High sensitive measurements of absorption coefficient and optical nonlinearities

Accurate knowledge of absorption coefficient of a sample is a prerequisite for measuring the third-order optical nonlinearity of materials, which can be a serious limitation for unknown samples. We introduce a method, which measures both the absorption coefficient and the third-order optical nonlinearity of materials with high sensitivity in a single experimental arrangement. We use a dual-beam pump-probe experiment and conventional single-beam z-scan under different conditions to achieve this goal with communication relevant wavelength. We also demonstrate a counterintuitive coupling of the non-interacting probe-beam with the pump-beam in pump-probe z-scan experiment.     

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.     

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.     

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.     

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.     

Optical and nonlinear optical characteristics of the Ge and GaAs nanoparticle suspensions prepared by laser ablation

The laser ablation of Ge and GaAs targets placed in water and ethanol was carried out using the fundamental radiation of nanosecond Nd:YLF laser. The results of preparation and the optical and nonlinear optical characterization of the Ge and GaAs nanoparticle suspensions are presented. The considerable shift of the band gap energy of the nanoparticles compared to the bulk semiconductors was observed. The distribution of nanoparticle sizes was estimated in the range of 1.5-10 nm on the basis of the TEM and spectral measurements. The nonlinear refractive indices and nonlinear absorption coefficients of Ge and GaAs nanoparticles were defined by the z-scan technique using second harmonic radiation of picosecond Nd:YAG laser (λ = 532 nm).     

Measurement of nonlinear properties and optical limiting ability of Rhodamine6G doped silica and polymeric samples

The third order nonlinear optical properties of Rhodamine6G (Rh6G) doped silica and polymeric samples have been investigated using single beam z-scan technique under excitation by the second harmonic of Nd:YAG laser beam (532 nm). The nonlinear refractive index, nonlinear absorption coefficient, real and imaginary parts of third order nonlinear susceptibility in the samples of silica and poly-methylmethacrylate (PMMA) matrices are measured. Thermal contribution to the nonlinear refractive index in case of undoped silica samples has been calculated in order to have better accuracy of the material response contribution to third order nonlinearity. The comparative study of the optical limiting performance of Rh6G doped silica and polymeric samples show that Rh6G doped silica is relatively superior for optical limiting applications.     

A neat semi-Gaussian laser beam with no diffraction fringes: Theoretical analysis

We propose a simple optical device to convert a Gaussian laser beam into a neat semi-Gaussian laser beam without any diffraction fringe by using a spatial light modulator and a thin, sharp blade, and numerically calculate the diffracted, relative intensity distributions of both the semi-Gaussian laser field and the semi-Gaussian, pseudo-thermal light. We also study the dependence of the border width of the semi-Gaussian beam on the waist of the Gaussian beam. Our study shows that the proposed scheme can be used to cancel all diffraction fringes from both the straight edge of the blade and a finite lens aperture in all the planes vertical to the z axis and obtain a neat semi-Gaussian beam without any diffraction fringe, and find that the border width w_B of the generated semi-Gaussian beam is not dependent on the waist of the incident Gaussian beam.     

Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam

We calculate the radiation force that is exerted by a focused continuous-wave Gaussian beam of wavelength λ on a non-absorbing nonlinear particle of radius a ? 50λ/π. The refractive index of the mechanically-rigid particle is proportional to the incident intensity according to the electro-optic Kerr effect. The force consists of two components representing the contributions of the electromagnetic field gradient and the light scattered by the Kerr particle. The focused intensity distribution is determined using expressions for the six electromagnetic components that are corrected to the fifth order in the numerical aperture (NA) of the focusing objective lens. We found that for particles with a < λ/21.28, the trapping force is dominated by the gradient force and the axial trapping force is symmetric about the geometrical focus. The two contributions are comparable with larger particles and the axial trapping force becomes asymmetric with its zero location displaced away from the focus and towards the beam propagation direction. We study the trapping force behavior versus incident beam power, NA, λ, and relative refractive index between the surrounding liquid and the particle. We also examine the confinement of a Kerr particle that exhibits Brownian motion in a focused beam. Numerical results show that the Kerr effect increases the trapping force strength and significantly improves the confinement of Brownian particles.     

Determination of the lens transmittance of nonabsorbing media using the optical matrix method

The geometrical optics approximation is shown for the first time to be sufficient for determining the lens transparency in the Z-scan method for nonabsorbing media. The diffraction effects are taken into account in calculating the cross section of a focused Gaussian beam. With the use of the matrix method, the lens transparency of a Z-scan scheme is determined as a quantity inverse to the square of its normalized optical power. At a small phase incursion, the expressions for the lens transparency obtained by different methods coincide.     

Z-scan technique for saturable absorption using diffraction method in γ-alumina nanoparticles

In this article, the z-scan method has been corrected for the case of saturation in absorption. Using the principle relations of the changes in the transmitted beam through a Kerr sample and Fresnel–Kirchoff integral method, a proper model is offered to evaluate the electric field in any point of the far field. This model contains both the saturation intensity and nonlinear refractive index simultaneously. Based on this study, a precise method to evaluate the nonlinear indices is obtained. Finally, this model is used in the precise study of z-scan curves for γ-Al₂O₃ nanocolloid and its saturation intensity and nonlinear refractive index have been obtained precisely.     

