A two-dimensional material stress nondestructive detection method based on polarization propagation matrix evolution

Abstract

This invention discloses a non-destructive testing method for stress in two-dimensional materials based on the evolution of the polarization propagation matrix. The testing system comprises a light source, chopper, polarizer, photoelastic modulator, microscope objective, detector, lock-in amplifier, and data processing module. During testing, a continuous laser beam is modulated and irradiates the two-dimensional material under test. Localized stress within the material induces perturbation of the dielectric tensor, causing the complex refractive index and polarization propagation matrix to evolve, resulting in polarization phase difference and polarization coupling effects. After photoelectric conversion, the reflected light is simultaneously demodulated by the lock-in amplifier to obtain the DC signal and the 2f harmonic signal. Combined with the differential reflection spectrum, and relying on the polarization propagation matrix model inversion, the numerical value and spatial distribution of localized stress in the sample can be obtained. This method is applicable to various two-dimensional materials and can detect various types of localized stress, such as thermal stress and residual stress. It employs non-contact detection, enabling full-domain stress scanning imaging of the sample. It has strong anti-interference capabilities, high detection accuracy, and a wide range of applications.

Description

Technical Field

[0001] This invention relates to the field of optical detection and polarization spectral characterization technology for two-dimensional materials, and in particular to a non-destructive testing method for stress in two-dimensional materials based on the evolution of polarization propagation matrix. Background Technology

[0002] Two-dimensional materials, with their unique lattice structure and excellent optoelectronic and mechanical anisotropy, have broad application prospects in microelectronics, optoelectronic devices, and flexible electronics. However, during the growth, mechanical exfoliation, artificial transfer, and device service processes, two-dimensional materials are prone to localized stresses such as thermal stress, interfacial residual stress, transfer stress, and mechanical bending stress. These localized stresses alter the lattice symmetry, electron orbital distribution, and band structure, modulating the dielectric response and polarization optical propagation characteristics, severely impacting the optoelectronic performance and structural stability of devices. Therefore, achieving high-precision, non-destructive, high spatial resolution, and identifiable quantitative detection and spatial distribution characterization of localized stresses in two-dimensional materials is a key technological requirement for both basic research and industrial applications.

[0003] Currently, the mainstream techniques for stress characterization of two-dimensional materials include Raman spectroscopy, photoluminescence spectroscopy, and differential reflectance spectroscopy. Raman spectroscopy relies on the vibrational properties of lattice phonons, inverting stress through changes in the position, width, and splitting of Raman characteristic peaks. Essentially, it is an indirect detection based on lattice vibrational frequencies. Its detection effectiveness is highly dependent on the material's Raman activity, excitation wavelength, and phonon mode intensity. For ultrathin two-dimensional materials, samples with weak Raman signals, or non-uniform stress distributions, it suffers from low signal-to-noise ratio, insufficient spatial resolution, and difficulty in distinguishing subtle stresses. Furthermore, Raman technology only focuses on changes in lattice vibrational frequencies, neglecting the modulation effect of localized stress on polarization propagation behavior, propagation phase, and polarization mode coupling. Therefore, it cannot establish a physical correlation between stress and polarization propagation evolution, nor can it achieve stress analysis and inversion based on polarization propagation mechanisms. Photoluminescence spectroscopy utilizes the modulation effect of stress on the band structure, characterizing stress through changes in exciton emission peak parameters. However, it is only applicable to semiconductor two-dimensional materials with strong exciton emission characteristics, limiting its applicability. Differential reflection spectroscopy, a polarization optics characterization technique, obtains the in-plane static optical anisotropy of a material by comparing the reflectance differences along orthogonal polarization directions. This technique treats two-dimensional materials as statically anisotropic reflective media, focusing only on the reflectance differences along orthogonal polarization directions and neglecting the modulation of polarization propagation paths and polarization state evolution by stress. Its models often employ diagonalized polarization response matrices, assuming independent polarization channels and failing to consider stress-induced polarization coupling and propagation phase mismatch. It can only detect crystal orientation and static anisotropy, but cannot explain polarization perturbations, mode mixing, and polarization rotation phenomena under stress. Furthermore, in practical applications, two-dimensional materials are often multilayer composite structures of material / interface / substrate. The propagation of polarized light between layers generates phase accumulation and interface interference effects. Local stress further modulates the complex refractive index and propagation phase of each layer, altering the overall polarization propagation response. However, existing techniques generally simplify two-dimensional materials to single-layer reflective media, lacking multilayer polarization transmission matrix models. This fails to characterize the modulation effect of interface propagation enhancement on stress signals, limiting the ability to detect local stress with high sensitivity and achieve high-precision spatial distribution imaging.

