Method and system for generating tunable flat-topped spectrum based on Flokey singular point

Abstract

The invention discloses a method and a system for generating a tunable flat-topped spectrum based on a Flokey singular point. The method comprises the following steps: forming two types of supermodes alternately arranged on a frequency axis by using a pair of coupled optical ring resonators; applying periodic dynamic complex modulation including real and imaginary components to the resonator; configuring the modulation frequency to be matched with the super-mode interval so as to construct a periodically quenched non-Hermite frequency lattice on the synthetic frequency dimension; and adjusting modulation parameters, and driving the quasi-energy band of the crystal lattice to present a linear dispersion relationship at the singular point, thereby generating the flat-topped spectrum. According to the method, the intensity and the broadening speed of the flat-topped spectrum are linearly controlled by adjusting the imaginary part modulation amplitude, and the flat-topped frequency comb formed by a single supermode is obtained by extracting signals at a specific moment in a modulation period. According to the method, flexible electric control tuning of the spectrum form, the broadening speed and the modal component is realized, the system can work under the weak non-Hermite condition, and the practicability and integration of the system are improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of integrated optics and spectral regulation, and particularly relates to a tunable flat-top spectrum generation method and system based on Floquet singular points. BACKGROUND

[0002] Integrated optics technology provides a key technical basis for modern optical communication, spectral analysis and quantum information processing by constructing micro resonant structures on a chip and accurately manipulating the modes and frequencies of light fields therein. In recent years, simulating condensed matter physical models in resonant systems by using synthetic frequency dimension has become a cutting-edge technical path. The core of this technology is that by applying specific forms of dynamic modulation (such as phase and amplitude modulation) to coupled optical resonators (such as ring resonators), an artificial synthetic periodic lattice structure, i.e. a frequency lattice, can be constructed on the frequency axis. This frequency lattice can simulate the transport behavior of electrons in a solid lattice, providing a highly flexible platform for realizing topologically protected transmission of photonic states, non-Hermitian singular point physics and new spectral manipulation. In particular, in a non-Hermitian optical system, by introducing controllable gain or loss, novel physical effects such as parity-time symmetry breaking can be achieved in the frequency lattice, opening up new avenues for generating optical frequency combs with special time-frequency characteristics, such as flat-top frequency combs.

[0003] However, the existing such schemes still have obvious limitations. First, the output flat spectrum is usually a mixed state of two basic optical modes, such as a mixed state of symmetric supermodes and antisymmetric supermodes, which cannot be separated into a single pure mode according to application requirements, limiting its use in high-precision scenarios. Second, to achieve non-Hermitian phase transition and generate a flat spectrum, existing technologies often rely on setting a high equivalent gain or loss, which not only increases the complexity and instability of the system, but also hinders the practical integration of the device. More critically, key characteristics such as spectral broadening behavior and output power are difficult to independently and flexibly adjust through simple electrical parameters, and there is coupling between performance parameters. Therefore, it is urgent to improve the existing technology to solve the problems of mode impurity, poor parameter tuning flexibility and strong dependence on high gain and loss conditions in existing flat spectrum generation techniques. SUMMARY

[0004] The present application aims to overcome the deficiencies of the prior art and provide a tunable flat-top spectrum generation method and system based on Floquet singular points to solve the problems of low mode purity, poor parameter tuning flexibility and strong dependence on high gain and loss conditions in existing flat spectrum generation techniques.

[0005] To achieve the above-mentioned purpose, the present application adopts the following technical solutions: In a first aspect, the present application provides a tunable flat-top spectrum generation method based on Floquet singular points, comprising: Step S100: providing a pair of mutually coupled optical ring resonators to form symmetric supermodes and anti-symmetric supermodes arranged alternately on a frequency axis; Step S200: applying a periodic dynamic complex modulation to the pair of optical ring resonators, the dynamic complex modulation comprising a real modulation component and an imaginary modulation component; Step S300: configuring a modulation frequency of the dynamic complex modulation to correspond to a frequency interval between the symmetric supermodes and anti-symmetric supermodes, thereby constructing a periodically quenched non-Hermitian frequency lattice on a synthetic frequency dimension; Step S400: adjusting a parameter of the dynamic complex modulation to drive a quasi-energy band of the non-Hermitian frequency lattice to exhibit a linear dispersion relation at a Floquet exceptional point, and generating a flat-top spectrum based on the linear dispersion relation.

[0006] Preferably, the step S100 comprises splitting a resonant frequency mode of a single optical ring resonator to form the symmetric supermodes and anti-symmetric supermodes by a coupling effect between the pair of optical ring resonators, the symmetric supermodes and anti-symmetric supermodes being arranged alternately with a first frequency interval and a second frequency interval on the frequency axis.

[0007] Further, the first frequency interval is associated with a coupling strength between the pair of optical ring resonators, and the second frequency interval is associated with a free spectral range of the optical ring resonators and the first frequency interval.

[0008] Preferably, the step S200 comprises generating the real modulation component by a phase modulator and fixing an initial phase of the real modulation component, and generating the imaginary modulation component by an amplitude modulator and an optical amplifier and controlling an initial phase of the imaginary modulation component to vary periodically with time to introduce a periodically switching sign non-Hermitian coupling term in the non-Hermitian frequency lattice.

[0009] Further, the step S300 comprises setting the dynamic complex modulation to comprise a first modulation frequency component and a second modulation frequency component, configuring the first modulation frequency component to correspond to the first frequency interval and the second modulation frequency component to correspond to the second frequency interval, and driving the symmetric supermodes and anti-symmetric supermodes to mutually couple by the first modulation frequency component and the second modulation frequency component to form the periodically quenched non-Hermitian frequency lattice.

[0010] Preferably, in the step S400, the quasi-energy band of the non-Hermite frequency lattice presents a linear dispersion relation at the Floquet exceptional point, comprising: dividing one modulation period of the dynamic complex modulation into a first time interval and a second time interval; adjusting the duration of the first time interval and the second time interval to be equal; by setting the equal duration, the non-Hermite frequency lattice is in a critical state of parity-time symmetry breaking, thereby exciting the Floquet exceptional point in the quasi-energy band.

