Optical detection of the ultrasound-induced pulsed thermal lens close to the ice-water phase transition.

Piezo-optic and thermo-optic coefficients are important material properties that play a critical role in the design and optimization of many optical devices. The ability to accurately measure and control these coefficients is essential for achieving high performance and reliability in a wide range of applications. In this article, we use the optical detection of the ultrasound-induced thermal lens effect to investigate these properties for water at low temperatures. The results show that the anomalous behavior of water around 4°C is easily observed. The thermal lens method is used to determine the temperature dependence of the piezo-optic and thermo-optic coefficients.

Laser induced thermoelastic surface displacement in solids detected simultaneously by photothermal mirror and interferometry.

We propose a combined pump-probe optical method to investigate heat diffusion properties of solids. We demonstrate single-shot simultaneous laser-induced thermoelastic surface displacement of metals detected by concurrent measurements using photothermal mirror and interferometry. Both methods probe the surface displacement by analyzing the wavefront distortions of the probe beams reflected from the surface of the sample. Thermoelastic properties are retrieved by transient analysis in combination with numerical description of the thermoelastic displacement and temperature rise in the sample and in the surrounding air. This technique presents a capability for material characterization that can be extended to experiments for quantitative surface mapping.

Modeling population and thermal lenses in the presence of Auger Upconversion for Nd(3+) doped materials.

We present a theoretical model to thermal (TL) and population (PL) lenses effects in the presence of Auger upconversion (AU) for analysis of Nd(3+) doped materials. The model distinguishes and quantifies the contributions from TL and PL. From the experimental and theoretical results, the AU cannot be neglected because it plays an important role on the excited state population and therefore on the temperature and polarizability difference between excited and ground states. Considering the extensive use of these techniques, the model presented here could be useful for the investigation of materials and also to avoid misleading analysis of lenses transients.

Discriminating the role of sample length in thermal lensing of solids.

Thermal lens (TL) is a key effect in laser engineering and photothermal spectroscopy. The amplitude of the TL signal or its dioptric power is proportional to the optical path difference (OPD) between the center and border of the beam, which is proportional to the heat power (Ph). Due to thermally induced mechanical stress and bulging of end faces of the sample, OPD depends critically on the geometry of the sample. In this investigation, TL measurements were performed as a function of the sample length keeping the same Ph. It is experimentally demonstrated that for materials with positive ∂n/∂T OPD increases typically 30 to 50% with the decrease of sample length (from long rod to thin-disk geometry). For materials with negative ∂n/∂T, this variation is much larger due to the cancelation of the different contributions to OPD with opposite signs. Furthermore, the experimental investigation presented here validates a recently proposed unified theoretical description of the TL effect.

Role of photophysics processes in thermal lens spectroscopy of fluids: a theoretical study.

Photophysics processes are ubiquitous in nature and difficult to be quantitatively characterized by conventional spectroscopy. Alternatively, pump-probe methods have been widely applied to study these complex processes. In this context, the thermal lens technique is a precise spectroscopic tool for material characterization and presents a wide range of applications in chemical analysis. Here, we present an all numerical approach to analyze the dynamics of photophysics processes and to identify the role of individual contributions of photoreaction and mass diffusion in the thermal lens experiments. The results are essential for a proper understanding of the dominant physical mechanisms in laser-induced photodegradation, which allow precise data analysis of the effects in photosensitive fluids.

Pulsed photothermal mirror technique: characterization of opaque materials.

The time-resolved thermal mirror technique is developed under pulsed laser excitation for quantitative measurement of thermal and mechanical properties of opaque materials. Heat diffusion and thermoelastic equations are solved analytically for pulsed excitation assuming surface absorption and an instantaneous pulse. Analytical results for the temperature change and surface displacement in the sample are compared to all-numerical solutions using finite element method analysis accounting for the laser pulse width and sample geometry. Experiments are performed that validate the theoretical model and regression fitting is performed to obtain the thermal diffusivity and the linear thermal expansion coefficient of the samples. The values obtained for these properties are in agreement with literature data. The technique is shown to be useful for quantitative determinations of the physics properties of metals with high thermal diffusivity.

