Theoretical study on stability of Z-scan technique by use of quasi-one-dimensional slit beam

The modified Z-scan technique using the quasi-one-dimensional slit (QODS) beam for characterizing the third-order optical nonlinearity has been reported recently. In the present work, we investigate the effect of the finite length of the slit in the QODS beam Z-scan for the practical experimental conditions, and then give an empirical expression that allows the direct estimation of nonlinear refraction coefficient from the measured normalized peak-valley transmittance difference. In particular, we explore relatively in detail the influences of the sample imperfection on the Z-scan traces, such as the hollow hole of the sample and the nonuniform nonlinearity. Compared with the other Z-scan techniques, such as the top-hat and Gaussian-beam Z-scans, we find that the QODS beam Z-scan has the great improvement for the sample imperfections. The results suggest that the QODS beam Z-scan is a more promising and useful technique for characterizing the optical nonlinearity of an imperfect sample.     

Direct measurement of free carrier nonlinearity in semiconductor-doped glass with picosecond pump-probe Z-scan experiment

We report the direct measurement of free carrier nonlinearity in a semiconductor-doped glass with picosecond pump-probe Z-scan experiment. A strong Z-scan signal from a weak and time delayed probe beam is observed. The probe beam Z-scan signal is comparable in magnitude to the Z-scan signal of the intense pump beam, clearly showing the dominance of the effective fifth order nonlinearity due to the pump beam generated free carriers in the overall nonlinear response of semiconductor-doped glass. The estimated magnitude of the fifth order nonlinearity is consistent with that obtained from earlier reported experiments.     

Theory of Z-scan technique using Gaussian-Bessel beams with a phase object

This paper reports the theoretical study of combining Z-scan technique with Gauss-Bessel (GB) beams beside a phase object (PO) to measure the third-order nonlinear susceptibility components.By using this method,the sign of refractive index which depends on the shape of the close aperture Z-scan curve can be easily determined.Meanwhile,the magnitude of nonlinear coefficients can also be deduced by theoretical fit.The proposed method is advantageous for high sensitivity and imposes a lower stress in the cases of fragile materials,since small pulse energy is enough for the measurement of nonlinear coefficients.Predictions of the models are compared with Gaussian Z-scan measurement and GB Z-scan measurement.By using GB beams with a PO,the sensitivity of Z-scan measurements is found to be a factor of over 60 times greater than for Gaussian beams and 2 times greater than for Gaussian-Bessel beams.     

Theoretical analysis of the off-axis Z-scan method for measuring nonlinear refractive indices

The results of a theoretical analysis of the off-axis Z-scan method for measuring nonlinear refraction are presented. The dependences of the normalized transmittance are calculated for different radii and positions of the aperture. The amplitude T _pv and the distance between the maximum and the minimum Z _pv are analyzed as functions of the aperture size.     

Data analysis of z-scan experiment using Fresnel–Kirchoff integral method in colloidal TiO2 nanoparticles

In this study, a precise method to evaluate nonlinear optical absorption and refraction of materials using z-scan method based on Fresnel–Kirchhoff integral method (FK method) has been offered. The real electric field of a Gaussian beam passing through a nonlinear sample having both nonlinear absorption and refraction has been investigated using FK method. Subsequently, the z-scan curves have been studied. This is the first time that FK method has been used for calculating the nonlinear absorption coefficient. Additionally, an appropriate numerical curve-fitting method for calculating the nonlinear optical coefficients based on z-scan method has been suggested. Z-scan curves and nonlinear optical coefficients have been obtained for TiO₂ nanoparticles in CW irradiation regime with the particle size ranges from 70 to 90 nm. This is the first experimental study which uses this analytical numerical method. Finally, all calculated results extracted from this new method have been compared with those of the previous methods.     

Optical nonlinearities of Au nanoparticles embedded in a zinc oxide matrix

Optical nonlinearities of Au nanoparticles embedded in zinc oxide (ZnO) matrix have been investigated by the Z-scan method at the wavelength of 532 nm using nanosecond Nd³⁺:YAG laser radiation. The nonlinear refractive index has been measured and the real part of the third-order nonlinear susceptibility is deduced. The results of the investigation of nonlinear refraction using the off-axis Z-scan configuration are presented and the mechanisms responsible for the nonlinear response are discussed. The nonlinear refraction is found to be negative (self-defocusing) in the vicinity of the surface plasmon resonance. Moreover, its strength is shown to be larger for materials having higher gold concentration. Finally, the prevailing influence of the electronic Kerr effect over the possible thermo-optical contribution is demonstrated.     

