A nanoresonator amplitude and phase response measurement device

Abstract

The application provides a response measuring device for amplitude and phase of a nanoresonator. The response measuring device comprises: an arbitrary waveform generator for generating a first waveform signal and a second waveform signal; a nanoresonator for generating a vibration signal; a first radio frequency power divider for transmitting an equalized first vibration signal to a first signal path and a second vibration signal to a second signal path; a first processing module for multiplying the first vibration signal with the first waveform signal, filtering high frequency components in a first resultant signal, and obtaining an I(t) signal; a second processing module for multiplying the second vibration signal with the second waveform signal, filtering high frequency components in a second resultant signal, and obtaining a Q(t) signal; and a signal acquisition system for determining an amplitude signal and a phase signal of the nanoresonator according to the I(t) signal and the Q(t) signal. The application can replace a vector network analyzer to obtain the amplitude signal and the phase signal of the nanoresonator.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of resonators, in particular to a device for measuring the amplitude and phase response of a nano-resonator. BACKGROUND

[0002] The nano-resonator has a very small size, with a cavity diameter generally ranging from several microns to tens of microns, and the thickness of the two-dimensional material therein can reach several nanometers. The amplitude and phase response are different at different driving frequencies. When the excitation frequency of the outside world is the same as the natural frequency, the amplitude response is the largest, and a phase jump of about 180 degrees occurs near the resonant frequency.

[0003] Currently, a vector network analyzer is usually used to detect the amplitude and phase response of the nano-resonator. The detection method is to set port 1 of the vector network analyzer as a radio frequency output channel and use it to drive the resonator, set port 2 as an input channel and connect it to the output end of a photoelectric detector, and use it to extract the response signal of the resonator. Then, the input signal of port 1 is swept, and the phase difference and amplitude ratio of the input signal and the output signal are calculated, so as to obtain the phase and amplitude response curves of the nano-resonator. However, the price of the complete set of vector network analyzer devices is very high, usually more than hundreds of thousands of yuan. SUMMARY

[0004] Therefore, the embodiments of the present application aim to provide a device for measuring the amplitude and phase response of a nano-resonator, comprising:

[0005] An arbitrary waveform generator is configured to generate a first waveform signal and a second waveform signal having a preset phase difference with the first waveform signal;

[0006] A nano-resonator is configured to generate a vibration signal under the action of an external signal;

[0007] A first radio frequency power divider is configured to equally divide the vibration signal, and transmit the equally divided first vibration signal to a first signal path and the equally divided second vibration signal to a second signal path;

[0008] A first processing module is arranged on the first signal path and configured to multiply the first vibration signal by the first waveform signal to obtain a first result signal, and filter out high-frequency components in the first result signal to obtain an I(t) signal;

[0009] A second processing module is arranged on the second signal path and configured to multiply the second vibration signal by the second waveform signal to obtain a second result signal, and filter out high-frequency components in the second result signal to obtain a Q(t) signal;

[0010] A signal acquisition system is configured to determine an amplitude signal and a phase signal of the nanoresonator based on the I(t) signal and the Q(t) signal.

[0011] Optionally, the first processing module comprises a first mixer and a first low-pass filter, and the first mixer is arranged between the first RF power divider and the first low-pass filter.

[0012] The first mixer is configured to calculate the first resultant signal according to the following formula:

[0013]

[0014] The first low-pass filter is configured to filter out high-frequency components with a frequency of and obtain the I(t) signal with a frequency of according to the following formula:

[0015]

[0016] wherein t represents time, φ represents a phase signal, A represents an amplitude signal, and represent different frequencies.

[0017] Optionally, the second processing module comprises a second mixer and a second low-pass filter, and the second mixer is arranged between the first RF power divider and the second low-pass filter.

[0018] The second mixer is configured to calculate the second resultant signal according to the following formula:

[0019]

[0020] The second low-pass filter is configured to filter out high-frequency components with a frequency of and obtain the Q(t) signal with a frequency of according to the following formula:

[0021]

[0022] wherein t represents time, φ represents a phase signal, A represents an amplitude signal, and represent different frequencies.

[0023] Optionally, the signal acquisition system calculates an amplitude signal and a phase signal according to the following formula:

[0024]

[0025]

[0026] wherein, is the frequency signal after the I(t) signal is multiplied by the signal and low-pass filtered, is the frequency signal after the Q(t) signal is multiplied by the signal and low-pass filtered.

