Photoelastic Coefficient Research Articles

Temperature-dependent photo-elastic coefficient of silicon at 1550 nm

This paper presents a study on the temperature dependent photo-elastic coefficient in single-crystal silicon with (100) and (110) orientations at a wavelength of 1550 nm. The measurement of the photo-elastic coefficient was performed using a polarimetric scheme across a wide temperature range from 5 to 300 K. The experimental setup employed high-sensitivity techniques and incorporated automatic beam path correction, ensuring precise and accurate determination of the coefficient’s values. The results show excellent agreement with previous measurements at room temperature, specifically yielding a value of dn/dsigma = -2.463 times 10^{-11} 1/Pa for the (100) orientation. Interestingly, there is a significant difference in photo-elasticity between the different crystal orientations of approximately 50%. The photo-elastic coefficient’s absolute value increases by approximately 40% with decreasing temperature down to 5 K. These findings provide valuable insights into the photo-elastic properties of silicon and its behavior under varying mechanical stress, particularly relevant for optomechanical precision experiments like cryogenic gravitational wave detectors and microscale optomechanical quantum sensors.

Experimental Study on the Photoelastic Coefficient and Its Wavelength Dispersion for Quantitative Imaging of Residual Strain in Commercial SiC Substrates

Experimental Study on the Photoelastic Coefficient and Its Wavelength Dispersion for Quantitative Imaging of Residual Strain in Commercial SiC Substrates

Characterization of the photoelastic dispersion coefficient using polarized digital holography.

The photoelastic dispersion coefficient represents the relationship between stress and the differences in refractive indices in a birefringent material. However, determining the coefficient using photoelasticity is challenging, as it is difficult to determine the refractive indices within photoelastic samples that are under tension. Here we present, for the first time, to our knowledge, the use of polarized digital holography to investigate the wavelength dependence of the dispersion coefficient in a photoelastic material. A digital method is proposed to analyze and correlate the differences in mean external stress with differences in mean phase. The results confirm the wavelength dependence of the dispersion coefficient, with an accuracy improvement of 25% compared to other photoelasticity methods.

Determination of the mean relative photoelastic dispersion factor by means of photoelasticity

This work proposed to determine the mean dispersion factor, < αC > , which is related to the relative photoelastic dispersion coefficient of a photoelastic material, subjected to consecutive external stresses, by means of a direct computational method associated with error theory. An important feature of photoelasticity, related to the light wavelength, is the photoelastic dispersion coefficient, which is determined in traditional methods by indirect statistical processes, as it depends on refractive indices, which are difficult to determine in photoelastic materials. Therefore, finding an alternative form to determine this coefficient is necessary and can help in the processes that involve the use of photoelasticity. The mean dispersion factor obtained was < αC > = (8,90 ± 0,42) x 10-5, which works as a system calibrator to allow the determination of the photoelastic dispersion coefficient of photoelastic materials by photoelasticity, with greater accuracy.

Photoelastic coefficient measurement method of optical glasses based on Mach–Zehnder interferometer

A method based on Mach–Zehnder interferometer and stress optical coefficients theory was proposed for measuring the photoelastic coefficients of optical glasses. The corresponding apparatus is built to measure the photoelastic coefficients of fused silica and As2S3 glasses, with p12 = 0.27 and 0.26 at 632.8 nm, respectively. The validity and accuracy of the present technique were tested on the samples of fused silica and As2S3 glass, with the relative error not exceeding 10% compared to that in previous studies and the causes of errors were analyzed. The photoelastic coefficients of tellurite glasses with component 75TeO2-20ZnO-5Na2O were measured, with p11 = 0.23 and p12 = 0.22. The acousto-optic (AO) figure of merit M2 of the three types of glass was calculated and the role of photoelastic coefficient in the equation was discussed, providing an effective technique for investigating the AO interaction in a glass.

Off-axis photoelasticity by anisotropic molecular deformation of uniaxially aligned cellulose nanofiber films

We report the angle dependence of the photoelasticity for unidirectionally aligned films of bacterial cellulose nanofibers (CNFs) by applying the off-axis stress at 0°–90° with respect to the CNF orientation. The photoelastic coefficient was positive when the stress direction was close to the CNF axial direction, and it was negative when the stress was applied close to the lateral direction. The positive to negative photoelasticity was also observed in the off-axis photoelasticity of the cellophane film and in the density functional theory (DFT) calculations for the stretching between two atoms in the cellobiose model. On the other hand, unlike the cellophane film, the CNF film showed a positively and negatively asymmetric photoelasticity of 5 to −10 TPa−1, reflecting the anisotropy of the crystal modulus tensor. We found that the presence or absence of cellulose crystals controls the anisotropy of photoelasticity by constraining the molecular deformation.

