Measurement Of Nonlinear Refraction Research Articles

Measurement of nonlinear refraction and absorption coefficient in BaGa2GeSe6 crystal

The coefficients of nonlinear absorption and nonlinear refraction of the quaternary barium chalcogenide crystal BaGa2GeSe6 at a wavelength corresponding to half the band gap, as well as their dependence on the pulse repetition rate and peak on-axis irradiance, were measured for the first time. The third-order nonlinear optical properties were studied using the single-beam Z-scan technique. An Nd: YLF laser at 1.053 μm with a pulse duration of approximately 5.2 ns was used as a radiation source. In addition, a thermal Z-scan was carried out to investigate thermal lensing in the BaGa2GeSe6 crystal, employing a continuous wave Nd: YAG laser at 1064 nm. These studies represent an important step in comprehending the nonlinear optical properties of barium chalcogenide crystals and their behavior at different pulse intensities. The results might be significant for the modelling and design of mid-infrared optical systems.

Probing the ultrafast gain and refractive index dynamics of a VECSEL

Typically, strong gain saturation and gain dynamics play a crucial role in semiconductor laser mode-locking. While there have been several investigations of the ultrafast gain dynamics in vertical-external-cavity surface-emitting lasers (VECSELs), little is known about the associated refractive index changes. Yet, such refractive index changes do not only have a profound impact on the pulse formation process leading to self-phase modulation, which needs to be compensated by dispersion, but they are also of particular relevance for assessing the feasibility of Kerr-lens mode-locking of VECSELs. Here, we measure both refractive index as well as gain dynamics of a VECSEL chip using the ultrafast beam deflection method. We find that, in contrast to the gain dynamics, the refractive index dynamics is dominated by an instantaneous (∼100 fs) and a very slow component (∼100 ps). The time-resolved measurement of nonlinear refraction allows us to predict a pulse-length dependent, effective nonlinear refractive index n2,eff, which is shown to be negative and on the order of 10−16m2/W for short pulse lengths (∼100 fs). It becomes positive for large excitation fluences and large pulse lengths (few ps). These results agree with some previous reports of self-mode-locked VECSELs for which the cavity design and pulse properties determine sign and strength of the nonlinear refractive index when assuming Kerr-lens mode-locking.

Direct observation of an irradiance dependent nonlinear refraction in CVD single layer graphene

The nonlinear optical properties of single layer graphene are studied via Z-scan. The measurements are carried out at 1045 nm with a 360 femtosecond highly stable Yb doped mode-locked fiber laser. Under laser illumination single-layer graphene exhibits both a transmittance increase due to saturable absorption and a nonlinear phase-shift due to nonlinear refraction. The nonlinear refraction measurements were carried out from 0.5 to 8 GW/cm2 revealing an expected irradiance-dependent nonlinear refraction. An effective nonlinear refractive index coefficient ñI is used to describe this and discriminate it from the conventional n2 coefficient usually measured by Z-scan. The saturation level of the nonlinear phase-shift where the nonlinear response becomes irradiance dependent is deduced from the experimental data.

Ultrafast nonlinear refraction measurements of infrared transmitting materials in the mid-wave infrared.

We utilize the conventional Z-scan technique to provide absolute measurements of third-order nonlinear refraction coefficients (n2) in the mid-wave infrared at 2 µm and 3.9 µm of common optical materials that have transparency windows spanning this regime. We study a variety of narrow band gap and wide band gap semiconductors, fluoride crystals (BaF2, CaF2, LiF, and MgF2) and optical glasses, and a series of chalcogenide glasses. The n2 is found to span on the order of ∼10-15 to ∼10-12 cm2/W for the semiconductors, ∼10-16 cm2/W for the fluoride crystals and glasses, and ∼10-14 to ∼10-13 cm2/W for the chalcogenides. The experimental results are compared to previous measurements of n2 conducted in the visible and near-infrared along with empirical and theoretical formulations.

Ultrafast nonlinear refraction measurements of infrared transmitting materials in the mid-wave infrared

Ultrafast nonlinear refraction measurements of infrared transmitting materials in the mid-wave infrared

Influence of strong light beams on the nonlinear refraction and absorption coefficients of transparent materials

We explore the effective nonlinear (NL) optical response of transparent materials illuminated by strong light beams. Two different setups were used to study the influence of the numerical aperture (NA) corresponding to the collecting lens on the measured coefficients in the open- and closed-aperture Z-scan transmittance. For that, we have reproduced experiments in ${{\rm CS}_2}$CS2 at 532 nm in the picosecond regime using the ${D}4\sigma$D4σ-Z-scan method. It is found that measurements of high-order NL coefficients are not possible after a limit defined by the self-focusing of light inside the cell, and that stimulated light scattering is not significant to explain alone the saturation behavior that occurs in the NL refraction measurements. Indications are given for future Z-scan-based experiments that may clarify the boundary conditions to be respected for the measurement.

