Giant Enhancement and Sign Inversion of Optical Kerr Nonlinearity in Random High Index Nanocomposites near Mie Resonances

High-index dielectric nanoantennas excited at Mie-type resonances have exhibited enormous enhancement of optical nonlinearity. Such nanostructures have been actively studied by researchers in recent years. Here, a numerical analysis study of the optical Kerr effect of nanocomposites consisting of high refractive index (GaP) spheres at the wavelength of 532 nm is presented. This is done by means of 3D finite-difference time-domain simulations. The effective nonlinear refractive index of 0.8 µm thick nanocomposites and metasurfaces is evaluated. It is shown that the optical Kerr nonlinearity of the nanocomposites rises by orders in proximity to Mie resonances and may exceed the second-order refractive index of the bulk material. It is revealed that the sign of the effective optical Kerr coefficient is inverted near the Mie resonances. This effect may be of interest in developing nonlinear optical metadevices.     

Theoretical study of saturable Kerr nonlinearity using top-hat beam Z-scan technique

Saturable Kerr nonlinearity is theoretically investigated by use of the top-hat beam Z-scan technique. The saturation intensity changes the nonlinear refractive profile and decreases the sensitivity of the Z-scan measurements, which were quantitatively analyzed. An empirical formula for the saturable Kerr nonlinearity, which gave the relationship between the light intensity and the peak-valley transmittance difference, was accomplished. A high-accuracy method to determine the nonlinear refractive index and the characteristic saturation intensity was proposed.     

Femtosecond filament induced birefringence in argon and in air: Ultrafast refractive index change

The birefringence of a linearly polarized femtosecond laser filament in gases has been previously established. In this work, we report the time-dependent refractive index measurements of the filament based upon the spectral modulation of a weak probe pulse in air and in argon gas at 1 atmospheric pressure. The polarization dependence of the refractive index modulation induced by the delayed molecular alignment and by the electronic Kerr effect is highlighted. A numerical simulation of the refractive indices, which takes into account the molecular alignment, the electronic Kerr non-linearity and the plasma, is in good agreement with the measurements.     

Size and dielectric dependence of the third-order nonlinear optical response of Au nanocrystals embedded in matrices

The third-order nonlinear optical response of Au nanocrystals embedded in BaTiO(3) and ZrO(2) matrices was investigated through the off-resonance femtosecond optical Kerr effect. Compared with pristine films, the nonlinearity of composite films shows an enhancement that depends on the sizes of Au particles and the refractive index of the matrices. We performed a calculation based on Lorenz-Mie scattering theory to explain the experimental results. Additionally, the nonlinearity was optimized by determination of the values of the particle size and the refractive index of the matrix.     

Microwave generator based on tunnel-coupled semiconductor-metamaterial structure

We propose a model of a tunable laser based on a tunnel-coupled waveguide semiconductormetamaterial structure. The waveguide semiconductor channel has a positive refractive index and a high Kerr nonlinearity coefficient. In the frequency range under investigation, the channel formed by the magnetoactive metamaterial is characterized by a negative refractive index. Computer simulation is used for investigating the peculiarities of generation of microwave radiation under pumping due to modulated instability in the semiconductor channel and a distributed feedback. The generation frequency is controlled using the dependence of the refractive index of the metamaterial on the external magnetic field.     

Measurement of the frequency response induced by electrostriction in optical fibers

Accurate measurements of the frequency response of the nonlinear refractive index induced by the combined effects of Kerr nonlinearity with electrostrictional excitation of acoustic waves in optical fibers are presented. A detailed experimental investigation of both standard (zero-dispersion wavelength,lambda(0) approximately 1.31microm) and dispersion-shifted (lambda(0)=1.55microm) single-mode fibers showed the presence of several resonant peaks induced by the electrostrictive nonlinearity in the fiber structure. This investigation has provided better insight into the frequency behavior of the electrostriction-induced acoustic waves in optical fibers.     

Zero-n gap soliton

Periodic structures consisting of alternating layers of positive-index and negative-index materials have a novel bandgap at the frequency at which the average refractive index is zero. We show that, in the presence of a Kerr nonlinearity, this zero-n gap can switch from low transmission to a perfectly transmitting state, forming a nonlinear resonance or gap soliton in the process. This zero-n gap soliton is omnidirectional, in contrast to the usual Bragg gap soliton of positive-index periodic structures.     