[0004] In summary, existing detection techniques such as Raman spectroscopy and differential reflection spectroscopy cannot analyze the local stress modulation law from the perspective of polarization propagation mechanism. They have shortcomings such as low sensitivity to weak stress, inability to characterize polarization coupling and phase evolution, lack of resolution capability for multi-layer interfaces, and limited spatial characterization accuracy. These limitations make it difficult to meet the practical needs of non-destructive high-precision stress detection of two-dimensional materials, mapping of stress distribution across the entire domain, and synergistic characterization of polarization propagation characteristics. Therefore, there is an urgent need to design a new non-destructive stress detection method for two-dimensional materials based on the evolution of polarization propagation matrix. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a non-destructive testing method for stress in two-dimensional materials based on the evolution of the polarization propagation matrix. By constructing a physical correlation model of stress-dielectric tensor-polarization propagation matrix-reflection differential response, and taking into account stress-induced polarization coupling, polarization propagation phase evolution, and the enhancement effect of polarization interference at multilayer interfaces, this method achieves high sensitivity, non-contact non-destructive testing, and high-precision spatial distribution inversion of local stress in two-dimensional materials. This effectively overcomes the shortcomings of existing technologies, such as low detection sensitivity, lack of mechanistic models, and insufficient spatial resolution, and is suitable for the precise stress detection needs of various two-dimensional materials and their composite structures.

[0006] The technical solution adopted by this invention to solve its technical problem is: a two-dimensional material stress non-destructive testing method based on polarization propagation matrix evolution. This testing method is implemented based on a two-dimensional material stress non-destructive testing system, which includes a light source, a chopper, a polarizer, a photoelastic modulator, a semi-reflective mirror I, an auxiliary light source, a mirror, a beam splitter, a microscope objective, a sample stage, a semi-reflective mirror II, a CCD, an analyzer, a detector, a lock-in amplifier, and a data processing module. The light source, chopper, polarizer, and photoelastic modulator are arranged coaxially along the main optical path. The output of the photoelastic modulator is connected to a beam splitter via a semi-reflective mirror I. The auxiliary light source is connected to the auxiliary optical path of the semi-reflective mirror I. The downstream of the beam splitter is connected to a microscope objective, and an adjustable sample stage is placed below the microscope objective. The sample reflected light passes through the microscope objective and the beam splitter, then is guided into the detection branch via a mirror, and sequentially passes through a semi-reflective mirror II and a polarizer before being connected to the detector. The detector, chopper, and photoelastic modulator are electrically connected to a lock-in amplifier. The lock-in amplifier is communicatively connected to the data processing module. The CCD is used to observe the spot quality and sample surface morphology in real time, and to assist in sample positioning and focusing. The two-dimensional material stress nondestructive testing method includes the following steps: S1. Provide a two-dimensional material sample to be tested, wherein the two-dimensional material sample contains localized stress. S2. The incident light is modulated into periodic pulse light by a chopper, and then converted into linearly polarized light by a polarizer. S3. The linearly polarized light is input into the photoelastic modulator for periodic polarization state modulation to obtain dynamically modulated polarized light; S4. Focus the dynamically modulated polarized light onto the surface of the two-dimensional material sample; S5. Localized stress within two-dimensional materials causes changes in lattice symmetry and electron orbital distribution, which in turn causes perturbation and evolution of the dielectric tensor of two-dimensional materials. S6. Based on the mathematical relationship between dielectric tensor and complex refractive index, the complex refractive index in different polarization directions is obtained by solving the perturbed dielectric tensor. The change in complex refractive index further drives the evolution of the polarization propagation matrix of the two-dimensional material. S7. Different polarization directions produce polarization propagation phase difference due to the difference in complex refractive index, and at the same time, local stress induces polarization mode coupling propagation effect. S8. The reflected polarized light after being reflected by the two-dimensional material passes through the analyzer and detector in sequence to complete the conversion of optical signal to electrical signal; S9. The lock-in amplifier synchronously receives the chopper reference frequency signal, the photoelastic modulator reference frequency signal and the detector output electrical signal, and synchronously demodulates and extracts the DC signal and the 2f harmonic modulation signal. S10. Establish a quantitative correspondence between the polarization propagation matrix and the reflected differential signal; S11. Based on the changes in the reflection differential spectral signal, the magnitude and spatial distribution of local stress in two-dimensional materials are obtained by inversion using the polarization propagation matrix model.

[0007] Furthermore, the two-dimensional material is any one of ReSe2, ReS2, MoS2, WSe2, or MoSe2; the localized stress originates from at least one of thermal stress, transferred stress, interfacial stress, residual stress, bending stress, or applied mechanical stress.

