Frequency Characterization of the Nonlinear Refractive Index in Optical Fiber

The Kerr and the electrostrictive contributions to the intensity-dependent nonlinear refractive index in optical fibers are discussed on both theoretical and experimental bases. Particular attention is devoted to the electrostrictive contribution that under particular conditions is enhanced by resonances. The resonant behavior of the electrostrictive effect is calculated, measured, and discussed for standard single-mode fibers and dispersion shifted fibers. Experimental results are also reported. Measure ments have been carried out with a simple and effective technique based on the cross-phase modulation effect that also allows one to evaluate the nonlinear refractive index at any bit rate. Electrostriction contributes 20 % to the total nonlinear refractive index but in the resonant regime becomes comparable to the Kerr effect.     

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.     

Dynamic lenses in femtosecond filament

We study, both experimentally and numerically, the variations of the refractive index at the filamentation of a femtosecond laser pulse in a fused silica. Using the polarigraphy and shadowgraphy techniques, we investigate the spatio-temporal variations of the refractive index induced by Kerr and plasma nonlinearities. The induced variations of the refractive index play the role of dynamic lenses: focusing for Kerr nonlinearity and defocusing for plasma nonlinearity. We show that intensity saturation occurs at the distance, where the total optical force of Kerr and plasma nonlinear lenses reaches its maximum.     

Non-linear optical properties and all optical switching of Congo red in solution

We present the results from investigations of the nonlinear properties of Congo red solutions using Z-scan technique with a continuous wave argon ion laser at 514 nm. The magnitude and sign of the third-order nonlinear refractive index n₂ of aqueous solution of Congo red were determined. The nonlinear refractive index was found to vary with concentration. Third-order nonlinearity is dominated by nonlinear refractive index, which leads to strong self-defocusing and self diffraction in the samples studied. A pump and probe technique was used to investigate the origin of nonlinearity. Furthermore the nonlinear refractive index effect was utilized to demonstrate all optical switching. The optical limiting behavior based on nonlinear refractive index was investigated.     

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.     

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.     

Nonlinear refractive index measurement of tris(acetylacetonato) manganese(III) solution

We present the results from investigations of the nonlinear refractive index and nonlinear absorption coefficient of tris(acetylacetonato)manganese(III) solution, using Z-scan technique with a low-power continuous-wave laser at 514 nm. We demonstrate that the light-induced nonlinear refractive index variation leads to strong self-focusing and self-defocusing. A pump and probe technique was used to investigate the cause of nonlinearity. Furthermore, the nonlinear absorption effect was utilized to demonstrate all optical switching.     

Optical bistability in Coumarin-450 doped polymeric samples

Experimental observations of optical bistability in Coumarin-450 dye molecule entrapped in polymeric (PMMA) host inside Fabry–Perot cavity have been reported. Efforts have been made to demonstrate the nonlinear behavior of optical materials in solid form using 532 nm of Nd: YAG laser. The nonlinearity in terms of optical bistability and excited state absorption (ESA) has been discussed. The nonlinearity in Coumarin-450 dye molecule originated from unique intensity dependence of the complex index of refraction. It has been observed that nonlinear refraction dominates over nonlinear absorption in giving rise to the optical bistability. Nonlinear refractive index in both polymeric and liquid samples has been calculated.     

Enhanced nonlinear optical responses in metal-glass nanocomposites

The “engineered” nonlinear nanocomposite materials with extremely large values of optical Kerr susceptibility and fast temporal responses that can be precisely tuned to satisfy the requirements of switching applications is of current interest in photonics. Metal quantum-dot composite glasses can exhibit enhanced optical susceptibility, χ⁽³⁾, whose real and imaginary parts are related to the intensity-dependent refractive index and two-photon absorption coefficient, respectively. Classical (dielectric) and quantum confinement effects come into play in the nonlinear optical responses of these nanocomposites. Metal nanocluster-glass composites have been synthesized by 200 keV Cu⁺ and 1.5 MeV Au⁺ ion implantations in fused silica glasses at a dose of 3 × 10¹⁶ ions/cm², followed by thermal annealing in reducing atmosphere to promote cluster growth. UV-Visible spectroscopy has revealed prominent linear absorption bands at characteristic surface plasmon resonance (SPR) frequencies signifying appreciable formation of copper and gold colloids in glass matrices. Third-order optical properties of the composite materials have been studied by Z-Scan and Anti-Resonant Interferometric Nonlinear Spectroscopy (ARINS) measurements. The sign of nonlinear refraction is readily obtained from the Z-Scan signatures. The ARINS technique utilizes the dressing of two unequal-intensity counter-propagating pulsed light beams with differential nonlinear phases, which occur upon traversing the sample if it exhibits nonlinear optical response. This difference in phase manifests itself in the intensity-dependent transmission. The nonlinear refractive index, nonlinear absorption coefficient, the real and imaginary parts of the third-order optical susceptibility have been extracted.     