[0011] Further, in the step S400, generating a flat-top spectrum based on the linear dispersion relation, comprising: adjusting the amplitude of the imaginary part modulation component to change the asymmetric coupling strength in the non-Hermite frequency lattice; by changing the asymmetric coupling strength, linearly adjusting the slope of the quasi-energy band near the Floquet exceptional point; according to the adjustment of the slope, controlling the group velocity and spectral width expansion velocity of the generated flat-top spectrum in the frequency domain.

[0012] Preferably, the method further comprises a step S500: monitoring the power evolution of the symmetric supermode and the antisymmetric supermode over time during the generation of the flat-top spectrum; within one modulation period of the dynamic complex modulation, when the power of the symmetric supermode reaches a peak and the power of the antisymmetric supermode is suppressed, extracting an optical signal to obtain a flat-top frequency comb mainly composed of the symmetric supermode; or, when the power of the antisymmetric supermode reaches a peak and the power of the symmetric supermode is suppressed, extracting an optical signal to obtain a flat-top frequency comb mainly composed of the antisymmetric supermode.

[0013] Preferably, in the step S400, the amplitude of the imaginary part modulation component is configured to be smaller than the amplitude of the real part modulation component.

[0014] In a second aspect, the present application also provides a system for implementing the above method, comprising: a double-ring resonator unit containing the pair of mutually coupled optical ring resonators; a dynamic modulation generation unit for generating and applying the periodic dynamic complex modulation to the double-ring resonator unit; a control and processing unit connected with the dynamic modulation generation unit, for configuring the parameters of the dynamic complex modulation, monitoring the power evolution of the symmetric supermode and the antisymmetric supermode, and controlling the extraction operation of the optical signal.

[0015] The application discloses a tunable flat-top spectrum generation method and system based on Floquet singular points, and the core of the application is that a non-Hermite lattice with periodic quenching dynamics is constructed and controlled in the synthetic frequency dimension through accurate matching dynamic complex modulation, and then a flat-top spectrum is generated by using the linear dispersion effect near the Floquet singular point. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0017] Figure 1 is a flowchart of a tunable flat-top spectrum generation method based on Floquet singular points provided by an embodiment of the present application; Figure 2 is a structural block diagram of a tunable flat-top spectrum generation system based on Floquet singular points provided by an embodiment of the present application; Figure 3 is a principle and modulation schematic diagram of a double-ring coupling system in an embodiment of the present application; wherein, Figure 3 a is a coupling double-ring system structure schematic diagram of the applied dynamic complex modulation, Figure 3 b is a frequency mode splitting and supermode alternating arrangement schematic diagram caused by coupling, Figure 3 c is a periodic variation waveform schematic diagram of the imaginary part modulation phase; Figure 4 is a spectrum and power evolution simulation result schematic diagram of a synthetic frequency lattice in an embodiment of the present application; wherein, Figure 4a is the time evolution of the flat-top spectrum driven by the Floquet topological singularity, Figure 4 b is the evolution curve of the total power of symmetric supermodes and antisymmetric supermodes showing anti-phase periodic oscillation over time, Figure 4 c is the time evolution of the flat-top spectrum driven by the Floquet topological singularity, Figure 4 b is the spectral power distribution diagram for verifying the modal purity taken at a specific moment in time; Figure 5 is a contrast schematic diagram of spectral evolution under different imaginary part modulation amplitudes in an embodiment of the present application.

[0018] Among them, the reference signs are explained as follows: 100, a double-ring resonator unit; 200, a dynamic modulation generation unit; 300, a control and processing unit. DETAILED DESCRIPTION

[0019] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0020] In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0021] At present, although the spectral generation technology based on the synthetic frequency dimension theoretically shows the potential of simulating the topological physical model, it is limited by the aliasing problem of photonic supermodes in practical application, resulting in that the output spectrum is often a mixed state, which is difficult to meet the demand of high-purity mode division multiplexing. At the same time, in order to induce phase transition, the existing scheme usually needs a strict high gain-loss ratio, which is difficult to achieve in integrated optical circuits. In addition, the bandwidth and group velocity of the spectrum and other key parameters are often locked by static physical structures, and there is a lack of flexible dynamic regulation means.

[0022] Based on this, in order to improve the problems in the related art, the present application provides a tunable flat-top spectrum generation method based on Floquet singularity, as shown in the figure, which comprises the following steps: Figure 1 Step S100: providing a pair of mutually coupled optical ring resonators to form alternating symmetric supermodes and antisymmetric supermodes on the frequency axis; ​Step S200: applying a periodic dynamic complex modulation to the pair of optical ring resonators, the dynamic complex modulation including a real modulation component and an imaginary modulation component; Step S300: configuring a modulation frequency of the dynamic complex modulation to correspond to a frequency interval between the symmetric supermode and the anti-symmetric supermode, thereby constructing a periodic quenched non-Hermitian frequency lattice in a synthetic frequency dimension; Step S400: adjusting parameters of the dynamic complex modulation to drive a quasi-energy band of the non-Hermitian frequency lattice to exhibit a linear dispersion relation at a Floquet anomaly point, and generating a flat-top spectrum based on the linear dispersion relation.

[0023] For ease of understanding, some key terms in the present embodiment are explained as follows: An optical ring resonator is a miniature optical device, usually composed of a waveguide in a ring structure, in which light signals are transmitted multiple times through total internal reflection. Its characteristic is that it has discrete resonant frequency modes, and when the frequency of the light signal matches the resonant frequency of the resonator, the optical energy will be efficiently coupled into the resonator and enhanced.

[0024] Supermode refers to the hybridization of the intrinsic modes of two or more independent resonators when they are coupled to each other, forming new collective modes. In the present embodiment, a pair of mutually coupled optical ring resonators will produce two main supermodes, namely symmetric supermode and anti-symmetric supermode. These supermodes exhibit an alternating arrangement on the frequency axis, reflecting the breaking of energy degeneracy in the coupled system.