[0027] Optionally, the signal is obtained according to the following calculation formula:

[0028]

[0029] The signal is obtained according to the following formula:

[0030]

[0031] wherein, t represents time, represents a phase signal, represents an amplitude signal.

[0032] Optionally, the response measurement device further comprises a photoelectric detector, a band-pass filter and a low-noise amplifier connected in sequence, and the low-noise amplifier is electrically connected with the first radio frequency power divider.

[0033] The photoelectric detector is used to convert the reflected light signal modulated by the nano-resonator into an electrical signal.

[0034] Optionally, the mean square value of the output voltage of the photoelectric detector is obtained according to the following formula:

[0035]

[0036] wherein, represents the product of the gain and responsivity of the photoelectric detector, represents the transmittance of the reflected light path, represents the optical power of the laser light source incident on the nano-resonator, represents the vibration displacement of the nano-resonator, represents the derivative of the reflectivity with respect to the vibration displacement of the resonator at the equilibrium position, represents the mean square value of the background noise.

[0037] Optionally, the response measurement device further comprises a laser light source, a polarization beam splitting cube, a quarter-wave plate and a microscope objective arranged in sequence.

[0038] The nanoresonator is located below the microscope objective, and the polarization beam splitter cube is also adjacent to the photodetector;

[0039] The circularly polarized light reflected by the nanoresonator is transformed into linearly polarized light with only a vertical component after passing through the quarter-wave plate, and then reflected into the photodetector through the polarization beam splitter cube.

[0040] Optionally, the response measurement device further comprises:

[0041] A direct current signal source for providing a direct current signal;

[0042] An MXG signal source for providing an MXG signal;

[0043] The nanoresonator is used to receive the signal after mixing of the direct current signal and the MXG signal.

[0044] Optionally, the response measurement device further comprises:

[0045] A second radio frequency power divider electrically connected to the output end of the MXG signal source;

[0046] A third radio frequency power divider electrically connected between the arbitrary waveform generator and the second mixer;

[0047] A third low-pass filter electrically connected to the input end of the signal acquisition system;

[0048] A third mixer with its input end connected to the second radio frequency power divider and the third radio frequency power divider respectively, and its output end connected to the third low-pass filter.

[0049] According to the scheme of the embodiment of the present application, the vibration signal generated by the nanoresonator is equally divided by the first radio frequency power divider and is divided into two parallel signals, then the first vibration signal is multiplied by the first waveform signal by the first processing module, and the high frequency components in the multiplied result are filtered out, so that the I(t) signal can be obtained, and the second vibration signal is multiplied by the second waveform signal by the second processing module, and the high frequency components in the multiplied result are filtered out, so that the Q(t) signal can be obtained, and then the signal acquisition system determines the amplitude signal and the phase signal of the nanoresonator according to the I(t) signal and the Q(t) signal, so that the phase and amplitude response can be obtained based on the IQ demodulation principle. It is found through comparison of the phase and amplitude response test using the vector network analyzer that the result obtained in the present application based on the IQ demodulation principle is basically consistent with the result obtained by using the vector network analyzer in the prior art, because it is found through experiment that the resonance peaks and the phase step positions measured by the two methods are basically coincident. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 Fig. 3 shows a schematic structure diagram of a response measurement device for amplitude and phase of a nano-resonator according to an embodiment of the present application;

[0051] Figure 2 Fig. 4 shows a microscope image of a nano-resonator to be measured according to an embodiment of the present application;

[0052] Figure 3 Fig. 5 shows a graph of I(t) and Q(t) components measured around the resonance frequency of a nano-resonator with average number of 100, 200, 400 and 1000 according to an embodiment of the present application, the driving frequency P used in the measurement is -15dBm; drive

[0053] Figure 4 Fig. 6 shows a graph of the phase response of a nano-resonator with respect to the average number at a fixed driving frequency;

[0054] Figure 5 Fig. 7 shows the amplitude response of a nano-resonator at a driving power of -30dBm, the hollow data points in the graph are the phase response measured by using the IQ demodulation principle in the present application, and the solid curve is the phase response measured by using the prior art VNA;

