A method for enhancing high-frequency coherent phonon signals in time-domain transient reflectance spectroscopy

Abstract

The application provides a method for enhancing high-frequency coherent phonon signals in time-domain transient reflection spectroscopy, and the method comprises the following steps: constructing an expression of coherent phonon damped oscillation, and performing time derivation operation on the expression of coherent phonon damped oscillation. The application has the beneficial effect that the application can amplify signals when the coherent phonon frequency is greater than 138GHz, and is convenient for data extraction, and the method of the application is extremely effective for weak ultrahigh-frequency oscillation signals.

Description

Technical Field

[0001] This invention relates to the field of detection and analysis technology, and in particular to a method for enhancing high-frequency coherent phonon signals in time-domain transient reflectance spectra. Background Technology

[0002] Pump-probe technology is a highly sensitive detection and analysis technique. Its principle involves exciting the sample with a pump laser pulse of high energy flux density, followed by probing with a probe laser pulse of much lower energy flux density to detect the internal state of the sample at a specific moment. Simultaneously, it can also detect the motion of atoms, i.e., phonons. The time delay is provided by a displacement platform. The actual data measured in the experiment is the change in reflectivity of the sample surface, i.e., the time-domain transient reflectance spectrum. The measured reflectivity change will vary depending on the material, the wavelength and power of the probe and pump beams, etc. The time-domain transient reflectance spectrum generally includes signal changes caused by electronic relaxation, lattice heating, and coherent phonon damped oscillations, with coherent phonon damped oscillations being the core of our research. A unit cell with N atoms has a total of 3N phonon modes, including 3 acoustic phonon modes and 3N-3 optical phonon modes. Generally, the energy (i.e., vibration frequency) of optical phonons is higher than that of acoustic phonons. In pump-probe experiments, laser pulses excite a large number of coherent phonon modes, and the probe light detects the modes located at the center of the Brillouin zone. However, for some coherent phonon modes with very low intensity, the pump-probe method with ordinary signal-to-noise ratio cannot detect them.

[0003] In the study of time-domain coherent phonons, to more accurately understand their characteristics, it is generally desirable to detect coherent phonon amplitudes as large as possible so that useful information can be extracted. To improve the amplitude of detected coherent phonons, one can approach the issue from two aspects: detection methods and excitation methods.

[0004] Firstly, there are excitation methods. One simple method is to increase the energy flux density of the pump pulse, which is usually the most significant way to increase the amplitude of coherent phonons. However, the drawback is also obvious: the sample is easily damaged. Another excitation method is to increase the energy of the pump photon. Under the same energy flux density, the carriers can be excited to a higher excited state, thereby enhancing the electron-phonon coupling strength and strengthening the amplitude of coherent phonons. The drawback is also that the sample is easily damaged. Alternatively, a photoacoustic transducer can be used to transfer the strain of some easily excited samples to samples that are not easily excited, thereby increasing the coherent phonon amplitude of the latter (e.g., Wang PJ, et al. Photoacoustics, 2023:100477. and Ma W, et al. The Journal of Physical Chemistry C, 2015, 119(9):5152-5159).

[0005] Secondly, the detection method can be selected according to the optical characteristics of the sample to improve the amplitude of the detected coherent phonons. For coherent acoustic phonons, the change of the detection wavelength will also change the frequency and detection depth of the coherent acoustic phonons (for example, CN115479921A "Method and apparatus for selecting the detection wavelength in time-domain Brillouin scattering experiment"). Summary of the Invention

[0006] This invention provides a method for enhancing high-frequency coherent phonon signals in time-domain transient reflection spectra. In the time-domain transient reflection spectrum, the expression for a coherent phonon damped oscillation is:

[0007]

[0008] Where ΔR / R is the relative change in reflectivity, A is the amplitude of the coherent phonon, t is the time interval between the pump pulse and the probe pulse, τ is the decoherence time of the coherent phonon, and f is the frequency of the coherent phonon. It is the initial phase of the oscillation;

[0009] Taking the time derivative of equation (1), the amplitude becomes:

[0010]

[0011] The initial phase becomes:

[0012]

[0013] The amplitude gain coefficient obtained by taking the time derivative of ΔR / R is:

[0014]

[0015] As a further improvement of the present invention, the initial phase of ΔR / R is... The restoration is obtained by solving equation (6).