[0025] Periodic dynamic complex modulation refers to applying a complex modulation signal that varies periodically with time to an optical system. The modulation signal usually includes a real modulation component and an imaginary modulation component. The real modulation component is mainly used to introduce coupling modulation, affecting the energy exchange between light fields in different modes or positions; the imaginary modulation component is used to introduce non-Hermitian modulation, simulating gain or loss effects, thereby changing the energy balance and symmetry of the system.

[0026] Non-Hermitian frequency lattice is an artificial lattice structure constructed in the synthetic frequency dimension. By applying periodic dynamic modulation to optical resonators, discrete frequency modes can be mapped to "lattice points" in the lattice, and the modulation introduces "coupling" between these lattice points. When non-Hermitian modulation is introduced, the lattice system no longer satisfies the Hermitian property, thereby exhibiting unique physical properties, such as parity-time symmetry breaking.

[0027] Floquet exceptional points refer to special points in the quasi-energy band structure of a periodically driven quantum or classical system. Near these exceptional points, the quasi-energy bands exhibit linear dispersion relations, similar to Dirac cone structures. Floquet exceptional points are often associated with topological properties or symmetry-breaking critical states of the system and can be used to precisely manipulate photonic states.

[0028] Quasi-energy bands are a description of the energy spectrum in a periodically driven system. Similar to energy bands in static systems, quasi-energy bands describe the allowed energy states of a system under periodic modulation. Their structure determines the transmission behavior of photons in the frequency lattice.

[0029] Linear dispersion relation refers to a linear relationship between frequency and wave vector (or equivalent composite dimension parameter) within a certain frequency range. Near Floquet exceptional points, the linear dispersion relation of the quasi-energy bands means that the group velocity of photons in this region is constant, which is important for achieving broadband and flat spectral output.

[0030] Flat-top spectrum refers to a spectrum with a relatively flat top within a certain frequency range, and a rapid decay outside this range. This spectrum has good flatness and steep edges, and has wide applications in optical communication, spectral filtering, and frequency comb generation.

[0031] The embodiment provides a tunable flat-top spectrum generation method based on Floquet exceptional points, and the specific implementation process is as follows: First, a pair of coupled optical ring resonators is established, as shown in the coupling double-ring system structure schematic diagram of applying dynamic complex modulation shown in Figure 3 a, the two ring resonators are coupled through evanescent field, and the coupling strength is denoted as Kappa The resonant frequency mode of a single ring resonator is , where Ω is the free spectral range (FSR). The coupling effect is used to form symmetric and antisymmetric supermodes arranged alternately on the frequency axis. Specifically, the coupling causes mode splitting, forming symmetric supermodes with a frequency of , and antisymmetric supermodes with a frequency of , as shown in Figure 3 b, the interval between adjacent symmetric and antisymmetric supermodes is the first frequency interval , and the interval between adjacent antisymmetric supermodes and the next symmetric supermode is the second frequency interval , thereby forming an alternating arrangement.

[0032] Second, periodic dynamic complex modulation is applied to the pair of optical ring resonators. The modulation can be realized by driving a modulator with an external electrical signal source.

[0033] As a specific implementation method, the dynamic complex modulation signal applied to the two rings can be specifically designed as follows: The first two cosine terms constitute the real part of the modulation component, which is implemented by a phase modulator, typically with its initial phase fixed (e.g., ...). The last cosine term constitutes the imaginary modulation component, which is achieved through a combination of an amplitude modulator and an optical amplifier, and its initial phase is controlled. It changes periodically over time, such as Figure 3 c shows 0 and π The periodic jumps between these terms introduce non-Hermitian coupling terms with periodic alternation of signs.

[0034] Furthermore, the modulation frequency of this dynamic complex modulation is configured to correspond to the alternating frequency interval characteristics between the symmetric and antisymmetric supermodes. This means that the modulation frequency needs to be... Configured to be spaced (2) from the first frequency Kappa If the modulation frequency is equal to the modulation frequency, then... Configured to be spaced from the second frequency (Ω-2) Kappa )equal.

[0035] Thus, a periodically quenched non-Hermitian frequency lattice is constructed in the synthesis frequency dimension. When the modulation frequencies are matched, the modulation signal can effectively couple adjacent supermodes. Under the rotating wave approximation, the system is mapped to a periodically quenched non-Hermitian SSH model. Subsequently, the parameters of this dynamic complex modulation are adjusted to drive the quasi-energy band of the non-Hermitian frequency lattice to exhibit a linear dispersion relation at the Flokai singularity.

[0036] As one specific implementation method, the driving process includes: converting one modulation cycle of dynamic complex modulation. T Divided into the first time interval With the second time interval ;adjust and The duration of, By setting this equal duration, the non-Hermitian frequency lattice is brought to a critical state of parity-time (PT) symmetry breaking, thereby enabling the quasi-energy band (e.g., in the...) Exciting the Flokai singularity at a certain point (e.g., at a specific location), the quasi-band exhibits an approximately linear dispersion relation in the vicinity of this Flokai singularity. This linear dispersion leads to a decrease in the group velocity of light diffusing in the frequency lattice. v g The constant frequency allows the initial narrowband optical signal to broaden uniformly along the frequency axis, thus forming a flat-top spectrum.

[0037] Its evolutionary process can be referenced. Figure 4 ,Figure 4 The results show the spectral and power evolution of the synthesized frequency lattice obtained through numerical simulation. In the simulation, initial conditions are set to correspond to specific excited states near the central wave vector; for example, the initial conditions are set to... The Gaussian wave packet distribution. Specifically, as shown... Figure 4 As shown in Figure a, this figure presents the numerical simulation results of the evolution of spectral intensity over time in the synthetic frequency lattice driven by the Flokai singularity. The horizontal axis represents the number of frequency modes, and the vertical axis represents the normalized evolution time. T It can be seen that the initially injected narrowband Gaussian beam diffuses to both sides at a constant speed along the frequency axis as the modulation period increases, exhibiting a significant linear broadening trend, and eventually evolves into a rectangular wave packet with a flat top, thus generating a flat-top spectrum. This intuitively verifies the shaping effect of the quasi-band linear dispersion relation on the diffusion of the light wave packet.

