Measurement Of Nonlinear Coefficient Research Articles

Measurement of nonlinear refraction and absorption coefficient in BaGa2GeSe6 crystal

The coefficients of nonlinear absorption and nonlinear refraction of the quaternary barium chalcogenide crystal BaGa2GeSe6 at a wavelength corresponding to half the band gap, as well as their dependence on the pulse repetition rate and peak on-axis irradiance, were measured for the first time. The third-order nonlinear optical properties were studied using the single-beam Z-scan technique. An Nd: YLF laser at 1.053 μm with a pulse duration of approximately 5.2 ns was used as a radiation source. In addition, a thermal Z-scan was carried out to investigate thermal lensing in the BaGa2GeSe6 crystal, employing a continuous wave Nd: YAG laser at 1064 nm. These studies represent an important step in comprehending the nonlinear optical properties of barium chalcogenide crystals and their behavior at different pulse intensities. The results might be significant for the modelling and design of mid-infrared optical systems.

Measurements of Nonlinear Absorption and Refraction Coefficients of Pure and Nd Doped Calcium Lanthanum Borate Glasses

Measurements of Nonlinear Absorption and Refraction Coefficients of Pure and Nd Doped Calcium Lanthanum Borate Glasses

Wavelength dependence of nonlinear optical susceptibility of ZnSe nanocrystalline film

The present work reports the nonlinear optical susceptibility of nanocrystalline ZnSe thin films with different thicknesses, measured using third-order harmonic technology at irradiation wavelengths λ of 1200–1900 nm. The results show that the third-order nonlinear susceptibility χ(3) of ZnSe thin films is a function of the pump wavelength and film thickness. The χ(3) values for the thinner 202-nm film generally decreased with the redshift of the wavelength and were approximately 10−20 m2/V2 at λ ≤ 1500 nm and 10−21 m2/V2 at λ > 1500 nm. The χ(3) values for the thicker 1021-nm film did not follow a decreasing trend, but instead exhibited local peaks at 1350, 1500 and 1750 nm, with a maximum value of approximately 2.4 × 10−19 m2/V2 at λ = 1750 nm. Within 1200–1900 nm, the χ(3) of the thicker film was always greater than that of the thinner film. In addition, a weak second-order harmonic at wavelengths within 1100–1300 nm was observed for the 1021 nm ZnSe thin film. The large difference in the nonlinear optical properties between the thinner and thicker film samples is conjectured to be caused by the increased density of geometric defects and the gradual formation of local anisotropy with increasing film thickness. Nonlinear optical coefficient measurements of ZnSe thin films with different thicknesses over a broad spectrum are important for the application of these films in nonlinear thin-film optoelectronic devices.

Optical force spectroscopy for measurement of nonlinear optical coefficient of single nanoparticles through optical manipulation.

Compared with manipulation of microparticles with optical tweezers and control of atomic motion with atom cooling, the manipulation of nanoscale objects is challenging because light exerts a significantly weaker force on nanoparticles than on microparticles. The complex interaction of nanoparticles with the environmental solvent media adds to this challenge. In recent years, optical manipulation using electronic resonance effects has garnered interest because it has enabled researchers to enhance the force as well as sort nanoparticles by their quantum mechanical properties. Especially, a precise observation of the motion of nanoparticles irradiated by resonant light enables the precise measurement of the material parameters of single nanoparticles. Conventional spectroscopic methods of measurement are based on indirect processes involving energy dissipation, such as thermal dissipation and light scattering. This study proposes a theoretical method to measure the nonlinear optical constant based on the optical force. The nonlinear susceptibility of single nanoparticles can be directly measured by evaluating the transportation distance of particles through pure momentum exchange. We extrapolate an experimentally verified method of measuring the linear absorption coefficient of single nanoparticles by the optical force to determine the nonlinear absorption coefficient. To this end, we simulate the third-order nonlinear susceptibility of the target particles with the kinetic analysis of nanoparticles at the solid-liquid interface incorporating the Brownian motion. The results show that optical manipulation can be used as nonlinear optical spectroscopy utilizing direct exchange of momentum. To the best of our knowledge, this is currently the only way to measure the nonlinear coefficient of individual single nanoparticles.

Nonlinear absorption property investigation into MAX phase Ti2AlC at 1.9 μm

An experimental and theoretical investigation into the nonlinear absorption properties of MAX phase Ti2AlC was conducted at 1900 nm wavelength. First, the nonlinear absorption coefficient measurement of Ti2AlC was carried out using an open-aperture (OA) Z-scan technique. This measurement revealed that the nonlinear absorption coefficient of Ti2AlC was ∼(-24.13×103) cm2/GW at 1900 nm. Subsequently, the energy band structure of the Ti2AlC was calculated through density functional theory (DFT) calculation. This calculation confirmed that Ti2AlC had a metallic band structure implying an ultrawide absorption bandwidth. Finally, the feasibility of fabricating an all-fiberized device of a saturable absorber (SA) using Ti2AlC was conducted with a side-polished fiber platform. The SA was successfully used for the generation of femtosecond soliton pulses with features of 17.91 MHz repetition rate, 4.3-nm bandwidth, and ∼960 fs pulse width at 1922 nm. To the best of authors’ knowledge, this is the first demonstration of the use of a MAX phase-based SA for femtosecond mode-locking in the 1.9 μm spectral region.

Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674074 and 61701133).

Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium. The bubbles show highly nonlinear properties under finite amplitude acoustic excitation, so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency, which shows that the nonlinear coefficient increases obviously. The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately. The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles. However, the stability of inversion is not high enough. In this paper, we introduce a new acoustic inversion method for bubble size distribution, which is based on the nonlinear coefficients of bubble medium. Compared with other inversion methods based on linear or nonlinear scattering cross section, the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.

Ultrafast nonlinear refraction measurements of infrared transmitting materials in the mid-wave infrared.

We utilize the conventional Z-scan technique to provide absolute measurements of third-order nonlinear refraction coefficients (n2) in the mid-wave infrared at 2 µm and 3.9 µm of common optical materials that have transparency windows spanning this regime. We study a variety of narrow band gap and wide band gap semiconductors, fluoride crystals (BaF2, CaF2, LiF, and MgF2) and optical glasses, and a series of chalcogenide glasses. The n2 is found to span on the order of ∼10-15 to ∼10-12 cm2/W for the semiconductors, ∼10-16 cm2/W for the fluoride crystals and glasses, and ∼10-14 to ∼10-13 cm2/W for the chalcogenides. The experimental results are compared to previous measurements of n2 conducted in the visible and near-infrared along with empirical and theoretical formulations.

Measurement of effective nonlinear coefficients in few-mode fibers.

Because of random mode coupling, the nonlinear coefficient in few-mode fibers (FMFs) is averaged to an effective value, which can be theoretically modeled and calculated by using the multi-mode Manakov equations. In this Letter, we experimentally measure the effective nonlinear coefficients in a 530-m-long FMF supporting two mode groups, namely, the $ {\rm LP}_{01} $LP01 and $ {\rm LP}_{11} $LP11 mode groups, by exploiting the self-phase and cross-phase modulations of pulsed fields. By using the nonlinear coefficient of the $ {\rm LP}_{01} $LP01 mode as a reference and comparing the spectral broadening of the pulsed fields, we obtain the intra-modal effective nonlinear coefficient of the $ {\rm LP}_{11} $LP11 mode and the inter-modal effective nonlinear coefficient between the $ {\rm LP}_{01} $LP01 and $ {\rm LP}_{11} $LP11 modes. The experimental results are in good agreement with the theoretical predictions of the multi-mode Manakov equations.

Properties of piezoceramic materials in high electric field actuator applications

In this paper, we compare the performance of 8 PZT ceramics and one PMN-PT material for typical bending actuator applications. This includes the measurement of nonlinear transverse charge coefficient at high electric field strength and related quantities such as the Young’s modulus, relative permittivity, coercive field and their temperature dependencies, and the Curie temperature. Most materials show much higher strains than what is expected from the datasheet values. We further study the operating region for fields against the polarization direction in different operating cycles and demonstrate a long-term stable quick re-poling method which increases the operating range of negative-only cycles from 50% of Ec to 66% of Ec.

Nonscanning Moiré deflectometry for measurement of nonlinear refractive index and absorption coefficient of liquids.

In this work, a nonscanning measurement technique is presented for determining the nonlinear refractive index and absorption coefficient of liquid media based on Moiré deflectometry. In the proposed method two lasers are used: a low power, wide beam as probe and a high power with specific wavelength as a pump. Interaction of the pump laser beam with the nonlinear sample changes the refractive index, which leads to change in convergence/divergence of the collimated incident probe laser beam. The induced deflection is monitored by Moiré deflectometry. If the pump laser has a Gaussian intensity profile, the refractive index profile of the sample is Gaussian, too. Measuring the deflection angle of the probe beam by Moiré fringes deflection, and by using the inverse Abel transform integral, the refractive index profile and nonlinear refractive index can be determined. This method is fast, easy, and insensitive to environmental noise and allows real-time measurement. Also, the refractive index profile of the interacted medium with pump laser can be achieved by this technique. As a liquid sample, a DCJ dye in water solution was studied. The value of nonlinear refractive index, n2, and absorption coefficient, α, were obtained -2.54×10-4 cm2 w-1 and 1.368 cm-1, respectively.

Measurement of non-linear optical coefficients of chalcogenide glasses near the fundamental absorption band edge

A time-resolved pump-probe method is used for the evaluation of non-linear optical coefficients of chalcogenide glasses from the As-S-Se and Ge-Se systems near their fundamental absorption band edges. The results are analyzed via comparison with the spectral dependencies of the non-linear optical coefficients of crystalline semiconductors; the role of electron transitions through the gap states of chalcogenide glasses is discussed.