Towards a comprehensive characterization of spatio-temporal dependence of light-induced electromagnetic forces in dielectric liquids.

The interaction of localized light with matter generates optical electrostriction within dielectric fluids, leading to a discernible change in the refractive index of the medium according to the excitation's light profile. This optical force holds critical significance in optical manipulation and plays a fundamental role in numerous photonic applications. In this study, we demonstrate the applicability of the pump-probe, photo-induced lensing (PIL) method to investigate optical electrostriction in various dielectric liquids. Notably, the thermal and nonlinear effects are observed to be temporally decoupled from the electrostriction effects, facilitating isolated observation of the latter. Our findings provide a comprehensive explanation of optical forces in the context of the recently introduced microscopic Ampère electromagnetic formalism, which is grounded in the dipolar approximation of electromagnetic sources within matter and characterizes electrostriction as an electromagnetic-induced stress within the medium. Here, the optical force density is re-obtained through a new Lagrangian approach.

Modeling the population lens effect in thermal lens spectrometry.

We report a theoretical model and experimental results for laser-induced lensing in solids. The model distinguishes and quantifies the contributions from population and thermal effects. Laser-induced lensing in ytterbium-doped fluorozirconate glass ZBLAN:Yb(3+) is measured, and the thermal and optical properties obtained from analyzing the data with the proposed model agree well with published values. Photothermal techniques are used extensively for the investigation of laser and laser-cooling materials, and the model developed here enables the interpretation of convoluted laser-induced lensing signals that have contributions from different sources.

Resonant excited state absorption and relaxation mechanisms in Tb3+-doped calcium aluminosilicate glasses: an investigation by thermal mirror spectroscopy.

Resonant excited state absorption (ESA) and relaxation processes in Tb(3+)-doped aluminosilicate glasses are quantitatively evaluated. A model describing the excitation steps and upconversion emission is developed and applied to interpret the results from laser-induced surface deformation using thermal mirror spectroscopy. The fluorescence quantum efficiency of level (5)D(4) was found to be close to unity and concentration independent while, for the level (5)D(3), it decreases with Tb(3+) concentration. Emission spectroscopy measurements supported these results. ESA cross sections are found to be more than three orders of magnitude higher than the ground state absorption cross section.

The role of electrostriction in the generation of acoustic waves by optical forces in water.

We present semi-analytical solutions describing the spatiotemporal distributions of temperature and pressure inside low-absorbing dielectrics excited by tightly focused laser beams. These solutions are compared to measurements in water associated with variations of the local refractive index due to acoustic waves generated by electrostriction, heat deposition, and the Kerr effect at different temperatures. The experimental results exhibited an excellent agreement with the modeling predictions, with electrostriction being the dominant transient effect in the acoustic wave generation. Measurements at 4 . 0 ∘ C show that the thermoelastic contribution to the optical signal is significantly reduced due to the low thermal expansion coefficient of water at this temperature.

Unveiling bulk and surface radiation forces in a dielectric liquid.

Precise control over light-matter interactions is critical for many optical manipulation and material characterization methodologies, further playing a paramount role in a host of nanotechnology applications. Nonetheless, the fundamental aspects of interactions between electromagnetic fields and matter have yet to be established unequivocally in terms of an electromagnetic momentum density. Here, we use tightly focused pulsed laser beams to detect bulk and boundary optical forces in a dielectric fluid. From the optical convoluted signal, we decouple thermal and nonlinear optical effects from the radiation forces using a theoretical interpretation based on the Microscopic Ampère force density. It is shown, for the first time, that the time-dependent pressure distribution within the fluid chiefly originates from the electrostriction effects. Our results shed light on the contribution of optical forces to the surface displacements observed at the dielectric air-water interfaces, thus shedding light on the long-standing controversy surrounding the basic definition of electromagnetic momentum density in matter.

Soret effect and photochemical reaction in liquids with laser-induced local heating.

We report a theoretical model and experimental results for laser-induced local heating in liquids, and propose a method to detect and quantify the contributions of photochemical and Soret effects in several different situations. The time-dependent thermal and mass diffusion equations in the presence and absence of laser excitation are solved. The two effects can produce similar transients for the laser-on refractive index gradient, but very different laser-off behavior. The Soret effect, also called thermal diffusion, and photochemical reaction contributions in photochemically reacting aqueous Cr(VI)-diphenylcarbazide, Eosin Y, and Eosin Y-doped micellar solutions, are decoupled in this work. The extensive use of lasers in various optical techniques suggests that the results may have significance extending from physical-chemical to biological applications.