[0038] As a specific implementation method, the broadening rate (group velocity) of the flat-top spectrum v g The output power and other parameters can be flexibly tuned through electrical parameters. This is achieved by adjusting the amplitude of the imaginary modulation component. J i This allows for linear alteration of the slope of the quasi-energy band near the Flokai singularity, thereby linearly controlling the spectral broadening rate. Even in J i Much smaller than the real modulation amplitude Under certain conditions (i.e., weak non-Hermitian region), the Frokai singularity and flat-top spectrum can still be generated stably, which reduces the difficulty of system implementation.

[0039] This pattern is in Figure 5 This has been verified. Figure 5 a- Figure 5 d are schematic diagrams comparing the spectral evolution under different imaginary modulation amplitudes, simulating the imaginary modulation amplitude respectively. J i The spectral evolution for different values ​​(e.g., 0.1, 0.5, 2, and 3). From Figure 5 It can be clearly observed that, with J i With the increase of , the broadening rate of the flat-top spectrum on the frequency axis increases significantly, and the generated spectral power also increases accordingly. This indicates that the slope of the quasi-band (i.e., the group velocity) is increasing. v g ) and asymmetric coupling strength J i The positive correlation verifies that adjusting electrical parameters... J i This allows for independent, linear control of spectral bandwidth and generation rate.

[0040] The application can generate flat-top spectrum with tunable characteristics by introducing periodic dynamic complex modulation in the coupled optical ring resonators and realizing linear dispersion relation of quasi-energy band at the Floquet singular point. The method effectively solves the problems of low output spectrum mode purity, strong dependence on high non-Hermite degree condition and insufficient performance parameter regulation freedom in the prior art. Specifically, the scheme can realize single pure mode flat-top spectrum output, reduces the demand for high gain or high loss, and provides a way to independently and flexibly adjust the spectrum broadening behavior and output power through electrical parameters, thereby improving the precision, stability and practicability of spectrum generation.

[0041] The application further proposes that the resonant frequency modes of a single optical ring resonator are split to form the symmetric supermode and the anti-symmetric supermode through the coupling effect between the pair of optical ring resonators; the symmetric supermode and the anti-symmetric supermode are alternately arranged with a first frequency interval and a second frequency interval on the frequency axis.

[0042] Specifically, the coupling effect refers to the phenomenon that two or more optical resonators interact through evanescent field, resulting in energy transfer between them. When two optical ring resonators are placed at a close enough distance, their respective resonant modes will hybridize to form new eigenmodes, i.e. supermodes. This hybridization effect causes the energy separation of the degenerate or non-degenerate resonant frequency modes of the original single resonator, which is manifested as frequency splitting. For example, when two identical optical ring resonators are coupled through waveguides or direct contact, each independent resonant mode will split into two new modes, corresponding to symmetric and anti-symmetric combination modes, which are the symmetric supermode and the anti-symmetric supermode. The degree of splitting is usually determined by the coupling strength between the resonators Kappa . The greater the coupling strength, the more significant the frequency splitting. Alternately arranged on the frequency axis means that in the optical spectrum, the resonant peaks of the symmetric supermode and the resonant peaks of the anti-symmetric supermode will appear periodically and are spaced apart. The first frequency interval refers to the frequency difference between adjacent symmetric supermodes and anti-symmetric supermodes, while the second frequency interval refers to the frequency difference between adjacent anti-symmetric supermodes and symmetric supermodes. This alternating arrangement is an inherent spectral feature of the coupled resonator system, and the specific interval size is determined by factors such as coupling strength, free spectral range of a single resonator and resonator geometry. For example, in an ideal case, if two resonators are completely identical and symmetrically coupled, the symmetric supermode and the anti-symmetric supermode may appear alternately with a fixed frequency interval.

[0043] By explicitly describing how a pair of optical ring resonators, through coupling, causes the individual resonator modes to split, thereby forming symmetric and antisymmetric supermodes, and further pointing out that these supermodes are arranged alternately on the frequency axis with a first frequency interval and a second frequency interval, a clear and controllable physical basis is provided for subsequent dynamic complex modulation.

[0044] This application further proposes that the first frequency interval is determined by the coupling strength between the pair of optical ring resonators, and the second frequency interval is determined by the difference between the free spectral range of the optical ring resonator and the first frequency interval.

[0045] Specifically, when a pair of coupled optical ring resonators couple, their respective resonant modes split, forming new normal modes, or supermodes. The degree of this mode splitting is directly related to the coupling strength between the two resonators. Kappa Relatedly, a stronger coupling strength results in more pronounced mode splitting, leading to a larger frequency spacing between supermodes. The coupling strength can be adjusted in various ways, such as changing the distance between the two ring resonators, adjusting the geometric parameters of the waveguide coupling region between them (e.g., coupling gap, coupling length), or by introducing tunable coupling elements. By precisely controlling the coupling strength, the first frequency spacing can be achieved. The precise setting of the frequency axis affects the distribution of the supermode.

[0046] Meanwhile, the free spectral range Ω of an optical ring resonator refers to the frequency interval between its adjacent resonant modes, which is determined by the perimeter of the ring resonator. L Group speed v g Decision (Ω=2) πv g / L In a coupled ring resonator system, the formation of supermodes is based on the free spectral range Ω of a single resonator and mode splitting caused by coupling. When symmetric and antisymmetric supermodes alternate along the frequency axis, the spacing between them is not a single value. The first frequency spacing... This is directly caused by the coupling split, and the second frequency interval... This reflects the distribution characteristics of the supermode throughout the entire free spectral range after considering coupling splitting, specifically... The free spectral range Ω is primarily determined by the perimeter and effective refractive index of the optical ring resonator. Once the physical dimensions of the ring resonator are determined, its free spectral range Ω is essentially fixed. Therefore, by pre-designing or measuring the free spectral range Ω of a single optical ring resonator, and combining it with a predetermined first frequency interval... (or coupling strength) Kappa The second frequency interval can then be calculated and determined. This determination ensures that the periodic distribution of supermodes along the frequency axis is self-consistent and predictable, providing an accurate frequency reference for subsequent dynamic complex modulation.