[0055] Figure 6 Fig. 8 shows the amplitude response of a nano-resonator at a driving power of -30dBm, the hollow data points in the graph are the amplitude response measured by using the IQ demodulation principle in the present application, and the solid curve is the amplitude response measured by using the prior art VNA;

[0056] Fig. 1: 1 - arbitrary waveform generator, 2 - nano-resonator, 21 - nanostructure, 22 - metal gate, 3 - first RF power divider, 4 - first processing module, 41 - first mixer, 42 - first low-pass filter, 5 - second processing module, 51 - second mixer, 52 - second low-pass filter, 6 - signal acquisition system, 7 - DC signal source, 8 - MXG signal source, 9 - laser light source, 10 - polarization beam splitting cube, 11 - quarter wave plate, 12 - microscope objective, 13 - vacuum cavity, 14 - photodetector, 15 - band-pass filter, 16 - low-noise amplifier, 17 - second RF power divider, 18 - third RF power divider, 19 - third low-pass filter, 20 - third mixer, 23 - fourth RF power divider. DETAILED DESCRIPTION

[0057] ​To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, it should be noted that, for ease of description, only the parts relevant to this application are shown in the accompanying drawings, not the entire structure. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this application.

[0058] The terms “comprising” and “having”, and any variations thereof, used in this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus.

[0059] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0060] Figure 1 A schematic structural diagram of a device for measuring the amplitude and phase response of a nanoresonator 2 according to an embodiment of the present invention is shown. Figure 1 As shown, the response measurement device includes an arbitrary waveform generator 1, a nanoresonator 2, a first radio frequency power divider 3, a first processing module 4, a second processing module 5, and a signal acquisition system 6. The arbitrary waveform generator 1 generates a first waveform signal and a second waveform signal with a preset phase difference from the first waveform signal. This preset phase difference can be, for example, 90°. The nanoresonator 2 generates a vibration signal under the influence of an external signal. The first radio frequency power divider 3 divides the vibration signal into equal parts, transmitting the divided first vibration signal to a first signal path and the divided second vibration signal to a second signal path. The first processing module 4 is located on the first signal path and multiplies the first vibration signal with the first waveform signal to obtain a first result signal, filtering out high-frequency components in the first result signal to obtain an I(t) signal. The second processing module 5 is located on the second signal path and multiplies the second vibration signal with the second waveform signal to obtain a second result signal, filtering out high-frequency components in the second result signal to obtain a Q(t) signal. The signal acquisition system 6 is used to determine the amplitude and phase signals of the nanoresonator 2 based on the I(t) and Q(t) signals.

[0061] According to the scheme of the embodiment of the application, the vibration signal generated by the nanoresonator 2 is equally divided by the first radio frequency power divider 3 and is divided into two parallel signals, then the first vibration signal is multiplied by the first waveform signal by the first processing module 4, and the high frequency components in the multiplied result are filtered out, so that the I(t) signal can be obtained, and the second vibration signal is multiplied by the second waveform signal by the second processing module 5, and the high frequency components in the multiplied result are filtered out, so that the Q(t) signal can be obtained, and then the signal acquisition system 6 determines the amplitude signal and the phase signal of the nanoresonator 2 according to the I(t) signal and the Q(t) signal, so that the phase and amplitude response can be obtained based on the IQ demodulation principle. It is found through the comparison of the phase and amplitude response test by using the vector network analyzer that the result obtained by using the IQ demodulation principle in the present application is basically consistent with the result obtained by using the vector network analyzer in the prior art, because it is found through the experiment that the resonance peak and the phase step position measured by the two methods are basically coincident.

[0062] In Figure 1 In the embodiment shown, the first processing module 4 includes a first mixer 41 and a first low-pass filter 42, and the first mixer 41 is arranged between the first radio frequency power divider 3 and the first low-pass filter 42. The first mixer 41 is used to multiply the first vibration signal by the first waveform signal to obtain a first result signal. The first low-pass filter 42 is used to filter out the high frequency components in the first result signal to obtain the I(t) signal. The second processing module 5 includes a second mixer 51 and a second low-pass filter 52, and the second mixer 51 is arranged between the first radio frequency power divider 3 and the second low-pass filter 52. The second mixer 51 is used to multiply the second vibration signal by the second waveform signal to obtain a second result signal. The second low-pass filter 52 is used to filter out the high frequency components in the second result signal to obtain the Q(t) signal.

