CN118971815B - Device and method for realizing modulated signal amplification based on stochastic resonance in nanomechanical resonator - Google Patents
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Abstract
本发明公开了一种基于纳米机械谐振器中的随机共振实现调制信号放大的装置及方法，具体涉及信号放大技术领域，其包括激光光束、以及用于传递激光光束的光路设置和测试组件，利用光学干涉的探测方法，通过对处于非线性状态下的基于原子级厚度的待测纳米机械谐振器施加一定的宽带噪声等步骤实现振幅调制信号的放大。本发明在纳米机械谐振器中实现了高达22.7 kHz的随机转换率，且基于这种高频转换将振幅调制信号的信噪比提高了2倍以上。
The present invention discloses a device and method for realizing modulated signal amplification based on random resonance in a nanomechanical resonator, which specifically relates to the field of signal amplification technology, including a laser beam, an optical path setting and a test component for transmitting the laser beam, and a detection method using optical interference, and amplifying the amplitude modulated signal by applying a certain broadband noise to the nanomechanical resonator to be tested based on atomic-level thickness in a nonlinear state. The present invention realizes a random conversion rate of up to 22.7 kHz in the nanomechanical resonator, and based on this high-frequency conversion, the signal-to-noise ratio of the amplitude modulated signal is increased by more than 2 times.
Description
Technical Field
The invention relates to a device and a method for realizing modulation signal amplification based on stochastic resonance in a nano mechanical resonator, and belongs to the technical field of signal amplification.
Background
Stochastic resonance (Stochastic resonance) is a technique that uses an amount of noise to amplify signals that periodically act on a bistable nonlinear system. In 1981 Benzi et al, for the first time, proposed this concept to explain the periodicity of glacial phase, after which stochastic resonance was widely used in the electrical, optical and superconducting fields.
The mechanism for achieving signal amplification using stochastic resonance is that as the applied excitation increases gradually, the response of the system no longer follows hooke's law, exhibiting the well-known Duffing bistable phenomenon. When the system is in a bistable region, its response is a multi-valued function having both low and high amplitude states, and external random fluctuations, such as white noise, cause the system response to undergo random transitions between the low and high amplitude states, which may be used to amplify the amplitude modulated signal.
However, due to the fact that the traditional micro-electro-mechanical system (MEMS) device is large in size, the conversion rate is only tens of hertz, the conversion rate is low, the human voice wave band (20 Hz-20000 Hz) is difficult to cover, if the conversion frequency can be expanded to thousands of hertz, and meanwhile, the energy dissipated by each conversion can be reduced, a new application scene, such as an audio amplifier, can be opened up for stochastic resonance in the audio field.
With the development of nano-fabrication technology, the advent of mechanical resonators based on atomic-scale thickness two-dimensional materials made possible the above assumptions, which have very little mass, very low bending stiffness and very large tensile stiffness, which make it easy to achieve Duffing nonlinearity, and whose random conversion rates can reach kHz orders at very low energy consumption.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a device and a method for amplifying a modulation signal based on stochastic resonance in a nano mechanical resonator, wherein the stochastic resonance is utilized to apply certain broadband noise to the nano mechanical resonator in a nonlinear state, so that the conversion rate of 22.7 kHz is realized, and the signal to noise ratio of the modulation signal is improved by more than 2 times based on the high-frequency conversion.
