts of the fifth-order nonlinear susceptibility.

Six-wave mixing phase-dispersion by optical heterodyne detection in dressed reverse N-type four-level system

We have investigated the dressed effects of non-degenerate four-wave mixing (NDFWM) and demonstrated a phase-sensitive method of studying the fifth-order nonlinear susceptibility due to atomic coherence in RN-type four-level system. In the presence of a strong coupling field, NDFWM spectrum exhibits Autler–Townes splitting, accompanied by either suppression or enhancement of the NDFWM signal, which is directly related to the competition between the absorption and dispersion contributions. The heterodyne-detected nonlinear absorption and dispersion of six-wave mixing signal in the RN-type system show that the hybrid radiation-matter detuning damping oscillation is in the THz range and can be controlled and modified through the colour-locked correlation of twin noisy fields.

Effective AC response of nonlinear metal/dielectric granular composites

T-matrix approach is generalized to study the AC response of nonlinear metal/dielectric granular composites. We have derived general expressions for effective AC response at the fundamental frequency ω and the third harmonic 3ω and the fifth harmonic 5ω. When the components possess real dielectric response, our theoretical work reduces to the one with perturbative method. We take one step forward to perform numerical calculations on the metal/dielectric composites, and the results show that the effective third-order and fifth-order nonlinear susceptibility for fundamental and third-harmonic and fifth-harmonic frequencies can achieve large enhancement near the surface plasmon resonant frequency. Moreover, the resonant frequency exhibits a red-shift with increasing volume fraction of the nonlinear component. In addition, the effect of dimensionality on the effective nonlinear responses is studied.

Characteristics of optical limiting in media with nonlinear absorption and scattering

A comparative study is performed for characteristics of optical limiting in the media with nonlinear absorption and scattering with the use of nanosecond-scale laser pulses. Two methods are proposed to analyze of experimental nonlinear transmittance curves. The experiments revealed differences in the shape of nonlinear transmittance curves in the media with different physical mechanisms of optical limiting. For optical limiting in suspensions of light-absorbing particles, it is concluded that the fifth-order nonlinear susceptibilities should be taken into account.

Spectral representation theory for higher-order nonlinear response in random composites

The higher-order nonlinear response of random two-phase composites is investigated within the spectral representation theory. Both components are assumed to be weakly nonlinear with a displacement ( D )—electric field ( E ) relation of the form D =ϵ i E +χ i| E | 2 E , where ϵ i is the linear dielectric constant and χ i is the third-order nonlinear response of the ith component ( i=1,2). The effective field-dependent dielectric response of the composites is defined as ϵ ̃ e=ϵ e+χ e| E 0| 2+η e| E 0| 4 , where ϵ e , χ e and η e are the effective linear dielectric constant, the effective third-order and fifth-order nonlinear susceptibilities, respectively. By taking into account the correction to the nonlinear local fields, general expressions are derived for χ e and η e to the second order of χ i . We perform numerical calculations on Au/SiO 2 composites with three typical microstructures, described by the Maxwell–Garnett approximation, Bruggeman effective medium approximation and differential effective medium one. Our formulae are then generalized to systems of arbitrary nonlinearity. In the dilute limit, the formulae reduce to those in previous works, as expected. For large volume fractions, our theoretical results are in good agreement with simulation data in nonlinear random resistor networks.

Studies of the fifth-order nonlinear susceptibility of ultraviolet-grade fused silica

Femtosecond transient absorption pump-probe spectroscopy has been used to study the third- and fifth-order nonlinear susceptibility of UV-grade fused silica. Theoretical simulations support the experimental evidence of interference between the third- and fifth-order contributions to the signal. Approximate values of the second-order nonlinear refractive index n(4) and of the three-photon absorption coefficient gamma are obtained.

Nondegenerate multiwave mixing in polydiacetylene: phase conjugation with frequency conversion

We present an analysis of optical phase conjugation with frequency doubling in terms of nondegenerate six-wave mixing fifth-order nonlinear susceptibility. We show how the Bragg phase-matching condition is achieved at small angles. The process under picosecond-pulse conditions in a polydiacetylene solution pumped at two-photon resonance and probed at one-photon resonance is experimentally demonstrated. Results are discussed in terms of a one-dimensional quantum three-level system. The proximity of one- and two-photon resonance in conjugated polymers makes these polymers efficient nonlinear-optical materials for this original application. The experiment permits artifact-free measurement of the two-photon state recovery time of the red form of polydiacetylene.

Nonlinear susceptibility of InSb at the wavelength of 10.6 µ

The nonlinear susceptibilities of InSb were determined at 10.6 µ and their relaxation times were found. In the case of noncoherent signal and reference waves the reflection due to the four-wave interaction was found to be dominated by the third-order nonlinear susceptibility χ(3) ≈10−7 cgs esu with a relaxation time ~10−11 sec. In the coherent interaction case the reflection was dominated by the fifth-order nonlinear susceptibility χ(5)≈10−8 cgs esu with a relaxation time ~10−8 sec.

The Anisotropy of Refraction Nonlinearity and Vector Self-Diffraction. In the Wide-Gap Semiconductors of CdS Type

An anisotropy of the third order nonlinear susceptibility χ(3) and fifth-order nonlinear susceptibility χ(5) is measured within a wide spectral range by the methods of a self interaction in the large gap A2B6-semiconductors. A high anisotropy χ(3) and χ(5) is observed in the vicinity of the absorption edge. The nature of observed anisotropy is studied. This great anisotropy nonlinear susceptibilities is used to record polarization holograms and to realize vector self-diffraction of the light waves with orthogonal polarization. [Russian Text Ignored].

Vector self-diffraction of light waves in cadmium sulfide crystals

Vector self-diffraction of light waves by polarization holograms was observed for the first time experimentally in CdS semiconductor crystals. These holograms were formed using the anisotropy of the fifth-order nonlinear susceptibility χ(5) related to the anisotropy of the two-photon absorption coefficient in the region of resonant contribution of the exciton states. The experimental results were interpreted allowing for the anisotropy of two-photon absorption.