Phase synchronization system and method

Abstract

A phase synchronization system according to the present invention comprises: a mechanical resonance unit (12) that has a simultaneous oscillation mechanism of a plurality of vibration modes; an optical resonance unit (11) that is configured such that an optical mode interacts with each of the plurality of vibration modes; and an optical control unit (10) that modulates the intensity of laser light introduced into the optical resonance unit (11). The optical control unit (10) modulates the intensity of the laser light in accordance with an intensity modulation signal at a frequency based on the difference frequencies of the plurality of vibration modes, thereby synchronizing a phase difference between the plurality of vibration modes to a desired phase through nonlinear interaction between the optical mode and the plurality of vibration modes.

Description

Phase-locked systems and methods

[0001] The present invention relates to a phase synchronization system and method for synchronizing the phases of multiple mechanical vibration modes in a state of simultaneous oscillation.

[0002] The oscillation state of mechanical vibrations plays a crucial role in high-sensitivity sensing applications using oscillators, as it enables the achievement of very large vibration amplitudes and narrow frequency linewidths. In particular, controlling the oscillation states of multiple natural vibration modes with different frequencies and spatial distributions can lead to further enhancements in sensing, such as spatial resolution and frequency resolution. As a control device for the simultaneous oscillation state of such multiple vibration modes, a phase-locked device based on electrical circuits has been proposed (Non-Patent Document 1).

[0003] However, the phase-locking device disclosed in Non-Patent Document 1 requires the nonlinearity necessary for phase locking to be realized by an electrical circuit, which necessitates adjustment of components and parameters according to the oscillation frequency, and also presents the problem that the circuit configuration becomes significantly more complex as the number of oscillation modes increases.

[0004] Matthew H. Matheny, Matt Grau, Luis G. Villanueva, Rassul B. Karabalin, MCCross, and Michael L. Roukes, “Phase Synchronization of Two Anharmonic Nanomechanical Oscillators”, Physical Review Letters, 112, 014101, 2014

[0005] The present invention has been made to solve the above problems and aims to provide a phase synchronization system and method that can easily synchronize the phases of multiple vibration modes in a simultaneously oscillating state.

[0006] The phase-locking system of the present invention comprises a mechanical resonant section having a mechanism for simultaneous oscillation of multiple vibration modes, an optical resonant section configured such that an optical mode interacts with each of the multiple vibration modes, and an optical control section configured to modulate the intensity of laser light introduced into the optical resonant section. The optical control section modulates the laser light in intensity according to an intensity modulation signal of frequency based on the difference frequencies of the multiple vibration modes, thereby synchronizing the phase difference of the multiple vibration modes to a desired phase through a nonlinear interaction between the optical mode and the multiple vibration modes.

[0007] According to the present invention, by adopting a configuration in which multiple vibration modes of a mechanical resonant section interact with the optical modes of an optical resonator, it becomes possible to synchronize the phase difference of multiple vibration modes in a simultaneously oscillating state to a desired phase through the nonlinearity inherent in the optical-mechanical coupling. The present invention makes it possible to synchronize the phase difference of multiple vibration modes of a mechanical resonant section using a single laser beam, achieving high scalability as the number of vibration modes increases. Furthermore, by configuring the system using a laser light source in the communication wavelength band, the present invention is expected to realize simple and scalable phase synchronization of IoT vibration sensors that can be connected to an optical network.

[0008] Figure 1 is a block diagram showing the configuration of the phase-locked system according to the present invention. Figure 2 is a diagram showing the phase difference between the intensity modulated signal, the oscillation amplitude of the mechanical resonant section, and the two vibration modes of the mechanical resonant section. Figure 3 is a block diagram showing the configuration of the phase-locked system according to the first embodiment of the present invention. Figure 4 is a diagram showing the intensity change of the beat signal according to the modulation frequency and modulation voltage. Figure 5 is a diagram illustrating the effect of phase locking by the phase-locked system according to the second embodiment of the present invention. Figure 6 is a block diagram showing the configuration of the phase-locked system according to the third embodiment of the present invention. Figure 7 is a diagram showing the locking probability when only the second harmonic signal is used. Figure 8 is a diagram showing the locking probability when the fundamental wave signal is used in addition to the second harmonic signal. Figure 9 is a diagram showing the transition of the locking phase when the phase of the fundamental wave signal is changed. Figure 10 is a diagram illustrating the effect of the phase-locked system according to the fifth embodiment of the present invention. Figure 11 is a block diagram showing the configuration of the phase-locked system according to the sixth embodiment of the present invention. Figure 12 is a schematic diagram illustrating the structure of the optical resonant section and the mechanical resonant section according to the sixth embodiment of the present invention.

