Laser Beam Deflection Research Articles

3D Femtosecond Laser Beam Deflection for High-Precision Fabrication and Modulation of Individual Voxelated PCM Meta-Atoms.

Optical metasurfaces have found widespread applications in the field of optoelectronic devices. However, achieving dynamic and flexible control over metasurface functionalities, while also developing simplified fabrication methods for metasurfaces, continues to pose a significant challenge. Here, the study introduces a PCM-only metasurface that exclusively consists of voxel units crafted from different phases of phase-change materials. Micro-nano regions, with varying phase states, are directly utilized as resonant elements and embedded in the material, forming the metasurface voxel meta-atoms. By manipulating the morphology, size, and arrangement of these meta-atoms, the study achieves both the fabrication and modulation of the PCM-only metasurface. Additionally, a 3D high-precision voxelated beam deflection method based on femtosecond laser phase modulation is introduced to streamline the fabrication and modulation of PCM-only metasurface. By using a spatial light modulator to load the blazed grating phase manipulation beam for precise deflection, high-precision deflection processing of individual meta-atom on metasurfaces can be achieved, with a deflection accuracy of up to 200nm. By loading Fresnel phase manipulation beams to move along the z-axis, perfect modulation of PCM sub-meta-atoms can be achieved. The 3D femtosecond laser beam deflection technology will bring many potential application opportunities in the fields of optoelectronic device fabrication and functional control.

On‐Chip Multidimensional Manipulations of Spatial Laser Fields by Jointly Controlling Amplitude and Phase of Metasurface

AbstractOver the past decades, metasurfaces have experienced rapid development controlling the propagation of electromagnetic waves. Seamlessly combining metasurfaces with semiconductor devices enhance the device's performance and expand functional diversity. Currently, vertical‐cavity surface‐emitting lasers integrated with metasurfaces (MS‐VCSELs) employed to generate various wavefronts. However, the existing MS‐VCSELs that use only phase modulation still face limitations and challenges in generating customized fields, especially in 3D space. Here, amplitude‐phase metasurfaces are proposed and joint amplitude‐phase modulations are employed to increase the degree of freedom in controlling laser fields. By using electron beam lithography (EBL) and inductively coupled plasma reaction ion etching (ICP‐RIE), metasurfaces are directly fabricated on the back‐emitting surface of VCSELs, enabling samples to realize diverse functions such as multi‐focus multi‐plane generation and intensity control, multi‐plane holographic images, and laser beam deflections with different intensities. Compared to traditional discrete metasurface configurations, the proposed scheme achieves on‐chip integration of amplitude‐phase metasurface with the light source, enhancing the multidimensional laser field modulation capabilities of MS‐VCSELs in the 3D space while further promoting the cross‐integration of metasurfaces with optoelectronic devices. It is believed that MS‐VCSELs with amplitude‐phase modulations hold significant promise for applications in 3D imaging, facial recognition, and laser communications.

Quantitative photothermal investigation of nonradiative recombination parameters in GaAs/InAs(QD)/GaAs quantum dot structures using a three-layer laser beam deflection model

In this paper, we developed a theoretical model for the photothermal deflection technique in order to investigate the electronic parameters of three-layer semiconductor structures. This model is based on the resolution of thermal and photogenerated carrier diffusion-wave equations in different media. Theoretical results show that the amplitude and phase of the photothermal deflection signal is very sensitive to the nonradiative recombination parameters. The theoretical model is applied to one layer of InAs quantum dots (QDs) inserted in GaAs matrix InAs/GaAs QDs in order to investigate the QD density effects on nonradiative recombination parameters in InAs through fitting the theoretical photothermal beam deflection signal to the experimental data. It was found that the minority carrier lifetime and the electronic diffusivity decrease as functions of increasing InAs QD density. This result is also related to the decrease in the mobility from 21.58 to 4.17 (±12.9%) cm2/V s and the minority carrier diffusion length from 0.62 (±5.8%) to 0.14 (±10%) μm, respectively. Furthermore, both interface recombination velocities S2/3 of GaAs/InAs (QDs) and S1/2 of InAs (QDs)/GaAs increase from 477.7 (±6.2%) to 806.5 (±4%) cm/s and from 75 (±7.8%) to 148.1 (±5.5%) cm/s, respectively.