[0016]

[0017] or

[0018]

[0019] The phase difference between equations (8) and (9) is π, which is the phase recovery value. When the time is right, choose to solve using either equation (8) or equation (9).

[0020] As a further improvement of the present invention, a displacement platform is added to the pump-probe optical path. The delay time in the transient reflection spectrum is determined by the displacement platform. The vibrator vibrates back and forth at a certain frequency within a set range with a time step of h to modulate the probe light. The data reading is determined by the vibrator. When the displacement platform moves by one point, the vibrator moves within a set range at that point. When it moves to the two endpoints, the reading point is taken. Let the data read at the endpoint far from the displacement platform be ΔR2 and the data read at the endpoint close to the displacement platform be ΔR1. The program is set so that the output value is equal to (ΔR2-ΔR1) / 2h, and the result of the approximate time derivative is obtained.

[0021] As a further improvement of the present invention, the method employs forward difference method, backward difference method, or central difference method.

[0022] As a further improvement of the present invention, the method employs the central difference method.

[0023] As a further improvement to this invention, the central difference method is selected as the basic algorithm for this operation, then:

[0024]

[0025] Where O(h) 2 ) is the square of the time step h 2 The error is proportional to the time step, where h is the time step.

[0026] As a further improvement of the present invention, for coherent optical phonons, the oscillation contains chirp, then equation (1) becomes:

[0027]

[0028] Where β is the chirp coefficient, the amplitude after processing by the central difference method becomes

[0029]

[0030] The initial phase becomes

[0031]

[0032] As a further improvement of the present invention, the set range is 100nm-5μm.

[0033] The beneficial effects of this invention are: it can amplify signals when the coherent phonon frequency is greater than 138 GHz, making it easier to extract data; and the method of this invention is extremely effective for weak ultra-high frequency oscillation signals. Attached Figure Description

[0034] Figure 1This is a graph showing the relationship between amplitude gain (Gain) and the decoherence time (τ) and frequency (f) of coherent phonons.

[0035] Figure 2 This is a diagram showing the position and trajectory of the vibrator in the pump-probe optical path;

[0036] Figure 3a It is a sinusoidal oscillation containing three different frequencies, amplitudes, and decoherence times. The inner plot is its spectrum after FFT processing.

[0037] Figure 3b Yes Figure 3a The processed signal obtained by central differential processing of the initial signal in the image is the spectrum of the signal after FFT processing.

[0038] Figure 3c This is the time-domain transient reflectance spectrum of single-crystal bismuth. The oscillations represented by the hollow circles are the raw data of bismuth under the conditions of 800nm ​​pump-800nm ​​detection, and the oscillations represented by the broken lines are the processed data obtained after the raw data has been processed by the central difference. Detailed Implementation

[0039] This invention discloses a method for enhancing high-frequency coherent phonon signals in time-domain transient reflection spectra. In the time-domain transient reflection spectrum, the expression for a coherent phonon damped oscillation can be written as:

[0040]

[0041] Where ΔR / R is the relative change in reflectivity, A is the amplitude of the coherent phonon, t is the time interval between the pump pulse and the probe pulse, τ is the decoherence time of the coherent phonon, and f is the frequency of the coherent phonon. It is the initial phase of the oscillation.

[0042] If we perform time differentiation on equation (1), we can obtain

[0043]

[0044] Note that two simple harmonic motions with the same frequency and a fixed phase difference, when combined, still result in a single simple harmonic motion.