Z-scan measurements of nonlinear refraction and absorption for aluminum-doped zinc oxide thin film.

In this paper, we investigate third-order nonlinearities in aluminum-doped zinc oxide (AZO) thin film by the Z-scan method at a wavelength of 1064nm. We carried out experiments under different pulse widths (26ns, 62ns, and 101ns) and energy densities (5.3 J/cm2, 10.6 J/cm2, and 15.9 J/cm2) and obtained the nonlinear absorption coefficient, nonlinear refractive index, and third-order nonlinear susceptibility of AZO thin film. The Z-scan results show that AZO thin film exhibits a larger nonlinear refractive index (-5.48×10-13 m2/W) and third-order nonlinear susceptibility (1.97×10-6 esu) than those of some other semiconductor materials at the wavelength of 1064nm. This suggests that AZO thin film may be a very promising nonlinear medium for nonlinear photonics applications in the tens of nanoseconds regime.

Measurements of nonlinear refraction in the mid-infrared materials ZnGeP2 and AgGaS2

Accurate values of the nonlinear index of refraction n 2 for the nonlinear optical crystals ZnGeP2 and AgGaS2 were measured using the Z-scan technique. The results were obtained using ~100-fs mid-infrared pulses from an OPA-DFG system driven by the 800-nm laser. The measured values of the AGS agree well with the theoretical values based on the two-band model for a direct band gap material. We confirmed the validity of the measured values for the indirect semiconductor ZGP by comparing the results with those obtained at ~1300 nm in a previous study. We have proved the broadening due to GVD is negligible in our experiments. We believe these nonlinear measurements of AGS and ZGP are meaningful for the analysis and design of optical systems in the mid-infrared region.

Comment on “Nonlinear refraction measurements of materials using the moiré deflectometry”

In an influential paper Jamshidi-Ghaleh and Mansour [1] (Opt. Commun. 234 (2004) 419), have reported on a new method for measuring the nonlinear refractive index of materials using the rotational moiré deflectometry technique. In the cited work, the authors apply the ray matrix theory for finding the beam deflection angle on the plane of the first grating in the used geometry. To this end, using the parabolic approximation, the exponential term in the beam irradiance is expanded and retaining the first two resultant terms, the nonlinear sample is treated as a thin lens with a position dependent focal length. In this comment, the effective focal length of the nonlinear sample has been rederived in detail using the Gaussian beam theory and it is shown that it must contain a correction factor. The relative error introduced by ignoring this factor can be as large as 73.5–84.4% in determining the nonlinear refractive index of thin samples.

Using pulse transit delay in Z-scan to discriminate between excited-state absorption and other nonlinear processes in ZnO nanocones

We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.

Measurement of nonlinear refraction of thick samples using nonlinear-imaging technique with a phase object

Abstract The third-order nonlinear refractive index of carbon disulfide (CS2) with different thicknesses is measured by a nonlinear-imaging technique with a phase object (NIT-PO). The propagating characteristics of the laser beam within thick medium are analyzed by numerically solving the electromagnetic wave equation. By theoretically calculating, we study the relationship of the phase shift induced by nonlinear refraction versus medium thicknesses. Fitting the output image with the help of the effective interaction length, the nonlinear refractive index n2 of CS2 can be determined, which suggests a one-single-shot method for the investigation of optical nonlinearity in thick medium.

Sensitivity enhancement for measurement of nonlinear refraction using top-hat beams

A simple and high-sensitivity technique is presented to investigate nonlinear refraction. In this technique, a combination of aperture and obscuration disk is introduced in the measurement system. Compared to the top-hat Z-scan, the curves of modified top-hat Z-scan for the nonlinear refraction show a single peak. Furthermore, the sensitivity of this new technique can be more than two orders of magnitude enhanced. Nonlinear refraction of Nd-doped phosphate glass is investigated using this technique with 19 ps pulses at wavelength of 532 nm.