Refractive Laser Beam Measuring Diffusion Coefficient of Concentrated Battery Electrolytes

A thorough understanding of electrolyte transport properties is crucial in the development of alternative battery technology. As a key parameter, the diffusion coefficient offers important insights into the behavior of electrolytes, especially for fast charge of high-energy batteries. Existing methods of measurement are often limited by redox species or offer questionable accuracy due to side reactions and/or disruption of the diffusion profile. A highly sensitive optical method was developed using a refractive laser beam through triangular diffusion column to measure the diffusion coefficient of concentrated battery electrolytes. The method based on Snell’s law can be applied to all liquid phase electrolytes since the refractive index is concentration dependent for all liquid electrolytes. This universal method relies on the deflection of a refractive laser beam passing through an electrolyte of a minor concentration gradient in a triangular diffusion column (Figure 1). A polarized HeNe laser was arranged to pass the beam through a right-angled triangular quartz precision cell, slightly rotated to the normal. The exact position of the refracted beam was located by a silicon photodiode-based position detector. Deflection calibration curves made simple conversion of beam position to concentration, and during the diffusion of two layered solutions, data points were collected every minute to produce a concentration profile descriptive of the 48-hour diffusion. Diffusion coefficients were calculated using a model based on OSM theory, accounting for multi-component concentrated systems in a restricted diffusion column.1 The measured diffusion coefficients are between 4.12x10-10 m2/s for 0.15 mol/kg ZnSO4 and 0.681x10-10 m2/s for 2.5 mol/kg ZnSO4 at 22.4 °C. The profile of concentration-dependent diffusion coefficients follows a non-linear inverse relationship described by the function D=4.943(1+m)-1.564 (Figure 2).Several other physicochemical properties of the same electrolytes were studied to correlate to the concentration-dependent diffusion coefficients, including refractive index, viscosity, conductivity, and microstructure analysis based on vibrational spectroscopy (Infrared and Raman). High concentration electrolytes with more ion pairs show increased viscosity which ultimately leads to smaller diffusion coefficients. A QCM-I instrument standard flow cell were used to determine the viscosity of ZnSO4 electrolyte and the concentration-dependent viscosity was fitted to the function η=1.06-0.476m+2.13m2-1.01m3+0.204m4. Interionic interactions also led to reduced conductivity at concentrations beyond 1.5mol/kg, despite the increased charge density of concentrated solutions. FT-IR spectrums allowed analyzation of increased charge density, which increased intensity of the O-H stretching peak in concentrated electrolytes, despite the decrease in the ratio of water. Competition between charge density and viscosity continues to challenge the efficiency of concentrated electrolytes.Lastly, we demonstrate the prototype in situ triangular cell to characterize the electrolyte in working batteries. The cell responds to short, low-voltage pulses with beam deflection and relaxation, and offers an opportunity as a novel in situ spectroscopic tool to characterize the battery electrolyte. Acknowledgments This work is supported by a grant from NSF (CBET-2243098).