[0047] Through the above technical solutions, the present application provides an accurate and controllable way to define and adjust the alternating frequency interval of supermodes along the frequency axis. This explicit physical mechanism enables more accurate correspondence between the modulation frequency of dynamic complex modulation and the alternating frequency interval feature of supermodes when configuring the modulation frequency, thereby constructing an accurate periodic quenching non-Hermitian frequency lattice.

[0048] The present application further proposes that when applying periodic dynamic complex modulation, the real part modulation component is generated using a phase modulator, and the initial phase of the real part modulation component is fixed; at the same time, the imaginary part modulation component is generated using an amplitude modulator and an optical amplifier, and the initial phase of the imaginary part modulation component is controlled to change periodically with time, so as to introduce a non-Hermitian coupling term with sign periodic alternation in the non-Hermitian frequency lattice.

[0049] Specifically, the phase modulator is a device that introduces modulation by changing the phase of an optical signal, for example, an electro-optic modulator can be used. By applying an electrical signal to the phase modulator, the phase of the output optical signal can be changed. Fixing the initial phase of the real part modulation component means that the phase of the component at time zero or a certain reference time remains unchanged throughout the modulation period. This can be achieved by precisely controlling the starting point of the modulation signal or using a stable reference clock. Fixing the initial phase helps to ensure that the coupling effect introduced by the real part modulation is deterministic, avoiding instability caused by phase drift, thereby providing a stable foundation for the accurate construction of the subsequent non-Hermitian frequency lattice.

[0050] Meanwhile, an amplitude modulator is used to change the amplitude of the optical signal, which can be an electro-absorption modulator or a Mach-Zehnder modulator, for example. An optical amplifier, such as an erbium-doped fiber amplifier (EDFA) or a semiconductor optical amplifier (SOA), is used to compensate for the loss in the modulation process or to enhance the signal strength. The imaginary part of the modulation component is usually associated with the gain or loss, so the combination of the amplitude modulator and the optical amplifier can effectively introduce such imaginary part modulation. Controlling the initial phase of the imaginary part modulation component to change periodically over time means that within each modulation period, the initial phase of the imaginary part modulation component will switch or evolve according to a predetermined periodic rule. This periodically changing initial phase, combined with the gain / loss introduced by the amplitude modulator and the optical amplifier, can generate a non-Hermitian coupling term with periodically alternating signs in the non-Hermitian frequency lattice. For example, gain (positive imaginary part) is introduced during part of the modulation period, and loss (negative imaginary part) is introduced during another part of the modulation period, and the phase (or sign) of these gain / loss is periodically inverted. Such a non-Hermitian coupling term with periodically alternating signs is the key to realizing a periodically quenched non-Hermitian frequency lattice, which can break the Hermiticity of the system, introduce the asymmetry of gain and loss, and thus create conditions for the excitation of the Fano exceptional point and the formation of linear dispersion relation.

[0051] By the above technical solution, the phase modulator is used to generate the real part modulation component and fix its initial phase, ensuring the stability and predictability of the coupling modulation and providing a solid foundation for the construction of the non-Hermitian frequency lattice.

[0052] The application further proposes that in the above step S300, the dynamic complex modulation includes a first modulation frequency component and a second modulation frequency component; the first modulation frequency component is configured to correspond to the first frequency interval, and the second modulation frequency component is configured to correspond to the second frequency interval; and the first modulation frequency component and the second modulation frequency component are used to drive the symmetric supermode and the antisymmetric supermode to be coupled to each other, so as to form the periodically quenched non-Hermitian frequency lattice.

[0053] Specifically, the dynamic complex modulation is no longer a single modulation signal, but is composed of two independent frequency components, i.e., a first modulation frequency component Ω mod1 and a second modulation frequency component Ω mod2 This design allows more precise control of the modulation behavior. For example, two independent signal generators can be used to generate electrical signals of different frequencies, which are then combined by a mixer or a multiplexer to form a composite dynamic complex modulation signal, which is then applied to the optical ring resonator. In the configuration process, the first modulation frequency component Ω mod1 is accurately configured to correspond to the first frequency interval corresponding. Meanwhile, the second modulation frequency component Ω mod2 is precisely configured to correspond to the second frequency interval This precise configuration can be achieved through pre-measurement or calculation and Then, the frequency of the two modulation frequency components is adjusted by the control unit.

[0054] Through the above technical solution, the dynamic complex modulation is decomposed into two independent modulation frequency components, and each is precisely matched with the two different frequency intervals between the symmetric supermode and the anti-symmetric supermode, thereby enabling precise control of the coupling between supermodes.

[0055] The application further proposes that the quasi-energy band of the non-Hermitian frequency lattice driven by the dynamic complex modulation exhibits linear dispersion relation at the Floquet singular point, comprising: dividing one modulation period of the dynamic complex modulation into a first time interval and a second time interval; adjusting the duration of the first time interval and the second time interval to be equal; by setting the equal duration, the non-Hermitian frequency lattice is in a symmetry breaking critical state, thereby exciting the Floquet singular point in the quasi-energy band.