Dissipative discrete spatial optical solitons in a system of coupled optical fibers with the Kerr and resonance nonlinearities

The propagation of monochromatic radiation in a system of weakly coupled single-mode optical fibers with saturable amplification and absorption and Kerr nonlinearity of the refractive index is analyzed. Conditions of stability and bistability of plane-wave regimes are determined. Discrete dissipative optical solitons are found and their stability is studied. The hysteresis dependences of the peak intensity of the discrete solitons on the value of the Kerr nonlinearity and the input beam intensity are demonstrated. The numerical estimates of the parameters of the spatial dissipative discrete solitons are presented.     

Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time

We investigated the spatiotemporal modulation instability (MI) in a medium with a non-instantaneous Kerr response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. The expression for the MI gain spectrum in non-instantaneous Kerr medium is obtained, which clearly reveals the influence of the finite time of the nonlinear response (relaxation effect) on the spatiotemporal MI. It is shown that, due to the relaxation effect, the spatiotemporal MI can appear for the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in instantaneous Kerr medium for the same case, and a new MI gain spectrum appears, adding to the conventional MI gain spectrum similar to that in an instantaneous Ker medium. In addition, the bandwidth of MI gain spectrum is extended and the maximum MI gain is reduced with increasing of the relaxation time. Interestingly, spatiotemporal MI can appear for any spatial frequencies in non-instantaneous Kerr medium for any combination of dispersion and nonlinearity. We have performed an experiment of MI in carbon disulfide (CS₂), a typical non-instantaneous Kerr medium, which shows quantitative agreement with the theoretical analyses.     

Surface waves in a crystal with switching Kerr nonlinearity

In this paper, we explore transverse electric surface waves propagating along the crystal with jump change of Kerr nonlinearity in dependence on field amplitude. The dielectric permittivity in the proposed model of nonlinearity is characterized by abruptly changing unperturbed dielectric constant and Kerr nonlinearity coefficient from one value to another when field amplitude exceeds the threshold value of the switching field. This allows to find exact solutions of model equations in different cases of nonlinearity signs, and to obtain the dependence of wave characteristics, including total power flux, on effective refractive index in explicit form. Such solutions describe two new types of nonlinear surface waves with specific structure depending on electric field amplitude. We derive the conditions of surface domain formation. It is found that the largest percentage of radiation is concentrated within the domain.     

Propagation characteristics of nonlinear optical fibers with complex refractive index. A transmission line model approach

The transmission line model has been modified in order to evaluate nonlinear waves guided by optical fibers with complex refractive index. It is proven that the proposed model is able to tackle fibers with losses or gain, under the presence of arbitrary nonlinearity. The method is applied for the calculation of weakly guided lossy nonlinear optical fibers considering various configurations and Kerr nonlinearity. Power depended propagation characteristics have been calculated and plotted for the fundamental mode and the potential use of the method in optical fiber amplifiers with index nonlinearity is also discussed.     

Saturation of the all-optical Kerr effect in solids

We discuss the influence of the higher-order Kerr effect (HOKE) in wide bandgap solids at extreme intensities below the onset of optically induced damage. Using different theoretical models, we employ multiphoton absorption rates to compute the nonlinear refractive index by a Kramers-Kronig transform. Within this theoretical framework we provide an estimate for the appearance of significant deviations from the standard optical Kerr effect predicting a linear index change with intensity. We discuss the role of the observed saturation behavior in practically relevant situations, including Kerr lens mode-locking and supercontinuum generation in photonic crystal fibers. Furthermore, we present experimental data from a multiwave mixing experiment in BaF2, which can be explained by the appearance of the HOKE.     

Observation of large Kerr nonlinearity at low light intensities

We report an experimental observation of large Kerr nonlinearity with vanishing linear susceptibilities in coherently prepared four-level rubidium atoms. Quantum coherence and interference manifested by electromagnetically induced transparency suppress the linear susceptibilities and greatly enhance the nonlinear susceptibilities at low light intensities. The measured Kerr nonlinearity is comparable in magnitude to the linear dispersion in a simple two-level system and is several orders of magnitude greater than the Kerr nonlinearity of a conventional three-level scheme under similar conditions.     