[0063] Figure 2A microscope image of a nano-resonator 2 under test according to one embodiment of the present application is shown. The nano-resonator 2 includes a nano-structure 21 and a metal gate 22 with a spacing from the nano-structure 21. The material of the nano-structure 21 can be, for example, graphene, molybdenum disulfide, transition metal dichalcogenide, carbon nanotube, or other one-dimensional or two-dimensional nanomaterials. The response measurement device further includes a DC signal source 7 and an MXG signal source 8. The DC signal source 7 is configured to provide a DC signal, and the MXG signal source 8 is configured to provide an MXG signal. The DC signal source 7 and the MXG signal source 8 are connected to the metal gate 22 of the nano-resonator 2 through a DC biaser (not shown in the figure). The DC signal provides a static pulling force to the nano-resonator 2, which in turn changes the internal stress of the nano-structure 21 of the nano-resonator 2 to tune the resonant frequency of the resonator. The MXG AC signal provides a simple harmonic driving force to the resonator, the frequency of which is the same as that of the AC signal, to generate resonance.

[0064] That is, the DC signal provides a DC bias voltage, which causes the nano-structure 21 film to deform, and the MXG AC signal provides a sinusoidal drive, which causes the nano-resonator 2 to vibrate periodically. The laser is incident on the device, and the reflected light signal modulated by the vibration is converted into an electrical signal by the photodetector 14. The response signal is transmitted to the mixer after being divided into two signals by the radio frequency power divider. The mixer down-converts the resonator under the response signal into two same-frequency quadrature signals, which are transmitted to the first channel and the second channel of the radio frequency input of the signal acquisition system 6, such as the Red Piyata STEMlab122-16 board, after filtering out the high-frequency components by the low-pass filter. By using Matlab to control the STEMlab122-16 board through SCPI (Standard Commands for Programmable Instruments), the original data collected by the first channel and the second channel on the board can be obtained, and the amplitude and phase responses of the resonator can be extracted by IQ demodulation of the two signals.

[0065] The response measurement device further includes a laser light source 9, a polarization beam splitting cube 10, a quarter-wave plate 11, and a microscope objective 12 arranged in sequence. The nano-resonator 2 is located below the microscope objective 12, and the polarization beam splitting cube 10 is adjacent to the photodetector 14. The nano-resonator 2 is disposed in a vacuum cavity 13, and the nano-structure 21 and the metal gate 22 form a Fabry-Perot interference cavity. When the nano-structure 21 vibrates, the spacing of the optical cavity changes, thereby achieving modulation of the reflected light. The reflected light is still circularly polarized light, which is transformed into linearly polarized light with only a vertical component after being reflected by the nano-resonator 2 and passing through the quarter-wave plate 11, and then reflected to the photodetector 14 through the polarization beam splitting cube 10. The mean square value of the output voltage of the photodetector 14 The mean square value of the output voltage of the photodetector 14 is calculated according to the following formula:

[0066]

[0067] wherein, represents the product of the gain and responsivity of the photodetector 14, represents the transmittance of the reflected light path, represents the optical power of the laser light source 9 incident on the nanoresonator 2, represents the vibrational displacement of the nanoresonator 2, represents the derivative of the reflectance with respect to the vibrational displacement of the resonator at the equilibrium position, represents the mean square value of the background noise.

[0068] The photodetector 14 converts the reflected light signal into an electrical signal, which is then split equally by the first RF power divider 3 after passing through the bandpass filter 15 and the low-noise amplifier 16. The first vibrational signal after being split is multiplied by the first waveform signal using the first mixer 41 to obtain the first resultant signal, which is calculated according to the following formula:

[0069]

[0070] The high-frequency component with a frequency of is filtered out using the first low-pass filter 42, and the I(t) signal with a frequency of is obtained according to the following formula:

[0071]

[0072] wherein t represents time, represents the phase signal, represents the amplitude signal, and represent different frequencies.

[0073] The second vibrational signal after being split is multiplied by the second waveform signal using the second mixer 51 to obtain the second resultant signal, which is calculated according to the following formula:

[0074]

[0075] The high-frequency component with a frequency of is filtered out using the second low-pass filter 52, and the Q(t) signal with a frequency of is obtained according to the following formula:

[0076]

[0077] wherein t represents time, represents the phase signal, represents the amplitude signal, and represent different frequencies.