[0056] Specifically, the dynamic complex modulation is periodic, and one modulation period T is the minimum time unit of the modulation repetition. The modulation period T is divided into a first time interval and a second time interval , which means that in a complete modulation cycle, there are two different operation stages or parameter setting stages. This division can be achieved by switching the waveform or parameters of the modulation signal in different time periods. For example, in a digital control system, a programmable timer or state machine can be used to precisely define the start and end of the two time intervals. Further, the duration of the first time interval and the second time interval is adjusted to be equal, that is , is the precise definition of the time interval division described above. This symmetrical division is crucial for achieving certain physical effects and can be achieved by precisely controlling the duty cycle or pulse width of the modulation signal. This usually requires a high-precision clock source and a digital signal processor (DSP) or field-programmable gate array (FPGA) for precise control to ensure time synchronization and accuracy of duration. By setting equal durations, it is possible to bring the non-Hermitian frequency lattice to a parity-time (PT) symmetry breaking critical state. In this critical state, the system exhibits great sensitivity to small perturbations. For the non-Hermitian system of the present application, this state is closely related to the appearance of the Floquet exceptional point. Equal duration is a key condition for reaching this critical state, which introduces a kind of symmetry in time within the modulation period, thereby affecting the effective Hamiltonian of the non-Hermitian frequency lattice, so that it satisfies the condition for the existence of the exceptional point. Finally, the Floquet exceptional point is excited in the quasi-energy band (e.g., at quasi-energy Epsilon =± π points). The Floquet exceptional point is a special point in a non-Hermitian system, characterized by the degeneracy of two or more eigenstates on the complex energy plane, and the eigenstates themselves also merge. Exciting the Floquet exceptional point in the quasi-energy band is crucial for achieving linear dispersion relations, as the transition from nonlinear to linear dispersion relations usually occurs near the exceptional point.

[0057] By precisely dividing one modulation period of the dynamic complex modulation into a first time interval and a second time interval with equal durations, the present application can effectively bring the non-Hermitian frequency lattice into a symmetry breaking critical state. This critical state is a key condition for exciting the Floquet exceptional point in the quasi-energy band, thereby ensuring that the linear dispersion relation can be stably presented at the Floquet exceptional point. Compared to the general control by adjusting parameters, this precise division of time intervals provides a more direct and reliable mechanism to trigger and locate the Floquet exceptional point, thereby laying a solid foundation for generating a tunable flat-top spectrum based on the linear dispersion relation, significantly improving the accuracy and controllability of the flat-top spectrum generation process.

[0058] The present application further proposes that when generating a flat-top spectrum based on the linear dispersion relation, the amplitude of the imaginary part modulation component is adjusted to change the asymmetric coupling strength in the non-Hermitian frequency lattice; by changing the asymmetric coupling strength, the slope of the quasi-energy band near the Floquet exceptional point is linearly adjusted; according to the adjustment of the slope, the group velocity and spectral broadening rate of the generated flat-top spectrum in the frequency domain are controlled.

[0059] Specifically, the imaginary part modulation component is an important part of the dynamic complex modulation, and its main function is to introduce non-Hermitian modulation, thereby generating gain or loss in the non-Hermitian frequency lattice, forming asymmetric coupling, the strength of which is determined by the amplitude Ji Characterization. By adjusting this J i The value can directly control the intensity of the introduced non-Hermitian effect. For example, it can be changed by adjusting the electrical signal power driving the amplitude modulator. J i This allows for precise control of the effective asymmetric coupling strength in the non-Hermitian frequency lattice. This adjustment allows the system to alter the energy distribution and mode interaction strength around the Flokai singularity while maintaining its existence. At the Flokai singularity, the quasi-band structure exhibits a linear dispersion relation. Asymmetric coupling strength is one of the key parameters affecting the quasi-band structure of the Flokai system. When the asymmetric coupling strength... J i When changes occur, the effective Hamiltonian near the Flokai singularity changes accordingly, leading to a change in the dispersion characteristics of the quasi-energy band. Specifically, this is achieved through fine-tuning... J i It can achieve the slope of the quasi-energy band near the Flokai singularity. v g Linear adjustment. This means the slope v g Changes and J i There is a predictable, approximately linear relationship between the changes in the quasi-energy band. v g The group velocity directly determines the group velocity of the optical signal in the frequency domain. Group velocity is a physical quantity describing the propagation speed of wave packets. For flat-top spectra, controlling the group velocity is crucial for achieving specific time-domain waveform shaping or signal transmission. For example, by increasing... J i To increase the slope v g This can correspondingly accelerate the group velocity of the optical signal, thus resulting in faster spectral broadening. Simultaneously, the dispersion characteristics of the quasi-bandgap, especially its slope, are also closely related to spectral broadening or compression. By adjusting the slope... v g This allows for effective control of the spectral broadening rate of the flat-top spectrum, enabling it to present a wider or narrower spectral width as needed, thereby meeting the requirements of different application scenarios for spectral shape and bandwidth. Furthermore, the power of the output spectrum also varies accordingly. J i It increases with the increase of [something].

[0060] By the technical solution, on the basis of generating the flat-top spectrum through the Floquet singular point, a means for fine control of the flat-top spectrum characteristics is further provided, which makes the method not only capable of generating the flat-top spectrum, but also capable of flexibly adjusting the transmission characteristics and spectral width of the flat-top spectrum according to actual application requirements, greatly enhancing the tunability and practicality of the flat-top spectrum.

[0061] The application further proposes that, in the process of generating the flat-top spectrum, the power evolution rules of the symmetric supermode and the antisymmetric supermode with time are monitored; within one modulation period of the dynamic complex modulation, when the power of the symmetric supermode reaches a peak value and the power of the antisymmetric supermode is suppressed, an optical signal is extracted to obtain a flat-top frequency comb mainly composed of the symmetric supermode; or when the power of the antisymmetric supermode reaches a peak value and the power of the symmetric supermode is suppressed, an optical signal is extracted to obtain a flat-top frequency comb mainly composed of the antisymmetric supermode.