Different modifier oxides effect on the photoluminescence and photoinduced piezooptics of Er3+-doped fluorotellurite glasses

Novel fluorotellurite glasses with composition 70TeO2·5MxOy·10P2O5·10ZnO·5PbF2 (mol %) containing 600 ppm Er2O3, where MxOy = (MgO, PbO, Bi2O3, Nb2O5, TiO2, BaO, WO3, SrO, CdO) have been prepared using the conventional melt-quenching method. Studies of the nonlinear optical refractive index and photoinduced piezooptics were carried out. The Mid-Infrared spectroscopy, optical transmission, photoluminescence and photoinduced changes of diagonal piezooptics and nonlinear optics refractive indices coefficient measurements were applied to determine the appropriate glass modifier to achieve the desirable optical properties and high performance. The glasses may be useful for operation by high-intensity laser pulses.

Optical nonlinearity in nanostructured carbon thin films fabricated by pulsed laser deposition technique

In the present paper, the measurement of nonlinear refractive index coefficient in nanostructured carbon thin films deposited via pulsed laser deposition (PLD) technique is reported. The PLD carbon thin films were characterized by micro-Raman spectroscopy and ellipsometry. Raman spectra showed characteristic D and G band around ~1350cm−1 and ~1580cm−1 respectively. The nonlinear refractive index of the carbon films was measured by closed aperture Z-scan technique using He-Ne laser. The nonlinear refractive index coefficient of carbon thin films was found to increase from (6.08±0.75)×10−4cm2/W to (1.69±0.13)×10−3cm2/W with the deposition temperature from room temperature to 750°C, respectively.

Nonlinear ultrasonic characterization of intergranular corrosion damage in super 304H steel tube

Purpose – Super304H steel is a new fine-grained austenitic heat-resistant stainless steel developed in recent years, and it is widely used in high temperature section superheater and reheater tubes of ultra-supercritical thermal power units’ boiler. Currently intergranular corrosion (IGC) has occurred in a few austenitic stainless steel tubes in ultra-supercritical units and led to boiler leakage. The purpose of this paper is to find a nondestructive method to quickly and easily detect IGC of austenitic stainless steel tube. Design/methodology/approach – This paper uses the nonlinear characteristics of ultrasonic propagation in steel tube to detect the IGC of Super304H tube. Findings – The experimental results show that the nonlinear coefficient generally increases sensitively with the degree of IGC; hence, the nonlinear coefficient can be used to assess IGC degree of tubes, and the nonlinear coefficient measurement method is repeatable for the same tube. Research limitations/implications – A theory of how IGC would affect the ultrasonic signals and lead to a nonlinear response needs further research. Practical implications – A nondestructive method to quickly and easily detect IGC is provided. Social implications – Using ultrasonic nonlinear coefficient to assess IGC degree of tubes is a new try. Originality/value – This paper provides a new way to test IGC.

Investigation on Z-Scan and its Application of Nonlinear Measurement

The principle of Z-scan and its application on nonlinear refractive index and absorption coefficient measurement are introduced. Besides, two methods of improving sensitivity of Z-scan are described.

Straightforward method for measuring optical fiber’s nonlinear coefficient based on phase mismatching FWM

A novel method for measuring optical fiber's nonlinear coefficient, based on phase mismatching four-wave mixing is proposed. Measurements for both high nonlinearity dispersion shifted fiber and low nonlinearity standard single mode fiber are demonstrated with simple setup. Chromatic dispersion is also measured with high precision simultaneously, and therefore its effect to the nonlinear coefficient measurement can be removed.

Measurement of nonlinear refractive index coefficient of inert gases with hollow-core fiber

A simple method of determining the nonlinear refractive index coefficient n 2 of inert gases is demonstrated. It is based on the accumulation of optical-Kerr-induced spectral broadening effect in gas-filled hollow-core fibers. By using this method, the values of n 2 of argon and neon at 800 nm and argon at 1.8 μm are determined.

Measurement of nonlinear refractive index coefficient using emission spectrum of filament induced by gigawatt-femtosecond pulse in BK7 glass

A beam of 33 fs laser pulse with peak power of 15-40 GW was employed to explore a convenient method to determine the nonlinear refractive index coefficient of an optical glass. It is rare to investigate nonlinearities of optical glass with such an extreme ultrashort and powerful laser pulse. According to our method, only a single beam and a few experimental apparatuses are necessary to measure the nonlinear refractive index coefficient. The results from our method are in reasonable agreement with the others, which demonstrates that this new method works well, and the nonlinear refractive index coefficient is independent of measuring technology. Meanwhile, according to our results and those obtained by others in different laser power ranges, it seems that the nonlinear refractive index coefficient has a weak dependence on the laser peak power.

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.

Measurement of second-order nonlinear optical coefficients of BaMgF_4

The three independent second-order nonlinear optical coefficients of BaMgF4 are determined by the Maker fringe method with a nanosecond pulsed Nd:YAG laser at 1064 nm wavelength. All the results are relative to the reference crystal congruent LiNbO3. The largest element in a second-order nonlinear optical matrix of BaMgF4 is d32, with the value of 0.36 pm/V.