Optical Detection of Underwater Propeller Wake Based on a Position-Sensitive Detector

The study of underwater vehicle wake detection is of significant importance within the field of target detection, localisation, and tracking of underwater vehicles. Given that propellers are the propellers of modern ships and underwater vehicles, the propeller wake field represents the principal target source for wake detection in underwater vehicles. The objective of this paper is to propose a method for measuring the wake of an underwater propeller based on a position-sensitive detector. A theoretical model of the relationship between the laser spot displacement and the change in the refractive index of the wake field is established on the basis of the principle of laser beam deflection. A prototype experimental setup for underwater propeller wake measurement was constructed based on the aforementioned optical measurement method. Furthermore, the simulation of the propeller wake flow field with strong density stratification and linear density stratification was conducted based on the experimental setup. Furthermore, experiments were conducted to detect the flow field of a propeller wake. The experimental results indicate that the wake dissipation times of the propeller in a strong density-stratified water environment are approximately 800 s and 750 s. Following the stabilisation of the wake field density, the laser spot position is observed to be stable at 0.341 mm and 0.441 mm, respectively, with a corresponding refractive index change of 2.99 × 10−6 RIU (refractive index unit) and 3.87 × 10−6 RIU, respectively. These experimental results are found to be in general agreement with the simulation results of the propeller wake field. A comparison of the experimental wake measurements based on the device with the wake measurements based on a CTD (conductivity–temperature–depth) device reveals a consistent trend. The realisation of this detection technique is of great significance for the advancement of research in the field of optical detection of underwater vehicle wake streams.

High-Sensitivity Seawater Refraction Index Optical Measurement Sensor Based on a Position-Sensitive Detector.

The refractive index of seawater is one of the essential parameters in ocean observation, so it is necessary to achieve high-precision seawater refractive index measurements. In this paper, we propose a method for measuring the refractive index of seawater, based on a position-sensitive detector (PSD). A theoretical model was established to depict the correlation between laser spot displacement and refractive index change, utilizing a combination of a position-sensitive detector and laser beam deflection principles. Based on this optical measurement method, a seawater refractive index measurement system was established. To effectively enhance the sensitivity of refractive index detection, a focusing lens was incorporated into the optical path of the measuring system, and simulations were conducted to investigate the impact of focal length on refractive index sensitivity. The calibration experiment of the measuring system was performed based on the relationship between the refractive index of seawater and underwater pressure (depth). By measuring laser spot displacement at different depths, changes in displacement, with respect to both refractive index and depth, were determined. The experimental results demonstrate that the system exhibits a sensitivity of 9.93×10-9 RIU (refractive index unit), and the refractive index deviation due to stability is calculated as ±7.54×10-9 RIU. Therefore, the feasibility of this highly sensitive measurement of seawater refractive index is verified. Since the sensitivity of the refractive index measurement of this measurement system is higher than the refractive index change caused by the wake of underwater vehicles, it can also be used in various applications for underwater vehicle wake measurement, as well as seawater refractive index measurement, such as the motion state monitoring of underwater navigation targets such as AUVs and ROVs.

Forward modelling of the Cotton-Mouton effect polarimetry on EAST tokamak

Measurement of plasma electron density by far-infrared laser polarimetry has become a routine and indispensable tool in magnetic confinement fusion research. This article presents the design of a Cotton-Mouton polarimeter interferometer, which provides a reliable density measurement without fringe jumps. Cotton-Mouton effect on Experimental Advanced Superconducting Tokamak (EAST) is studied by Stokes equation with three parameters . It demonstrates that under the condition of a small Cotton-Mouton effect, parameter contains information about Cotton-Mouton effect which is proportional to the line-integrated density. For a typical EAST plasma, the magnitude of Cotton-Mouton effects is less than 2 for laser wavelength of 432 . Refractive effect due to density gradient is calculated to be negligible. Time modulation of Stokes parameters ( , ) provides heterodyne measurement. Due to the instabilities arising from laser oscillation and beam refraction in plasmas, it is necessary for the system to be insensitive to variations in the amplitude of the detection signal. Furthermore, it is shown that non-equal amplitude of X-mode and O-mode within a certain range only affects the DC offset of Stokes parameters ( , ) but does not greatly influence the phase measurements of Cotton-Mouton effects.