[0008] Furthermore, the incident light in step S2 is a 532nm single-longitudinal-mode continuous laser; the polarizer is a Glan Taylor prism, and the polarization direction of the polarizer is set at a 45° angle with the main axis of the photoelastic modulator; the modulation frequency of the photoelastic modulator is set to 50kHz; the sample stage is equipped with a three-dimensional electric displacement platform, which can realize full-area scanning of the sample surface and complete the detection of local stress mapping distribution; the detector is any one of a photomultiplier tube, avalanche photodiode, or silicon photodetector; the lock-in amplifier is configured with a dual-channel reference frequency input interface, which is respectively connected to the chopper frequency reference signal and the photoelastic modulator frequency reference signal to realize synchronous demodulation of DC signal and 2f harmonic signal.

[0009] Furthermore, in step S5, the expression for the dielectric tensor of the two-dimensional material under stress-free conditions is: ; When a local stress σ exists inside a two-dimensional material, the stress will change the lattice spacing and electron orbital distribution, thereby causing a disturbance in the dielectric tensor of the material. The dielectric tensor expression for a two-dimensional material after perturbation is: ; In the formula, ε x ε y These are the dielectric response parameters of the two-dimensional material along different crystal axis directions under stress-free conditions; , This refers to the change in dielectric constant caused by stress. This is a stress-induced polarization coupling term; This represents the localized stress in a two-dimensional material.

[0010] Furthermore, in step S6, since the dielectric tensor and complex refractive index of the two-dimensional material satisfy: ; Therefore, under localized stress, the complex refractive index corresponding to different polarization directions evolves as follows: In the formula, , , respectively, are the real parts of the complex refractive index in the x and y polarization directions; , The imaginary parts of the complex refractive index in the x and y polarization directions are called the extinction coefficients; i is the imaginary unit. And the complex refractive index does not need to satisfy the polarization direction .

[0011] Furthermore, the expression for the polarization propagation matrix of a two-dimensional material is: ; Where: r x r y For complex reflection coefficients in different polarization directions; , The phase of polarization propagation; The x-polarization to y-polarization coupling coefficient; The coupling coefficient from y-polarization to x-polarization is denoted as .

[0012] Furthermore, the polarization propagation phase in a two-dimensional material is determined by the complex refractive index, and the expressions for the polarization propagation phase in the x and y directions are: ; In the formula, d is the equivalent optical thickness of the two-dimensional material; λ is the wavelength of the incident light. , The complex refractive index in the x and y polarization directions is modulated by local stress; Due to the stress, it satisfies This results in an orthogonal polarization phase difference: .

[0013] Furthermore, for two-dimensional material samples with multi-layered composite structures, a multi-layered cascaded polarization propagation matrix is ​​used to characterize the overall polarization propagation process. The overall polarization propagation matrix J... total This can be expressed as the product of the polarization propagation matrices of each layer: ; Where N is the number of layers, J1, J2, ..., J N These are the polarization propagation matrices for the first to Nth layers, respectively.

[0014] Furthermore, in step S10, the formula for calculating the reflectance differential spectrum is: ; In the formula, , Reflectivity in the x and y polarization directions, respectively. , Let x and y be the output polarization electric field components after evolution by the polarization propagation matrix, respectively.

[0015] The beneficial effects of this invention are: This invention introduces localized stress in two-dimensional materials into the polarization propagation process, establishing a complete physical model of "stress-dielectric tensor-polarization transmission matrix-reflection differential signal," thus realizing direct non-destructive testing of stress based on polarization propagation behavior. By introducing stress-induced polarization coupling terms into the polarization propagation matrix and combining high-frequency modulation and demodulation techniques of photoelastic modulators and lock-in amplifiers, it can detect weak localized stresses with high sensitivity, effectively overcoming the limitations of existing technologies that rely solely on lattice vibration frequencies or static reflectivity differences. Meanwhile, this invention proposes a detection mechanism where stress is propagated by a phase difference caused by changes in the complex refractive index in different polarization directions. This allows stress to be characterized not only by changes in reflection intensity but also by phase changes, providing an additional dimension for detection. For practical multilayer structures, this invention employs a multilayer cascaded polarization transmission matrix to describe the overall propagation behavior and utilizes interface interference and phase accumulation effects to enhance the signal, thereby improving spatial resolution and detection sensitivity. Furthermore, through two-dimensional scanning and polarization propagation matrix inversion, this invention can obtain a continuous spatial distribution map of localized stress on the sample surface and analyze the stress propagation direction and coupling strength, providing an effective non-destructive testing tool for two-dimensional material stress analysis. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the structure of the two-dimensional material stress non-destructive testing system in this invention.