In order to achieve the above purpose, the invention is realized by adopting the following technical scheme:
on one hand, the invention provides a device for realizing modulation signal amplification based on stochastic resonance in a nano mechanical resonator, which comprises a helium-neon laser, wherein the helium-neon laser is used for emitting laser beams towards an optical fiber coupling assembly, the optical fiber coupling assembly is used for expanding and collimating the laser beams and transmitting the laser beams to a half-wave plate, the half-wave plate is used for adjusting the energy duty ratio of horizontal component p waves and vertical component s waves in the beams, the laser beams are transmitted to a polarization beam splitting cube after passing through the half-wave plate and are reflected by a reflecting assembly, the polarization beam splitting cube is used for reflecting the vertical component s waves out of a light path and enabling the horizontal component p waves to pass through, the horizontal component p waves are incident to an objective lens through a quarter-wave plate, and the other side of the objective lens is provided with a vacuum cavity, and the objective lens is used for focusing the laser beams and transmitting the vacuum cavity to the nano mechanical resonator to be tested;
The polarization beam splitting cube is connected with a photoelectric detector, the photoelectric detector is connected with a spectrum analyzer, the photoelectric detector is used for receiving the optical signals of the polarization beam splitting cube, converting the optical signals into electric signals and transmitting the electric signals to the spectrum analyzer, and the spectrum analyzer is used for receiving the electric signals and displaying the electric signals in a frequency domain;
The vacuum cavity is provided with a radio frequency connector, the radio frequency connector is connected with a microwave biaser, the microwave biaser comprises a DC end and an RF end, the DC end is connected with a direct current voltage source, the RF end is connected with an arbitrary waveform signal generator and a sine wave signal generator, the arbitrary waveform signal generator is used for outputting wide bandwidth noise voltages with different amplitudes, and the sine wave signal generator is used for outputting sine wave signals.
Further, the optical fiber coupling assembly comprises a polarization-maintaining single-mode fiber and two optical fiber couplers which are placed in opposite directions, wherein the two optical fiber couplers are connected through the polarization-maintaining single-mode fiber, and the polarization-maintaining single-mode fiber is used for transmitting a laser beam focused by one optical fiber coupler to the other optical fiber coupler for beam expansion and collimation.
Further, the reflecting component comprises two reflecting mirrors, the two reflecting mirrors are symmetrically arranged, and the reflecting mirrors are used for reflecting the laser beam twice by 90 degrees and then making the laser beam enter the polarization beam splitting cube in the direction opposite to the initial emitting direction.
Further, the device also comprises a beam calibration assembly and a neutral density filter;
The neutral density filter is arranged between the helium-neon laser and the optical fiber coupling assembly and is used for carrying out partial attenuation on the laser beam power;
The beam calibration component is used for calibrating the position of the laser beam incident on the nano mechanical resonator to be measured and comprises a reversible beam splitter, a lens, a camera and a white light source;
The white light source is used for emitting white light to the beam splitter, the beam splitter is used for enabling the white light to enter the objective lens after passing through the reversible beam splitter, reflecting the white light reflected by the nano mechanical resonator to be detected and part of laser beams to enter the camera through the lens, and the reversible beam splitter is arranged between the objective lens and the quarter wave plate and used for reflecting the emitted white light into the objective lens and simultaneously reflecting the white light reflected by the resonator and part of laser beams to the camera.
In another aspect, the present invention provides a method for amplifying a modulation signal based on stochastic resonance in a nanomechanical resonator, which is implemented by the device for amplifying a modulation signal based on stochastic resonance in a nanomechanical resonator, comprising:
placing the nano mechanical resonator to be tested in the vacuum cavity, and starting a helium-neon laser;
Starting a direct-current voltage source and a spectrum analyzer, setting the output voltage of the direct-current voltage source to be a fixed value, setting the frequency range of the spectrum analyzer to be 10 MHz, and setting the resolution bandwidth to be 5 Hz;