Refractive Laser Beam Measuring Diffusion Coefficient of Concentrated Battery Electrolytes

A thorough understanding of electrolyte transport properties is crucial in the development of alternative battery technology. As a key parameter, the diffusion coefficient offers important insights into the behavior of electrolytes, especially for fast charge of high-energy batteries. Existing methods of measurement are often limited by redox species or offer questionable accuracy due to side reactions and/or disruption of the diffusion profile. This work provides a novel optical method for measuring diffusion coefficients of liquid-phase concentrated battery electrolytes without electrochemical reactions. The method relies on the deflection of a refractive laser beam passing through an electrolyte of a minor concentration gradient in a triangular diffusion column. The diffusion coefficient, D, for a range of zinc sulfate electrolytes was successfully extracted by correlating the position of the laser beam to its concentration. Several other physicochemical properties of the same electrolytes are studied to correlate to the concentration-dependent diffusion coefficients, including viscosity, conductivity, and microstructure analysis based on vibrational spectroscopy (Infrared and Raman). Also included is the future application of the triangular column for in situ electrochemical measurements.

Characterizing air-coupled gas discharge acoustic transducers by using scanning laser Doppler refracto-vibrometry

Scanning laser Doppler vibrometry (SLDV) is an effective tool for characterizing acoustic transducers and visualizing acoustic waves, in particular, when using air-coupled ultrasonic emitters. Refraction of laser beams in the areas of oscillating air pressure enables measuring amplitude-frequency parameters of propagating waves in a wide range of frequencies. The technique of refracto-vibrometry has been used for non-contact measurement of phase and frequency parameters of vibration signals generated by a pulsed gas discharge in the ambient air. The proposed gas discharge acoustic transducer operates on the base of the electro-thermoacoustic effect accompanying the flow of spark discharge current in the air at atmospheric pressure. A feature of the proposed device is that the emitter membrane contains a central through-hole that allows the discharge plasma to propagate beyond the electrode space of the emitter. Such configuration of the emitter allows the generation of acoustic waves in the ultra-wide frequency range from 50 Hz to 4 MHz. The spectrum of generated oscillations is essentially non-uniform that is explained by the presence of both resonance peaks and absorption bands of acoustic waves in the device elements. The proposed technique was checked in the inspection of impact damage in a hybride CFRP/flax composite.

Ultrashort pulse laser micro processing strategies for fast beam deflection with acousto-optical deflectors

Acousto-optical deflectors (AOD) enable laser pulse-synchronous beam deflection up to the MHz range, which can deviate from the usual path control and raster scan strategies. Where the small working field of the AODs is not sufficient, a combination with a galvo scanner or an axis system can be used. Laser micromachining with modern ultrashort pulse lasers with a high pulse repetition rate is increasingly faced with the challenge of applying the laser power to the workpiece without too much heat remaining locally in the surface. AOD-based beam deflection can help here by quickly distributing the laser pulses on the surface, which is equivalent to a locally reduced laser pulse repetition rate without reducing the laser’s repetition rate. We provide an overview of the technology and present examples of innovative machining strategies resulting from the use of acousto-optical laser beam deflection.

Use of the Laser Beam Deflection Technique for Thermo-Optic Coefficients Study in Gadolinium-Yttrium Oxyorthosilicate Doped with Erbium Ions