[0017] Figure 2 This is a flowchart of the two-dimensional material stress non-destructive testing method of the present invention.

[0018] In the diagram: 1. Light source; 2. Chopper; 3. Polarizer; 4. Photoelastic modulator; 5. Semi-reflective mirror I; 6. Auxiliary light source; 7. Mirror; 8. Spectroradiometer; 9. Microscope objective; 10. Sample stage; 11. Semi-reflective mirror II; 12. CCD; 13. Analyzer; 14. Detector; 15. Lock-in amplifier; 16. Data processing module. Detailed Implementation

[0019] The present invention will be further described in detail below with reference to the accompanying drawings.

[0020] This invention discloses a two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution.

[0021] Reference Figure 1 and Figure 2 A two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution is proposed. This testing method is implemented based on a two-dimensional material stress nondestructive testing system, which includes: a light source 1, a chopper 2, a polarizer 3, a photoelastic modulator 4, a semi-reflective mirror I 5, an auxiliary light source 6, a mirror 7, a beam splitter 8, a microscope objective 9, a sample stage 10, a semi-reflective mirror II 11, a CCD 12, a polarizer 13, a detector 14, a lock-in amplifier 15, and a data processing module 16.

[0022] In this system, light source 1, chopper 2, polarizer 3, and photoelastic modulator 4 are arranged coaxially along the main optical path. The output of photoelastic modulator 4 is connected to beam splitter 8 via semi-reflective mirror I5. Auxiliary light source 6 is connected to the auxiliary optical path of semi-reflective mirror I5. Downstream of the optical path of beam splitter 8 is connected to microscope objective 9, and a sample stage 10 with two-dimensional displacement adjustment is set below microscope objective 9. The sample reflected light passes through microscope objective 9 and beam splitter 8, and is then guided into the detection branch via mirror 7, and sequentially connected to detector 14 via semi-reflective mirror II 11 and analyzer 13. Detector 14, chopper 2, and photoelastic modulator 4 are electrically connected to lock-in amplifier 15. Lock-in amplifier 15 is communicatively connected to data processing module 16. CCD 12 is positioned at a suitable location in the imaging optical path split by beam splitter 88 to observe the spot quality and sample surface morphology in real time, and to assist in sample positioning and focusing. By introducing a photoelastic modulator 4 and a lock-in amplifier 15, the system achieves high-frequency modulation of the polarization state and synchronous demodulation of weak signals, thereby improving the detection sensitivity of stress-induced polarization disturbances.

[0023] The process of performing two-dimensional material stress nondestructive testing using the above system specifically includes the following steps: S1. Provide a two-dimensional material sample to be tested; the two-dimensional material sample contains localized stress; the two-dimensional material to be tested can be any one of ReSe2, ReS2, MoS2, WSe2, or MoSe2, or other two-dimensional materials with in-plane optical response characteristics. These materials all have significant in-plane optical anisotropy response characteristics. The two-dimensional material can be transferred to different substrate surfaces or grown directly on the substrate. The localized stress in the sample can originate from at least one of thermal stress, transferred stress, interface stress, residual stress, bending stress, or applied mechanical stress. In actual operation, the sample is fixed on the sample stage 10, and the sample can be scanned and moved with high precision through a three-dimensional electric displacement platform to achieve stress detection and imaging in different regions.

[0024] S2. The incident light is modulated into periodic pulses by chopper 2, and then converted into linearly polarized light by polarizer 3. The incident light is generated by a 532nm light source 1, preferably a 532nm single-longitudinal-mode continuous laser to ensure high spatial coherence and temporal stability. The 532nm laser first propagates along the main optical path into chopper 2. Chopper 2 is electrically connected to the control module, which drives the blades of chopper 2 to rotate periodically, converting the continuous laser into a periodic pulse signal. This pulse signal is used to improve the system's noise immunity and also serves as the reference synchronization frequency signal for lock-in amplifier 15. The output of chopper 2 is coaxially connected to polarizer 3. Polarizer 3 is used to convert unpolarized laser light into stable linearly polarized light. Polarizer 3 preferably uses a Glan Taylor prism, and its polarization direction is preferably set to form a 45° angle with the main axis of the photoelastic modulator 4 to improve polarization modulation efficiency. After passing through polarizer 3, the incident light becomes linearly polarized light with a defined polarization direction.