[0078] The signal acquisition system 6 calculates the amplitude signal and the phase signal according to the following formulas:

[0079]

[0080]

[0081] wherein, is the frequency signal obtained by multiplying the I(t) signal by the signal and low-pass filtering, is the frequency signal obtained by multiplying the Q(t) signal by the signal and low-pass filtering.

[0082] The signal is obtained according to the following calculation formula:

[0083]

[0084] The signal is obtained according to the following formula:

[0085]

[0086] wherein, t represents time, φ represents the phase signal, A represents the amplitude signal.

[0087] In one embodiment, the response measuring device further comprises a second RF power divider 17, a third RF power divider 18, a third low pass filter 19, a third mixer 20 and a fourth RF power divider 23. The second RF power divider 17 is electrically connected to the output of the MXG signal source 8. The third RF power divider 18 is electrically connected between the arbitrary waveform generator 1 and the second mixer 51. The third low pass filter 19 is electrically connected to the input of the signal acquisition system 6. The input of the third mixer 20 is electrically connected to the second RF power divider 17 and the third RF power divider 18 respectively, and the output of the third mixer 20 is electrically connected to the third low pass filter 19. The fourth RF power divider 23 is electrically connected between the first mixer 41 and the arbitrary waveform generator 1. Since the RF signal output from the MXG signal source 8 will be divided into two signals by the second RF power divider 17, one of which is used to drive the nanoresonator 2, and the other of which is used to transmit the frequency converted signal through the third mixer 20 and the third low pass filter 19 as a trigger signal to the external trigger channel of the STEMlab 122-16 development board, so that the signals collected each time are kept in phase, and then the signal average technique is used to eliminate the random noise in the signals I(t) and Q(t). At the same time, the signal source clock reference output is connected with the arbitrary waveform generator (AWG) clock reference input, so as to greatly improve the frequency accuracy.

[0088] Figure 3 The graphs of I(t) and Q(t) components measured near the resonance frequency of the nanoresonator 2 when the average number is 100, 200, 400 and 1000 are shown according to one embodiment of the present application, and the driving frequency P drive =-15dBm is used during the measurement. The I(t) and Q(t) components are tested under the conditions of average numbers of 100, 200, 400 and 1000 near the resonance frequency of the nanoresonator 2 according to the embodiment of the present application, as shown in Figure 3 , it is found that the signal improves better with the increase of the average number. The accuracy of the amplitude response and the phase response of the nanoresonator 2 needs enough average number to remove the random noise, but too many average numbers will make the measurement time too long, so it is necessary to select a suitable average number. Therefore, the phase response of the graphene resonator is measured under the condition of fixed driving frequency, as shown in Figure 4 , it is found that the phase tends to be stable when the average number is greater than 500, so the average number is set to 500.

[0089] Figure 5 The amplitude response of the nanoresonator 2 under the condition of driving power of -30dBm is shown, and the hollow data points in the figure are the phase response measured by using the IQ demodulation principle in the present application, and the solid curve is the phase response measured by using the prior art VNA. Figure 6The amplitude response of the nanoresonator 2 is shown with a driving power of -30dBm. The hollow data points in the figure are the amplitude responses measured using the IQ demodulation principle in this application, and the solid curves are the amplitude responses measured using the existing VNA technology.

[0090] Depend on Figure 5 and Figure 6 It can be seen from the comparison of amplitude and phase response curves that the phase response changes at the maximum rate with the driving frequency at its resonant frequency. When the driving frequency is far from the resonant frequency, the rate of change of its phase response tends to be gradual, and there is a phase jump of about 180° near the resonant frequency of the resonator.

[0091] To verify the accuracy of the phase and amplitude responses obtained through the IQ demodulation principle in this application, a Vector Automatic Network Analyzer (VNA) was used to test the phase and amplitude responses of the resonator. The measurement results are as follows: Figure 5 and Figure 6 The actual curves are shown. By comparing the phase and amplitude response curves obtained using IQ demodulation technology and VNA (vector network analyzer), it was found that the resonance peak and phase step position measured by the two methods basically coincide. This verifies the accuracy of the phase frequency and amplitude frequency curves of the resonator measured by our IQ demodulation technology.

