Fresnel diffraction model for mode-mismatched thermal lens with top-hat beam excitation

A theoretical model, based on the Fresnel diffraction integral, is developed to describe the thermal lens (TL) signal in a mode-mismatched collinear configuration, which is optimized for a near field detection scheme and excitation by a cw modulated laser beam with a top-hat profile. The TL amplitudes obtained with both top-hat and Gaussian beam excitations are numerically computed and compared, and the dependence of the TL amplitude on the experimental parameters is discussed. Numerical results show that the top-hat beam TL instrument is more sensitive than the Gaussian beam TL instrument, with a potential doubling of the sensitivity. The use of the top-hat beam excitation with TL detection is a significant improvement because a top-hat beam can be easily obtained with a low-cost, wide-spectral emission white-light source. The use of incoherent light sources as the excitation sources would substantially expand the applicability of the TL technique to the general area of chemical analysis.This revised version was published online in March 2005. In the previous version, the published online date was missing     

A precise data processing method for extracting χ from Z-scan technique

We present a precise data processing method, in the Z-scan experiments using a Gaussian beam and trimmed Airy beam, for directly extracting nonlinear refraction from the closed aperture Z-scan trace with the aid of the open aperture Z-scan trace when the materials exhibit nonlinear refraction and nonlinear absorption simultaneously. This method is still applicable when the nonlinear absorption is dominant and the closed aperture Z-scan curve degenerates into a single valley configuration, which is a salient advantage over other methods. In addition, we give gracefully empirical formulas with very high precision, which have good practicability for characterizing the optical nonlinearities of materials by use of the Gaussian beam and trimmed Airy beam Z-scan technique, respectively.     

Fourier transforms method for measuring thermal lens induced in diluted liquid samples

Drawing on interferometry and Fourier analysis, this paper describes the use of a two-beam thermal lens technique for measuring thermo-optical properties in optical materials. The procedure consists of yield interference patterns deformed by a localized photothermal effect. The photothermal phase shift is locally induced by the pump beam focused on a tested sample located on an on-axis probe beam, which is the first arm of a Mach-Zehnder interferometer. The plane where the effect is localized is imaged onto a CCD camera. Then two interferograms are recorded: one without effect and the other one with the induced photothermal phase. Fourier analysis performed on these interferograms allow us to plot the thermal lens map and, therefore, to estimate thermo-optic constant of Malachite Green in water solution. The method is applied to measure low linear absorptions of a diluted sample of Rhodamine B in water solution at 633 nm, showing that the proposed technique allows to measure photothermal phase shift as low as 3.1 mrad at 8 mW of input power in diluted materials.     

Laser induced thermal profiles in thermally and optically thin films

The temperature field generated by the weak absorption of a gaussian laser beam in an optically and thermally thin film bounded by two transparent plates is discussed. An analytical solution of the problem is presented together with an algorithm for the numerical integration. The influence of the finite thermal conductivity of the plates is shown in an example.     

Laser Mode-Dependent Size of Plasma Zones Induced by Femtosecond Laser Pulses in Fused Silica

We carry out the numerical simulations of femtosecond laser propagation with TEMoo mode, TEM10 mode and a beam combining both the modes in fused silica. It is found that the transverse size of plasma zones induced by laser pulses with the TEM10 mode is smaller than that induced by the TEM00 mode, while the longitudinal size is almost the same, and the saturated plasma density is higher. The transverse size, the longitudinal size and the ratio of the longitudinal to transverse size, for the beam combining both the modes, all could be reduced at the same time in comparison with the TEM00 mode under the same focusing conditions.     

Photorefraction in the ultraviolet: Materials and effects

Doped as well as nominally pure crystals of Lithium Niobate (LiNbO₃), -Arginine Phosphate (LAP), Lithium Iodate (LiIO₃), Potassium Dihydrogen Phosphate (KDP), Lithium Formate (LFM), Beta-Barium Borate (BBO), and lithium tetra borate were grown and investigated for photorefractive effects at ultraviolet wavelengths down to 333 nm. In nominally undoped LiNbO₃ crystals strong beam coupling effects were observed. In contrast to the visible we revealed a diffusion-dominated charge transport mechanism based on holes, and a low photovoltaic field in the order of 550 V/cm. With such a crystal we investigated the modulation transfer function of a lensless image projection system based on a phase conjugation scheme. A spatial frequency response beyond 2800 line pairs per millimeter was observed. Photorefractive beam coupling was also obtained in LiIO₃. Light-induced scattering was detected in iron-doped LiIO₃ whereas as-grown LAP material did not exhibit any observable photorefractive effects. However, 100 kV X-ray irradiation seems to induce material defects which can lead to weak light-induced scattering at 351 nm. In all other above-mentioned materials, doped as well as undoped, light-induced scattering could not be observed. On the other hand, this is appreciated in all the applications where the crystals are used as nonlinear material for optical frequency conversion.     

Efficient ultraviolet photorefraction in LiNbO3

A nominally undoped LiNbO₃ crystal with a slightly broadened absorption edge is used to study beam coupling effects in the UV at 351 nm. At this wavelength the crystal exhibits a diffusion-dominated charge transport mechanism, which allows steady state beam amplification of up to 700 times, comparable to BaTiO₃ in the visible. The used crystal material was characterized by an absorption coefficient =2.68 cm^–1 at 351 nm and a maximal gain coefficient =13.94 cm^–1. This high gain value in the UV can be attributed to a hole diffusion-dominated charge transport mechanism together with a low bulk photovoltaic effect. We measured photovoltaic fields of the order of 550 V/cm.     

