Method and application of frequency comb generation based on magnon-magnon ultrastrong coupling

Abstract

The present invention discloses a method and application for generating a frequency comb based on superstrong coupling of magnons and magnons, which belongs to the field of spin electronics technology. In a system of two superstrongly coupled magnons, when a pumping magnetic field with a frequency close to the frequency of the high-frequency branch magnon is applied, the system enters a nonlinear state. According to the amplitude of the pumping magnetic field, the system presents a frequency comb, period-doubling bifurcation and chaotic frequency comb. As the strength of the magnon-magnon coupling increases, the nonlinearity of the system is significantly enhanced, thereby reducing the demand for external power. Unlike traditional methods that rely on the weak nonlinearity of the material itself and require high power density to exceed the starting threshold, the superstrong coupling system provides an ideal platform for studying chaotic frequency combs. Chaotic systems have high sensitivity and noise resistance, and play an important role in signal detection. The present invention provides a new idea for the application of the magnon-magnon coupling mechanism in the fields of high-precision frequency measurement, information processing and sensitive detection.

Description

Technical Field

[0001] The present invention belongs to the field of spin electronics technology, and particularly relates to a method for generating a frequency comb and a chaotic frequency comb based on magnon-magnon ultrastrong coupling, and an application of the method in identifying signals in noise. Background Art

[0002] Frequency combs are spectra composed of a series of discrete, equally spaced frequency components. They were first discovered in optical systems. After more than two decades of development, they have become an important technology in fields such as atomic clocks, satellite navigation, molecular fingerprinting, metrology, and optical spectroscopy. Inspired by optical frequency combs, frequency combs have now been intensively studied in other physical systems. Among them, magnon frequency combs, generated by nonlinear coupling between magnons of different modes, have been reported both theoretically and experimentally. Currently, chaotic frequency combs derived from nonlinear interactions within optical microresonators have been shown to have significant application potential in a variety of fields, including metrology, spectroscopy, and coherent communications. However, chaotic frequency combs have not yet been realized in spin systems. Summary of the Invention

[0003] The technical problem solved by the present invention is to provide a method for generating a frequency comb, period-doubling bifurcation and chaotic frequency comb in a spin system and to achieve signal recognition with high sensitivity and noise resistance.

[0004] Technical solution: In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0005] This invention proposes a magnon frequency comb and a chaotic frequency comb based on the superstrong coupling mechanism of magnons in a spin system. By studying the nonlinear interaction between the upper and lower branches of magnon polaritons in a synthetic antiferromagnetic (SAF) system, the feasibility of the proposed magnon chaotic frequency comb is demonstrated both theoretically and numerically. Through period-doubling cascade bifurcations of the comb tooth spacing, the invention observes the transition of the frequency comb to chaos. The robustness of the chaotic frequency comb is demonstrated by the Poincaré cross section, bifurcation diagram, and maximum Lyapunov exponent. In addition, the significant advantages of the chaotic system are reflected in its high sensitivity to small perturbations and strong resistance to noise, which are verified in the successful identification of periodic signals from background noise. The research results of this invention provide a new paradigm for magnetic systems for the potential application of nonlinear dynamics in fields such as metrology, sensing, information processing, and quantum spin electronics.

[0006] The present invention provides a method for generating a frequency comb based on superstrong coupling of magnons and magnons. In a system of two superstrongly coupled magnons, when a pumping magnetic field with a frequency close to the frequency of the high-frequency branch magnon is applied, the system enters a nonlinear state. Depending on the amplitude of the pumping magnetic field, the system exhibits typical nonlinear dynamic phenomena, including frequency combs, period-doubling bifurcations, and chaotic frequency combs.

[0007] Furthermore, when the pump intensity is low, the spectrum of the magnon frequency comb is:

[0008] ;

[0009] Among them, lf p Indicates the center frequency of the lth comb tooth, n and f d Indicates the distance between the nth comb teeth.

[0010] Furthermore, after the high-frequency branch magnon polaritons are excited by the pump field, they interact with the low-frequency branch magnon polaritons to generate a sum frequency (f p +f d ) and difference frequency (f p -f d ) mode; as this cascade process continues, the system eventually generates a comb spacing of f d frequency comb.

