Thermo-optical effects in Z -scan measurements using high-repetition-rate lasers

Nonlinear study of indolamines: A hidden property that might have possible implications in neurodegeneration

Indolamines (e.g., serotonin and melatonin) are tryptophan-derived class of neurotransmitters and neuromodulators that play crucial roles in mood regulation, sleep-wake cycles, and gastrointestinal functions. These biogenic amines exert their effects by binding to specific receptors in the central nervous system, influencing neuronal activity and signalling cascades. Indolamines are vital in maintaining homeostasis, and imbalances in their levels have been implicated in various neurological and psychiatric disorders. Hence, in the present study, we have investigated the nonlinear properties of indolamines under a continuous wave (CW) and pulsed laser excitation using the closed-aperture (CA) Z-scan technique. The CA Z-scan is a cost-effective and sensitive analytical tool for investigating nonlinear properties. It is observed that indolamines show negative refractive and positive absorptive nonlinearity under in vitro physiological conditions. The origin of nonlinearity is ascribed to the thermo-optical effect governed by the saturated atomic absorption and molecular orientation mechanisms under CW and pulsed laser excitation, respectively. The strength of nonlinearity is found to vary linearly with the concentration of indolamines. Overall, serotonin possesses stronger nonlinearity than melatonin. The maximum nonlinearity (refractive index (n2) & absorption coefficient (β)) for melatonin under CW and pulsed laser excitations are (-1.266 × 10-12 m2W-1 and -1.883 × 10-17 m2W-1) & (8.046 × 10-8 mW-1 and 1.516 × 10-13 mW-1), respectively. Meanwhile, the maximum n2 and β under pulsed laser excitation for serotonin are obtained as -3.195 × 10-17 m2W-1 and 6.149 × 10-12 mW-1, respectively. The outcome of the results may be utilized in understanding processes mediated by indolamines and designing therapeutic interventions.

Hematin anhydride (β-hematin): An analogue to malaria pigment hemozoin possesses nonlinearity

Hematin anhydride (β-hematin), the synthetic analogue of the malaria pigment, "hemozoin", is a heme dimer produced by reciprocal covalent bonds among carboxylic acid groups on the protoporphyrin-IX ring and the iron atom present in the two adjacent heme molecules. Hemozoin is a disposal product formed from the digestion of hemoglobin present in the red blood cells infected with hematophagous malaria parasites. Besides, as the parasites invade red blood cells, hemozoin crystals are eventually released into the bloodstream, where they accumulate over time in tissues. Severe malaria infection leads to significant dysfunction in vital organs such as the liver, spleen, and brain in part due to the autoimmune response to the excessive accumulation of hemozoin in these tissues. Also, the amount of these crystals in the vasculature correlates with disease progression. Thus, hemozoin is a unique indicator of infection used as a malaria biomarker and hence, used as a target for the development of antimalarial drugs. Hence, exploring various properties of hemozoin is extremely useful in the direction of diagnosis and cure. The present study focuses on finding one of the unknown properties of β-hematin in physiological conditions by using the Z-scan technique, which is simple, sensitive, and economical. It is observed that hemozoin possesses one of the unique material properties, i.e., nonlinearity with a detection limit of ∼ 15 µM. The self-defocusing action causes β-hematin to exhibit negative refractive nonlinearity. The observed data is analyzed with a thermal lensing model. We strongly believe that our simple and reliable approach to probing the nonlinearity of β-hematin will provide fresh opportunities for malaria diagnostics & cure in the near future.

Solvent-Driven Variations of Third-Order Nonlinear Thermo-Optical Features of Glutaric Acid-Directed Self-Healing Supramolecular Ni(II) Metallogels

The generation of solvent-directed self-healing supramolecular Ni(II) metallogels of glutaric acid (i.e., Ni-Glu-DMF and Ni-Glu-DMSO) is described in this article. Polar aprotic solvents like N,N'-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) are separately entrapped into the Ni(II)-acetate salt and glutaric acid-mediated networks to attain the semisolid flexible scaffolds. The gel nature of the fabricated materials is experimentally proven through different rheological tests such as amplitude sweep, frequency sweep, and thixotropic (time sweep) measurements. The self-repairing strategy and load-bearing features of the synthesized metallogel are studied in this work. The different supramolecular noncovalent interactions working within the soft scaffold are clearly explored. The formation strategy and the microstructural features of these synthesized metallogels are scrutinized through a Fourier transform infrared (FT-IR) spectroscopy study and field-emission scanning electron microscopy (FESEM) morphological analyses. The FT-IR spectroscopy observation displays a considerable amount of shifting of the infrared (IR) peaks of the xerogel samples of both the metallogels Ni-Glu-DMF and Ni-Glu-DMSO. The electrospray ionization (ESI)-mass spectroscopy result demonstrates the plausible construction of the metallogel network. In order to examine the nonlinear optical characteristics of the two synthesized self-healing metallogels Ni-Glu-DMSO and Ni-Glu-DMF, Z-scan measurements are carried out with a continuous wave (CW) diode-pumped solid-state (DPSS) laser at 532 nm. The nonlinear refractive index, nonlinear absorption coefficient, thermo-optical coefficient, and third-order susceptibility of these metallogels were evaluated by analyzing the experimental data from the Sheik-Bahae formalism. The nonlinear thermo-optical study reveals that these solvent-dependent metallogels show negative signs of nonlinear refractive index and nonlinear absorption coefficient. The figure of merit calculated for these compounds shows good agreement for their use in nonlinear photonic devices.