Third-order nonlinear-optical parameters of gold nanoparticles in different matrices

Third-order nonlinear-optical properties of gold nanoparticles embedded in Al₂O₃, ZnO and SiO₂ have been investigated by the Z-scan method at the wavelength of 532 nm using nanosecond Nd³⁺:YAG laser radiation. The nonlinear refractive index, nonlinear absorption coefficient, and the real and imaginary parts of the third-order nonlinear susceptibility are deduced. The results of the investigation of nonlinear refraction using the off-axis Z-scan configuration are presented and the mechanisms responsible for the nonlinear response are discussed. The prevailing influence of the electronic Kerr effect over the possible thermo-optical contribution is demonstrated.     

Investigation on z-scan experiment by use of partially coherent beams

Z-Scan experiment using partially coherent beams is investigated theoretically. We derive the expression for the cross-spectral density of the Gaussian Schell-model (GSM) beam passing through the nonlinear thin sample. Then the influences of the aperture radius and the spatial degree of coherence on the z-scan curves are analyzed. We find that transmittance difference ΔT_p-v between the peak and valley in z-scan curves decreases gradually with the increment of the aperture radius, which is similar to the case of the fully coherent beams. It is also shown that ΔT_p-v is getting bigger with the increment of the spatial degree of coherence α₀, and when α₀ is larger than a certain value, ΔT_p-v becomes almost unchanged. The results show that the z-scan experiment with partially coherent beams may provide a feasible method for measuring the spatial degree of coherence.     

Nonlinear optical properties of gold nanoparticles dispersed in different optically transparent matrices

The nonlinear optical properties of gold nanoparticles dispersed in optically transparent matrices Al₂O₃, ZnO, and SiO₂ are investigated using the classical and off-axis techniques of the Z-scan method at a wavelength of 532 nm (radiation from a nanosecond Nd: YAG laser). The experimental data on the nonlinear refraction in composite materials are obtained. The nonlinear refractive indices and the light absorption coefficients are determined, and the real and imaginary parts of the third-order nonlinear susceptibility for the structures under investigation are calculated. It is demonstrated that, for the composite materials under consideration, the nonlinear properties of the medium under the chosen conditions of laser irradiation are predominantly determined by the Kerr effect and the contribution of this effect exceeds the contribution of the thermal lens.     

Nonlinear properties of polyurethane-urea/multi-wall carbon nanotube composite films

The third-order nonlinear optical properties of polyurethane-urea/multiwalled carbon nanotube composites (PU/MWNT) films with different MWNT concentrations are investigated by the use of the Z-scan technique at a wavelength of 532 nm with a pulse duration of 8 ns. The results reveal that the nonlinear refraction and absorption coefficients are linearly dependent on the MWNT concentration. The negative nonlinear refraction effect is validated from the closed-aperture Z-scan measurements. We find that PU/MWNT films are promising nonlinear optical materials, and the nonlinear coefficients can be controlled.     

Optical characteristics of semiconductor saturable absorber mirrors investigated by the reflection Z-scan technique

Recently, the semiconductor saturable absorber mirror (SESAM) has become a key component of passive mode-locked solid-state lasers. Here we present a simple method based on the reflection Z-scan technique to measure the key optical parameters of SESAM such as saturation fluence and modulation depth. The experimental results demonstrate that our method is able to perform with a high accuracy of 10⁻⁴ and a dynamic range of over four orders of magnitude.     

Nonlinear optical studies of a newly synthesized copolymer containing oxadiazole and substituted thiophenes

We investigated the third-order nonlinear optical properties of a newly synthesized soluble copolymer containing oxadiazole and thiophene units using Z-scan and Degenerate Four Wave Mixing (DFWM) techniques. The measurements were performed at 532 nm with 7 ns pulses from a Nd:YAG laser. We found a good agreement between the values of χ⁽³⁾ determined from both experiments. Z-scan results indicate a negative nonlinear refractive index, n₂, whose magnitude is of the order of 10⁻¹⁰ esu. The copolymer exhibits strong nonlinear absorption and good optical limiting properties at 532 nm, and hence may be a potential material for optical limiting applications.     

Comparative study between interferometric and Z-scan techniques for thermal lensing characterization

This work presents an original, comparative study between two optical techniques for the analysis of thermal lensing induced by a low-power, cw laser beam focused onto a sample cell containing a weak absorbing medium. It deals with an interferometric technique and a Z-scan technique in real time. The interferometric method permits the determination of the spatial profile of the thermal lens. The development of the work puts in evidence the high sensitivity of both techniques for the detection and measurement of low absorption coefficients and refractive index changes in dye solutions at very low concentrations. Improvements in the sensitivity of both methods can make possible the measurement of very small phase shift distortions of the wavefront. One shows also the mutual complementary character of two techniques for the characterization and measurement of linear and nonlinear properties of materials.     