[0011] Furthermore, when the pump intensity increases, the system begins to show a period-doubling cascade bifurcation, and the comb tooth spacing changes from f d Gradually evolved into f d / 2, f d / 3, f d / 4; when the pump intensity h p When it increases above a certain critical value, the system enters a chaotic state, the spacing between the comb teeth becomes irregular, and a chaotic frequency comb is formed.

[0012] Furthermore, when the detuning is small, the system's path to chaos begins with the frequency comb and evolves gradually through a series of pitch bifurcations, during which periodic oscillations and chaotic states alternate repeatedly. When the detuning is large, the system transitions directly to chaos without undergoing period-doubling bifurcations.

[0013] Furthermore, when f p Less than f u When f p Greater than f u When f p Close to f u When , the system will show the phenomenon of frequency comb and period doubling cascade, which eventually leads to chaos.

[0014] The application of frequency comb in identifying signals in noise, applying a reference signal to make the system at the boundary between periodic oscillation and chaos c , when there is a periodic signal with amplitude s0 in the system, it will affect the total signal amplitude h0. When h0 is close to h c -s0, the system exhibits periodic oscillations; when h0 is close to h c At +s0, the system transitions to chaotic oscillation; therefore, when there is a frequency difference between the periodic signal and the reference signal In the case of h0, h0 is periodically greater than or less than h c , intermittent chaos will occur; this intermittent chaos is stable and has a fixed periodicity.

[0015] Furthermore, the periodicity is given by the following formula:

[0016] .

[0017] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0018] (1) This paper explores the generation mechanism of magnon chaotic frequency combs in an ultrastrongly coupled magnon-magnon system. As the strength of the magnon-magnon coupling increases, the nonlinearity of the system significantly increases, thereby reducing the need for external power. Unlike traditional methods that rely on the inherently weak nonlinearity of the material and require high power density to exceed the activation threshold, ultrastrongly coupled systems provide an ideal platform for studying chaotic frequency combs.

[0019] (2) Chaotic systems have high sensitivity and noise immunity, playing an important role in signal detection. This paper demonstrates noise-resistant signal recognition by utilizing the transition of a magnon chaotic comb from periodic oscillation to chaos (or vice versa). Even when the signal to be identified is buried in Gaussian noise, the results remain consistent with those in the absence of noise, demonstrating the robustness of the system and its immunity to noise interference.

[0020] (3) The present invention provides the possibility of realizing magnon chaotic frequency comb under ultrastrong coupling conditions, which provides a new idea for the application of magnon-magnon coupling mechanism in the fields of high-precision frequency measurement, information processing and sensitive detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the magnon chaotic frequency comb.

[0022] Figure 2 Schematic diagram of a synthetic antiferromagnet in a spin-tilted state and its resonance spectrum.

[0023] Figure 3 is in f p = 8 GHz and hp = 2, 6, 8, 9, 11.2, 12 mT, nonlinear characteristics of SAF: m x Time domain variation, m x and m z Poincaré cross section, and magnon spectrum of synthetic antiferromagnets.

[0024] Figure 4 is different detuning f p -f u = 0.05 GHz, f p -f u = -0.7 GHz dispersion diagram and h p , as well as the corresponding bifurcation diagram (blue dots) and LLE (green line).

[0025] Figure 5 is the magnon dispersion diagram with f p Changes, (a) and (b) h p =6 mT, (c) and (d) h p =8 mT, (e) and (f)h p =12 mT. The right figures (b), (d) and (f) are enlarged views of the corresponding dotted boxes in the left figures (a), (c) and (e). The nonlinear phenomenon appears at f u There are thresholds on both sides, as h p As the value of α increases, the threshold distance also expands.

[0026] Figure 6 The phase diagram shows the relationship between the state of the system and h p and f p relationship.