Nonlinear Optical Properties of Zinc Oxide Nanoparticle Colloids Prepared by Pulsed Laser Ablation in Distilled Water

The nonlinear optical properties of zinc oxide nanoparticles (ZnONPs) in distilled water were measured using a femtosecond laser and the Z-scan technique. The ZnONPs colloids were created by the ablation of zinc bulk in distilled water with a 532 nm Nd: YAG laser. Transmission electron microscopy, an ultraviolet-visible spectrophotometer, and atomic absorption spectrophotometry were used to determine the size, shape, absorption spectra, and concentration of the ZnONPs colloids. The nonlinear absorption coefficient and nonlinear refractive index were measured at different excitation wavelengths and intensities. The nonlinear absorption coefficient of the ZnONPs colloids was found to be positive, caused by reverse saturable absorption, whereas the nonlinear refractive index was found to be negative due to self-defocusing in the ZnONPs. Both laser parameters, such as excitation wavelength and input intensity, and nanoparticle features, such as concentration and size, were found to influence the nonlinear optical properties of the ZnONPs.

Excitation Wavelength and Colloids Concentration-Dependent Nonlinear Optical Properties of Silver Nanoparticles Synthesized by Laser Ablation

We reported experimental results from investigations that employed the Z-scan method to explore the dependence of silver nanoparticles' (AgNPs) nonlinear optical properties on the excitation wavelength, AgNP concentration, and size. Using a 532 nm Nd: YAG laser beam at 100 mJ/pulse for different ablation times, AgNPs were synthesized from a silver target immersed in distilled water. UV-Vis spectroscopy and an atomic absorption spectrometer are used to characterize the optical properties of laser-synthesized AgNPs as well as their concentrations. The AgNPs' size and shape are determined using a transmission electron microscope (TEM). The laser-synthesized AgNPs are spherical, with an average particle size of 12 to 13.2 nm. Whatever the ablation time, the AgNP colloids exhibit reversed saturable absorption and a negative nonlinear refractive index (n₂). Both n₂ and the nonlinear absorption coefficient (α₃) increase as the AgNP concentration increases. As the excitation wavelength and average size of the AgNPs increase, n₂ and α₃ decrease.

Faris H, Ahmed H, Mamdouh S, Thambiratnam K, Mohamed T. Using Femtosecond Laser Pulses to Explore the Nonlinear Optical Properties of Au NP Colloids That Were Synthesized by Laser Ablation

In this study, we experimentally investigated the nonlinear optical properties of Au nanoparticles (Au NPs) that were prepared in pure distilled water using the laser ablation method. The Au NPs were prepared using a nanosecond Nd:YAG laser with an ablation time of 5 or 10 min at a constant laser energy of 100 mJ. The structure and the linear optical properties of the Au NPs were investigated using a transmission electron microscope (TEM) and UV-visible spectrophotometer analysis, respectively. The TEM measurements showed that the average size of the Au NPs varied from 20.3 to 14.1 nm, depending on the laser ablation time. The z-scan technique was used to investigate the nonlinear refractive index (n2) and nonlinear absorption coefficient (γ) of the Au NPs, which were irradiated at different excitation wavelengths that ranged from 740 to 820 nm and at different average powers that ranged from 0.8 to 1.6 W. The Au NP samples exhibited a reverse saturable absorption (RSA) behavior that increased when the excitation wavelength and/or incident laser power increased. In addition, the Au NPs acted as a self-defocusing material whenever the excitation wavelength or incident power were modified.

Investigating the effects of intermolecular interactions on nonlinear optical properties of binary mixtures with high repetition rate femtosecond laser pulses

Measurements of nonlinear optical (NLO) properties of different binary mixtures having carbon disulfide (CS2) as the common component, namely CS2-acetone, CS2-cyclopentanone, CS2-toluene, and CS2-carbon tetrachloride (CCl4), are carried out by using the z-scan technique. Open-aperture z-scan (OAZS) and close-aperture z-scan (CAZS) experiments are performed to determine the nonlinear absorption coefficient (β) and nonlinear refractive index (n2) of all binary liquid mixtures at various compositions of the components by employing a pulsed, high repetition rate (HRR) femtosecond laser. Also, we were able to use the flowing liquid to measure NLO properties in the CS2-acetone binary mixture to remove the cumulative thermal effects produced due to the pulsed HRR laser light. Nonlinear refractive index (n2) values are found to be influenced by the weak dipole-induced dipole intermolecular interactions between the nonpolar CS2 and polar acetone as well as cyclopentanone of the respective binary mixtures. On the contrary n2 values are not found to be affected by the intermolecular interactions in CS2-toluene and CS2-CCl4 binary mixtures. In comparison, the nonlinear absorption coefficient (β) values are not found to be affected by the same in all different sets of binary mixtures.