Results of use of the laser beam deflection technique for determination of thermo-optic coefficients (TOCs) of the Er3+-doped gadolinium-yttrium oxyorthosilicate crystal (Er3+:(GdY) SiO– Er:GYSO) are presented. A 0.1 at.% Er-doped gadolinium-yttrium oxyorthosilicate crystal was grown by the Czochralski method under nitrogen atmosphere. Raw materials such as Er2O3, Gd2O3, Y2O3, and SiO2 were weighed according to the formula (Er0.001Gd0.8995Y0.0995)2SiO5. Optical properties of the biaxial Er:GYSO crystal are described within the frame of the optical indicatrix with orthogonal principal axes Np , Nm , and Ng . To characterize the anisotropy of the TOCs a sample from the grown Er:GYSO crystal was prepared in a shape of a rectangular parallelepiped with dimensions of 7.0 (Np ) × 8.0 (Nm ) × 8.5 (Ng ) mm3. Each face of the sample is perpendicular to one of the optical indicatrix axes Np , Nm and Ng . For determination of the TOCs the laser beam deflection technique for a material with a linear temperature gradient is used. Measurements are performed at the wavelength of 632.8 nm. The thermal coefficient of the optical path (TCOP) for the Er:GYSO crystal measured at the wavelength of 632.8 nm at different light polarization E and propagation direction k were obtained. The TCOP values are positive for all directions of the light propagation k // Np , Nm , Ng . This means that the sign of the thermal lens which is directly related to the TCOP value will also be positive, and the positive thermal lens is then expected for Np Nm-, and Ng -cut Er:GYSO. Applying an analysis of the thermal lensing the dn /dT value for Yb:GYSO is estimated to be 6.5×10–6 K–1.

Two-Axial Measurement of the Angular Microdeflection of a Laser Beam Using One Single-Axis Sensor.

The majority of current methods for measuring the angular deflection of a laser beam enable measurement only in one selected plane. However, there are tasks in which measurements of laser beam deflections in 3D are required. In this paper, we present a way of enabling two-axial measurements of the deflection of a beam based on a single-axis sensor. The key idea is to direct a laser beam, alternately, into one of two arms of a measurement system. In the first arm, the beam is transmitted directly to the angular sensor, while in the second, the beam is directed to the sensor via a special optical element that rotates the plane of the beam deflection; in other words, this element changes the deflection in the horizontal plane into a deflection in the vertical plane, and vice versa. To alternate the path of the beam, a variable phase retarder and a polarising beamsplitter are used. The proposed technique was experimentally verified, and the results confirm its effectiveness.

Young’s modulus of V3O5 thin films

Vanadium oxide V3O5 exhibits an insulator-to-metal transition (IMT) near 430 K, which is the highest value for all vanadium oxides exhibiting IMTs. This makes it interesting for advanced electronic applications. However, the properties of V3O5 have been little studied, and, in particular, there are no reports of experimentally determined mechanical properties. In this work, Young’s modulus of sputter-deposited V3O5 thin films has been determined by measuring the fundamental resonant frequency of V3O5-coated silicon microcantilevers using a laser beam deflection technique. After deposition, the films were characterized by x-ray diffraction, resistivity measurements, and atomic force microscopy. The value of Young’s modulus experimentally determined for V3O5 was 198 ± 14 GPa, which is slightly lower than the computationally derived values for bulk crystal V3O5.

Laser Thermal Wave Diagnostics of the Thermal Resistance of Soldered and Bonded Joints in Semiconductor Structures.

This paper is a review of recent applications of a laser photothermal mirage technique for sensing and measuring the thermal resistance of joint layers in modern electronic devices. A straightforward theoretical model of the interfacial thermal resistance based on the formation of a thin intermediate layer between jointed solids is described. It was experimentally shown that thermal properties of solder layers cannot be evaluated simply on the base of averaging the thermal properties of solder components. The review presents the laser thermal wave methodology for measuring thermal parameters of soldered and adhesively bonded joints. The developed theoretical model makes it possible to carry out a quantitative estimation of local thermal conductivities of joints and their thermal resistances by fitting theoretical results with experimental data obtained by the laser beam deflection method. The joints made with lead-containing and lead-free solders were studied. The anomalous distribution of thermal properties in the solder layer is explained by the diffusion of various atoms detected by energy dispersive X-ray spectroscopy. The laser beam deflection method made it possible to reveal a strong influence of the surface pretreatment quality on the interfacial thermal resistance.