[0009] [Principle of the Invention] Figure 1 is a block diagram showing the configuration of the phase-locked system according to the present invention. The phase-locked system of the present invention comprises an optical control unit 10, an optical resonant unit 11, and a mechanical resonant unit 12 having a mechanism for simultaneous oscillation of multiple vibration modes. The optical control unit 10 controls the difference frequency (Ω) of the multiple vibration modes of the mechanical resonant unit 12. ２ -Ω １ The laser light is intensity-modulated in response to the intensity-modulated signal of the ), and the intensity-modulated light 20 is input to the optical resonator 11. This synchronizes the phase difference of the multiple vibration modes to a desired phase through the nonlinear interaction between the optical modes of the optical resonator 11 and the multiple vibration modes of the mechanical resonator 12.

[0010] Figure 2(a) shows the intensity modulated signal, Figure 2(b) shows the oscillation amplitude of the mechanical resonant section 12, and Figure 2(b) shows the phase difference between the two vibration modes of the mechanical resonant section 12. According to the present invention, the phase difference φ of the two vibration modes ｄｉｆｆ The phase φ of the intensity modulation signal ｍｏｄ This matches.

[0011] Regarding the interaction between the optical mode and the vibration mode that is essentially related to the same period, a distributed interaction, which is a general optomechanical interaction, is assumed. Assuming that the vibration modes of the mechanical resonance part 12 are two modes 1 and 2, and the dynamics of the optical resonance part 11 are much faster than the dynamics of the mechanical vibration and the optical resonance mode is always in a steady state, the equations of motion for the displacements of the mechanical vibration modes 1 and 2 are as shown in equations (1) and (2) respectively.

[0012]

[0013] x ｊ is the displacement of mode j, Γ ｊ is the damping coefficient of mode j, Ω ｊ is the vibration frequency of mode j, g ｊ is the optomechanical coupling constant of mode j. g ｊ f ＯＭ (・) represents the radiation pressure. f ＯＭ (・) is a non-linear function derived from the steady state of the optical resonance part 11 and is expressed as in equation (3).

[0014]

[0015] The Taylor expansion of equation (3) has all polynomial degrees with respect to the displacements x １ , x ２ of modes 1 and 2. When equation (3) is Taylor-expanded up to the third order, it becomes as shown in equations (4) and (5).

[0016]

[0017] In equations (4) and (5), β ｎ = f （ｎ） (X)| Ｘ→０ , tilde Ω ｊ ２ = Ω ｊ ２ + β １ g ｊ ２ is. Here, the "~" attached to the letter is called a tilde. From equations (4) and (5), it can be seen that the Duffing non-linearity for the two modes is generated by the optomechanical coupling. x ｊ (t) = a ｊ (t)e－ｉωｊｔ Set it as +c.c. (j = 1, 2), and assume that the dynamics of the amplitude and phase are much slower than rotation (dot a ｊ ≪Ω ｊ ). Then, it can be described as in equations (6) and (7).

[0018]

[0019] Here, the "·" attached to the characters is called a dot. Since the non - linear term is given by a polynomial, it can be formally described as in equation (8).

[0020]

[0021] ω ｍｏｄ = rω ｄ + Δ (Δ≪ω ｄ , r ∈ Z). If so, the slowest dynamics to be considered is on a time scale of about the reciprocal of Δ. That is, it becomes as in equations (9) and (10).

[0022] ・・(9) ・・(10) <00ZZZ110> a ｊ (t) = A ｊ (t)e －ｉθｊ Decompose the complex amplitude into the real amplitude and phase as, and establish the equation of motion for the phase from the imaginary part of the equation. Then, equations (11) and (12) are obtained.

[0024] ・・(11) ・・(12)

[0025] Here, f ｑ，ｐ [[ID=Z9]] = tilde f ｜ｑ｜，｜ｐ｜ e ｉｑθ１＋ｉｐθ２ is expanded. Considering the degree of the polynomial, for |q| + |p| < |q'| + |p'|, tilde f ｜ｑ｜，｜ｐ｜ ≫ tilde f ｜ｑ｜，｜ｐ｜ ≫ tilde f ｜ｑ’｜，｜ｐ’｜ It should be noted that there seems to be an unclear "ZZZ" in the original text at line 31 which might be an error. I've tried to translate as accurately as possible based on the available context.The following holds true. Therefore, equations (11) and (12) can be approximated as equations (13) and (14).