[0092] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A device for measuring the amplitude and phase response of a nanoresonator, characterized in that, include: An arbitrary waveform generator is used to generate a first waveform signal and a second waveform signal having a preset phase difference with the first waveform signal; A DC signal source is used to provide DC signals; MXG signal source, used to provide MXG signals; A nano-resonator is used to generate a vibration signal under the action of an external signal and to receive the signal after the DC signal and the MXG signal are mixed. The first radio frequency power divider is used to divide the vibration signal into equal parts, and transmit the divided first vibration signal to the first signal path, and transmit the divided second vibration signal to the second signal path. The second radio frequency power divider is electrically connected to the output terminal of the MXG signal source; A first processing module is disposed on the first signal path, used to multiply the first vibration signal and the first waveform signal to obtain a first result signal, and filter out the high-frequency components in the first result signal to obtain an I(t) signal; the first processing module includes a first mixer and a first low-pass filter, the first mixer being disposed between the first radio frequency power divider and the first low-pass filter; The second processing module is disposed on the second signal path and is used to multiply the second vibration signal and the second waveform signal to obtain a second result signal, and filter out the high-frequency components in the second result signal to obtain a Q(t) signal; the second processing module includes a second mixer and a second low-pass filter, the second mixer being disposed between the first RF power divider and the second low-pass filter; A signal acquisition system is used to determine the amplitude signal and phase signal of the nanoresonator based on the I(t) signal and the Q(t) signal; The third radio frequency power divider is electrically connected between the arbitrary waveform generator and the second mixer; The third low-pass filter is electrically connected to the input terminal of the signal acquisition system. The third mixer has its input terminals connected to the second RF power divider and the third RF power divider, respectively, and its output terminal connected to the third low-pass filter.

2. The response measurement device according to claim 1, characterized in that, The first mixer is used to calculate the first result signal according to the following formula: The first low-pass filter is used to filter out frequencies of The high-frequency components are obtained according to the following formula, with the frequency being... The I(t) signal: Where t represents time. Indicates phase signal, Indicates amplitude signal, and Indicates different frequencies.

3. The response measuring device according to claim 2, characterized in that, The second mixer is used to calculate the second result signal according to the following formula: The second low-pass filter is used to filter out frequencies of The high-frequency components are obtained according to the following formula, with the frequency being... The Q(t) signal: Where t represents time. Indicates phase signal, Indicates amplitude signal, and Indicates different frequencies.

4. The response measuring device according to any one of claims 1-3, characterized in that, The signal acquisition system calculates the amplitude signal according to the following formula. and phase signal : in, For the I(t) signal and the signal The frequency signal after multiplication and low-pass filtering, The Q(t) signal and the signal The frequency signal after multiplication and low-pass filtering.

5. The response measuring device according to claim 4, characterized in that, Signal The following calculation formula is used to obtain it: Signal Calculated using the following formula: Where t represents time. Indicates phase signal, This indicates the amplitude signal.

6. The response measuring device according to any one of claims 1-3 and 5, characterized in that, It also includes a photodetector, a bandpass filter, and a low-noise amplifier connected in sequence, wherein the low-noise amplifier is electrically connected to the first radio frequency power divider; The photodetector is used to convert the reflected light signal modulated by the nanoresonator into an electrical signal.

7. The response measuring device according to claim 6, characterized in that, The mean square value of the output voltage of the photodetector Calculated using the following formula: in, This represents the product of the photodetector's gain and responsivity. Indicates the transmittance of the reflected light path. This represents the optical power of the laser source incident on the nanoresonator. This represents the vibration displacement of the nanoresonator. This represents the derivative of the resonator's reflectivity with respect to the vibrational displacement at the equilibrium position. This represents the mean square value of the background noise.

8. The response measuring device according to claim 7, characterized in that, It also includes a laser source, a polarizing beam splitter cube, a quarter glass slide, and a microscope objective arranged in sequence; The nanoresonator is located below the microscope objective, and the polarization beam splitter is also adjacent to the photodetector. The circularly polarized light reflected by the nanoresonator is transformed into linearly polarized light with only a vertical component after passing through the quarter glass plate, and then reflected by the polarization beam splitter into the photodetector.

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