[0062] To achieve this goal, it is first necessary to monitor the power evolution rules of the symmetric supermode and the antisymmetric supermode with time. This can be achieved by setting photodetectors on the symmetric and antisymmetric supermode output channels of the optical ring resonator system, collecting the intensity information of the optical signal in real time, and recording the instantaneous power change of the optical signal within the dynamic complex modulation period by using a high-speed data acquisition system. As shown in FIG. 2b, the figure records the evolution curves of the total power of the symmetric supermode and the total power of the antisymmetric supermode with time. It is obvious that the two present opposite periodic oscillation characteristics in the time domain: when the power of the symmetric supermode reaches a peak value, the power of the antisymmetric supermode is at a valley value (tends to zero), and vice versa. Figure 4 Figure 4 c further shows the spectrum power distribution snapshots taken at two specific time points (for example, the 19th cycle Figure 4 b). and ) in the process shown in FIG. 2b. The results show that at the first time point ( ), the output spectrum is almost completely composed of the symmetric supermode; and at the second time point ( ), the output spectrum is almost completely composed of the antisymmetric supermode. This fully proves that the time gating mechanism of the system can separate a single-mode flat-top frequency comb with high purity from the mixed state.

[0063] Specifically, when it is monitored that the power of the symmetric supermode reaches a peak value and the power of the antisymmetric supermode (the antisymmetric supermode) is suppressed to near zero, for example, at a specific time point (such as Figure 4 ) in the cycle shown in FIG. 2b, an optical signal is extracted to obtain a flat-top frequency comb mainly composed of the symmetric supermode; or when it is monitored that the power of the antisymmetric supermode reaches a peak value and the power of the symmetric supermode is suppressed to near zero, for example, at a specific time point (such as ​nearby), the light signal from the symmetric supermode output channel can be extracted within this specific time window by a high-speed optical switch or time-gating device, so as to obtain a flat-top frequency comb mainly composed of symmetric supermodes. Conversely, when the power of the antisymmetric supermode is monitored to reach a peak value and the power of the symmetric supermode is suppressed, for example Figure 4 nearby), the light signal from the antisymmetric supermode output channel can be extracted within the corresponding specific time window, so as to obtain a flat-top frequency comb mainly composed of antisymmetric supermodes. This extraction mechanism ensures the purity of the output frequency comb and avoids mutual interference between different supermodes. nearby), the light signal from the antisymmetric supermode output channel can be extracted within the corresponding specific time window, so as to obtain a flat-top frequency comb mainly composed of antisymmetric supermodes. This extraction mechanism ensures the purity of the output frequency comb and avoids mutual interference between different supermodes.

[0064] By means of the above technical solutions, the present application can accurately identify and utilize the instantaneous evolution characteristics of the supermode power within the dynamic complex modulation period, so as to realize selective extraction of a flat-top frequency comb composed of specific supermodes.

[0065] The present application further proposes that, when performing the step of adjusting the parameters of the dynamic complex modulation to drive the quasi-energy band of the non-Hermite frequency lattice to exhibit a linear dispersion relation at the Floquet singular point and generate a flat-top spectrum, the amplitude of the imaginary part modulation component is configured to be smaller than the amplitude of the real part modulation component. The imaginary part modulation component is mainly responsible for introducing the non-Hermite modulation, and the amplitude J i determines the strength of the non-Hermite effect, such as the degree of gain or loss, or the strength of the asymmetric coupling. The real part modulation component is used to introduce the coupling modulation, and the amplitude reflects the strength of the coupling between supermodes. By configuring the amplitude J i of the imaginary part modulation component to be smaller than the amplitude and of the real part modulation component, it can be ensured that the non-Hermite effect remains within a controlled range during the entire modulation process, avoiding its excessive dominance over the dynamics of the system. The technical solutions of the present application show that, even under the condition that J i is much smaller than and (for example J i = 0.1, ), through the aforementioned periodic quenching mechanism and symmetric duty cycle setting, the Floquet singular point can still be stably excited and a high-quality flat-top spectrum can be generated.

[0066] By the above technical solution, the amplitude of the imaginary part modulation component is limited to be less than the amplitude of the real part modulation component, which can effectively suppress the system instability that may be caused by the non-Hermitian effect. This makes the quasi-energy band structure of the non-Hermitian frequency lattice near the Floquet singular point maintain a stable and predictable linear dispersion relationship, thereby ensuring that the generated flat-top spectrum has higher quality and better controllability. This configuration helps to accurately regulate the dispersion characteristics at the Floquet singular point, avoids the distortion or instability of the quasi-energy band caused by the over-strong non-Hermitian effect, thereby improving the robustness and performance of the flat-top spectrum generation method, while reducing the performance requirements for high-gain / loss modulation devices and improving the practical potential of the system.

[0067] Further, the embodiments of the present application also disclose a system for implementing the above method, as shown in Figure 2 , comprising: a double-ring resonator unit 100, which comprises the pair of mutually coupled optical ring resonators; a dynamic modulation generation unit 200, configured to generate and apply the periodic dynamic complex modulation to the double-ring resonator unit 100; a control and processing unit 300, connected with the dynamic modulation generation unit 200, configured to configure modulation parameters, monitor supermode power evolution, and control light signal extraction operation.

[0068] The double-ring resonator unit 100 is composed of a pair of optical ring resonators connected with each other through evanescent wave coupling, and the coupling causes the splitting of the resonant frequency mode of a single optical ring resonator, forming symmetric supermodes and antisymmetric supermodes arranged alternately on the frequency axis with a spacing of . The dynamic modulation generation unit 200 comprises a phase modulator and a combination of an amplitude modulator and an optical amplifier, configured to generate a periodic dynamic complex modulation signal comprising a real part modulation component and an imaginary part modulation component; wherein the real part modulation component is generated by the phase modulator and has a fixed initial phase, for introducing coupling modulation; the imaginary part modulation component is generated by the amplitude modulator and the optical amplifier, and its initial phase changes periodically with time, for introducing a non-Hermitian coupling term with periodically alternating signs. The control and processing unit 300 is electrically connected with the dynamic modulation generation unit 200, configured to accurately configure the modulation frequency parameters and of the dynamic complex modulation, the amplitude parameters , J 1、 J i and the duty cycle of the modulation period T (set to ), so as to construct a periodic quenched non-Hermitian frequency lattice in the synthetic frequency dimension; meanwhile, the control and processing unit 300 monitors the power evolution of symmetric and antisymmetric supermodes over time in real time, and triggers the high-speed optical switch to perform optical signal extraction operation when the power of symmetric supermodes reaches the peak and the power of antisymmetric supermodes is suppressed, or when the power of antisymmetric supermodes reaches the peak and the power of symmetric supermodes is suppressed, within one modulation period of dynamic complex modulation, to obtain a flat-top frequency comb mainly composed of a single supermode.