[0027] Figure 7 This is a proof-of-concept demonstration of noise signal recognition. (a) Schematic diagram of three different input conditions: only the reference signal, the reference signal and the signal to be recognized, and the reference signal and the signal to be recognized buried in Gaussian noise. x The time evolution of the short-time Fourier transform (SFT) is shown in the figure: (b) With only the reference signal, the response of m exhibits periodic oscillations. (c) The simultaneous presence of the reference signal and the periodic target signal leads to intermittent chaos. (d) The simultaneous presence of the reference signal, the target signal, and noise results in persistent intermittent chaos. The frequency difference between the reference signal and the target signal is Δf = 0.01 GHz. The dotted box indicates the occurrence of intermittent chaos. DETAILED DESCRIPTION

[0028] The present invention will be further illustrated below with reference to specific examples. The examples are implemented based on the technical solutions of the present invention. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0029] Example 1

[0030] This embodiment provides a method for generating a frequency comb based on magnon-magnon ultrastrong coupling, which can generate frequency combs, period-doubling bifurcations, and chaotic frequency combs.

[0031] In the system of ultrastrongly coupled magnons, the eigenfrequencies are f u and f d When the applied frequency is close to the high frequency branch magnetic oscillator frequency f p ≈f u When the pump magnetic field is high, the system enters a nonlinear state. p The system exhibits typical nonlinear dynamic phenomena, including frequency comb, period-doubling bifurcation and chaotic behavior.

[0032] At low pump intensities (typically less than 10 mT), the spectrum of the magnon frequency comb appears as follows:

[0033] .

[0034] Among them, lf p Indicates the center frequency of the lth comb tooth, n and f d represents the nth comb tooth and the distance between the comb teeth. In this case, the formation of the frequency comb can be attributed to the three-magnon process. After the high-frequency branch magnon polaritons are excited by the pump field, they interact with the low-frequency branch magnon polaritons to generate the sum frequency (f p +f d ) and difference frequency (f p -f d ) pattern. As this cascade process continues, the system eventually generates a comb spacing of f d When the pump intensity increases, the system begins to show a period-doubling cascade bifurcation, and the comb tooth spacing is changed from f d Gradually evolved into f d / 2, f d / 3, f d / 4, etc. When the pump intensity h p When it increases above a certain critical value, the system enters a chaotic state, the spacing between the comb teeth becomes irregular, and a chaotic frequency comb is formed.

[0035] These nonlinear dynamical phenomena can be characterized using Poincaré cross sections in phase space. At selected cross sections, the magnetic moment trajectory exhibits distinct patterns: a single closed curve corresponds to a single-periodic quasiperiodic oscillation, three closed curves correspond to a triple-periodic oscillation, and chaotic trajectories correspond to a chaotic frequency comb. These phenomena fully demonstrate the nonlinear evolutionary characteristics of the system.

[0036] The dynamics of ferrimagnetic, antiferromagnetic, and SAF systems can be described by two coupled Landau-Lifshitz-Gilbert (LLG) equations:

[0037] ;

[0038] ;

[0039] Among them, m i (i=1,2) represents two normalized magnetic moments, γ and α i They are gyromagnetic ratio and Gilbert damping respectively, and the effective magnetic field includes the external magnetic field H ext , anisotropy field H k,1(2) =H k,1(2) m 1(2) and exchange field H ex,1(2) = H ex m 2(1) Here, H k and H ex are the total anisotropy field and the interlayer coupling field, respectively. Since the system contains high-order nonlinear terms, under the action of near-resonant pumping, significant nonlinear interactions are excited between the upper and lower branches of the magnon polaritons.

[0040] In order to further analyze the nonlinear behavior and coupling strength of the system, the present invention adopts the generalized Hopfield Hamiltonian to describe the magnon-magnon coupling system:

[0041]

[0042] in, is the reduced Planck constant, ω + and ω - They correspond to two magnon angular frequencies respectively, and i is an imaginary unit. ( ) corresponds to the annihilation operator of the +(-) magnon mode, ( ) corresponds to the generation operator of the +(-) magnon mode. Here, "+magnon mode" and "-magnon mode" refer to different magnon modes. g1 and g2 correspond to the strength of the corotating coupling and the counterrotating coupling, respectively. When the coupling strength reaches an ultrastrong state, the nonlinear effect between the upper and lower branches of the magnon polaritons is enhanced, and the three-magnon process is strengthened, resulting in various nonlinear phenomena.

[0043] Currently, experimental reports of ultrastrong magnon-magnon coupling have been published in compensated ferromagnetic and SAF systems. To develop a magnon analogue of a chaotic frequency comb, this study examines the nonlinear dynamics of SAFs. SAFs are three-layer structures consisting of two ferromagnetic layers separated by a nonmagnetic intermediate layer, with interlayer exchange coupling dominated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction.