Scattering behavior of nonabsorbing metallic nanoparticles

The optical property of nanosized metallic particles is unique and size-dependent, which cause color variation. In this work, the relationship between diameter and refractive index of nonabsorbing metallic nanoparticles and their scattering properties is studied by using Mie theory. Obtained results indicate that the optical scattering of metallic nanoparticle depends on their refractive index and diameter. The effect of refractive index on optical scattering depends on the nanoparticle diameter. So that, for very fine nanoparticle (10 nm diameter) the effect of refractive index on scattering is not significant. But the effect of refractive index of large size nanoparticle (700–900 nm diameter) on their optical scattering is higher than fine and medium size nanoparticles. The wavelength with maximum scattering depends on refractive index and nanoparticles diameter. In addition, the colorimetric study indicates that the color of nanoparticle depends on their size and refractive index. So that, the lightness, hue, and colorfulness of nanoparticles is changed by changing size and refractive index.     

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.     

Nonlinear refraction and nonlinear absorption of silver aggregates in a polymeric matrix

The nonlinear optical characteristics of silver aggregates in a polymeric matrix are studied by the Z-scan method at the wavelength λ = 1064 nm. The nonlinear refractive index and the third-order nonlinear susceptibility of a sample with silver aggregates are measured. It is shown that the nonlinear refraction in the sample is related to the Kerr effect. The character of the nonlinear absorption process is discussed.     

Enhanced nonlinearity for filamentation in gold-nanoparticle-doped water

We report a universal approach based on the surface plasmon resonances(SPRs) attained in filamentation in water doped with gold nanoparticles for enhancing the nonlinear refractive index. The filament-induced supercontinuum spectrum in water overlaps with SPRs of gold nanospheres, which further leads to a modification on the Kerr nonlinear refractive index. In our experiment, the measured nonlinear refractive index(n_2) in water doped with gold nanoparticles increases by six times, as compared with that in pure water. Such enhancement may be useful for filament-induced nonlinear applications with modest incident intensity.     

水溶性CdTe量子点的三阶光学非线性极化特性

利用超短脉冲Z扫描技术和光学Kerr效应研究了以巯基丙酸为稳定剂的CdTe量子点水溶液的三阶光学非线性极化特性. 在532nm,30ps和800nm,130fs脉冲激光激发下, 发现分别具有正负相反取值的三阶光学非线性折射率,自由载流子吸收和双光子吸收分别是这两种脉冲激光激发下三阶光学非线性吸收的起因. 测量得到CdTe量子点的三阶光学非线性极化率约为CS₂的32倍, 在520—700nm光谱区的CdTe量子点的光学响应时间小于400fs. 关键词： CdTe量子点(QDs) Z扫描 三阶光学非线性极化特性 双光子吸收     

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.     

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.     

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.     

Nonlinear refractive index of some anthraquinone dyes in 1294-1b liquid crystal

Third order nonlinear refractive index of three anthraquinone dyes, i.e., Solvent Blue 59, Solvent Blue 35 and Solvent Green 3 doped in 1294-1b nematic liquid crystal (NLC) were studied by the single beam Z-scan technique using a continuous-wave He–Ne laser at 632.8 nm. The negative nonlinear refractive index (n₂) in the order of 10^? 5 cm²/w for all samples was obtained. We believe that, this large nonlinearity is owing to Janossy effect and the difference in the nonlinear refractive index of our dyes can be described by the structures of dyes and the interactions between dyes and 1294-1b molecules. So as to understand the effect of dye structure on nonlinearity enhancement, the dichroic ratio of these dyes in 1294-1b was measured using polarized spectroscopy.     

Nonlinear Refractive Index of Er3+-Doped Fiber and Its Application to Nonlinear Fiber Coupler

A large change in the refractive index originating in the transition absorption of erbium ions is induced in an Er³⁺-doped fiber. It is shown that the Er³⁺-doped fiber exhibits the nonlinear refractive index of n₂=7.4 × 10⁻¹⁵ m²/W, which is 10⁵−10⁶ times larger than that caused by the optical Kerr effect in a usual silica fiber at the pumping, wavelength of 514.5 nm. The large nonlinear refractive index occurred in a fiber directional coupler fabricated with the Er³⁺-doped fiber optically changes the coupling condition. The coupling ratio changes up to 0.16 by increasing the pumping power up to 0.7 mW.