[0026]

[0027] The logarithmic equation relating to the phase difference is given by equation (15).

[0028] ... (15)

[0029] Finally, in order to directly capture the detuned portion in terms of dynamics, if we set δφ = Δt / r - δθ, we get equation (16).

[0030]

[0031] In equation (16), tilde Δ≡-((g ２ Tilde f ０，１ ) / (2ω ２ A ２ ) - (g １ Tilde f １，０ ) / (2ω １ A １ )) + Δ / r. When extending the above expansion to the case of multiple intensity modulations, (1 + εsinω ｍｏｄ The light intensity modulation term of t) is (1 + Σε ｊ sinω ｍｏｄ，ｊ This can be changed to t). Considering that the entire derivation is a linear operation due to the additivity of this light intensity modulation term, it can be written as equation (17).

[0032]

[0033] Here, the amplitude A of vibration modes 1 and 2. １ , A ２ Assuming that is constant under steady conditions, equations (16) and (17) are consistent with the Kuramoto model which describes general synchronization phenomena, indicating that the phase difference between the two vibration modes 1 and 2 is fixed, i.e., the two vibration modes 1 and 2 are synchronized.

[0034] [First Embodiment] Hereinafter, embodiments of the present invention will be described with reference to the drawings. Figure 3 is a block diagram showing the configuration of a phase-locked system according to the first embodiment of the present invention. In this embodiment, a bottle-shaped optical resonator 13 fabricated on silica glass was used. The optical resonator 13 has an optical resonant section 11 and a mechanical resonant section 12 formed in a single element structure. Each of the multiple vibration modes of the mechanical resonant section 12 is coupled via radiation pressure to a whispering optical resonant mode orbiting around the bottle-shaped optical resonant section 11. Such an optical resonator 13 configuration is disclosed, for example, in the literature "Asano, Motoki et al., "Evanescent coupling between a bottle optical resonator and an electromechanical resonator," Proceedings of the 65th Spring Meeting of the Japan Society of Applied Physics, March 2018," international publication WO2022 / 264395, etc.

[0035] The optical control unit 10 consists of a laser light source 100, an optical intensity modulator 101, and a signal generator 102. The optical intensity modulator 101 modulates the laser light from the laser light source 100 according to the intensity modulation signal output from the signal generator 102. The intensity-modulated light emitted from the optical intensity modulator 101 propagates through the thinned optical fiber 14. The evanescent light seeping out from the thinned optical fiber 14 is then introduced into the optical resonant section 11. The mechanical resonant section 12 in this embodiment has an oscillation frequency of around 47 MHz and has two vibration modes spaced approximately 480 kHz apart.

[0036] An intensity-modulated signal with a frequency near 480 kHz generated by the signal generator 102 was applied to the optical intensity modulator 101, and the laser light input to the optical resonator 11 was intensity-modulated to synchronize the phase difference between the two vibration modes with the phase of the intensity-modulated signal.

[0037] In this embodiment, a phase-synchronized evaluation unit 15 is provided to evaluate the phase difference between the two vibration modes of the mechanical resonant section 12. The phase-synchronized evaluation unit 15 consists of a photodetector 150 that converts the output light from the thinned optical fiber 14 into an electrical signal, a mixer 151 that mixes the two output signals from the photodetector 150, and a lock-in amplifier 152 that takes the output signal from the mixer 151 and a reference signal output from the signal generator 102 as inputs and detects the beat signals of the two vibration modes of the mechanical resonant section 12 from the output signal of the mixer 151.

[0038] By splitting the intensity-modulated signal output from the signal generator 102 and using it as the reference signal for the lock-in amplifier 152, the beat signal of the difference frequency between the two vibration modes can be detected. Figure 4 shows the intensity of the beat signal obtained by lock-in detection when the modulation frequency and modulation voltage (frequency and voltage of the intensity-modulated signal) of the light intensity are swept. Figure 4 shows that the intensity of the beat signal increases as the brightness increases.

[0039] As shown in Figure 4, a triangular region appears where the intensity of the beat signal increases, centered around the case where the modulation frequency is 480 kHz. This region indicates that the phase difference between the two vibration modes of the mechanical resonant section 12 is synchronized with the phase of the intensity-modulated signal. Furthermore, this triangular distribution in the parameter space closely matches the distribution trend of the synchronization phenomenon, which is the most well known phenomenon in nonlinear dynamics. As described above, according to this embodiment, it is possible to synchronize the phase difference between multiple independently oscillating vibration modes of the mechanical resonant section 12 using an external laser beam to which intensity modulation has been applied.