Z-scan analysis and theoretical studies of dopamine under physiological conditions

Dopamine (DA) is a widely researched catecholamine best known for its role in motor, motivation, addiction, and reward. Disruption in dopamine homeostasis and signaling within the central nervous system (CNS) can lead to disorders such as attention deficit hyperactivity disorder (ADHD), schizophrenia, Parkinson's disease, and obsessive-compulsive disorder. In the periphery, circulating DA is stored in blood platelets, and its disruption correlates with pathological conditions such as head and neck paragangliomas, Huntington's chorea, and schizophrenia. Various methods to sensitively and selectively detect dopamine have been reported, but sparse attempts have been made to exploit its intrinsic properties. Previously, we have harnessed dopamine's natural mid-ultraviolet auto-fluorescence to carry out its label-free imaging in live brain tissues. Recently, we used the closed-aperture (CA) Z-scan method to provide the first line of evidence on the existence of dopamine nonlinearity. Here, we utilized this simple, sensitive, and straightforward CA Z-scan technique and coupled this with theoretical simulations to further investigate the nonlinear photophysical properties of DA under physiological conditions. Our combined approach revealed that the nonlinear property of dopamine is governed by the thermo-optical effects, and the CA Z-scan profiles can be modulated by parameters such as phase-shift, orders of absorption, and time dependency. Simple and physiologically relevant systems, such as the platelets, are amenable to Z-scan analysis, thereby empowering us to scrutinize in the future if nonlinearity and its alterations, if any, have a direct bearing on DA homeostasis and associated diseases.

Nonlinear thermal lensing of high repetition rate ultrafast laser light in plasmonic nano-colloids

We report on experimental observations of phenomenological self-trapping in plasmonic colloids of varying plasmon peaks in the visible/near infrared. A femtosecond (fs) oscillator is used in both pulsed (35 fs, 76 MHz) and continuous wave (cw) operation for comparison. We show that for both modes and for all examined colloids (and under typically applied external focusing conditions in self-trapping studies in colloidal media) nonlinear propagation is governed by thermal defocusing of the focused beam, which precedes the steady-state regime reached by particle diffusion, even far from the plasmon resonance (or equivalently for non-plasmonic colloids, even for low absorption coefficients). A strategy for the utilization of high repetition fs pulses to mitigate thermal lensing and promote gradient force-induced self-trapping is discussed. Notably, nonlinear thermal lensing is further accompanied by natural convection due to the horizontal configuration of the setup. Under resonant illumination, for both fs and cw cases, we observe mode break-up of the beam profile, most likely due to azimuthal modulation instability. Importantly, time-resolved observations of the break-up indicate that in the fs case, thermal convection heat transfer is reduced in magnitude and significantly decoupled in time from thermal conduction, presumably due to temperature increase confinement near the particles. We anticipate that our findings will trigger interest toward the use of high repetition fs pulses for self-channeling applications in nano-colloids.

Hyperspectral z-scan: Measurement of spectrally resolved nonlinear optical properties

Broadband hyperspectral z-scan using a supercontinuum light source is a convenient technique to obtain spectrally resolved nonlinear optical properties of the materials under investigation. Post-processing and segregation of the data obtained from the supercontinuum based hyperspectral z-scan measurement aids in determining the nonlinear optical properties with high spectral resolution. However, few data models exist to store and represent the large amount of information acquired from the hyperspectral z-scan measurement. In this paper, a 3D data model for representing the data obtained from broadband z-scan measurements and analysis is presented. This method would help in the quick characterization of spectrally resolved nonlinear optical properties of materials from a single z-scan measurement. The proposed model is used for obtaining the spectrally resolved nonlinear optical properties of rhodamine 6G.

Norepinephrine exhibits thermo-optical nonlinearity under physiological conditions

Norepinephrine (NE), a crucial modulatory neurotransmitter, plays a significant role in human physiology. Here, we use the Z-scan technique to investigate the nonlinear properties of NE at physiological conditions. Results reveal that NE exhibits thermo-optical nonlinearity. Outcomes can be utilized to investigate noradrenergic processes in correlation with various diseases.

Nonlinear and thermo-optical characterisation of bareimidazoliumionic liquids

Nonlinear optical (NLO) and thermo-optical properties of two pure ionic liquids, BMIOMe.NTf2and BMIOMe.N(CN)2, were examined in this study. This was the first nonlinear refractive index determination of a pristine ionic liquid by a standard self-refraction experiment. The NLO characterisations were performed using Z-scan and EZ-scan techniques in the thermally managed approach, with a mode-locked femtosecond laser source. Thermal properties were analysed concomitantly, and the thermo-optical coefficient, thermal characteristic time, and lens strength were characterised. These results define the parameters to be adopted in the method of nanoparticles formation by laser ablation in an ionic liquid solution and indicate that BMIOMe.NTf2is a prominent material to be engineered for photonics applications.