Control of Group Velocity via Spontaneous Generated Coherence and Kerr Nonlinearity

A four-level N-type atomic medium is considered to study the effect of spontaneous generated coherence(SGC) and Kerr nonlinearity on light pulse propagation. A light pulse is propagating inside the medium where each atom follows four-level N-type atom-field configuration of rubidium(85Rb) atom. The atom-field interaction leads to electromagnetically induced transparency(EIT) process. The atom-field interaction is accompanied by normal dispersion and in the presence of SGC and Kerr nonlinearity the dispersion property of the proposed atomic medium is modified,which leads to enhancement of positive group index of the medium. The enhancement of positive group index then leads to slow group velocity inside the medium. A more slow group velocity is also investigated by incorporated the collective effect of SGC and Kerr nonlinearity. The control of group velocity inside a four-level N-type atomic medium via collective effect of SGC and Kerr nonlinearity is the major part of this work.     

Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption

3 crystal have been measured using Z-scan technique with picosecond pulses at 532 nm. The nonlinear absorption coefficient and nonlinear refractive index are determined to be 2.5×10^-10 cm/W and 5.3×10^-15 cm²/W, respectively. Both sign and magnitude of the measured refractive nonlinearity are considerably different from the reported Z-scan results in LiNbO₃ obtained with cw laser beam at 514 nm. The nonlinearities in LiNbO₃ induced by 532 nm picosecond pulses are believed to be mainly due to two-photon absorption and bound electronic Kerr effect associated with the two-photon absorption. Received: 4 July 1996     

Enhancement of Kerr nonlinearity via spontaneously generated coherence in a four-level N-type atomic system

A theoretical investigation is carried out into the effect of spontaneously generated coherence (SGC) on Kerr nonlinearity of a four-level N-type system. It’s found that the Kerr nonlinearity can be obviously enhanced with SGC present. We attribute the enhancement of Kerr nonlinearity mainly to the generation of extra coherences induced by the superposition of the two SGC channels, and when the superposition is controlled by the interference between two SGC channels properly, the maximal Kerr nonlinearity does not only enter the electromagnetically induced transparency window as the spontaneous generated coherences intensify, but also gets enhanced about 10 times with very large SGC coefficients than that with no SGC effect.     

Control of Group Velocity via Spontaneous Generated Coherence and Kerr Nonlinearity

A four-level N-type atomic medium is considered to study the effect of spontaneous generated coherence (SGC) and Kerr nonlinearity on light pulse propagation. A light pulse is propagating inside the medium where each atom follows four-level N-type atom-field configuration of rubidium (⁸⁵Rb) atom. The atom-field interaction leads to electromagnetically induced transparency (EIT) process. The atom-field interaction is accompanied by normal dispersion and in the presence of SGC and Kerr nonlinearity the dispersion property of the proposed atomic medium is modified, which leads to enhancement of positive group index of the medium. The enhancement of positive group index then leads to slow group velocity inside the medium. A more slow group velocity is also investigated by incorporated the collective effect of SGC and Kerr nonlinearity. The control of group velocity inside a four-level N-type atomic medium via collective effect of SGC and Kerr nonlinearity is the major part of this work.     

A Quantum Interpretation of Light Scattering near the Boundary between Transparent Media with Kerr Nonlinearity

The transformation of light by a nonlinear beamsplitter is considered. The beamsplitter is formed by a plane interface between two transparent dielectrics, at least one of which has a Kerr nonlinearity; i.e., its refractive index depends on the intensity of the penetrating radiation. It is shown that the interpretation of the result of calculation of quantum fields at the outputs from such a beamsplitter indicates a violation of the principle of causality in the sense that a subsequent event affects the previous one.     

Photoconductivity,photoluminescence and optical Kerr nonlinear effects in zinc oxide films containing chromium nanoclusters

Chromium doped zinc oxide thin solid films were deposited on soda–lime glass substrates. The photoconductivity of the material and its influence on the optical behavior was evaluated. A non-alkoxide sol–gel synthesis approach was used for the preparation of the samples. An enhancement of the photoluminescence response exhibited by the resulting photoconductive films with embedded chromium nanoclusters is presented. The modification in the photoconduction induced by a 445 nm wavelength was measured and then associated with the participation of the optical absorptive response. In order to investigate the third order optical nonlinearities of the samples, a standard time-resolved Optical Kerr Gate configuration with 80 fs pulses at 830 nm was used and a quasi-instantaneous pure electronic nonlinearity without the contribution of nonlinear optical absorption was observed. We estimate that from the inclusion of Cr nanoclusters into the sample results a strong optical Kerr effect originated by quantum confinement. The large photoluminescence response and the important refractive nonlinearity of the photoconductive samples seem to promise potential applications for the development of multifunctional all-optical nanodevices.