[0025] Step S3: Linearly polarized light is input to the photoelastic modulator 4 for periodic polarization state modulation to obtain dynamically modulated polarized light. The photoelastic modulator 4 is electrically connected to the lock-in amplifier 15, and the control module outputs a high-frequency sinusoidal driving voltage to the photoelastic modulator 4. In this embodiment, the modulation frequency of the photoelastic modulator 4 is set to 50kHz. Under the action of the high-frequency driving voltage, the crystal inside the photoelastic modulator 4 periodically generates a stress birefringence effect, thereby dynamically modulating the incident linearly polarized light. Specifically, when the photoelastic modulator 4 is working, it causes the incident polarization state to change periodically between two orthogonal polarization directions, forming a corresponding 2f polarization modulation signal. This dynamic modulation process enables subsequent detection to extract weak polarization modulation responses using lock-in amplification technology, thereby significantly improving the signal-to-noise ratio and weak stress detection capability.

[0026] Step S4: The dynamically modulated polarized light is focused onto the surface of the two-dimensional material sample. The modulated polarized light enters the main microscope optical path through a semi-reflective mirror I5. The semi-reflective mirror I5 is used to adjust the coupling relationship between the main detection optical path and the auxiliary observation optical path, and its transmitted light continues to propagate to the beam splitter 8. It should be noted that the auxiliary light source 6 is set in the auxiliary optical path. The illumination light emitted by the auxiliary light source 6 is coupled into the microscope system through the semi-reflective mirror I5 for real-time imaging, positioning, and focusing observation of the sample. There is no signal interference between the auxiliary light source 6 and the main detection optical path; it is only used for auxiliary microscopic observation. At the same time, the CCD 12 receives the imaging light from the sample surface and can display the spot quality and sample surface morphology in real time, which facilitates precise adjustment of the focus and selection of the detection area. The modulated main detection light enters the microscope objective 9 after passing through the beam splitter 8. The beam splitter 8 is used to separate the incident light and the reflected light: the incident light enters the microscope objective 9 after passing through the beam splitter 8, while the sample reflected light is reflected by the beam splitter 8 into the detection branch. The microscope objective 9 is preferably a high numerical aperture microscope objective 9, used to focus modulated polarized light onto the surface of the two-dimensional material sample, while simultaneously collecting the reflected light from the sample. The focused polarized light illuminates the surface of the two-dimensional material sample on the sample stage 10.

[0027] Step S5: Localized stress within the two-dimensional material alters lattice symmetry and electron orbital distribution, thereby perturbing and evolving the dielectric tensor of the two-dimensional material. When modulated polarized light irradiates the surface of the two-dimensional material, the localized stress changes the lattice spacing and electron orbital distribution within the material, resulting in a change in the dielectric tensor. In the stress-free state, the dielectric tensor of the two-dimensional material can be expressed in diagonal form: ; When a local stress σ exists inside a two-dimensional material, the stress will change the lattice spacing and electron orbital distribution, thereby causing a disturbance in the dielectric tensor of the material. The dielectric tensor expression for a two-dimensional material after perturbation is: ; In the formula, ε x ε y These are the dielectric response parameters of the two-dimensional material along different crystal axis directions under stress-free conditions, respectively, and are dimensionless. , This refers to the change in dielectric constant caused by stress. This is a stress-induced polarization coupling term, dimensionless; This represents the localized stress in a two-dimensional material, expressed in Pa. Off-diagonal terms. The introduction of this concept is one of the key aspects of this invention. It characterizes how stress disrupts the original orthogonal symmetry of the material, thereby causing coupling between two originally independent polarization directions.

[0028] Step S6: Based on the mathematical relationship between dielectric tensor and complex refractive index, the complex refractive index of different polarization directions is obtained by solving the perturbed dielectric tensor. The change in complex refractive index further drives the evolution of the polarization propagation matrix of the two-dimensional material.

[0029] Since the dielectric tensor and complex refractive index of two-dimensional materials satisfy: ; Therefore, under localized stress, the complex refractive index corresponding to different polarization directions evolves as follows: In the formula, , , respectively, are the real parts of the complex refractive index in the x and y polarization directions; , The imaginary parts of the complex refractive index in the x and y polarization directions are called the extinction coefficients; i is the imaginary unit. Due to the presence of stress, the complex refractive index is not equal in different polarization directions; that is, the complex refractive index in different polarization directions satisfies... This difference is a direct manifestation of stress-induced optical anisotropy and the physical basis for the subsequent evolution of the polarization propagation matrix.

[0030] Based on this, this invention uses the Jones polarization transfer matrix to describe the propagation behavior of polarized light in two-dimensional materials. The expression for the polarization propagation matrix of a two-dimensional material is: ; Where: r x r y For complex reflection coefficients in different polarization directions, denoted as dimensionless; , The polarization propagation phase is expressed in rad. The x-polarization to y-polarization coupling coefficient is dimensionless. is the y-polarization to x-polarization coupling coefficient, which is dimensionless.