Temperature evaluation of colloidal nanoparticles by the thermal lens technique

The use of highly sensitive thermometric methods is essential for the evaluation of nanoplatforms for photothermal therapy. In this study, the thermal lens technique was introduced to assess the optically induced temperature changes in colloidal samples of gold nanoparticles. Thermal lens measurements also allowed the acquisition of the nanoparticle absorption cross-section value, regardless of knowing the nanostructure scattering properties. The developed thermometric system exhibited 0.2 °C^-1 sensitivity and was capable of measuring temperature variations of metallic colloidal samples with a resolution of 0.01 °C. Measuring colloidal temperature changes allows for the estimation of the localized temperature variation reached by each nanoheater, before thermalization of the excitation volume. Our results establish a practical and effective method to evaluate optically induced temperature changes on metallic colloids.

Thermal lensing effects and nonlinear refractive indices of fluoride crystals induced by high-power ultrafast lasers

Thermo-optical and nonlinear property characterization of refractive optical components is essential for endoscopic instrumentation that utilizes high-power, high-repetition-rate ultrafast lasers. For example, ytterbium-doped fiber lasers are well suited for ultrafast laser microsurgery applications; however, the thermo-optical responses of many common lens substrates are not well understood at 1035 nm wavelength. Using a z-scan technique, we first measured the nonlinear refractive indices of CaF₂, MgF₂, and BaF₂ at 1035 nm and found values that match well with those from the literature at 1064 nm. To elucidate effects of thermal lensing, we performed z-scans at multiple laser repetition rates and multiple average powers. The results showed negligible thermal effects up to an average power of 1 W and at 10 W material-specific thermal lensing significantly altered z-scan measurements. Using a 2D temperature model, we could determine the source of the observed thermal lensing effects. Linear absorption was determined as the main source of heating in these crystals. On the other hand, inclusion of nonlinear absorption as an additional heat source in the simulations showed that thermal lensing in borosilicate glass was strongly influenced by nonlinear absorption. This method can potentially provide a sensitive method to measure small nonlinear absorption coefficients of transparent optical materials. These results can guide design of miniaturized optical systems for ultrafast laser surgery and deep-tissue imaging probes.

A Novel Tool to Investigate the Early and Late Stages of α-Synuclein Aggregation

The accumulation of an inherently disordered protein α-synuclein (α-syn) aggregates in brain tissue play a pivotal role in the pathology and etiology of Parkinson's disease. Aggregation of α-syn has been found to be complex and heterogeneous, occurring through multitudes of early- and late-stage intermediates. Because of the inherent complexity and large dynamic range (between a few microseconds to several days under in vitro measurement conditions), it is difficult for the conventional biophysical and biochemical techniques to sample the entire time window of α-syn aggregation. Here, for the first time, we introduced the Z-scan technique as a novel tool to investigate different conformations formed in the early and late stage of temperature and mechanical stress-induced α-syn aggregation, in which different species showed its characteristic nonlinear characteristics. A power-dependent study was also performed to observe the changes in the protein nonlinearity. The perceived nonlinearity was accredited to the thermal-lensing effect. A switch in the sign of the refractive nonlinearity was observed for the first time as a signature of the late oligomeric conformation, a prime suspect that triggers cell death associated with neurodegeneration. We validate Z-scan results using a combination of different techniques, like thioflavin-T fluorescence assay, fluorescence correlation spectroscopy, Fourier-transform infrared spectroscopy, and atomic force microscopy. We believe that this simple, inexpensive, and sensitive method can have potential future applications in detecting/monitoring conformations in other essential peptides/proteins related to different neurodegenerative and other human diseases.

On the measurement of the nonlinear optical response of graphene dispersions using fs lasers

In this work, the nonlinear optical (NLO) response of some graphene dispersions is investigated under low (i.e., 10 Hz) and high (i.e., 80 MHz) repetition rate femtosecond (fs) laser excitation conditions, using ${Z}$Z-scan, optical Kerr effect (OKE), and a combination of ${Z}$Z-scan and thermal lensing techniques. It is shown, that the NLO response of graphene dispersions is negligible under low repetition rate fs laser excitation, while it becomes very large under high repetition rate laser excitation. In the latter case, it is shown that the observed very large NLO response arises entirely from thermal cumulative effects.

Discrimination between two distinct nonlinear effects by polarization-resolved Z-scan measurements

We investigated how the Z-scan technique can be explored to distinguish two types of nonlinear refractive effects by employing two distinct laser polarizations. It is possible that pure electronic, molecular orientation and thermal nonlinear effects may occur simultaneously during light-matter interaction. We found a way to discriminate and quantify two distinct nonlinear processes from Z-scan signals measured with linear and circular polarizations. This paper provides analytical equations for nonlinear refractions and in order to test them, we carried out measurements in CS₂ and in a rhodamine-B solution, where electronic and orientational, and electronic and thermal nonlinearities mixing, respectively, are present.