[0040] [Second Embodiment] Next, a second embodiment of the present invention will be described. In this embodiment as well, the configuration of the phase-locking system is the same as in the first embodiment, so it will be described using the reference numerals in Figure 3. The signal generator 102 in this embodiment outputs an intensity-modulated signal with a frequency that is n times (n is a natural number of 2 or more) the difference frequency of the two vibration modes of the mechanical resonant section 12. This makes it possible to realize multiple phase-locking states in which the phase difference between the two vibration modes has a different value. The first embodiment corresponds to the case where n = 1.

[0041] To verify the multiple-stable synchronization of this embodiment, the phase slip phenomenon occurring at the parameter boundary where the synchronization phenomenon occurs was utilized. The phase slip phenomenon is a phenomenon in which the phase state dynamically shifts from one synchronization phase to the next synchronization phase due to the imperfection of the conditions necessary for the synchronization phenomenon. Figure 5 shows the results of observing the phase slip of two vibration modes while the laser light was intensity-modulated with intensity-modulated signals of frequencies that are natural multiples of the difference frequency of the two vibration modes. Figure 5 shows the phase slip when using an intensity-modulated signal (fundamental wave signal) with the same frequency as the difference frequency, 52 shows the phase slip when using an intensity-modulated signal (second harmonic signal) with twice the frequency of the difference frequency, 53 shows the phase slip when using an intensity-modulated signal (third harmonic signal) with three times the frequency of the difference frequency, and 54 shows the phase slip when using an intensity-modulated signal (fourth harmonic signal) with four times the frequency of the difference frequency.

[0042] In synchronization using a fundamental wave signal, as in the first embodiment, the phase difference between the two vibration modes changes by 2π in one slip (unit step on the horizontal axis in Figure 5). That is, there is only one synchronization phase of the difference frequency between the two vibration modes for one period of the fundamental wave. On the other hand, in synchronization using an nth harmonic signal, the phase difference between the two vibration modes changes by 2π / n in one slip. This change suggests that there are n synchronization phases for one period of the fundamental wave. Thus, in this embodiment, by using an intensity modulation signal with a frequency n times the difference frequency of the two vibration modes, it is possible to realize multiple phase synchronization states in which the phase difference between the two vibration modes has a different value.

[0043] [Third Embodiment] Figure 6 is a block diagram showing the configuration of a phase-locked system according to a third embodiment of the present invention. The phase-locked system comprises an optical control unit 10a and an optical resonator 13. The optical control unit 10a consists of a laser light source 100, an optical intensity modulator 101, signal generators 102 and 103, and a multiplexer 104.

[0044] Similar to the first embodiment, the signal generator 102 outputs an intensity-modulated signal (fundamental wave signal) with the same frequency as the difference frequency between the two vibration modes of the mechanical resonant section 12. The signal generator 103 outputs an intensity-modulated signal (second harmonic signal) with a frequency twice the difference frequency. The multiplexer 104 combines the fundamental wave signal and the second harmonic signal. The optical intensity modulator 101 modulates the laser light from the laser light source 100 according to the signal output from the multiplexer 104.

[0045] This embodiment explains that by using a signal obtained by combining a fundamental wave signal and a second harmonic signal, it is possible to design the probability that the phase difference of two vibration modes will synchronize with multiple phases. As explained in the second embodiment, when only the second harmonic signal is used, there are two synchronization phases separated by π. As shown in Figure 7, the probability that the phase difference of two vibration modes will synchronize with the two phases is the same.

[0046] On the other hand, when a fundamental wave signal is used in addition to the second harmonic signal, as shown in Figure 8, the probability of the phase difference between the two vibration modes synchronizing with each of the two phases can be set to different values. Thus, in this embodiment, it is possible to arbitrarily design the probability of the phase difference between the two vibration modes synchronizing with each of multiple phases. Figures 7 and 8 show the results of calculating the probability density by sampling the phase difference between the two vibration modes when the signal strength is ON and OFF with a fixed value of 0.

[0047] [Fourth Embodiment] Next, a fourth embodiment of the present invention will be described. In this embodiment as well, the configuration of the phase-locked system is the same as in the third embodiment, so the reference numerals in Figure 6 will be used for explanation. The signal generators 102 and 103 in this embodiment change the relative phase of the fundamental wave signal and the second harmonic signal over time. Here, the relative phase of the fundamental wave signal and the second harmonic signal is changed linearly. Specifically, the phase θ of the fundamental wave signal ｒ The value of = 2πt / T was varied in the range 0 < t < T. By setting the modulation period T to be sufficiently larger than the reciprocal of the difference frequency of the two vibration modes of the mechanical resonant section 12, an adiabatic state change can be promoted.