Effect of water absorption on the structure and properties of isosorbide-based polycarbonate

The structure and properties of isosorbide-based polycarbonate (ISB-PC), and its responses to water absorption were investigated. Although the glass transition temperature of an ISB-PC film decreased as its water content increased, its Young's modulus increased as the strain at break decreased. The tensile yield stress of the polymer decreased following water absorption. Optical properties such as the refractive index and the photoelastic coefficient in the glassy state were also affected by water absorption. The refractive index increased with the water content, although the refractive index of water is lower than that of the polymer. The photoelastic coefficient reached a maximum at a specific water content. These phenomena can be explained by the interaction between water molecules and the carbonyl groups in the polymer, which affect the segmental mobility and polarizability anisotropy of ISB-PC. Basic properties such as entanglement molecular weight were also determined.

Investigation of Photoelastic Property and Stress Analysis for Optical Polyimide Membrane through Stress Birefringence Method

Optical polyimide (PI) membranes have been increasingly attractive in optoelectronic substrate and optical element material applications. Controlled stress distribution is very important to optical PI membrane-based optics. However, nondestructive absolute stress measurement inside optical PI membranes remains challenging. In this letter, we adopted the stress birefringence method to experimentally investigate the correlation between stress and retardation in uniaxially, biaxially, and circularly stretched PI membranes. The calculated value of the photoelastic coefficient was found to be around 400 nm/Mpa·cm. A theoretical model was established where the retardation angle is the negative arctan of the principal stress ratio in the biaxially stretched membrane. We also found that the average retardation angle is an important parameter for evaluating the uniformity of stretching force in the circularly stretched membrane. This work provides a better understanding of the stress birefringence measurement of membrane materials.

Measurement of Mechanical and Thermal Strains by Optical FBG Sensors Embedded in CFRP Rod

The present study intends to provide the photoelastic coefficient and thermal expansion coefficient needed to use an FBG-embedded CFRP rod (smart rod) as strain sensor. Due to the monolithic combination of the FBG sensor with a CFRP rod, the smart rod is likely to exhibit thermal and mechanical properties differing from those of the bare FBG sensor. A tensile test showed that the photoelastic coefficient of the smart rod is 0.204, which is about 7.3% lower than the 0.22 value of the bare optical FBG. Moreover, the thermal expansion coefficient of the smart rod obtained through a thermal test appeared to be negative with a low value of −0.190×10−6/°C. Consequently, the temperature dependence of the smart rod is mainly expressed by means of the thermooptic coefficient. Compared to the bare FBG sensor, the smart rod is easier to handle and can measure compressive strains, which make it a convenient sensor for various concrete structures.

Acousto-optical modulation of thin film lithium niobate waveguide devices

Due to its strong piezoelectric effect and photo-elastic property, lithium niobate is widely used for acousto-optical applications. However, conventional bulk lithium niobate waveguide devices exhibit a large footprint and limited light–sound interaction resulting from the weak guiding of light. Here, we report the first acousto-optical modulators with surface acoustic wave generation, phononic cavity, and low-loss photonic waveguide devices monolithically integrated on a 500 nm thick film of lithium niobate on an insulator. Modulation efficiency was optimized by properly arranging the propagation directions of surface acoustic waves and optical guided modes. The effective photo-elastic coefficient extracted by comparing the first and third harmonic modulation signals from an on-chip Mach–Zehnder interferometer indicates the excellent acousto-optical properties of lithium niobate are preserved in the thin film implementation. Such material property finding is of crucial importance in designing various types of acousto-optical devices. Much stronger amplitude modulation was achieved in a high Q (>300,000) optical resonator due to the higher optical sensitivity. Our results pave the path for developing novel acousto-optical devices using thin film lithium niobate.