Unraveling the molecular dependence of femtosecond laser-induced thermal lens spectroscopy in fluids

Fluid systems exhibit thermal lens effects due to laser irradiation accompanied by convection and in contrast primarily conductive heat dissipation is observed in solids. The presence of a significant convective mode modifies the temperature gradient in fluids resulting in a deviation of the experimental results from theories that are based on pure conduction. Herein, we present a carefully designed femtosecond laser experiment that keeps the heat generation process constant in order to account for the effect of molecular properties on thermal dissipation. We derive a theoretical model that introduces and characterizes the additional convective heat transfer in thermal lens (TL) spectroscopy which explains our observed experimental results. We measured the TL signal for a series of liquid aliphatic alkanes, ranging from hexane to decane, and their comparison has proven the validity of our model. The influence of convective heat transfer on the TL signal is predicted in terms of the dimensionless Peclet number (PE). The lower values of PE for alkanes with longer carbon chains indicate that the convective flow of heat slows down substantially for larger molecules.

Third-order nonlinear optical properties of a multi-layer Al2O3/ZnO for nonlinear optical waveguides

This is a report of a study of the nonlinear optical properties of samples based on multiple Al₂O₃/ZnO bilayers fabricated by atomic layer deposition (ALD) in silica. The multi-layer configuration for samples consists of alternated layers of constant thickness of Al₂O₃ (Δx) and ZnO (Δy) nanolaminates with a total thickness of ∼ 500 nm. The physical properties of the samples were characterized by means of TEM, spectrophotometry and variable angle spectroscopic ellipsometry. The absorptive and refractive contributions to the nonlinearity of the samples were studied by means of z-scan technique using a 100 fs at 800 nm. The nonlinear parameters, β and n₂, are studied using different values of the layers thickness, Δx and Δy, in the nanolaminated stack. The possible applications in optical signal processing system are discussed by means of the figures of merit W and T.

Large optical nonlinearity of ITO/Ag/ITO sandwiches based on Z-scan measurement

Indium tin oxide (ITO)-based sandwich structures with the insertion of silver (ITO/Ag/ITO) show large nonlinear optical enhancement of both nonlinear refraction and saturable absorption. Here optical nonlinearity is measured using a Z-scan experiment with a 1310 nm pulsed laser at normal incidence. The nonlinear refractive index (n₂=15.43×10^-16  m²/W) for an ITO/Ag/ITO sandwich with a 14 nm silver interlayer and the nonlinear absorption coefficient (β=-648×10^-11  m/W) for an ITO/Ag/ITO sandwich with a 10 nm silver interlayer are about 18 and 16 times greater than that of a single-layer ITO, respectively. Meanwhile, a large figure of merit and modulation depth values hinted that ITO/Ag/ITO sandwiches are promising saturable absorber materials to switch continuous laser waves into laser pulses. These novel nonlinear optical properties make ITO/Ag/ITO sandwiches a promising candidate for all-optical modulation devices at optical communication wavelengths.

Exploring adaptive optics on focus-scan for nonlinear materials characterization

Z-scan is a well-established technique used to measure the nonlinear refractive index and absorption coefficient of thin and transparent materials. The method requires the displacement of the sample along the focus of a laser beam. Therefore, the Z-scan is not suitable for experiments where the sample cannot be axially translated. Here, we explore a deformable mirror to create controllable defocus aberrations, translating the focus of the beam through the sample, alternatively to the sample displacement. The technique is based on time behavior analysis of the light beam transmitted by the nonlinear sample, at different defocus configurations. The method is validated by measuring reference samples (CS₂ and SiO₂) and comparing them with the conventional Z-scan technique.

Gold nanoparticle-decorated graphene as a nonlinear optical material in the visible and near-infrared spectral range

There have been numerous reports of boosting nonlinear optical phenomena in plasmonic nanostructures through local-field enhancement as well as through intrinsic metal nonlinearities. Here, we study the possibility of plasmonic enhancement of graphene's nonlinear absorption by creating a composite material: gold nanoparticle-decorated graphene dispersed in water. To evaluate the additive effect of combining the two materials on the saturable absorption efficiency we performed a series of f-scan (modified Z-scan) measurements using femtosecond laser pulses in the broad spectral range from 530 to 1600 nm. These studies are supplemented by TEM, UV-vis, ATR and Raman spectroscopy, revealing the mechanisms behind the formation of the composite material.

Ultra-fast dynamics in the nonlinear optical response of silver nanoprism ordered arrays

In this work we present the study of the ultra-fast dynamics of the nonlinear optical response of a honeycomb array of silver triangular nanoprisms, performed using a femtosecond pulsed laser tuned with the dipolar surface plasmon resonance of the nanoarray. Nonlinear absorption and refraction, and their time-dependence, were explored using the z-scan and time-resolved excite-probe techniques. Nonlinear absorption is shown to change sign with the input irradiance and the behavior was explained on the basis of a three-level model. The response time was determined to be in the picosecond regime. A technique based on a variable frequency chopper was also used in order to discriminate the thermal and electronic contributions to the nonlinearity, which were found to have opposite signs. All these findings propel the investigated nanoprism arrays as good candidates for applications in advanced ultra-fast nonlinear nanophotonic devices.