[0031] Unlike existing technologies that only use a diagonal matrix model, this invention explicitly introduces stress-induced polarization coupling terms into the off-diagonal elements. and This allows even minute stresses to be detected with high sensitivity by inducing polarization mode mixing.

[0032] Step S7: Different polarization directions generate polarization propagation phase difference due to the difference in complex refractive index, and at the same time, local stress induces polarization mode coupling propagation effect.

[0033] The polarization propagation phase in a two-dimensional material is determined by the complex refractive index, and the expressions for the polarization propagation phase in the x and y directions are: ; In the formula, d is the equivalent optical thickness of the two-dimensional material, in nm; λ is the incident light wavelength, in nm. , The complex refractive index in the x and y polarization directions is modulated by local stress; Due to the stress, it satisfies This results in an orthogonal polarization phase difference: .

[0034] This phase difference causes the two orthogonal polarization components to accumulate different phase delays during propagation, thereby changing the polarization state of the output light. Simultaneously, stress-induced off-diagonal coupling terms... and This causes energy exchange and mode mixing between the originally independent x-polarization and y-polarization modes.

[0035] The incident polarized electric field can be expressed as: ; When polarized light passes through a two-dimensional material, its output polarization electric field satisfies: ; After unfolding, we get: This shows that stress not only changes the propagation phase in different polarization directions, but also leads to the coupling propagation between different polarization modes.

[0036] For common two-dimensional material / interface / substrate multilayer structures in practice, this invention further employs a multilayer cascaded polarization transfer matrix to characterize the overall polarization propagation process. The overall polarization propagation matrix J total This can be expressed as the product of the polarization propagation matrices of each layer: ; Where N is the number of layers, J1, J2, ..., J N These are the polarization propagation matrices for the first to Nth layers, respectively.

[0037] Step S8: The reflected polarized light after being reflected by the two-dimensional material passes through the analyzer and detector in sequence to complete the conversion of optical signal to electrical signal.

[0038] The reflected light is collected again by the microscope objective 9 and returns to the beam splitter crystal 8, which guides the reflected light to the detection branch. The reflected light first changes direction via the reflector 77, and then enters the polarization analysis system via the semi-reflective mirror II 11. The semi-reflective mirror II 11 is used to adjust the detection light intensity and the propagation direction of the reflected light. The reflected light then enters the analyzer 13, which analyzes the polarization state of the reflected light. Its polarization direction is preferably at a specific angle to the polarizer 3 to improve the detection sensitivity of the reflected differential signal. After passing through the analyzer 13, the reflected light enters the detector 14, which is preferably any one of a photomultiplier tube, an avalanche photodiode, or a silicon photodetector, used to convert the optical signal into an electrical signal. The output of the detector 14 is electrically connected to the input of the lock-in amplifier 15 via a signal line.

[0039] Step S9: Lock-in amplifier 15 synchronously receives reference frequency signal from chopper 2, reference frequency signal from photoelastic modulator 4 and output electrical signal from detector 14, and synchronously demodulates and extracts DC signal and 2f harmonic modulation signal.

[0040] The lock-in amplifier 15 is equipped with dual reference frequency input interfaces, connecting to the frequency reference signals of chopper 2 and photoelastic modulator 4 respectively. The reference frequency of chopper 2 corresponds to the fundamental frequency of the pulsed light, and the reference frequency of photoelastic modulator 4 corresponds to the polarization modulation frequency (50kHz). The lock-in amplifier 15 extracts the DC signal and 2f harmonic signal from the electrical signal output by detector 14 through synchronous demodulation. The DC signal represents the average reflection intensity, reflecting the overall reflectivity of the sample; the 2f harmonic signal represents the differential reflection response corresponding to polarization modulation, corresponding to the stress-induced change in the polarization propagation matrix. Since local stress in different regions of the two-dimensional material causes changes in the propagation phase and polarization coupling terms in the polarization propagation matrix, the 2f signal intensity corresponding to different regions will also change accordingly.

[0041] Step S10: Establish a quantitative correspondence between the polarization propagation matrix and the reflection differential signal.

[0042] The formula for calculating differential reflectance spectroscopy is: ; In the formula, , Reflectivity in the x and y polarization directions, respectively. , Let x and y be the output polarization electric field components after evolution by the polarization propagation matrix, respectively.

[0043] The reflected differential signal Directly related to the polarization propagation matrix in step S7 Correlation. Through theoretical calculations, response curves or lookup tables between the polarization propagation matrix and the reflection differential signal under different stress states can be established in advance, thus providing a quantitative basis for subsequent stress inversion.