Enhanced Sensitivity of Silicon-Photonics-Based Ultrasound Detection via BCB Coating

Ultrasound detection via silicon waveguides relies on the ability of acoustic waves to modulate the effective refractive index of the guided modes. However, the low photo-elastic response of silicon and silica limits the sensitivity of conventional silicon-on-insulator sensors, in which the silicon core is surrounded by a silica cladding. In this paper, we demonstrate that the sensitivity of silicon waveguides to ultrasound may be significantly enhanced by replacing the silica over-cladding with bisbenzocyclobutene (BCB)-a transparent polymer with a high photo-elastic coefficient. In our experimental study, the response to ultrasound, in terms of the induced modulation in the effective refractive index, achieved for a BCB-coated silicon waveguide with TM polarization was comparable to values previously reported for polymer waveguides and an order of magnitude higher than the response achieved by an optical fiber. In addition, in our study, the susceptibility of the sensors to surface acoustic waves and reverberations was reduced for both TE and TM modes when the BCB over-cladding was used.

Post-implantation depth profiling using time-domain Brillouin scattering

The unique capabilities of time domain Brillouin scattering (TDBS) for studying post-implantation effects on optical and opto-elastic properties of semiconductors are discussed. This method utilizes coherent acoustic phonons to measure depth-dependent optical and opto-elastic changes arising from structural damage caused by ion implantation. This non-destructive technique is shown to be two orders of magnitude more sensitive than Rutherford backscattering spectrometry. Results are presented for silicon carbide (SiC), gallium arsenide (GaAs) and diamond. Using the TDBS approach, we have obtained depth-dependent profiles of the complex refractive index in hydrogen implanted 4H-SiC, and of the photoelastic coefficient in hydrogen implanted GaAs. In helium implanted diamond samples, both the complex refractive index and the photoelastic coefficient have been determined. A comparison between indirect (4H-SiC, diamond) and direct (GaAs) band gap semiconductors shows the sensitivity of TDBS to the particular optical properties of different semiconductors. These studies provide basic insight into the dependence of optical properties on defect densities created by ion implantation, which is of relevance to the fabrication of photonic and optoelectronic devices. Further development of TDBS shows promise for measuring the depth dependent positions of specific defects (color centers) in wide band gap semiconductors.

Photoelastic birefringence of copolymers with non-planar structure

We demonstrate the utility of nonplanar building blocks to tune the polymer photoelastic birefringence and obtain near zero and negative photoelastic coefficients. Photoelastic properties of two novel random copolymers systems: 2-vinlypyridene (2VP)-hydroxyadmantyl methacrylate (HAMA) and vinyl pyrrollidone (VP)-isobornylacrylate (iBOA) were investigated at a function of comonomer composition. Photoelastic coefficient of the copolymers could be facilely tuned by changing the copolymer composition. In particular, we show that negative stress optic coefficient could be obtained from VP - iBOA copolymers and near zero stress optic coefficient could be obtained from 2VP -HAMA copolymers. In addition, we investigate the effect of addition of triethylene glycol (TEG) as a plasticizer on the photoelastic properties for the 2VP-HAMA copolymers. We found that addition of TEG led to a reduction in both the polymer Tg and photoelastic coefficient. Our study indicates that bulky non-planar side groups in the polymer backbone tend to induce negative photoelastic birefringence and can be utilized as important building blocks for the design of optical polymers.

Basic Study on Photoelastic Stress Measurement for Surgery Simulator using Gel Materials