[0044] The SAF system has two intrinsic uniform magnon modes: an acoustic mode (AM) that precesses in phase and an optical mode (OM) that precesses in antiphase. The dynamics of the two magnetic moments in the system are determined by equation (1) (including (1a) and (1b)). By introducing an asymmetry in the magnetic anisotropy between the two ferromagnetic layers, the magnon-magnon ultrastrong coupling is achieved, f u and f d The magnon polaritons in the branch are generated by the coupling of AM and OM. Figure 2 Schematic diagram of SAF is shown, with an external in-plane magnetic field H applied along the x-axis. x , in order to keep the static magnetic moment in the spin tilt state. Here, the present invention mainly studies the characteristics of the net magnetization m = (m1 + m2) / 2 to discuss g1 / ω0= g2 / ω0=0.495, H x =120mT. In this case, the high frequency support f u =8GHz, low frequency support f d =0.5GHz. At the same time, the chirality of the magnetic moment precession also exchanges in different frequency branches: at f d When f u At this point, the chirality of m1 and m2 is exchanged. When the frequency of the applied pump magnetic field is close to f u 45° in the xy plane, with amplitude h p As m increases, behaviors such as periodic oscillations, frequency combs, period-doubling bifurcations, and chaos appear. x In the time domain change of h p In the Figure 3In the example, except for the chaotic behavior which lacks clear periodicity, all other behaviors are shown as m x The time variation of one cycle.

[0045] In order to understand the evolution of the dynamics, the present invention describes the Poincaré cross section of the system. Here, the present invention records the Poincaré cross section of the system for each m x The trajectory point when the local maximum is reached. Initially, the graph has only one point, indicating periodic oscillation. p When the temperature increases to 6 mT, the Poincaré cross section changes from a single point to a closed curve, indicating the transition from periodic to quasi-periodic behavior. This is followed by double-periodic, quadruple-periodic, and triple-periodic bifurcations, represented by two, four, and three closed curves, respectively. At about h p =12mT, the closed curve turns into a chaotic graph. In the frequency domain, when h p When it is small, only the pump frequency f p = 8GHz. p =6mT, the spectrum appears with f d =0.5, f p =8 and 2f p =16GHz, and there are three main peaks centered at low frequency f. d =0.5GHz clear frequency comb. p As the comb teeth increase, the spacing becomes 0.25, 0.17, and 0.125 GHz, representing double-period, triple-period, and quadruple-period bifurcations, respectively. p =12mT, the spectrum becomes disordered and enters a chaotic state.

[0046] In order to study the path to chaos in the system, the present invention characterizes the dynamic characteristics under different detuning conditions by analyzing the dispersion diagram, bifurcation diagram and maximum Lyapunov exponents (LLEs). First, we focus on the case where the detuning is small (f p -f u =0.05GHz). Figure 4 The dispersion diagram is shown as a function of the pump field intensity h p Changes in h p = 4.2mT, the system first appears a frequency comb; as h pAs the frequency comb increases, the system experiences a two-period bifurcation around 7.1 mT, and further a four-period bifurcation around 8.7 mT. Chaos is first observed at 9.2 mT, where the trajectory begins to diverge significantly. This is followed by a three-period bifurcation around 9.8 mT, and finally, above 11.7 mT, the system enters a persistent chaotic state. Research indicates that the path to chaos begins with the frequency comb and evolves gradually through a series of pitch bifurcations. During this process, periodic oscillations and chaotic states alternate repeatedly.

[0047] To further reveal the transition between periodic and chaotic behavior, the present invention extracts the local maximum of the wave packet and draws a bifurcation diagram, showing the three main transition stages from periodic oscillation to chaos. The chaotic behavior is quantitatively characterized by LLE, which is defined as:

[0048]

[0049] Here, δm represents the difference between the two initially close magnetization trajectories, i.e. , J is the Jacobian matrix derived from the LLG equation, which depends on the magnetization vector m(t) and time t.