Thermo-optical characteristics and concentration quenching effects in Nd3+ doped yttrium calcium borate glasses.

In this work we present a comprehensive study of the spectroscopic and thermo-optical properties of a set of samples with composition xNd(2)O(3)-(5-x)Y(2)O(3-)40CaO-55B(2)O(3) (0 ≤ x ≤ 1.0 mol%). Their fluorescence quantum efficiency (η) values were determined using the thermal lens technique and the dependence on the ionic concentration was analyzed in terms of energy transfer processes, based on the Förster-Dexter model of multipolar ion-ion interactions. A maximum η = 0.54 was found to be substantially higher than for yttrium aluminoborate crystals and glasses with comparable Nd(3+) content. As for the thermo-optical properties of yttrium calcium borate, they are comparable to other well-known laser glasses. The obtained energy transfer microparameters and the weak dependence of η on the Nd(3+) concentration with a high optimum Nd(3+) concentration put this system as a strong candidate for photonics applications.

Nonlocal model for nematic liquid-crystal elastomers.

We have developed a fully nonlocal model to describe the dynamic behavior of nematic liquid-crystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these order parameters is taken into account through nonlocal interactions rather than through the use of gradient expansions. We also give an expression for the Rayleigh dissipation function. The equations of motion for displacement and orientational order are obtained from the free energy and the dissipation function by the use of a Lagrangian approach. We examine the free energy and the equations of motion in the limit of long-wavelength and small-amplitude variations of the displacement and the orientational order parameter. We compare our results with those in the literature. If the scalar order parameter is held fixed, we recover the usual viscoelastic theory for nematic liquid crystals.

General solution of the diffusion equation with a nonlocal diffusive term and a linear force term.

We obtain a formal solution for a large class of diffusion equations with a spatial kernel dependence in the diffusive term. The presence of this kernel represents a nonlocal dependence of the diffusive process and, by a suitable choice, it has the spatial fractional diffusion equations as a particular case. We also consider the presence of a linear external force and source terms. In addition, we show that a rich class of anomalous diffusion, e.g., the Lévy superdiffusion, can be obtained by an appropriated choice of kernel.

Logarithmic diffusion and porous media equations: a unified description.

In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a Lorentzian form, consequently this equation characterizes a superdiffusion like a Lévy kind. In addition an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension, is obtained. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.

Investigation into photostability of soybean oils by thermal lens spectroscopy.

Assessment of photochemical stability is essential for evaluating quality and the shelf life of vegetable oils, which are very important aspects of marketing and human health. Most of conventional methods used to investigate oxidative stability requires long time experimental procedures with high consumption of chemical inputs for the preparation or extraction of sample compounds. In this work we propose a time-resolved thermal lens method to analyze photostability of edible oils by quantitative measurement of photoreaction cross-section. An all-numerical routine is employed to solve a complex theoretical problem involving photochemical reaction, thermal lens effect, and mass diffusion during local laser excitation. The photostability of pure oil and oils with natural and synthetic antioxidants is investigated. The thermal lens results are compared with those obtained by conventional methods, and a complete set of physical properties of the samples is presented.

Average entropy of a subsystem from its average Tsallis entropy.

In the non-extensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem [Phys. Rev. Lett. 71, 1291 (1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space dimension is mn, is considered, the average Tsallis entropy of an m-dimensional subsystem is obtained. This demonstration is expected to be useful to study systems where the usual entropy does not give satisfactory results.

q-exponential distribution in urban agglomeration.

Usually, the studies of distributions of city populations have been reduced to power laws. In such analyses, a common practice is to consider cities with more than one hundred thousand inhabitants. Here, we argue that the distribution of cities for all ranges of populations can be well described by using a q-exponential distribution. This function, which reproduces the Zipf-Mandelbrot law, is related to the generalized nonextensive statistical mechanics and satisfies an anomalous decay equation.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.