Method for measurements of second-order nonlinear optical coefficient based on Z-scan

The method for measuring second-order nonlinear optical coefficients based on well-known Z-scan is presented. The influence of linear absorption coefficients on normalized transmittance is discussed. Using this method, we obtained the second-order nonlinear coefficient d₃₁(5%MgO:LiNbO₃) = 4.5 × 10⁻¹² m/v at 1064 nm, which agrees well with theoretical calculations and previous well-known values.     

The nonlinear refraction and absorption dependence on the thermal effect for 4 ns pulse duration in binuclear Zn(II) phthalocyanine solution

The influence of thermal effect on the third-order nonlinear optical properties of binuclear Zn(II) phthalocyanine in chloroform solution was studied. The nonlinear refraction and absorption of the sample was measured by using Z-scan technique with 4 ns laser pulses at 532 nm wavelength. The opposite signs of the effective nonlinear refraction index were observed by changing the focal length of focusing lens from 10 cm to 20 cm in the experimental setup. Changing the focusing lens increased the beam waist radius from 7 μm to 20 μm. The nonlinear absorption coefficient was reduced about 200 times based on changing the fluence or beam waist radius. The drastic changes in the third-order nonlinear optical parameters were attributed to thermal effect. To investigate the role of thermal effects even further the effective nonlinear refraction and absorption coefficients were studied by using different repetition rates, input powers and concentrations.     

一种新型非晶态分子材料的非线性光学折射率和吸收特性

用单光束扫描法测量了在532nm处一种新型非晶态分子材料5,5′Bis(dimesitylboryl)2,2′bithiophene的非线性折射率和吸收系数样品非线性透射特性的分析表明,在靠近线性吸收区的532nm处有饱和吸收存在由三能级饱和模型和Zscan法确定了饱和强度、非线性折射率的实部和虚部研究结果表明:这种新型非晶态分子材料具有非常好的光子学应用前景.     

Nonlinear optical characteristics of colloidal solutions of metals

Results of the study of nonlinear optical parameters of colloidal solutions of silver, gold, platinum, and copper by the Z-scan method are presented. The nonlinear refractive indices of these solutions at the wavelength of the Nd:YAG laser (λ=1064 nm) and its second harmonic (λ=532 nm) were measured. The two-photon absorption of these solutions and their nonlinear susceptibilities were studied.     

Nonlinear optical characteristics of polymethine dyes

Nonlinear refraction, nonlinear absorption, and saturated absorption of a number of polymethine dyes are studied and their nonlinear optical parameters are measured by the Z-scan method (λ=1064 nm). Simultaneous occurrence of several nonlinear optical processes in the case of excitation of dye solutions by picosecond pulses is analyzed. Saturated absorption of dye solutions is considered in terms of different models.     

Nonlinear optical and optical power limiting studies on a new thiophene-based conjugated polymer in solution and solid PMMA matrix

An experimental investigation of the third-order nonlinear optical properties of new poly{2-{5-[3,4-ditetradecyloxy-5-(1,3,4-oxadiazol-2-yl)thiophen-2-yl]-1,3,4-oxadiazol-2-yl}pyridine} (P) in tetrahydrofuran (THF) solution and in solid poly(methylmethacrylate) (PMMA) matrix, by Z-scan technique is reported. The Z-scan traces reveal that the composite films exhibit large negative nonlinear refractive index of the order 10⁻¹⁰ esu. The excited-state absorption cross-section was found to be larger than the ground-state absorption indicating that the operating nonlinear process is reverse saturable absorption (RSA). The new polymer P exhibits good optical power limiting properties in the nanosecond regime in solution and as well in solid PMMA matrix.     

Preparation and the optical nonlinearity of surface chemistry improved titania nanoparticles in poly(methyl methacrylate)-titania hybrid thin films

With 800-nm, 120-fs laser pulses, optical nonlinearity has been studied in a series of thin films containing poly(methyl methacrylate) (PMMA), filled with surfactant acetylacetone (Acac) capped TiO₂ nanoparticles, which were synthesized by a simple in situ sol-gel/polymerization process, assisted by spin coating and multi-step baking. The resulting nanohybrid thin films have highly optical transparency and demonstrate a unique nonlinear optical (NLO) response. The highest nonlinear refractive index (n₂) is observed up to 6.55 × 10⁻² cm² GW⁻¹ in the nanohybrid thin film of 60 wt% Ti(OBu)₄ in PMMA, with a negligible two-photon absorption (TPA), as confirmed by the Z-scan technique. The titanium precursor loading combined with the nature of the capping molecules are used to influence the ability of nanoparticles to nonlinear optical response. Indeed, the ligands at the nanoparticles’ surface can not only control the extent of the interaction between the organic molecules and the embedded nanoparticles but also influence the optical nonlinearities of nanoparticles.