starting an arbitrary waveform signal generator, setting the arbitrary waveform signal generator to output wide bandwidth noise voltage signals with different amplitudes, and measuring by a spectrum analyzer to obtain response spectrums of the nano mechanical resonator to the wide bandwidth noise voltages with different amplitudes in a set frequency range, wherein the set frequency range comprises frequency ranges of expansion several MHz on two sides of a resonance frequency of the nano mechanical resonator to be measured as a center frequency;
obtaining the relation between the effective temperature and the noise voltage of the nano mechanical resonator to be measured according to the response frequency spectrum of the nano mechanical resonator for the wide bandwidth noise voltages with different amplitudes in the set frequency range;
Closing an arbitrary waveform signal generator, starting the sine wave signal generator, changing the output frequency of the sine wave signal generator, enabling the output frequency of the sine wave signal generator to be scanned from low frequency to high frequency in a fixed step length and from high frequency to low frequency in the same step length, recording the maximum value of a frequency spectrum at each output frequency, displaying the relation of amplitude change along with time at the center frequency by a frequency spectrum analyzer in a mode, and obtaining a frequency response curve of the nano mechanical resonator to be tested, wherein the frequency response curve of the nano mechanical resonator to be tested comprises a hysteresis area;
Setting a frequency spectrum analyzer to be in a frequency bandwidth mode of 0 Hz by taking the driving frequency at the middle position of the hysteresis area as the output frequency of a sine wave signal generator, starting an arbitrary waveform signal generator according to the relation that the amplitude at the center frequency changes along with time, taking the noise voltage at the uppermost curve in the frequency spectrum under the wide bandwidth noise voltages with different amplitudes in the set frequency range as the noise voltage output by the arbitrary waveform signal generator, and measuring by the frequency spectrum analyzer to obtain a jump curve of the frequency response of the nano mechanical resonator to be measured along with time;
according to the jump curve conversion of the frequency response of the nano mechanical resonator to be detected along with time, obtaining random conversion rate curves at different driving frequencies in a hysteresis region;
Taking the driving frequency of the highest point of the random conversion rate curve at different driving frequencies in the hysteresis area as the output frequency of the sine wave signal generator, setting the random waveform signal generator to output wide bandwidth noise voltages with different amplitudes, and obtaining the random conversion rate curve under the wide bandwidth noise voltages with different amplitudes;
Setting the output mode of a sine wave signal generator as amplitude modulation output, wherein the carrier frequency is the driving frequency of the highest point of a random conversion rate curve under different driving frequencies in a hysteresis region, the modulation frequency is set to be about 1/2 of the conversion rate according to the random conversion rate curve under the wide bandwidth noise voltage with different amplitudes, the center frequency of a frequency spectrum analyzer is set as the carrier frequency, the frequency range is set to be a plurality of times of the modulation frequency, and the modulation signal frequency spectrum under the wide bandwidth noise voltage with different amplitudes is obtained through the frequency spectrum analyzer;
Calculating according to the frequency spectrums of the modulation signals under the wide bandwidth noise voltages with different amplitudes to obtain the signal-to-noise ratio of the modulation signals output by the to-be-detected nano mechanical resonator under the wide bandwidth noise voltages with different amplitudes;
Obtaining the relation between the signal-to-noise ratio of the nano mechanical resonator to be measured and the effective temperature according to the signal-to-noise ratio of the modulation signal output by the nano mechanical resonator to be measured under the wide bandwidth noise voltage with different amplitudes and the relation between the effective temperature of the nano mechanical resonator to be measured and the noise voltage;
And determining an effective temperature value when the signal-to-noise ratio is maximum according to the relation between the signal-to-noise ratio of the modulation signal output by the nano mechanical resonator to be detected and the effective temperature, and amplifying the modulation signal to achieve the maximum value at the moment.