[0069] The whole system is composed of a dual-ring resonator unit 100, a dynamic modulation generation unit 200, and a control and processing unit 300. The dual-ring resonator unit 100 contains a pair of mutually coupled optical ring resonators. The dynamic modulation generation unit 200 is used to generate and apply the above-mentioned periodic dynamic complex modulation to the dual-ring resonator unit 100. The control and processing unit 300 is connected with the dynamic modulation generation unit 200, used to configure the modulation parameters, monitor the supermode power evolution, and control the extraction operation of the optical signal, ensuring accurate execution and efficient operation of the whole method.

[0070] The above only describes the embodiments of the present application and is not used to limit the protection scope of the present application. For those skilled in the art, the present application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for generating tunable flat-top spectra based on Flokai singularities, characterized in that, include: Step S100: Establish a pair of mutually coupled optical ring resonators, and use the coupling effect to make the pair of optical ring resonators used to form symmetric supermodes and antisymmetric supermodes that are alternately arranged on the frequency axis; Step S200: Apply periodic dynamic complex modulation to the pair of optical ring resonators, the dynamic complex modulation including a real modulation component for introducing coupling modulation and an imaginary modulation component for introducing non-Hermitian modulation; Step S300: Configure the modulation frequency of the dynamic complex modulation to correspond to the alternating frequency interval characteristics between the symmetric supermode and the antisymmetric supermode, thereby constructing a periodically quenched non-Hermitian frequency lattice in the synthesized frequency dimension. Step S400: Adjust the parameters of the dynamic complex modulation to drive the quasi-energy band of the non-Hermitian frequency lattice to exhibit a linear dispersion relation at the Flokai singularity, and generate a flat-top spectrum based on the linear dispersion relation.

2. The method according to claim 1, characterized in that, Step S100 includes: The coupling between the pair of optical ring resonators splits the resonant frequency mode of a single optical ring resonator to form the symmetric supermode and the antisymmetric supermode. The symmetric and antisymmetric supermodes are arranged alternately on the frequency axis at a first frequency interval and a second frequency interval.

3. The method according to claim 2, characterized in that, The first frequency interval is determined by the coupling strength between the pair of optical ring resonators, and the second frequency interval is determined by the difference between the free spectral range of the optical ring resonators and the first frequency interval.

4. The method according to claim 1, characterized in that, Step S200 includes: The real modulation component is generated using a phase modulator, and the initial phase of the real modulation component is fixed. The imaginary modulation component is generated using an amplitude modulator and an optical amplifier, and the initial phase of the imaginary modulation component is controlled to change periodically over time, so as to introduce non-Hermitian coupling terms with periodically alternating signs in the non-Hermitian frequency lattice.

5. The method according to claim 2 or 3, characterized in that, Step S300 includes: The dynamic complex modulation is configured to include a first modulation frequency component and a second modulation frequency component; The first modulation frequency component is configured to correspond to the first frequency interval, and the second modulation frequency component is configured to correspond to the second frequency interval; The first modulation frequency component and the second modulation frequency component drive the symmetric supermode and the antisymmetric supermode to couple with each other to form the periodically quenched non-Hermitian frequency lattice.

6. The method according to claim 1, characterized in that, In step S400, driving the quasi-energy band of the non-Hermitian frequency lattice to exhibit a linear dispersion relation at the Flokai singularity includes: One modulation period of the dynamic complex modulation is divided into a first time interval and a second time interval; Adjust the duration of the first time interval and the second time interval to make them equal; By setting the equal duration, the non-Hermitian frequency lattice is brought to a symmetry-breaking critical state, thereby exciting the Flokai singularity in the quasi-energy band.

7. The method according to claim 6, characterized in that, In step S400, generating a flat-top spectrum based on the linear dispersion relation includes: The amplitude of the imaginary modulation component is adjusted to change the asymmetric coupling strength in the non-Hermitian frequency lattice; The slope of the quasi-energy band near the Flokai singularity is linearly adjusted by changing the asymmetric coupling strength. Based on the adjustment of the slope, the group velocity and spectral broadening rate of the generated flat-top spectrum in the frequency domain are controlled.

8. The method according to claim 1, characterized in that, The method further includes step S500: During the generation of the flat-top spectrum, the power evolution of the symmetric and antisymmetric supermodes over time is monitored. Within one modulation cycle of the dynamic complex modulation, when the power of the symmetric supermode reaches its peak and the power of the antisymmetric supermode is suppressed, the optical signal is extracted to obtain a flat-top frequency comb mainly composed of the symmetric supermode; or, When the power of the antisymmetric supermode reaches its peak and the power of the symmetric supermode is suppressed, the optical signal is extracted to obtain a flat-top frequency comb mainly composed of the antisymmetric supermode.

9. The method according to claim 1, characterized in that, When performing step S400, the amplitude of the imaginary modulation component is configured to be smaller than the amplitude of the real modulation component.

10. A system for implementing the method according to any one of claims 1 to 9, characterized in that, include: A dual-ring resonator unit comprising the pair of mutually coupled optical ring resonators; A dynamic modulation generation unit is used to generate and apply the periodic dynamic complex modulation to the dual-ring resonator unit; The control and processing unit, connected to the dynamic modulation generation unit, is used to configure modulation parameters, monitor the evolution of supermode power, and control the extraction operation of optical signals.

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