[0044] Step S11: Based on the changes in the reflection differential spectral signal, the magnitude and spatial distribution of local stress in the two-dimensional material are obtained by inversion using the polarization propagation matrix model.

[0045] The data processing module 16 receives the DC signal and 2f signal output from the lock-in amplifier 15 and calculates the reflection differential signal according to the formula in step S10. The data processing module 16 has built-in polarization propagation matrix operation program, multi-layer interface matrix fitting program, and reflection differential spectrum stress inversion program. By fitting and optimizing the experimentally measured reflection differential signal with the theoretical model, the magnitude of the local stress σ in each region of the two-dimensional material can be inverted. Simultaneously, since the sample stage 10 can achieve high-precision three-dimensional scanning movement in x, y, and z directions, the local stress distribution map of the entire sample surface can be obtained by scanning point by point. The inversion process of this invention is essentially a polarization propagation matrix inversion method, that is, deriving the propagation phase in the polarization propagation matrix from the measured reflection differential signal. , and coupling coefficient , This allows for the calculation of stress values. Compared to simple peak-position fitting or reflectivity comparison in existing technologies, this method provides richer stress information, including stress direction, polarization coupling strength, and propagation enhancement regions in multilayer interfaces.

[0046] Based on the above embodiments, the present invention can also be adaptively adjusted according to different two-dimensional material types and stress sources. For example, for materials with strong in-plane anisotropy, such as ReSe2, the intrinsic dielectric tensor varies greatly, and the stress-induced relative change is more significant, thus improving the detection sensitivity. For non-uniform stress fields caused by bending stress or applied mechanical stress, the spatial scanning function of this method can clearly present the stress concentration region and its propagation path.

[0047] In summary, this invention establishes a complete physical model from the dielectric tensor to the polarization transmission matrix and then to the reflection differential signal by introducing local stress into the polarization propagation process, thus achieving highly sensitive and high-resolution non-destructive testing of stress in two-dimensional materials. Its core lies in employing a Jones matrix with off-diagonal elements containing stress-induced coupling terms, and considering the propagation phase accumulation and polarization interference effects in multilayer interfaces, thereby overcoming the limitations of existing technologies that rely solely on lattice vibration frequencies or static reflectivity differences.

[0048] Those skilled in the art should understand that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution, characterized in that: The detection method is implemented based on a two-dimensional material stress non-destructive testing system, which includes a light source (1), a chopper (2), a polarizer (3), a photoelastic modulator (4), a semi-reflective mirror I (5), an auxiliary light source (6), a mirror (7), a beam splitter (8), a microscope objective (9), a sample stage (10), a semi-reflective mirror II (11), a CCD (12), a polarizer (13), a detector (14), a lock-in amplifier (15), and a data processing module (16). The light source (1), chopper (2), polarizer (3), and photoelastic modulator (4) are arranged coaxially along the main optical path. The output end of the photoelastic modulator (4) is connected to the beam splitter (8) via a semi-reflective mirror I (5). The auxiliary light source (6) is connected to the auxiliary optical path end of the semi-reflective mirror I (5). The downstream of the optical path of the beam splitter (8) is connected to the microscope objective (9). A movable and adjustable sample stage (10) is set below the microscope objective (9). The sample reflected light passes through the microscope objective (9) and the beam splitter (8), and is then introduced into the detection branch via the reflector (7). It then passes through the semi-reflective mirror II (11) and the analyzer (13) in sequence and is connected to the detector (14). The detector (14), chopper (2), and photoelastic modulator (4) are electrically connected to the lock-in amplifier (15). The lock-in amplifier (15) is communicatively connected to the data processing module (16). CCD(12) is used to observe the spot quality and sample surface morphology in real time, and to assist in sample positioning and focusing; The two-dimensional material stress nondestructive testing method includes the following steps: S1. Provide a two-dimensional material sample to be tested, wherein the two-dimensional material sample contains localized stress. S2. The incident light is modulated into periodic pulse light by the chopper (2), and then converted into linearly polarized light by the polarizer (3). S3. The linearly polarized light is input to the photoelastic modulator (4) for periodic polarization state modulation to obtain dynamically modulated polarized light; S4. Focus the dynamically modulated polarized light onto the surface of the two-dimensional material sample; S5. Localized stress within two-dimensional materials causes changes in lattice symmetry and electron orbital distribution, which in turn causes perturbation and evolution of the dielectric tensor of two-dimensional materials. S6. Based on the mathematical relationship between dielectric tensor and complex refractive index, the complex refractive index in different polarization directions is obtained by solving the perturbed dielectric tensor. The change in complex refractive index further drives the evolution of the polarization propagation matrix of the two-dimensional material. S7. Different polarization directions produce polarization propagation phase difference due to the difference in complex refractive index, and at the same time, local stress induces polarization mode coupling propagation effect. S8. The reflected polarized light after being reflected by the two-dimensional material passes through the analyzer (13) and the detector (14) in sequence to complete the conversion of optical signal to electrical signal; S9, Lock-in amplifier (15) synchronously receives chopper (2) reference frequency signal, photoelastic modulator (4) reference frequency signal and detector (14) output electrical signal, synchronously demodulates and extracts DC signal and 2f harmonic modulation signal; S10. Establish a quantitative correspondence between the polarization propagation matrix and the reflected differential signal; S11. Based on the changes in the reflection differential spectral signal, the magnitude and spatial distribution of local stress in two-dimensional materials are obtained by inversion using the polarization propagation matrix model.