Catheterization procedure is a typical example of minimally invasive medical treatment. This has the advantage that the physical burden on the patient can be remarkably reduced as compared with the conventional medical treatment method involving craniotomy or hemorrhage etc. However, on the other hand, since visual and tactile restrictions are limited at the time of surgery, physicians are required to have expert skill and many experiences. To raise the success rate of surgery irrespective of the amount of surgical experience, we have conducted a simple model using a glass tube and a simulation operation using an experimental animal, but they have low bio-reproducibility and ethical problems was there. In recent years, due to the development of new materials and the appearance of 3D printers, shape reproducibility has improved. A more desirable function of the surgical simulator is to visualize the force applied to the vessel wall surface by the catheter. This is because there is a danger of attracting vascular occlusion etc. when a large force is applied to the wall surface of the blood vessel. Therefore, it is considered important to quantitatively evaluate the operational feeling for simulated surgery. Therefore, we aim to manufacture a vascular surgical simulator with high bio-reproducibility that enables real-time stress measurement. In this research, stress visualization method using photoelastic effect is applied to surgical simulator. By using the photoelastic effect, it becomes possible to check the stress state of the entire field of view, and it is possible to obtain a stress state when a medical instrument such as a coil or a stent is inserted. Therefore, it is useful not only for training but also for the development of medical instruments. Heretofore, examples using PDMS and polyurethane elastomer as a surgical simulator material have been reported, but the longitudinal modulus of elasticity is high and it is unsuitable for a blood vessel model. Therefore, we focused on PVA hydrogel as surgical simulator material. PVA (polyvinyl alcohol) hydrogel is a material that can be expected to reproduce vascular tissue because its physical properties can be easily changed by changing the compounding ratio and degree of polymerization of powdered PVA. By changing the compounding ratio of powdered PVA in the range of 4-15 wt.%, We realized PVA hydrogel's longitudinal elastic modulus of 60-450 kPa. Since the longitudinal elastic modulus of human vascular tissue is 20-3000 kPa, PVA hydrogel is useful for reproducing soft vascular tissue. Further, the average photoelastic coefficient of PVA hydrogel is 2.30 × 10-9 Pa-1, which has a photoelastic coefficient greater than that of polyurethane elastomer which is a photoelastic material useful for photoelastic stress measurement. (photoelastic coefficient of polyurethane elastomer is 1.45 × 10-9 Pa-1.) Therefore, it was confirmed that it is a useful material for stress measurement using photoelastic effect. In this study, a simple blood vessel model was prepared using PVA hydrogel and simulated surgery using a catheter was performed. In addition, a photoelastic observation system was constructed for stress measurement, and a method for correcting the influence due to the presence of incident light, ambient light, and initial stress was examined. As a result, we successfully extracted and visualized the stress applied to the simple blood vessel model.

(Invited) Development of Stress Measurable Vessel Model using Photoelastic Materials

Today, intravascular catheter surgeries, which are kind of minimally invasive procedures, are widely used surgical techniques. As compared to conventional open surgery, incision size is small, and burden on patients is reduce. Therefore, the wounds associated with pain is small, and time to heal is also short. On the other hand, since operative field was restricted during surgery, operators need to have sufficient skill for intravascular catheter surgeries. To obtain it, operators must practice using artificial surgical simulators. Materials for surgical simulators are requires having physical properties as like human organs. Although lab animals have similar physical properties, they are not appropriate from an ethical perspective. Moreover, recently, silicone-based materials are used for surgical simulators, but their physical properties do not mimic those of human organs. Gel materials are expected for materials of surgical simulators, because their mechanical properties are similar to human organs and they contain large amounts of moisture. Besides, gel material can apply for fabrication of the complicate shape of human organs using 3D printer. The issue of practice using conventional surgical simulators is quantitative evaluation of operator skill. In the case of intravascular catheter surgeries, measurement of applied force to vessel wall by catheter and guide wire is an important function. Since vessel walls of patients are delicate, if devices applied excess force, and unexpected accidents such as vascular occlusion are attracted. In this study, we focused on the photoelasticity of gel materials. If vessel models are made of these gel materials, it is possible them to evaluate quantitative score of operator skill. To realize these surgical simulators, we developed the stress measurement system for photoelasticity of gel materials. Besides, we evaluated the physical properties such as mechanical properties and photoelastic coefficient of several gel materials using our developed system. We constructed new stress measurement system for photoelasticity of gel materials Our system consisted of several polarizers and wave plates, and it could measure the value of stress and direction of stress in X-Y plane from RGB values on color map. In order to minimize the overlap ratio of the same color in the color map, two 1 wave plates were insert to conventional observation system of circularly polarized wave and the insertion angle of two 1 wave plates is 30 degrees. We suggested analysis algorithm which enables to eliminate the effects of incident light and ambient light. As the results, we succeed to measure the tensile stress by our system during the tensile test of PVA hydrogel. Measurement error was less than 6.3% at the stress range from 0 to 80 kPa, and it is sufficient measurement resolution for evaluate stress during practice of intravascular catheter surgeries. Generally, Young’s moduli of human vessels depend on the organ and/or symptoms, and they are ranged from 0.02 to 3 MPa. Although mechanical properties of gel material can be adjusted by changing kinds of formulas and their concentrations, it is difficult that only one type gel coverall the range of Young’s moduli of human vessels. Therefore, the materials of surgical simulators are selected on demand from patient of case history. Finally, we investigated the Young’s moduli and photoelastic coefficients of two types of designable gels such as inter cross-linking network gels and double networks gels. As the results, two type gels exhibited photoelasticity. Young’s moduli of inter cross-linking network gels are approximately 1 MPa and the effect of formula concentration was slightly. On the other hand, the range of Young’s modulus of double networks gels was 0.12 to 0.77 MPa for strain range from 0 to 15%, and it was within the range of Young’s modulus of human vessels. Their photoelastic coefficients were 0.012 to 0.022 ×10-9 Pa-1. The measurement error of our system was 7.3%, and was acceptable.