[0045]

[0046] Substituting equation (2) into equation (3) yields

[0047]

[0048] As can be seen from equation (4), after performing a time derivative operation on the coherent phonon damped oscillation, the result is still a damped oscillation with the same decoherence time, at which point the amplitude becomes

[0049]

[0050] The initial phase becomes

[0051]

[0052] Therefore, the amplitude gain coefficient obtained by differentiating ΔR / R over time is:

[0053]

[0054] Equation (7) is plotted as a three-dimensional graph showing the change of amplitude gain coefficient with decoherence time and coherent phonon frequency, as follows: Figure 1 As shown, when the decoherence time is not very small, the gain coefficient of the amplification is almost proportional to the coherent phonon frequency. Typically, even the shortest-lived coherent optical phonons have decoherence times exceeding 1 ps. Therefore, we can approximately ignore the effect of the decoherence time on the amplitude gain. Furthermore, when τ = 2 ps and the coherent phonon frequency f > 138 GHz, the amplitude gain coefficient Gain > 1, meaning that for coherent phonon oscillation signals with frequencies exceeding 138 GHz, the amplitude can be gained when differentiated with respect to time. Therefore, this method can also be used as a high-pass filter, and the higher the phonon frequency, the greater the gain, which is beneficial for extracting the time-domain information of the coherent phonons. Since the signal is amplified proportionally, fitting the obtained signal becomes very easy. The frequency f and decoherence time τ of the coherent phonon oscillation are easily extracted from the fitting equation, and the amplitude reconstruction is readily achieved.

[0055] For the initial phase of ΔR / R The restoration can be obtained by solving equation (6).

[0056] or

[0057]

[0058] The phase difference between equations (8) and (9) is π, which is the phase recovery value. When choosing between equation (8) or equation (9) to solve the problem, one should consider the actual situation.

[0059] To implement the aforementioned time derivative operation in the optical path, we can add a piezoelectric displacement platform to the pump-probe optical path, acting as a "vibrator," such as... Figure 2As shown. The delay time in the transient reflection spectrum is still determined by the displacement platform. The difference is that the "vibrator" modulates the probe light by vibrating back and forth at a certain frequency within a set range (e.g., the set range is 100nm-5μm) with a time step of h. Data reading is determined by the "vibrator". When the displacement platform moves one point, the vibrator moves within the set range (e.g., the set range is 100nm-5μm) at that point. When it moves to the two endpoints, a reading point is taken. Let the data read from the endpoint farther from the displacement platform be ΔR2, and the data read from the endpoint closer to the displacement platform be ΔR1. The program is set so that the output value is equal to (ΔR2-ΔR1) / 2h. At this time, the approximate time derivative result can be obtained. Depending on the definition of the zero point of time, the above method can be the forward difference method, the backward difference method, or the central difference method. Since the central difference method has the smallest error among the three, it is selected as the basic algorithm for this operation.

[0060]

[0061] Where O(h) 2 ) is the square of the time step h 2 The error is proportional. Considering that coherent phonon damped oscillations are relatively smooth functions, the smaller the time step h is in this operation, the more accurate the data will be theoretically.

[0062] To verify the feasibility of the central difference method in this experiment, we set up a damped oscillation with three different frequencies, amplitudes, and decoherence times.

[0063]

[0064] Let A1 = 1, A2 = 4, A3 = 10; τ1 = 4 ps, τ2 = 8 ps, τ3 = 20 ps; f1 = 3 THz, f2 = 0.8 THz, f3 = 0.05 THz, the resulting composite oscillation is as follows: Figure 3a As shown in the figure, the initial signal exhibits strong low-frequency oscillations and weak high-frequency oscillations. The inner plot is the spectrum obtained after performing a Fast Fourier Transform (FFT) on this composite oscillation; the peak at 3THz is almost invisible. Subsequently, the initial signal was subjected to center difference processing with a time step of h = 0.01ps, and its spectrum was analyzed, as shown below. Figure 3bAs shown. After central difference processing, the high-frequency oscillations are enhanced, and the amplitudes of the three peaks at 0.05, 0.8, and 3 THz are amplified by 0.312, 5.013, and 18.647 times, respectively, which is consistent with the prediction of equation (7). It is worth mentioning that when the time step is 0.01 ps, the vibration step of the piezoelectric displacement platform in reality is 1.5 μm, which can be easily met by existing technology. At this time, the error between the experimental value and the theoretical value is less than 0.4%. Further reducing the vibration step will yield more accurate data.