[0048] Phase θ of the fundamental wave signal ｒFigure 9 shows the change in the synchronization phase when the phase θ is changed. According to Figure 9, the phase θ ｒ By changing this for one period, the state in which the two vibration modes were initially synchronized with a phase difference of 0 becomes θ ｒ It can be seen that slips occur at π / 2 and 3π / 2 respectively, and the synchronization phase changes from 0 → -π → 0. Thus, in this embodiment, by changing the light intensity modulation over time, the synchronization state of the two vibration modes can be changed to different synchronization phases, making it possible to select any synchronization phase at any time.

[0049] [Fifth Embodiment] Next, a fifth embodiment of the present invention will be described. In this embodiment as well, the configuration of the phase-locked system is the same as in the first embodiment, so the reference numerals in Figure 3 will be used for explanation. In this embodiment, the frequency of the laser light output from the laser light source 100 is detuned to be slightly higher than the optical resonance frequency of the optical resonance unit 11. This makes it possible to simultaneously oscillate two vibration modes by parametric oscillation. Figure 10 shows the results of this embodiment. According to this embodiment, by adjusting the power and frequency of the laser light source 100 used for synchronization, simultaneous oscillation of multiple vibration modes of the mechanical resonance unit 12 can be achieved.

[0050] [Sixth Embodiment] In this embodiment, we will explain how optical-mechanical coupling between optical modes and natural vibration modes can be realized by constructing a system that can be coupled with multiple mechanical vibration modes via an optical near-field, and how phase difference synchronization via nonlinear interaction can be achieved. Figure 11 is a block diagram showing the configuration of the phase synchronization system according to this embodiment. The phase synchronization system comprises an optical control unit 10, an optical resonance unit 11a, and a mechanical resonance unit 12a.

[0051] In this embodiment, a micro-spherical optical resonator made of silica glass is used as the optical resonator 11a having a near field. In addition, a mechanical resonator having two mechanical oscillators with a cantilever structure that are placed in close proximity is used as the mechanical resonator 12a. In this embodiment, a structure is adopted in which there is no coupling of vibration modes between the cantilevers.

[0052] As shown in Figure 12, the micro-spherical optical resonator 11a is positioned close to the two cantilever structures 120 and 121 of the mechanical resonator 12a, and the whispering gallery optical modes are spatially superimposed with the cantilever structures 120 and 121. This creates a finite optical-mechanical coupling. By increasing the intensity of the external laser light introduced into the optical resonator 11a, it is possible to create a nonlinear coupling between the light and the vibration modes. Note that 110 in Figure 12 shows the evanescent light seeping from the optical resonator 11a.

[0053] An optical control unit 10, as described in the first embodiment, is provided in front of the thinned optical fiber 14 for introducing external laser light into the optical resonant section 11a. By modulating the optical intensity with an intensity modulation signal having the same frequency as the difference frequency of the fundamental vibration modes of the two cantilever structures 120 and 121, phase synchronization similar to that in the first embodiment can be achieved. Thus, according to this embodiment, it becomes possible to synchronize multiple oscillation states of the mechanical oscillator of the mechanical resonant section 12a, which is independent of the optical resonant section 11a, via optical-mechanical coupling by an optical near-field.

[0054] Some or all of the above examples may also be described as follows, but are not limited to the following:

[0055] (Note 1) The phase-locking system of the present invention comprises a mechanical resonant section having a mechanism for simultaneous oscillation of a plurality of vibration modes, an optical resonant section configured such that an optical mode interacts with each of the plurality of vibration modes, and an optical control section configured to modulate the intensity of laser light introduced into the optical resonant section, wherein the optical control section modulates the intensity of the laser light in accordance with an intensity modulation signal of frequency based on the difference frequencies of the plurality of vibration modes, thereby synchronizing the phase difference of the plurality of vibration modes to a desired phase through a nonlinear interaction between the optical mode and the plurality of vibration modes.

[0056] (Note 2) In the phase-locked system described in Note 1, the optical control unit comprises a laser light source configured to output laser light, a signal generator configured to generate the intensity modulation signal having a frequency that is a natural number multiple of the difference frequency of the plurality of vibration modes, and an optical intensity modulation unit configured to modulate the laser light from the laser light source according to the intensity modulation signal.