[0050] The Jacobian matrix describes the evolution rate between adjacent orbits. A positive LLE indicates a rapid divergence between adjacent orbits, which in turn indicates that the system is in a chaotic state. The green dotted line plot in the figure shows the calculated LLEs, which are consistent with the bifurcation diagram. Through these calculations, the present invention can further confirm whether the system has entered a chaotic state and the transition process of its dynamic behavior.

[0051] Different from the above cases, when the detuning is large, the path of the system leading to chaos exhibits different characteristics. Figure 4 In the example, the detuning is (f p -f u =-0.7GHz) shows that the frequency comb and period-doubling bifurcation phenomena disappear, and the system directly transitions from periodic oscillation of about 10.2mT to chaotic behavior. p At approximately 10.2 mT, the LLE becomes positive, indicating that the system enters a chaotic state. This phenomenon demonstrates that the change in detuning significantly affects the system's dynamic behavior, causing the periodic behavior to directly transition to chaos without undergoing a period-doubling bifurcation stage.

[0052] Figure 5 Describes the u Magnonic dispersion diagrams when the nearby pump field is detuned, including different h p=6, 8, 12 mT. From the perspective of the overall image, the nonlinear phenomenon occurs at high frequencies. u There are two thresholds on both sides of p = 6mT, only the frequency comb phenomenon appears, and it can be observed that f p and 2f p , and in f u and f d The intensity is highest at the comb teeth, the interval frequency is about 0.5GHz, and the threshold is between 7.5GHz and 8.75GHz. p When the frequency increases to 8 mT, the system shows frequency comb, period-doubling bifurcation and chaos. p =16GHz, 1 / 2f can be observed p The threshold value changes to 7.4GHz and 9.1GHz. When 7.4≤ f p When ≤ 8.2GHz, the system shows period doubling bifurcation; when 8.2 ≤f p When f ≤ 8.75 GHz, the system presents a frequency comb; and when 8.75 ≤ f p When h≤9.1GHz, the system enters a chaotic state. p When the frequency increases to 12 mT, chaotic behavior becomes the main phenomenon and 3f p At this time, the threshold changes again to 7.25GHz and 9.25GHz. From these results, we can see that as h p As the threshold distance increases, it is easier to stimulate nf p Frequency mode.

[0053] To gain a deeper understanding of the effects of these behaviors, the present invention studies the p and frequency f p The status of the system at that time. Figure 6 The different states of the system are summarized, and the colored areas represent the nonlinear response of the system. The nonlinear regions include the magnon frequency comb region, the period-doubling bifurcation region, and the chaotic region, which are marked with different colors. The results show that when f p Less than f u When f p Greater than f u When f p Close to f u When , the system will show the phenomenon of frequency comb and period doubling cascade, which eventually leads to chaos.

[0054] Example 2

[0055] This embodiment provides an application of the frequency comb generated in Example 1 to identify signals in noise. Chaotic systems have high sensitivity and noise resistance, and play an important role in signal detection. Here, the present invention uses the transition of the magnon chaotic comb from periodic oscillation to chaos (or from chaos to periodic oscillation) to demonstrate noise-resistant signal recognition. In the application, the pump magnetic field is called the reference signal. c At the critical amplitude, the system transitions from periodic oscillation to chaos.

[0056] The present invention assumes that only the reference signal h(t)=h p sin(2πf p t +φ), the oscillation of m is periodic. If there is a periodic signal s=s0sin(2πf s t+β), the total signal is expressed as h t =h+s=h0sin(2πf0t +φ+ε), where the amplitude h0 and phase ε are:

[0057]

[0058]

[0059] Where t represents time, φ and β are the phases of the reference signal and the periodic signal respectively, and s0 is the amplitude of the periodic signal. p >>s0, the phase change ε ​​becomes negligible (i.e., ε ~ 0), so the phase change can be ignored in the analysis. According to formula (4), it can be found that the periodic signal will affect the amplitude h0. When h0 is close to h c -s0, the system exhibits periodic oscillations; when h0 is close to h c +s0, the system transitions to chaotic oscillation. Therefore, in the presence of frequency difference f p -f s =Δf, h0 is periodically greater than or less than h c , intermittent chaos will occur. This intermittent chaos is stable and has a fixed periodicity, and its periodicity is given by the following formula:

[0060]