Effect of fibre orientation on the light scattering during laser transmission welding

During laser welding of thermoplastic (LTW) composites reinforced with short fibres, a divergence of the laser beam is observed due to internal refraction of the beam at each matrix–fibre interface. This phenomenon leads to scattering of the laser beam in this heterogeneous medium, resulting in reduction of energy reaching the weld interface. This work presents a numerical study of the effect of fibre orientation in fibre-reinforced composites during the laser transmission welding simulation. A three dimensional (3D) numerical structure is generated to take into account the real microstructure of a composite material reinforced with short fibres. The information of fibre volume fraction, fibre length distribution and fibre orientation distribution is extracted from injection moulding simulations. Fibre orientation distribution function is extracted from fibre orientation tensors. An algorithm is implemented to trace rays propagating through composite material at two scales: microscopic and macroscopic. This algorithm uses optical properties of the composite material to simulate laser beam reflection and refraction in a complex structure. Laser beam scatter at the weld interface is simulated in 3D geometries with various fibre orientation distributions. The effect of fibre orientation on the light scattering phenomenon of laser is compared for different cases of fibre orientation. The simulation results are validated experimentally.

Electromagnetic biaxial scanning mirror based on 3D printing and laser patterning

Scanning mirror, as an optical vector scanning actuator, which can control the deflection and reflection of laser beam, and plays an important role in laser scanning, laser imaging and laser radar. However, the current stage of micro-electro-mechanical systems (MEMS) micromirror suffers from high cost and long preparation cycle. In order to solve these problems, a novel and lost-cost electromagnetic biaxial scanning mirror is proposed based on 3D printing and laser patterning. The mechanical structure of the biaxial scanning mirror is made of acrylonitrile butadiene styrene (ABS) material. The copper foil accurately patterned by ultraviolet (UV) laser is used as the driving coil, and the annular neodymium magnet set provides the radial magnetic field. The experimental results show that the scanning mirror can achieve vertical scanning with an optical angle of 32.4° and horizontal scanning with an optical angle of 16.5° under the resonance excitation of 119 Hz and 250 Hz, respectively. The proposed biaxial scanning mirror has the advantages of low cost and rapid preparation, which has potential applications in intelligent household, regional monitoring, industrial cameras, etc. A novel and lost-cost electromagnetic biaxial scanning mirror is proposed based on 3D printing and laser patterning. The mechanical structure of the biaxial scanning mirror is made of acrylonitrile butadiene styrene (ABS) material. The copper foil accurately patterned by ultraviolet (UV) laser is used as the driving coil, and the annular neodymium magnet set provides the radial magnetic field. The scanning mirror can achieve vertical scanning with an optical angle of 32.4° and horizontal scanning with an optical angle of 16.5°, which has low cost, short preparation cycle, and has potential applications in intelligent household, regional monitoring, industrial cameras, and intelligent household appliances. • A novel biaxial electromagnetic scanning mirror based on 3D printing and laser patterning is proposed, which has the advantages of low cost and rapid preparation. • The mechanical structure of the biaxial scanning mirror is made of acrylonitrile butadiene styrene (ABS) material. The copper foil accurately patterned by ultraviolet (UV) laser is used as the driving coil. These make the scanning mirror have lower cost and faster preparation cycle. • The scanning mirror can achieve vertical scanning with an optical angle of 32.4° and horizontal scanning with an optical angle of 16.5°. Compared with similar polymer scanning mirrors, it has a larger angle.

A quality improvement method for complex component fine manufacturing based on terminal laser beam deflection compensation

A quality improvement method for complex component fine manufacturing based on terminal laser beam deflection compensation

Reconstruction of optical parameter fields in graded refractive index media based on laser beam deflection and attenuation measurement.