[0057] (Note 3) In the phase-locked system described in Note 2, the signal generator generates a plurality of intensity-modulated signals of different frequencies, the optical control unit further comprises a multiplexer configured to combine the plurality of intensity-modulated signals, and the optical intensity modulation unit modulates the laser light from the laser light source in accordance with the signal output from the multiplexer.

[0058] (Note 4) In the phase-locked system described in Note 3, the signal generator changes the relative phase of the plurality of intensity-modulated signals over time.

[0059] (Note 5) In the phase-locked system described in Note 1, the optical control unit comprises a laser light source configured to output laser light with a frequency higher than the optical resonance frequency of the optical resonant unit, a signal generator configured to generate the intensity modulation signal, and an optical intensity modulation unit configured to modulate the laser light from the laser light source according to the intensity modulation signal.

[0060] (Note 6) The phase-locked system described in Note 1 is configured with the optical resonant section and the mechanical resonant section as independent elements, and uses evanescent light seeping from the optical resonant section to induce a nonlinear interaction between the optical mode and the natural vibration mode.

[0061] (Note 7) The phase synchronization method of the present invention includes a first step of modulating the intensity of laser light and a second step of introducing the intensity-modulated laser light into an optical resonant section configured such that the optical mode interacts with each of the plurality of vibration modes of a mechanical resonant section, wherein the phase difference of the plurality of vibration modes is synchronized to a desired phase through a nonlinear interaction between the optical mode and the plurality of vibration modes by intensity-modulating the laser light in accordance with an intensity-modulated frequency signal based on the difference frequencies of the plurality of vibration modes.

[0062] 10, 10a... Optical control unit, 11, 11a... Optical resonator, 12, 12a... Mechanical resonator, 13... Optical resonator, 14... Thinned optical fiber, 15... Phase-locked evaluation unit, 100... Laser light source, 101... Optical intensity modulator, 102, 103... Signal generator, 104... Multiplexer, 120, 121... Cantilever structure.

Claims

1. A phase-locking system comprising: a mechanical resonant section having a mechanism for simultaneous oscillation of multiple vibration modes; an optical resonant section configured such that an optical mode interacts with each of the multiple vibration modes; and an optical control section configured to modulate the intensity of laser light introduced into the optical resonant section, wherein the optical control section modulates the intensity of the laser light in accordance with an intensity modulation signal of the frequency based on the difference frequencies of the multiple vibration modes, thereby synchronizing the phase difference of the multiple vibration modes to a desired phase through a nonlinear interaction between the optical mode and the multiple vibration modes.

2. A phase-locking system according to claim 1, wherein the optical control unit comprises a laser light source configured to output laser light, a signal generator configured to generate the intensity modulation signal having a frequency that is a natural number multiple of the difference frequency of the plurality of vibration modes, and an optical intensity modulation unit configured to modulate the laser light from the laser light source according to the intensity modulation signal.

3. A phase-locked system according to claim 2, wherein the signal generator generates a plurality of intensity-modulated signals of different frequencies, the optical control unit further comprises a multiplexer configured to combine the plurality of intensity-modulated signals, and the optical intensity modulation unit modulates the laser light from the laser light source in accordance with the signal output from the multiplexer.

4. A phase-locking system according to claim 3, characterized in that the signal generator changes the relative phase of the plurality of intensity-modulated signals over time.

5. A phase-locked system according to claim 1, wherein the optical control unit comprises a laser light source configured to output laser light with a frequency higher than the optical resonance frequency of the optical resonant unit; a signal generator configured to generate the intensity modulation signal; and an optical intensity modulation unit configured to modulate the laser light from the laser light source according to the intensity modulation signal.

6. A phase-locked system according to claim 1, characterized in that the optical resonant portion and the mechanical resonant portion are configured as independent elements, and a nonlinear interaction between an optical mode and an eigenmode is induced using evanescent light leaking from the optical resonant portion.

7. A phase synchronization method comprising: a first step of modulating the intensity of a laser beam; and a second step of introducing the intensity-modulated laser beam into an optical resonant section configured such that the optical mode interacts with each of a plurality of vibration modes of a mechanical resonant section, wherein the phase difference of the plurality of vibration modes is synchronized to a desired phase via a nonlinear interaction between the optical mode and the plurality of vibration modes by intensity-modulating the laser beam in accordance with an intensity-modulated frequency signal based on the difference frequencies of the plurality of vibration modes.

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