Enhancement of nonlinear optical properties of BaTiO3 nanoparticles by the addition of silver seeds: comment

This is a comment on the previously published paper "Enhancement of nonlinear optical properties of BaTiO3 nanoparticles by the addition of silver seeds," [Opt. Express20, 26511 (2012)10.1364/OE.20.026511]. An erroneous equation given in the manuscript is corrected with a more accurate equation in this comment.

Measurement of pure optical nonlinearity in carbon disulfide with a high-repetition-rate femtosecond laser

Using the close-aperture Z-scan technique, the pure nonlinear refractive index (n₂) of carbon disulfide is measured with a 76 MHz repetition rate femtosecond laser. Strong interference of thermal effects exists with high-repetition-rate lasers that result in negative values of n₂. We remove the thermal effect completely by continuously increasing the sample flow rate (F) in a sample cell as indicated by the change in sign of n₂ from negative to positive. The positive value of n₂ is due to Kerr-type nonlinearity. At sufficiently high values of F of >25 ml/min, all thermal effects are removed, resulting in an n₂ value that matches low-repetition-rate experiments.

Measuring the nonlinear refractive index of graphene using the optical Kerr effect method

By means of the ultrafast optical Kerr effect method coupled to optical heterodyne detection (OHD-OKE), we characterize the third-order nonlinear response of graphene and compare it to experimental values obtained by the Z-scan method on the same samples. From these measurements, we estimate a negative nonlinear refractive index for monolayer graphene, n₂=-1.1×10^-13  m²/W. This is in contradiction to previously reported values, which leads us to compare our experimental measurements obtained by the OHD-OKE and the Z-scan method with theoretical and experimental values found in the literature and to discuss the discrepancies, taking into account parameters such as doping.

Nonlinear optical response of platinum nanoparticles and platinum ions embedded in sapphire

We report on the fabrication of sapphire samples containing platinum nanoparticles (Pt-NPs) and platinum ions (Pt-ions) and the investigation of their third-order nonlinear (NL) optical properties. The presence of Pt-NPs was confirmed by electronic microscopy and by the linear absorption spectrum that shows a localized surface plasmon band centered at 290 nm. A sample without NPs but containing Pt-ions was also studied. The absorptive and refractive contributions to the nonlinearity were studied using the z-scan technique with 100 fs pulses at 800nm. The experiments revealed a NL refractive index, +3.8×10^-13 < n₂ < +1.3×10^-12cm²/W and NL absorption coefficient (β < 9.3 cm/GW). The results show enhancement of about five orders of magnitude with respect to the NL refractive index of sapphire.

Techniques for nonlinear optical characterization of materials: a review

Various techniques to characterize the nonlinear (NL) optical response of centro-symmetric materials are presented and evaluated with emphasis on the relationship between the macroscopic measurable quantities and the microscopic properties of photonic materials. NL refraction and NL absorption of the materials are the phenomena of major interest. The dependence of the NL refraction and NL absorption coefficients on the nature of the materials was studied as well as on the laser excitation characteristics of wavelength, intensity, spatial profile, pulse duration and pulses repetition rate. Selected experimental results are discussed and illustrated. The various techniques currently available were compared and their relative advantages and drawbacks were evaluated. Critical comparisons among established techniques provided elements to evaluate their accuracies and sensitivities with respect to novel methods that present improvements with respect to the conventional techniques.

Shape-Dependent Nonlinear Optical Properties of Anisotropic Gold Nanoparticles

This Letter reports the shape-dependent third-order nonlinear optical properties of anisotropic gold nanoparticles. We characterized the nonlinear absorption coefficients of nanorods, nanostars, and nanoshells using femtosecond Z-scan measurements. By comparing nanoparticle solutions with a similar linear extinction at the laser excitation wavelength, we separated shape effects from that of the localized surface plasmon wavelength. We found that the nonlinear response depended on particle shape. Using pump-probe spectroscopy, we measured the ultrafast transient response of nanoparticles, which supported the strong saturable absorption observed in nanorods and weak nonlinear response in nanoshells. We found that the magnitude of saturable absorption as well as the ultrafast spectral responses of nanoparticles were affected by the linear absorption of the nanoparticles.