Further, the obtaining the relation between the effective temperature and the noise voltage of the to-be-measured nano mechanical resonator according to the frequency spectrum in the set frequency under the wide bandwidth noise voltage with different magnitudes includes:
The response rate of the nano mechanical resonator to be measured is calculated, and the expression is as follows:
wherein, The method comprises the steps of representing the response rate of a nano mechanical resonator to be measured, G representing the conversion gain of a photoelectric detector, P APD representing the laser power received by the photoelectric detector, R representing the reflectivity of the nano mechanical resonator to be measured, dR/dz representing the optical response rate of the nano mechanical resonator to be measured, and the physical meaning of the method is the absolute value of the change rate of the reflectivity along with the displacement of the resonator in the z direction;
Dividing the ordinate of a frequency spectrum in a set frequency range under the wide bandwidth noise voltage with different magnitudes by the resolution bandwidth of a spectrum analyzer to obtain the power spectrum density of the noise voltage, subtracting the measured background noise from the power spectrum density of the voltage, and dividing the power spectrum density by the response rate of the nano mechanical resonator to be measured to obtain a power spectrum density curve of the displacement of the nano mechanical resonator to be measured in the set frequency under the wide bandwidth noise voltage with different magnitudes, wherein the set frequency range comprises frequency ranges of expansion several MHz respectively at two sides of the resonance frequency of the nano mechanical resonator to be measured as the center frequency;
Calculating the area covered by the power spectral density of the displacement of the nano mechanical resonator to be measured in a set frequency range under the wide bandwidth noise voltage with different amplitudes to obtain the mean square value of the displacement in time t, wherein the expression is as follows:
wherein, Representing the power spectral density of the noise voltage,Representing the background noise and,The power spectral density representing the displacement of the nanomechanical resonator to be measured,Mean square value representing displacement in time t;
and calculating the relation between the effective temperature and the noise voltage of the nano mechanical resonator to be measured by the mean square value of displacement in time t, wherein the expression is as follows:
wherein, Indicating the effective temperature of the nanomechanical resonator to be measured,Representing the effective mass of the nanomechanical resonator to be measured,Representing the nth order resonant frequency of the nanomechanical resonator to be measured,Representing the boltzmann constant.
Further, the background noise is obtained by measuring the average value of the spectrum at a position far from the formants.
Further, the step of obtaining the frequency random conversion rate curve in the hysteresis region under different driving frequencies according to the frequency response time-dependent jump curve of the nano mechanical resonator to be measured includes:
the jump from high amplitude to low amplitude in the jump curve of the frequency response of the nano mechanical resonator to be measured along with time is regarded as one-time conversion;
And calculating the conversion times of the frequency response of the nano mechanical resonator to be measured along with time in a certain measurement time as the conversion rate, and obtaining a random conversion rate curve in a hysteresis region under different driving frequencies.
Further, the calculating the signal-to-noise ratio according to the modulated signal spectrum includes dividing the signal voltage value of the highest point of the modulated signal spectrum by the background noise to obtain the signal-to-noise ratio.
Further, after starting the helium-neon laser, the test is started, and the test also comprises a beam calibration operation, wherein the beam calibration operation comprises the steps of turning over the turnover beam splitting mirror, opening the white light source and the camera, adjusting the distance between the objective lens and the resonator, observing through the camera to enable the nano mechanical resonator to be tested to be positioned on the focal plane of the nano mechanical resonator, adjusting the relative position of the objective lens in the direction vertical to the horizontal plane, enabling the laser beam to be positioned at the center position of the resonator, turning off the white light source after the adjustment is completed, turning over the turnover beam splitting mirror to enable the turnover beam splitting mirror to be parallel to the horizontal plane, and enabling the laser beam not to pass through the beam splitting mirror at the moment;
Compared with the prior art, the invention has the beneficial effects that:
The invention provides a device for realizing modulation signal amplification based on stochastic resonance in a nano mechanical resonator, which is used for transmitting laser beams through a designed light path and making the laser beams incident on the surface of the nano mechanical resonator, modulating the incident laser beams by stochastic resonance in the nano mechanical resonator and reflecting the incident laser beams, and testing the light beams reflected by the nano mechanical resonator to be tested through a photoelectric detector and a spectrum analyzer to realize modulation signal amplification of the nano mechanical resonator;
According to the graphene film resonator based on atomic-level thickness, a certain broadband noise is applied to the nano mechanical resonator to be detected in a nonlinear state by utilizing an optical interference detection method, so that the conversion rate of 22.7 kHz is realized, the high-frequency adjustable conversion rate can be used for a random number generator in the field of calculation, and the conversion rate can cover the frequency band of human voice by controlling the amplitude of the applied noise voltage, which cannot be achieved by the traditional silicon-based micro mechanical resonator. The signal to noise ratio of the modulated signal is improved by more than 2 times based on the high frequency random conversion.