Composite spatial solitons in a saturable nonlinear bulk medium

We review the generation of the recently predicted multi-component spatial optical solitons in a saturable nonlinear bulk medium. We present numerical simulations for an effectively isotropic model and experimental results for a set of different combinations of a Gaussian beam co-propagating incoherently with a beam of a more complex internal structure, such as a higher order transverse laser mode. We discuss the different formation processes and the general properties of a variety of different dipole-mode composite solitons and expand our investigations to the generation of a quadrupole-mode composite soliton. Received: 1 December 2000 / Revised version: 12 January 2001 / Published online: 21 March 2001     

Thermal diffusivity measurements in a lyotropic discotic nematic phase

The present work is focused on thermal diffusivity (D)$(D)$ measurements, via Z  -scan experiment, in a discotic nematic phase of the lyotropic mixture comprised of potassium laurate, decanol and D₂O${\text{D}}_2\text{O}$. In this experiment, the nematic sample is translated through the focal region of a focused Gaussian laser beam. The experimental data are analyzed according to the thermal lens model and the ratio between the thermal diffusivities parallel (D_∥)$(D_{\parallel })$ and perpendicular (D_⊥)$(D_{\perp })$ to the director of the nematic sample has been found to be smaller than one. The results are compared to others obtained with different liquid crystals and explained by using a simple model where this ratio is correlated to the shape anisotropy of the micelles.     

Measurement of nonlinear optical coefficients by the z-scan technique: Correctness of the technique and investigation of a new compound-lutetium diphthalocyanine complex

Correctness of z-scan measurements of nonlinear refractive indices for optical media is considered. It is shown that accuracy of these measurements is greatly affected by the thickness of the nonlinear medium layer (as compared with the diffraction length of the laser beam). Nonlinear refractive indices of nitrobenzene are measured at different laser pulse durations (7 ns and 350 ps); the nonlinearity mechanism is discussed. It is shown that at the pulse duration 350 ps the orientation mechanism of nonlinearity is less effective than at the pulse duration 7 ns due to its time lag. Nonlinear refractive indices are measured for the solution of a new synthesized compound-hexadecabutyl-substituted lutetium diphthalocyanine.     

Biphotonic effect of azo-dye-doped liquid crystals using the sequential Z-scan technique

This study investigates the biphotonic effect of azo-dye-doped liquid crystals (ADDLCs) using the sequential Z-scan technique. A spot on the sample is illuminated by a green light for 6 s, and then the same spot is illuminated simultaneously with a red light and a green light for 6 s. Measurements are made by scanning the sample near the beam waist of the green laser. The results show that the biphotonic effect is important to the nonlinear coefficient of the sample. The variations of the optical Kerr constant with intensity of red light are measured. Measurement results demonstrate that the molecular reorientation of liquid crystals induced by the photoisomerization of the azo dyes dominates at low red-light intensity, but the thermal effect compensates for the molecular reorientational nonlinearity of the sample at high red-light intensity.     

A novel approach for analyzing open Z-scan experiments

In this work, a novel method for analyzing open Z-scan experiments is presented. It is based on the calculation of the nonlinear absorption parameter q directly from the transmittance measurements. Specifically, we have found an analytic formula describing the dependence of the parameter q on the normalized transmittance. The influence of noise has been studied and the method was proved robust even under conditions of relatively high noise. Extension to the general case of an elliptic Gaussian incident beam has also been realized. The technique has been experimentally tested by analyzing transmittance measurements obtained from a recently synthesized pyrylium salt, illuminated by a femtosecond laser system. The results are in very good agreement with those obtained by the standard Z-scan analysis, especially regarding the nonlinear absorption coefficient β.     

Time analogue of the z-scan technique suitable to waveguides

We propose a new technique to perform measurements of nonlinearities in optical waveguides based on the variation of an optical pulse chirp. This technique is analogous to the z-scan technique in the time domain. We analyze the new experimental method analytically and numerically, obtaining an useful expression relating the nonlinearity with a peak-valley structure. Practical ways to implement the technique are discussed. Received 13 March 2001     

Propagation and interaction of beams with initial phase-front curvature in highly nonlocal media

In this paper, an exact Gaussian solution with initial phase-front curvature for the 1 + 2D Snyder–Mitchell linear model is presented. It is found that the propagation of the beam in bulk strongly nonlocal media is deeply affected by the initial phase-front curvature, which can cause the pulsating behavior of Gaussian beam, and lead to the occurrence of the periodic interference pattern during the interaction of two Gaussian beams. It is useful for further understanding the properties of optical beam in strongly nonlocal media and may be applied to precision measurement.     

Boosting quantum efficiency using multi-stage parametric amplification

We develop a numerical simulation to demonstrate increased quantum efficiency that can be achieved by using a second stage, phase matched crystal to convert signal energy to the idler wavelength. A pair of ZnGeP₂ crystals with walkoff and pump absorption were simulated leading to a tripling of the idler output energy. The output beam characteristics are close to a Gaussian beam with an M² around 1.1.