Thermal lensing effect of CS2 studied with femtosecond laser pulses

By chopping 820 nm 18 femtosecond (fs)-laser pulses, continuously generated by a self-mode locked Ti:Al2O3 laser at 82 MHz, into trains with both train-width and train-to-train separation considerably longer than the thermal diffusivity time constant τth of CS2, we conducted Z-scan measurements on it at various times relative to the leading pulse of each train (T's). As a result, we observed negative nonlinear refraction strengthening with T within τth and gradually stabilizing with T exceeding τth. We quantitatively explain the experimental results in terms of the thermal lensing effect. In particular, we attribute the heat generation to non-radiative relaxation of libration excited by individual 18 fs-pulses via stimulated Raman scattering. In contrast to the commonly held view of multi-photon excitation, we propose and verify a new heat-generating mechanism for the thermal lensing effect in CS2.

Nonlinear characterization of Ge₂₈Sb₁₂Se₆₀ bulk and waveguide devices

Single-mode Ge₂₈Sb₁₂Se₆₀ strip waveguides, fabricated with thermal evaporation and lift-off, were demonstrated at 1.03 µm. The linear and nonlinear optical properties of these waveguides were shown to be similar to bulk samples, with differences attributed to small variations in composition of ~4 atomic % or less. From z-scan measurements at 1.03 µm using circularly polarized, ~200 fs pulses at 374 kHz, Ge₂₈Sb₁₂Se₆₀ was found to have a nonlinear refractive index ~130 x fused silica and a two-photon absorption coefficient of 3.5 cm/GW. Given the large two-photon absorption coefficient, this material shows promise for optical limiting applications at 1 µm.

Eliminating thermal effects in z-scan measurements of thin PTCDA films

We investigate the two-photon absorption (TPA) and nonlinear refraction of a micrometer thick 3,4,9,10-perylentetracarboxyl-dianhydride (PTCDA) film using z-scans with tightly focused 100 fs laser pulses. The PTCDA film was grown by organic molecular beam deposition on a Pyrex substrate. To study the influence of sample heating, the pulse repetition rate was varied between 4 MHz and 50 kHz with an acousto-optic pulse selector. We find that thermal effects diminish for pulse repetition times longer than 5 and 0.75 µs when using a 10x or 20x microscope lens, respectively, resulting in a TPA coefficient of 6 cm/GW and a nonlinear refractive index of 1.2 x 10⁻¹³ cm²/W at a wavelength of 820 nm.

Femtosecond pulse train shaping improves two-photon excited fluorescence measurements

Measurements of two-photon absorption (TPA) cross sections are greatly confounded by even very weak linear absorption, for example from hot bands. In this case, the experimental power dependence of fluorescence from amplified and mode-locked laser systems can differ drastically, even if the peak intensity is adjusted to be the same in both cases. A simple pulse train shaping method suppresses linear contributions and extracts the nonlinear absorption cross section, demonstrated here for a meso-to-meso ethyne-bridged bis[(porphinato)zinc(II)] fluorophore (DD) at 800 nm. This approach permits reliable TPA cross-section measurement, even with standard modelocked lasers under conditions identical to that used for multiphoton microscopy.

Optical Kerr phase shift in a nanostructured nickel-doped zinc oxide thin solid film

The optical Kerr effect exhibited by a nickel doped zinc oxide thin solid film was explored with femto- and pico-second pulses using the z-scan method. The samples were prepared by the ultrasonic spray pyrolysis technique. Opposite signs for the value of the nonlinear refractive index were observed in the two experiments. Self-defocusing together with a two-photon absorption process was observed with 120 ps pulses at 1064 nm, while a dominantly self-focusing effect accompanied by saturated absorption was found for 80 fs pulses at 825 nm. Regarding the nanostructured morphology of the resulting film, we attribute the difference in the two ultrafast optical responses to the different physical mechanism responsible of energy transfer generated by multiphoton processes under electronic and thermal effects.

Third order nonlinear optical properties of phthalocyanines in the presence nanomaterials and in polymer thin films

Third order nonlinear optical properties were determined for phthalocyanine complexes 1–10 containing In , Ga and Zn central metals and tetra- or octa-substituted with benzyloxyphenoxy, phenoxy, tert-butylphenoxy and amino groups at peripheral or non-peripheral positions. The phthalocyanines were embedded in poly (methyl methacrylate) polymer in the presence of CdTe quantum dots. All complexes 1–10 were studied in the presence of CdTe quantum dots and embedded in poly (methyl methacrylate) to form thin films. Complex 3 tetrasubstituted with tert-butylphenoxy groups at non-peripheral positions was also studied in the presence of CdS , CdSe quantum dots, fullerenes, single walled carbon nanotubes. Third order nonlinear optical parameters generally increase for Pcs in the presence of CdTe quantum dots.

Enhancement of nonlinear optical properties of BaTiO3 nanoparticles by the addition of silver seeds

Barium titanate (BaTiO3) is a technologically important material because of its nonlinear properties, such as its strong second harmonic generation and high third order susceptibility. While many nonlinear effects have been extensively studied on the bulk scale, there are still questions regarding the strength of nonlinear effects in nanoparticles. The nonlinear properties of BaTiO3 nanoparticles and nanorods have been studied using the closed aperture z-scan technique. Silver was then grown photochemically on the surface of the BaTiO3 nanoparticles, and it was found that the third order susceptibility increases dramatically.