Drawings
FIG. 1 is a schematic diagram of an apparatus for amplifying a modulation signal based on stochastic resonance in a nanomechanical resonator according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a voltage power spectral density curve of a nanomechanical resonator to be tested at different wide bandwidth noise voltages of different magnitudes within a set frequency of a method for implementing modulated signal amplification based on stochastic resonance in the nanomechanical resonator according to an embodiment of the present invention;
FIG. 3 is a schematic diagram showing the relationship between the effective temperature and the noise voltage of a nanomechanical resonator to be tested according to a method for amplifying a modulation signal based on stochastic resonance in the nanomechanical resonator according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a frequency response curve of a nanomechanical resonator to be tested in a nonlinear state according to a method of implementing modulated signal amplification based on stochastic resonance in the nanomechanical resonator according to an embodiment of the present invention;
FIG. 5 is a graph showing a jump curve of frequency response of a nanomechanical resonator to be measured over time according to a method of amplifying a modulation signal based on stochastic resonance in the nanomechanical resonator according to an embodiment of the present invention;
FIG. 6 is a graph showing random slew rates at different driving frequencies in a hysteresis region of a method for implementing modulated signal amplification based on stochastic resonance in a nanomechanical resonator according to one embodiment of the invention;
FIG. 7 is a graph showing the random slew rate at different effective temperatures for a method of implementing modulated signal amplification based on stochastic resonance in a nanomechanical resonator according to one embodiment of the invention;
FIG. 8 is a schematic diagram showing the relationship between the signal-to-noise ratio and the effective temperature of the nanomechanical resonator to be tested according to the method of amplifying the modulation signal based on stochastic resonance in the nanomechanical resonator according to an embodiment of the present invention;
In the figure, a 1-helium-neon laser, a 2-neutral density filter, a 3-optical fiber coupler, a 4-polarization maintaining single-mode optical fiber, a 5-half wave plate, a 6-reflecting mirror, a 7-polarization beam splitting cube, an 8-quarter wave plate, a 9-reversible beam splitting mirror, a 10-beam splitting mirror, a 11-white light source, a 12-lens, a 13-camera, a 14-objective lens, a 15-vacuum cavity, a 16-nanometer mechanical resonator to be measured, a 17-microwave bias device, an 18-arbitrary waveform signal generator, a 19-sine wave signal generator, a 20-direct current voltage source, a 21-photoelectric detector and a 22-spectrum analyzer are shown.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.
In the description of the present invention, unless explicitly stated or limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected, mechanically connected, electrically connected, directly connected, indirectly connected via an intervening medium, or in communication between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art in a specific case.
Example 1
As shown in fig. 1, the device for amplifying a modulation signal based on stochastic resonance in a nanomechanical resonator according to an embodiment of the present invention includes a helium-neon laser 1, where the helium-neon laser 1 is used to emit a laser beam. The laser beam enters the optical fiber coupling assembly after power attenuation through the neutral density filter 2.
In this embodiment, the optical fiber coupling assembly includes a polarization-maintaining single-mode fiber 4 and two opposite optical fiber couplers 3, where the two optical fiber couplers 3 are connected by the polarization-maintaining single-mode fiber 4, and the polarization-maintaining single-mode fiber 4 is used to transmit the laser beam focused by one optical fiber coupler 3 to the other optical fiber coupler 3 for beam expansion and collimation.
The optical fiber coupling assembly transmits the laser beam to the half-wave plate 5, and the half-wave plate 5 is used for adjusting the energy ratio of the horizontal component p wave and the vertical component s wave in the beam, and adjusting the fast axis direction of the half-wave plate 5 so as to maximize the power of the laser beam.