Graded refractive index media (GRIM) are widely applied as special functional materials in many practical engineering fields. Accurate knowledge of the optical parameters is key to using GRIM. In this study, simultaneous reconstruction of the refractive index and absorption coefficient fields of GRIM based on laser beam deflection and attenuation measurement is studied. A set of rays from the given positions along the given directions transits GRIM, and the deflection and attenuation of rays at the exit boundary are recorded as measurement information. A two-step reconstruction strategy is proposed to reconstruct the refractive index and absorption coefficient fields. First, the refractive index field is reconstructed from the ray deflection measurement information. Then, the ray trajectory can be obtained by the Runge-Kutta ray tracing technique based on the reconstructed refractive index field. Afterwards, the absorption coefficient field is reconstructed from the ray attenuation measurement according to the Bouguer law. The regularization technique based on the generalized Gaussian Markov random field model is employed to improve the reconstruction results. All test results show that the two-step reconstruction strategy is accurate and can be regarded as a promising reconstruction technique.

Refractive index and temperature coefficient of refractive index of Al2O3- and SiO2-water nanofluids

• Measurements are made of the refractive index and temperature coefficient of refractive index (∂n/∂T) for two nanofluids, Al 2 O 3 -water and SiO 2 -water. • For both nanofluids, the refractive index decreases with increasing temperature and increases with increasing particle concentration. • The variation of refractive index is approximately linear with concentration. • ∂n/∂T for Al 2 O 3 -water nanofluids can be approximated as that of water with an accuracy better than ±5% for a concentration φ < 1%. • For SiO2-water nanofluid, ∂n/∂T can be approximated as that of water with an accuracy of better than ±5% for a concentration φ < 4%. Measurements are made of the refractive index and temperature coefficient of refractive index (∂n/∂T) for two nanofluids, Al 2 O 3 -water and SiO 2 -water, over the temperature range 20–40°C at a wavelength of 632.8 nm. These optical properties are needed for refractive index-based temperature and heat transfer measurements, particularly laser interferometry. A laser beam deflection technique is used to measure the refractive index of the nanofluids. The temperature coefficient of refractive index is determined by measuring the phase change with temperature, using Mach-Zehnder interferometry. Measurements are made for Al 2 O 3 -water nanofluids up to a weight-based concentration of ϕ = 20% and for SiO 2 -water nanofluids up to a weight-based concentration of ϕ = 40%. The refractive index data are used to quantify the errors in interferometric temperature measurements produced by non-homogenous nanofluid suspensions. In the literature, the optical properties of dilute water-based nanofluids are sometimes assumed to be equal to those of water for interferometry experiments. The limits of this approximation are estimated. The current measurements indicate that ∂n/∂T for Al 2 O 3 -water nanofluids can be approximated as that of water with an accuracy better than ±5% for a concentration ϕ < 1%. For SiO 2 -water nanofluid, ∂n/∂T can be approximated as that of water with an accuracy of better than ±5% for a concentration ϕ < 4%.

Reconstruction of the gradient field in the cross-section of an acoustic wave and its usefulness in processing acoustic wave fields.

This paper proposes a method of reconstructing the gradient field in a cross-section of the acoustic wave using the laser beam deflection tomography, then verifing that the simultaneous acquisitions of the relative acoustic pressure distribution and the gradient field can make the direct employment of Kirchhoff's integral theorem feasible. Specifically, a position-sensitive detector (PSD) is used to sense the deflection of a laser beam impinging on a propagating acoustic wave. The deflection of the laser beam can be divided into two parts; one is in the plane that laser beams go through, and the other is perpendicular to the plane. Combining the tomographic results using the two parts of the deflection, the gradient field of the propagating acoustic wave in a cross-section is obtained, which is an extended version of beam deflection tomography. Based on the gradient of a wavefield along with the relative sound pressure distribution, Kirchhoff's integral theorem can be directly employed to calculate and analyze the wavefield further, which was hardly achieved in the past due to the lack of dense gradient sensing regimes. To verify the usefulness, two experiments are conducted, whose results indicate that the densely and precisely acquired gradient field of an acoustic wave is useful in solving the problem of port and starboard ambiguity, and the problem of accurate near-field prediction can also be well addressed, which in a deeper sense benefit from the direct employment of Kirchhoff's integral theorem in practical applications.