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.     

Modeling of two-photon absorption in nonlinear photonic crystal all-optical switch

We present an approach of taking the two-photon absorption effect into account and apply it to analyze an all-optical switch by means of the finite-difference time-domain method. It is shown for a shortened model of the device that the impact of the two-photon absorption on the functionality of the device is drastic. Therefore, under realistic conditions, it should be borne in mind when designing all-optical devices.     

Velocity of pulse propagation in media with amplitude nonlinearity

The propagation velocity of optical wave fronts can be accelerated by the influence of gain saturation. We report systematic measurements for the specific case of Brillouin gain in optical fibers. A simplified analytic rate equation approach permits a qualitative understanding of the observations in terms of a pure amplitude nonlinearity. We point out that there is a close analogy to a mode-locked laser with gain saturation. Pursuing this analogy, we can explain why the changes in propagation velocity are hardly measurable for synchronously pumped lasers, but easily amount to several percent for amplifiers or lasers based on stimulated Brillouin scattering.     

Concatenation of plasma filaments created in air by femtosecond infrared laser pulses

We report the first observation of the attachment of two single plasma filaments created collinearly in the atmosphere by IR femtosecond laser pulses. The linked filamentary structure is electrically conductive and emits sub-THz radiation over its entire length. Concatenation is achieved only for a specific time ordering between the two initial laser pulses. The pulse producing the filament closer to the laser source must be retarded with respect to the other pulse. This special time ordering is attributed to the acceleration of light in a self-guided pulse. Received: 4 March 2003 / Published online: 14 May 2003 RID="*" ID="*"Corresponding author. Fax: +33-1/6931-9996, E-mail: stzortz@ensta.fr     

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.     

Spatio-temporal structure formation and self-diffraction in CdS using laser-induced thermal gratings

The semiconductor CdS is well known to show various kinds of photo-thermal and photo-electric optical nonlinearities. We present here to our knowledge first results of spatiotemporal structure formation using laser-induced thermal gratings in CdS. By the means of an optical multi-channel analyzer the spatial resolution of transverse dynamic switching processes was observed directly. Spatially and time resolved self-diffracted signals were measured in the far-field. The experimental results agree very well with calculations obtained by solving the heat-flow equation and using a fast Fourier transformation. The calculations verify the experimental parameters, in particular the thermal diffusivity D0.1 cm²/s at room temperature. To obtain a better transverse structuring, CdS samples were also investigated which were fixed on a sapphire substrate for longitudinal heat sinking.     

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r)∼E²(r). For ultrathin films of thickness d?λ, the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region.     

Femtosecond filamentation in air at low pressures: Part I: Theory and numerical simulations

We investigate numerically the influence of the pressure on femtosecond filamentation in air. We show that femtosecond filamentation occurs at low pressure and compute the features of the plasma channel generated in the wake of the pulse. We discuss the influence of the pulse duration, chirp and input beam shape on the length of the plasma channels. These calculations constitute a prerequisite for laboratory experiments over short distances as well as for vertical femtosecond filamentation at high altitude on which light detection and ranging techniques or lightning protection rely.     

Measurement of two-photon absorption using the photo-thermal lens effect

We report on new schemes for pump-probe photo-thermal lens methods aimed for measuring the two-photon absorption coefficient of a given material. We show that by focusing a probe beam in the presence of a nearly collimated pump beam, we create a thermal lens which yields measurement of the two-photon absorption coefficient of nitrobenzene of (3.9 ± 0.3) 10⁻¹⁰ cm/W at 532 nm. We also show that when the pump field is focused in the presence of a nearly collimated probe beam the width of the z-scan signature of a two-photon absorption process is nearly one order of magnitude smaller than that of a one-photon process. We show experimental evidence of the effect obtained for nitrobenzene.     

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.     

Femtosecond filamentation in air at low pressures. Part II: Laboratory experiments

We present experimental studies of filamentation of a femtosecond laser pulse in air at low pressures. The evolution of the filament has been studied by measuring along the propagation axis the conductivity and the sub-THz emission from the plasma channel. We show experimentally that the filamentation process occurs at pressures as low as 0.2 atm in agreement with numerical simulations. Experimental and numerical results [A. Couairon, M. Franco, G. Méchain, T. Olivier, B. Prade, A. Mysyrowicz, Opt. Commun., submitted for publication] are compared and the possible sources of discrepancy are discussed.     

Sensitivity enhancement in thermal lens laser spectrometry

A novel experimental configuration for thermal lens detection is described. The method makes use of optical filtering of the probe beam by means of a circular aperture. This considerably reduces noise associated with intensity fluctuations of the probe beam. The technique provides an enhancement of the signal-to-noise ratio by almost one order of magnitude as compared to other thermal lens laser spectrometers. A theoretical calculation of the signal enhancement associated with optical filtering of the probe beam is presented. Furthermore, experiments on methyl blue dissolved in ethylalcohol are described which verify the theoretical predictions.