After passing through the half wave plate 5, the laser beam is reflected by the reflection assembly and then transmitted to the polarization beam splitting cube 7. In this embodiment, the reflecting assembly includes two reflecting mirrors 6, and the two reflecting mirrors 6 are symmetrically disposed, and are used to make the laser beam incident into the polarization beam splitting cube 7 in a direction opposite to the initial emission direction after being reflected twice by 90 °. The polarization beam splitting cube 7 is used for reflecting the vertical component s wave out of the optical path and allowing the horizontal component p wave to pass through, and the horizontal component p wave is incident to the objective lens through the quarter wave plate 8. In this embodiment, the fast axis direction of the quarter wave plate 8 is 45 ° to the horizontal, which maximizes the reflected laser energy.
The other side of the objective lens 14 is provided with a vacuum cavity 15, the vacuum cavity 15 is used for placing a nano mechanical resonator 16 to be measured, and the objective lens 14 is used for focusing laser beams and transmitting the vacuum cavity 15 to be incident on the nano mechanical resonator 16 to be measured.
The polarization beam splitting cube 7 is connected with a photoelectric detector 21, the photoelectric detector 21 is connected with a spectrum analyzer 22, the photoelectric detector 21 is used for receiving the optical signals of the polarization beam splitting cube 7, converting the optical signals into electric signals and transmitting the electric signals to the spectrum analyzer 22, and the spectrum analyzer 22 is communicated with a computer through a GPIB interface and is used for receiving the electric signals and displaying the electric signals in a frequency domain.
The vacuum cavity 15 is provided with a radio frequency connector, the radio frequency connector is connected with a microwave bias device 17, the microwave bias device 17 comprises a DC end and an RF end, the DC end is connected with a direct current voltage source 20, the RF end is connected with an arbitrary waveform signal generator 18 and a sine wave signal generator 19, the arbitrary waveform signal generator 18 is used for outputting wide bandwidth noise voltages with different amplitudes, and the sine wave signal generator 19 is used for outputting sine wave signals.
Example 2
Based on embodiment 1, the present embodiment further includes a beam calibration component, which is used for calibrating the position of the laser beam incident on the nano mechanical resonator 16 to be measured, and includes a reversible beam splitter 9, a beam splitter 10, a lens 12, a camera 13, and a white light source 11, where in the present embodiment, the camera 13 is a CCD camera.
The white light source 11 is used for emitting white light onto the beam splitter 10, the beam splitter 10 is used for making the white light enter the objective lens 14 after passing through the reversible beam splitter 9, reflecting the white light and part of laser beams reflected by the nano mechanical resonator 16 to be tested to enter the camera 13 through the lens 12, and the reversible beam splitter 9 is arranged between the objective lens 14 and the quarter wave plate 8 and used for reflecting the emitted white light into the objective lens 14, and simultaneously reflecting the white light and part of laser beams reflected by the nano mechanical resonator 16 to be tested to the camera 13.
After the beam alignment is completed, the reversible beam splitter 9 needs to be removed from the optical path.
Example 3
On the basis of embodiment 1, the present embodiment provides a method for amplifying a modulation signal based on stochastic resonance in a nanomechanical resonator, which includes the following steps:
the nanomechanical resonator 16 to be tested is placed inside the vacuum chamber and the helium-neon laser 1 is turned on.
The direct current voltage source 20 and the spectrum analyzer 22 were started, the output voltage of the direct current voltage source 20 was set to a fixed value, the frequency range of the spectrum analyzer 22 was set to 10 MHz, and the resolution bandwidth was set to 5 Hz.
The arbitrary waveform signal generator 18 is started, the arbitrary waveform signal generator 18 is set to output wide bandwidth noise voltages with different amplitudes, and after the power of the helium-neon laser 1 is stable, the spectrum analyzer 22 measures the frequency spectrum under the wide bandwidth noise voltages with different amplitudes within the set frequency range.
It should be noted that the set frequency range includes frequency ranges of several MHz spread on both sides of the resonance frequency of the nanomechanical resonator 16 to be measured as a center frequency.