Experimental techniques using 4f coherent imaging system for measuring nonlinear refraction

In this paper we briefly review experimental techniques exploiting all-optical Fourier image processing inside the 4f system in order to characterize nonlinear refractive indices. Advantages and inconveniences of imaging characterization methods are outlined and their sensitivities are compared in the context of thin films measurements (that is small nonlinear phase-shift). Comparison of imaging methods with well-known nonlinear characterization techniques such as degenerate four wave mixing, I-scan and Z-scan is also done. The influence of nonlinear absorption on sensitivity of nonlinear refraction measurements is discussed.

Measurement of nonlinear refraction using a reversal 4f coherent imaging system with phase objects

A reversal 4f coherent imaging system with phase objects is presented to measure nonlinear refraction of the materials. The modified system can increase the sensitivity compared with the conventional nonlinear-imaging technique with phase objects. The sensitivity enhancement of the modified system is about two times greater than the conventional technique within 0 ≤ Δφ NL ≤ 1. CS 2 is used to demonstrate the measurement using the reversal 4f coherent imaging system with phase objects.

Simple measurement of nonlinear refraction by using a single pulse and beam

A very simple technique, by which both the magnitude and the sign of nonlinear refraction can be determined through using only one single pulse and beam with a phase object, is presented. Using this technique, only the transmittance of an aperture in the far field is investigated. We study the nonlinear refraction of the carbon disulfide by using the presented technique with 21 ps pulses at a wavelength of 532 nm as a test.

Simultaneous measurements of nonlinear refraction and nonlinear absorption using a 4f imaging system

A method is reported to simultaneously measure the nonlinear absorption and refraction coefficients of materials using a nonlinear-imaging technique with a phase object. In this technique, the sign and magnitude of both the nonlinear absorption and refraction can be acquired conveniently from the analysis of three experiment images: the linear image, the nonlinear image and the image without sample. In order to validate our approach, we demonstrate this method for ZnSe at 532 nm where two-photon absorption is present and the nonlinear refractive index n 2 is negative. The values of β (nonlinear absorption coefficient) and n 2 we measured are very close to the values found in other literature.

Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry

Recently the nonlinear effects of the azo-dye doped liquid crystals have attracted much interest. In this paper the nonlinear refractive indices, n 2, of two dyes (Sudan Black B, Sudan III) doped nematic liquid crystal were measured at low laser powers using moiré deflectometry technique. The results show when a nonlinear sample is placed in moiré deflectometry setup, the moiré fringe patterns will rotate around the beam center because of self-focusing effect in the sample. By measuring this rotation, the magnitude and the sign of nonlinear refractive index were calculated. The n 2 values for Sudan black B is larger than Sudan III, because of some differences in molecular structure and molecular polarization.

Optimization of phase objects in 4f coherent imaging system for nonlinear refraction measurements

We numerically analyze the effects of radius and phase shift of phase objects on the diffraction image of the 4f coherent imaging system, a system used for measuring the third-order nonlinear refractive index. The selection of the aperture radius is discussed. We prove that when the phase object radius is 0.1 time of the aperture radius and the phase change of the phase object is 0.57π, one can get the highest sensitivity for nonlinear refraction measurement.

Nonlinear refraction measurements in presence of nonlinear absorption using phase object in a 4f system

We report a technique to measure the value of the nonlinear refractive index of materials in presence of nonlinear absorption using a phase object at the entry of a 4f coherent imaging system. We show that it is possible to obtain a signal approximately due only to the induced nonlinear refraction in presence of two photon absorption. Experimental and simulated Z-scan transmittance profiles with and without phase object, as well as acquired and calculated images are presented here in order to validate our approach. We show also that the use of a reference material simplifies the measurement procedure avoiding computer fits.

Femtosecond Z-scan measurements of nonlinear refraction in amino acid solutions

Abstract We report an investigation of third-order optical nonlinearities in several amino acid solutions using the Z-scan technique with femtosecond laser pulses at 775 nm. The amino acid solutions studied are usually employed for crystal growth, which can be used for ultrashort-pulse second-harmonic generation. The nonlinear refractive index n 2 in these aqueous solutions has been determined to be in the range from 10 −17 to 10 −16 cm 2 /W (second hyperpolaribality γ ranging from 0.9×10 −36 to 3.3×10 −36 esu). No two-photon absorption was observed. The experimental second molecular hyperpolarizabilities obtained for each amino acid are in good agreement with semi-empirical AM1 calculations.