2. The two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to claim 1, characterized in that: The two-dimensional material is any one of ReSe2, ReS2, MoS2, WSe2, or MoSe2; the localized stress originates from at least one of thermal stress, transferred stress, interfacial stress, residual stress, bending stress, or applied mechanical stress.

3. The two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to claim 1, characterized in that: The incident light in step S2 is a 532nm single-mode continuous laser; the polarizer (3) adopts a Glan Taylor prism, and the polarization direction of the polarizer (3) is set at a 45° angle with the main axis of the photoelastic modulator (4); the modulation frequency of the photoelastic modulator (4) is set to 50kHz; the sample stage (10) is equipped with a three-dimensional electric displacement platform, which can realize full-area scanning of the sample surface and complete the detection of local stress mapping distribution; the detector (14) adopts any one of photomultiplier tube, avalanche photodiode or silicon photodetector; the lock-in amplifier (15) is configured with a dual-channel reference frequency input interface, which is connected to the frequency reference signal of the chopper (2) and the frequency reference signal of the photoelastic modulator (4) respectively, so as to realize synchronous demodulation of DC signal and 2f harmonic signal.

4. A two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to any one of claims 1-3, characterized in that: In step S5, the expression for the dielectric tensor of the two-dimensional material under stress-free conditions is: ； When a local stress σ exists inside a two-dimensional material, the stress will change the lattice spacing and electron orbital distribution, thereby causing a disturbance in the dielectric tensor of the material. The dielectric tensor expression for a two-dimensional material after perturbation is: ； In the formula, ε x ε y These are the dielectric response parameters of the two-dimensional material along different crystal axis directions under stress-free conditions; , This refers to the change in dielectric constant caused by stress. This is a stress-induced polarization coupling term; This represents the localized stress in a two-dimensional material.

5. The two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to claim 4, characterized in that: In step S6, since the dielectric tensor and complex refractive index of the two-dimensional material satisfy: ； Therefore, under localized stress, the complex refractive index corresponding to different polarization directions evolves as follows: In the formula, , , respectively, are the real parts of the complex refractive index in the x and y polarization directions; , The imaginary parts of the complex refractive index in the x and y polarization directions are called the extinction coefficients; i is the imaginary unit. And the complex refractive index does not need to satisfy the polarization direction .

6. The two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to claim 5, characterized in that: The expression for the polarization propagation matrix of a two-dimensional material is: ； Where: r x r y For complex reflection coefficients in different polarization directions; , The phase of polarization propagation; The x-polarization to y-polarization coupling coefficient; The coupling coefficient from y-polarization to x-polarization is denoted as .

7. The two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to claim 6, characterized in that: The polarization propagation phase in a two-dimensional material is determined by the complex refractive index, and the expressions for the polarization propagation phase in the x and y directions are: ; In the formula, d is the equivalent optical thickness of the two-dimensional material; λ is the wavelength of the incident light. , The complex refractive index in the x and y polarization directions is modulated by local stress; Due to the stress, it satisfies This results in an orthogonal polarization phase difference: 。 8. The two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to claim 7, characterized in that: For two-dimensional material samples with multi-layered composite structures, a multi-layered cascaded polarization transfer matrix is ​​used to characterize the overall polarization propagation process. The overall polarization propagation matrix J total This can be expressed as the product of the polarization propagation matrices of each layer: ； Where N is the number of layers, J1, J2, ..., J N These are the polarization propagation matrices for the first to Nth layers, respectively.

9. A two-dimensional material stress nondestructive testing method based on polarization propagation matrix evolution according to claim 8, characterized in that: In step S10, the formula for calculating the reflectance differential spectrum is: ; In the formula, , Reflectivity in the x and y polarization directions, respectively. , Let x and y be the output polarization electric field components after evolution by the polarization propagation matrix, respectively.

Images