Nanomechanical resonators of different sizes and structures respond differently to the same noise voltage, so effective temperature is needed to measure the level of fluctuation. Therefore, the relationship between the effective temperature and the noise voltage of the to-be-measured nanomechanical resonator 16 needs to be obtained according to the frequency spectrum in the set frequency under the wide bandwidth noise voltage with different magnitudes, specifically including:
The response rate of the nanomechanical resonator 16 to be measured is calculated as follows:
wherein, The response rate of the nano-mechanical resonator 16 to be measured is represented by G, the conversion gain of the photodetector 21 is represented by P APD, the laser power received by the photodetector 21 is represented by |dr/dz| and the optical response rate of the nano-mechanical resonator 16 to be measured is represented by |dr/dz|, and the physical meaning is the absolute value of the change rate of the reflectivity along with the displacement of the resonator in the z direction.
The ordinate of the spectrum at the wide bandwidth noise voltages of different magnitudes within the set frequency range is divided by the resolution bandwidth of the spectrum analyzer 22 to obtain the power spectral density of the noise voltage, and the power spectral density of the voltage is subtracted by the measured background noise and divided by the response of the nanomechanical resonator 16 to be measured to obtain the voltage power spectral density curve of the nanomechanical resonator 16 to be measured at the wide bandwidth noise voltages of different magnitudes within the set frequency, as shown in fig. 2.
Calculating the area covered by the power spectral density of the displacement of the nano mechanical resonator 16 to be measured in a set frequency range under the wide bandwidth noise voltage with different amplitudes to obtain the mean square value of the displacement in time t, wherein the expression is as follows:
wherein, Representing the power spectral density of the noise voltage,Representing the background noise and,The power spectral density representing the displacement of the nanomechanical resonator 16 to be measured,Representing the mean square value of the displacement over time t.
And calculating the relation between the effective temperature and the noise voltage of the nano mechanical resonator to be measured by the mean square value of displacement in time t, wherein the expression is as follows:
wherein, Indicating the effective temperature of the nanomechanical resonator 16 to be measured,Representing the effective mass of the nanomechanical resonator 16 to be measured,Representing the nth order resonant frequency of the nanomechanical resonator 16 to be measured,Representing the boltzmann constant.
Through the above calculation processing steps, the effective temperature values corresponding to the to-be-measured nano mechanical resonator 16 under the wide bandwidth noise voltages with different magnitudes can be obtained, as shown in fig. 3.
Then, the arbitrary waveform signal generator 18 is turned off, the sine wave signal generator 19 is turned on, and the output frequency of the sine wave signal generator 19 is changed, so that the output frequency of the sine wave signal generator 19 is scanned from a low frequency to a high frequency (solid line in fig. 4) in a fixed frequency step size and from the high frequency to the low frequency (dashed line in fig. 4) in the same step size, the maximum value of the frequency spectrum of each output frequency is recorded, and the frequency response curve of the nano-mechanical resonator 16 to be measured is obtained, as shown in fig. 4, the y-axis is the voltage at the output end of the photodetector 21, and the x-axis is the output frequency of the sine wave signal generator 19, that is, the driving frequency of the nano-mechanical resonator 16 to be measured.
As can be seen from fig. 4, the frequency response curve of the nanomechanical resonator 16 to be measured includes a hysteresis region, and there is a portion of misalignment of the response amplitudes from low frequency to high frequency and from high frequency to low frequency, which just encloses a closed region, i.e., the hysteresis region. This is due to the nanomechanical resonator, as the applied excitation increases, so does the deformation of the graphene film. Above a certain threshold, the strain and applied stress cannot be described by hooke's law.
Taking the driving frequency at the middle position of the hysteresis region as the output frequency of the sine wave signal generator 19, the spectrum analyzer 22 is set to a frequency bandwidth (zero span) mode of 0Hz which shows the relationship of the amplitude at the center frequency with time, and in this embodiment, the bandwidth resolution of the spectrum analyzer 22 is set to 10 kHz and the measurement time is 10 ms. In the 0Hz frequency bandwidth mode, the abscissa of the spectrum measured by the spectrum analyzer 22 is the measurement time.