Measurement of the two-photon absorption cross section by means of femtosecond thermal lensing

We present a variation of the single-beam thermal lensing experiment to determine the two-photon absorption cross sections of classical fluorophores. The approach is based on comparison of two thermal lensing signals simultaneously induced by a one- and two-photon absorption process from a high-repetition-rate femtosecond laser system. As a consequence of this comparison, a simplified expression independent of the several experimental parameters is obtained. Additionally, because of the low incident power levels required, undesirable optical effects such as Kerr or Raman scattering are avoided. Our experimental results agree well with those recently published for luminescent methods, validating the approach.

Discriminating thermal effect in nonlinear-ellipse-rotation-modified Z-scan measurements

We report that a modified Z-scan method by nonlinear ellipse rotation (NER) can be used to discriminate true nonlinear refraction from thermal effect in the transient regime and steady state. The combination of Z-scan and NER allows us to measure the third-order nonlinear susceptibility component without the influence of thermal-optical nonlinearity. The experimental results of pure CS(2) and CS(2) solutions of nigrosine verify that the transient thermal effect can be successfully eliminated from the NER-modified Z-scan measurements. This method is also extended to the case in which thermal-optical nonlinearities depend on a high repetition rate of femtosecond laser pulses for the N,N-dimethylmethanamide solutions of graphene oxide.

Nonlinear refractive index of porcine cornea studied by z-scan and self-focusing during femtosecond laser processing

We have investigated the nonlinear refractive index of ex-vivo pig cornea by a combined approach using the standard z-scan technique on extracted corneas or corneal slices, as well as studying the deviations caused by self-focusing during femtosecond laser processing of the pig eyes. The experiments yield consistently an upper limit of 1.2 MW for the critical power of self-focusing in porcine cornea, and a value of 2 x 10(-19) m(2)/W for its nonlinear refractive index. We also demonstrate that due to this nonlinear refraction the cutting depth of typical fs-laser surgery processing in cornea may depend considerably, albeit in a well controllable way, on the laser parameters.

Femtosecond two-photon absorption measurements based on the accumulative photo-thermal effect and the Rayleigh interferometer

A rapid, straightforward method for measuring the two-photon absorption cross sections in liquid samples based on both the accumulative photo-thermal effect and the Rayleigh interferometery is described and demonstrated. This technique combines the sensitivity of the thermal lens approach and the accuracy of interferometry techniques. Focusing a high repetition rate laser beam in the sample, generating a localized change in its refractive index, induces the photo-thermal phase shift. By recording and processing two interference patterns, this technique allows the rapid estimation of the two-photon absorption cross section of the sample. Significantly, the experimental results demonstrate that this new method can be used with both fluorescent and non-fluorescent samples.

Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics

We apply ultrafast single beam Z-scan technique to measure saturation absorption coefficients and nonlinear-refraction coefficients of primary alcohols at 1560 nm. The nonlinear effects result from vibronic transitions and cubic nonlinear-refraction. To measure the pure total third-order nonlinear susceptibility, we removed thermal effects with a frequency optimized optical-chopper. Our measurements of thermal-relaxation dynamics of alcohols, from 1560 nm thermal lens pump and 780 nm probe experiments revealed faster and slower thermal-relaxation timescales, respectively, from conduction and convection. The faster timescale accurately predicts thermal-diffusivity, which decreases linearly with alcohol chain-lengths since thermal-relaxation is slower in heavier molecules. The relation between thermal-diffusivity and alcohol chain-length confirms structure-property relationship.

Thermally managed eclipse Z-scan

We report a new variation of the conventional Z-scan method to characterize the third-order optical nonlinearity of photonic materials. By exploiting the combination of the eclipse Z-scan with a thermal nonlinearity management technique, we demonstrate an improvement in sensitivity and flexibility of the method to simultaneously characterize the thermal and nonthermal nonlinearity of optical materials. The method is demonstrated by measuring the nonlinear refractive index in CS(2), SiO(2) and H(2)O, standard materials, and also in a biomaterial, the amino acid Tryptophan in water solution, using a femtosecond Ti-Sapphire laser operating at 76MHz repetition rate.

Nonlinear refraction and saturable absorption in Au:BaTiO3 composite films

Composite thin films Au:BaTiO3, comprising nanometer-sized gold particles embedded in barium titanate matrices, were synthesized on MgO (100) substrates with the pulsed laser deposition technique. The nanostructure of the films and the size distributions of the Au particles were analyzed by high-resolution transmission electron microscopy. Crystal lattice fringes from the Au nanocrystals and the BaTiO3 matrices were observed. The nonlinear optical properties of the Au:BaTiO3 films were measured with the z-scan method at a wavelength of 532 nm, which was closed to the surface plasmon resonance of nanoscale Au particles. The features of the closed-aperture z-scan transmittance curves were affected by the ratio, which increased greatly at a high metal concentration, of the imaginary part to the real part of the third-order nonlinear susceptibility chi(3).