The photoelastic coefficient {P}_{12} of H+ implanted GaAs as a function of defect density

The photoelastic phenomenon has been widely investigated as a fundamental elastooptical property of solids. This effect has been applied extensively to study stress distribution in lattice-mismatched semiconductor heterostructures. GaAs based optoelectronic devices (e.g. solar cells, modulators, detectors, and diodes) used in space probes are subject to damage arising from energetic proton (H+) irradiation. For that reason, the effect of proton irradiation on photoelastic coefficients of GaAs is of primary importance to space applied optoelectronics. However, there yet remains a lack of systematic studies of energetic proton induced changes in the photoelastic properties of bulk GaAs. In this work, the H+ energy and fluence chosen for GaAs implantation are similar to that of protons originating from the radiation belts and solar flares. We present the depth-dependent photoelastic coefficient {P}_{12} profile in non-annealed H+ implanted GaAs obtained from the analysis of the time-domain Brillouin scattering spectra. The depth-dependent profiles are found to be broader than the defect distribution profiles predicted by Monte Carlo simulations. This fact indicates that the changes in photoelastic coefficient {P}_{12} depend nonlinearly on the defect concentrations created by the hydrogen implantation. These studies provide insight into the spatial extent to which defects influence photoelastic properties of GaAs.

Optic, acoustic and acousto-optic properties of tellurium in close-to-axis regime of diffraction

We examined the optic, acoustic, photoelastic and acousto-optic (AO) properties of single crystal tellurium. We also determined the Bragg angle dependences on the acoustic frequency at 10.6 μm. The phenomenon of optical activity and its influence on the Bragg matching condition during anisotropic diffraction near the optic axis of the crystal are discussed in detail. Based on the results of our calculations, we designed, fabricated and characterized an AO cell to determine parameters of the anisotropic interaction with longitudinal acoustic waves propagating along the X axis in the crystal. In our experiments, we also measured the value of one of the important photoelastic coefficient in tellurium, p41 = 0.14 ± 0.01 and demonstrated that this coefficient determines the efficiency of the anisotropic diffraction in the employed geometry.

Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators

We realise a circular gray-field polariscope to image stress-induced birefringence in thin (sub-micron thick) silicon nitride membranes and strings. This enables quantitative mapping of the orientation of principal stresses and stress anisotropy, complementary to, and in agreement with, finite element modeling. Furthermore, using a sample with a well-known stress anisotropy, we extract a value for the photoelastic (Brewster) coefficient of silicon nitride, C ≈ (3.4 ± 0.1) × 10−6 MPa−1. We explore possible applications of the method to analyse and quality-control stressed membranes with phononic crystal patterns.

Electro-optic effect and photoelastic effect of feroelectric relaxors

To understand the origin of the electro-optic effect (EO-effect) of ferroelectric relaxors, the relationships among the quadratic EO-coefficient, photoelastic coefficient, and electron density were elucidated. The quadratic EO-coefficient is given by the product of the photoelastic and electrostrictive coefficients. Materials consisting of heavy elements normally exhibit high refractive indices and large photoelastic effects, indicating that the photoelastic coefficient increases with electron density of materials. The photoelastic coefficient was calculated as a function of the electron density of materials. The equations derived in this study were experimentally confirmed using lanthanum-added lead–zirconate–titanate (PLZT) transparent ceramics. It was found that the origin of the EO-effect in ferroelectric relaxors was the photoelastic effect coupled with electric-field-induced strain via the piezoelectric and electrostrictive effects.

On the optimization of fiber Bragg grating optical sensor using genetic algorithm to monitor the strain of civil structure with high sensitivity

The effect of strain on civil structures is experimentally studied using fiber Bragg grating (FBG). The genetic algorithm is implemented to optimize the multiple parameters (Poisson’s ratio, photoelastic coefficient P11, and photoelastic coefficient P12) of the proposed sensor. The optimized results helped in increasing the sensitivity in terms of wavelength shift. It is observed that the proposed FBG provides maximum wavelength shift of 38.16 nm with Poisson’s ratio of 1.94, photoelastic coefficient P11 of 1.994, and photoelastic coefficient P12 of 1.8103.