Taking the noise voltage at the uppermost curve in the frequency spectrum under the wide bandwidth noise voltages with different amplitudes in the set frequency range as the noise voltage output by the arbitrary waveform signal generator 18, the frequency response time jump curve of the nano mechanical resonator 16 to be measured is measured by the spectrum analyzer 22, as shown in fig. 5.
As shown in fig. 5, the hopping frequency at 44.2 MHz is up to 22.7 kHz, and within 1 MHz, the hopping frequency can be adjusted from a few Hz to 22.7 kHz.
The random conversion rate curves at different driving frequencies in the hysteresis region are obtained according to the transition curve of the frequency response of the nano mechanical resonator 16 to be measured along with time, specifically comprising:
The transition from a high amplitude to a low amplitude in the transition curve of the frequency response of the nanomechanical resonance 16 to be measured over time is considered as a transition.
The frequency response of the nano-mechanical resonator 16 to be measured in a certain measurement time is calculated as the conversion rate along with the time conversion times, and a random conversion rate curve in a hysteresis region under different driving frequencies is obtained, as shown in fig. 6.
The driving frequency at which the highest point of the random conversion rate curve at the different driving frequencies in the hysteresis region is located is taken as the output frequency of the sine wave signal generator 19, and in this embodiment, the driving frequency at which the highest point of the random conversion rate curve at the different driving frequencies in the hysteresis region is located is 44.2 MHz. The arbitrary waveform signal generator 18 is set to output wide bandwidth noise voltages of different magnitudes to yield a random slew rate curve at different effective temperatures, as shown in fig. 7.
The output mode of the sine wave signal generator 19 is set to be amplitude modulation output, the carrier frequency is the driving frequency where the highest point of the random conversion rate curve under different driving frequencies in the hysteresis region is located, the modulation frequency is set to be about 1/2 of the conversion rate according to the random conversion rate curve under the wide bandwidth noise voltage with different amplitudes, the center frequency of the spectrum analyzer 22 is set to be the carrier frequency, the frequency range is set to be a plurality of times of the modulation frequency, the arbitrary waveform signal generator 18 is set to output the wide bandwidth noise voltage with different amplitudes, and the modulation signal spectrum under the wide bandwidth noise voltage with different amplitudes is obtained through the spectrum analyzer 22.
According to the modulating signal frequency spectrum under the wide bandwidth noise voltage with different amplitude values, the signal-to-noise ratio of the modulating signal output by the to-be-detected nano mechanical resonator 16 under the wide bandwidth noise voltage with different amplitude values is obtained by calculating the signal voltage value of the highest point of the modulating signal frequency spectrum divided by the background noise.
According to the signal-to-noise ratio of the nano mechanical resonator 16 to be measured under the wide bandwidth noise voltage with different amplitudes and the relation between the effective temperature of the nano mechanical resonator 16 to be measured and the noise voltage, the relation between the signal-to-noise ratio of the nano mechanical resonator 16 to be measured and the effective temperature is obtained, as shown in fig. 8.
The effective temperature value when the signal-to-noise ratio is maximum is determined according to the relation between the signal-to-noise ratio of the modulation signal output by the nano mechanical resonator 16 to be measured and the effective temperature, and at this time, the amplification of the modulation signal achieves the maximum value.
Example 4
On the basis of embodiment 3, this embodiment further includes a beam calibration operation after starting the helium-neon laser 1 before starting the test, which includes:
The turnable beam splitter 9 is turned over so as to be parallel to the beam splitter.
The white light source 11 and the camera 13 are turned on, the distance between the objective lens 14 and the resonator is observed and adjusted by the camera, so that the nanomechanical resonator 16 to be measured is positioned on the focal plane thereof, and the relative position of the objective lens 14 is adjusted in the direction perpendicular to the horizontal plane, so that the laser beam is positioned at the center position of the resonator 16.
After the adjustment is finished, the white light source 11 is turned off, the turnover beam splitter 9 is turned over to enable the turnover beam splitter 9 to be parallel to the horizontal plane, and at the moment, laser beams cannot pass through the beam splitter 9 so as to facilitate subsequent operation.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (9)
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