[0061] In order to verify the above theory, the present invention calculates the oscillation of m under three input conditions, such as Figure 7 (a) shows: (i) only the reference signal, h p =8.3mT, f p =7.49GHz; (ii) the reference signal is combined with the signal to be identified (s0 = 0.5 mT); (iii) the reference signal and the signal to be identified are buried in Gaussian noise with a standard deviation of σ = s0 = 0.5 mT.c =8.5 mT, f p =7.5GHz, the system transitions from periodic oscillation to chaotic behavior. When the reference signal and the periodic signal to be identified coexist, intermittent chaos occurs. From the period of intermittent chaos T ≈ 100 ns, according to formula (6), the frequency difference Δf is about 0.01GHz. Given that the frequency of the reference signal is f p =7.49GHz, signal to be identified f s The frequency is 7.5 GHz. p =f s =7.5 GHz, the intermittent chaos disappears. Moreover, even when the signal to be identified is buried by Gaussian noise, the results are still consistent with the noise-free state, which demonstrates the robustness of the model and its immunity to noise interference.

[0062] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for generating a frequency comb based on magnon-magnon ultrastrong coupling, characterized by: In the system of ultrastrongly coupled magnons, the eigenfrequencies are the high frequency branch frequencies f u and low-frequency support f d , when the frequency of the applied pump magnetic field f p Close to the high frequency branch magnetic oscillator frequency: f p ≈ f u When , the system enters a nonlinear state. Depending on the amplitude of the pump magnetic field, the system exhibits typical nonlinear dynamic phenomena, including frequency comb, period-doubling bifurcation, and chaotic frequency comb. The generation of the frequency comb is attributed to the three-magnon process. After the high-frequency branch magnon polaritons are excited by the pump field, they interact with the low-frequency branch magnon polaritons to generate the sum frequency ( f p + f d ) and difference frequency ( f p - f d ) mode; then the newly generated sum frequency and difference frequency modes f p ± f d Will continue with f d Interaction, producing f p ± f d ) ± f d ,for f p ± 2 f d ; The newly generated sum and difference frequency patterns will continue to f d As this cascade process continues, the system eventually generates a comb spacing of f d frequency comb; when the pump intensity is less than 10mT, the spectrum of the magnon frequency comb is: lf p ± nf d ， l = 0、1、2...； n = 0、1、2...； in, lf p Indicates the l The center frequency of the comb teeth, n Indicates the n comb teeth, f d is the low-frequency branch frequency in the eigenfrequency, and is also the spacing between the teeth of the magnon frequency comb; When the pump intensity increases, the system begins to show a period-doubling cascade bifurcation, and the comb tooth spacing changes from f d Gradually evolved into f d / 2、 f d / 3. f d / 4; when the pump intensity h p When it increases above a certain critical value, the system enters a chaotic state, the spacing between the comb teeth becomes irregular, and a chaotic frequency comb is formed.

2. The method for generating a frequency comb based on magnon-magnon superstrong coupling according to claim 1, characterized in that: When the frequency of the applied pump magnetic field f p High-frequency branch frequencies less than the eigenfrequency f u When the frequency of the applied pump magnetic field is f p High-frequency branch frequencies greater than the eigenfrequency f u When the frequency of the pump magnetic field is applied, the system is more likely to enter chaos through the frequency comb. f p High-frequency branch frequencies close to the eigenfrequency f u When , the system will show the phenomenon of frequency comb and period doubling cascade, which eventually leads to chaos.

3. Application of the frequency comb in identifying signals in noise according to any one of claims 1 to 2, characterized in that: The reference signal puts the system on the boundary between periodic oscillation and chaos h c , when there is an amplitude of s The periodic signal of 0 will affect the total signal amplitude h 0, when h 0 close h c - s At 0, the system exhibits periodic oscillations; when h 0 close h c + s 0, the system transitions to chaotic oscillation; therefore, when there is a frequency difference between the periodic signal and the reference signal f p - f s =Δ f In the case of h 0 is periodically greater than or less than h c , intermittent chaos will occur; this intermittent chaos is stable, has a fixed periodicity, and is not affected by noise.

4. The use of a frequency comb for identifying signals in noise according to claim 3, characterized in that: The periodicity of intermittent chaos is given by the following formula: T=1 / D f 。

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