[0065] For coherent optical phonons, oscillations are generally accompanied by chirping, so equation (1) becomes

[0066]

[0067] Where β is the chirp coefficient, the amplitude after processing by the central difference method becomes

[0068]

[0069] The initial phase becomes

[0070]

[0071] This experiment uses single-crystal bismuth (Bi) as the demonstration object, with a wavelength of 800 nm and an energy flux density of 4.33 mJ / cm². 2 Pumped by light pulses, and detected by light pulses with a wavelength of 800 nm, the initial signal obtained is compared with the processed signal obtained by performing a center difference operation on the signal with a time step of h = 0.032 ps. Figure 3c As shown. Figure 3c Both the initial signal represented by the hollow circle and the processed signal represented by the broken line clearly show high-frequency coherent optical phonon oscillations within 12 ps. Damped sinusoidal oscillation fitting was performed on the two signals respectively, and the results are shown in Table 1.

[0072] Table 1 shows the data fitting for the time-domain coherent phonon oscillations of Bi.

[0073]

[0074] When t = 0, substituting the fitted data into equations (13) and (14) yields the theoretical amplitude amplification Gain = 17.97 and phase change, respectively. The amplification and phase change obtained after center differential processing with a time step h = 0.032 ps are Gain' = 17.18 and 1.032 ps, respectively. The error between the experimental and theoretical values ​​is less than 4.4%, therefore the method is highly feasible.

[0075] In actual measurements, noise can also amplify the signal. Noise is a high-frequency signal, so this method will amplify it. In simulations, when the signal-to-noise ratio (SNR) reaches 50% or higher, the effect of noise can be largely ignored. Therefore, improving the SNR of the system is the primary goal of this method.

[0076] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for enhancing high-frequency coherent phonon signals in a time-domain transient reflectance spectrum, characterized in that: In the time-domain transient reflection spectrum, the expression for a coherent phonon damped oscillation is: Where ΔR / R is the relative change in reflectivity, A is the amplitude of the coherent phonon, t is the time interval between the pump pulse and the probe pulse, τ is the decoherence time of the coherent phonon, and f is the frequency of the coherent phonon. It is the initial phase of the oscillation; Taking the time derivative of equation (1), the amplitude becomes: The initial phase becomes: The amplitude gain coefficient obtained by taking the time derivative of ΔR / R is: A piezoelectric displacement platform is added to the pump-probe optical path to act as an oscillator. The delay time in the transient reflection spectrum is still determined by the displacement platform. The difference is that the oscillator modulates the probe light by vibrating back and forth at a certain frequency within a set range with a time step of h. Data reading is determined by the oscillator. When the displacement platform moves to a point, the oscillator moves within a set range at that point. When it moves to the two endpoints, the data points are read. Let the data read from the endpoint far from the displacement platform be ΔR2 and the data read from the endpoint close to the displacement platform be ΔR1. The program is set so that the output value is equal to (ΔR2-ΔR1) / 2h, and the approximate time derivative result is obtained.

2. The method according to claim 1, characterized in that: The initial phase of ΔR / R The restoration is obtained by solving equation (6). or The phase difference between equations (8) and (9) is π, which is the phase recovery value. When the time is right, choose to solve using either equation (8) or equation (9).

3. The method according to claim 1, characterized in that: This method employs either forward difference, backward difference, or central difference.

4. The method according to claim 1, characterized in that: This method employs the central difference method.

5. The method according to claim 4, characterized in that: This method uses the central difference method as the basic algorithm for this operation, then: Where O(h) 2 ) is the square of the time step h 2 The error is proportional to the time step, where h is the time step.

6. The method according to claim 4, characterized in that, For coherent optical phonons, the oscillation contains chirp, then equation (1) becomes: Where β is the chirp coefficient, the amplitude after processing by the central difference method becomes The initial phase becomes 7. The method according to claim 1, characterized in that, The setting range is 100nm-5μm.

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