Multi-mode compression analysis method based on lithium niobate micro-ring resonant cavity second-order frequency comb

Abstract

The invention discloses a multi-mode compression analysis method based on a lithium niobate micro-ring resonant cavity second-order frequency comb, and the method constructs a second-order frequency comb generation model, the model is based on an MATLAB simulation environment, and is used for simulating and representing the evolution process of the second-order frequency comb based on the structure of a micro-ring resonant cavity. Wherein a second-order coupling average field theoretical model containing interaction of a pumping field and a semi-harmonic field is adopted in simulation; and carrying out multi-mode compression degree calculation and super-mode decomposition coefficient distribution analysis on the generated second-order frequency comb by adopting an analytic Bloch-Mapse decomposition algorithm so as to quantitatively evaluate the quantum compression characteristic and mode coupling rule of the frequency comb. The invention lays a key technical foundation for the application of the lithium niobate micro-ring resonant cavity in the fields of quantum optics, optical communication and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of nonlinear optics and quantum optics, and particularly relates to a second-order frequency comb generation based on a lithium niobate micro-ring resonator and a quantum multimode compression characteristic analysis technology, and is particularly suitable for application scenarios of frequency comb generation and quantum characteristic regulation in the fields of integrated optics, quantum communication, precision measurement, etc. BACKGROUND

[0002] As a light source with equally spaced frequency spectrum lines, frequency comb plays an irreplaceable role in the fields of quantum communication, precision spectral analysis, optical clock, etc. due to its high frequency stability and wide spectral coverage. With the rapid development of integrated photonics, chip-level quantum optical systems have become a research hotspot, and micro-ring resonators have become the core devices for generating frequency combs due to their strong optical confinement ability and enhanced nonlinear interaction, providing a key platform for realizing miniaturized and high-performance quantum light sources.

[0003] In recent years, significant progress has been made in the research of micro-ring resonator quantum light sources based on various material platforms. In silicon nitride micro-rings, orthogonal squeezed vacuum states and photon number difference squeezed states can be generated through threshold spontaneous four-wave mixing, and heralded single-photon sources and scalable multi-user quantum networks have been realized. In silicon carbide micro-rings, multimode entanglement is achieved using soliton micro-comb dynamics. In addition, gallium nitride, aluminum gallium arsenide, and integrated nanophotonic platforms have also been proven to be useful for preparing high-purity quantum light sources. These studies have promoted the development of quantum frequency comb control technology, from the non-equilibrium driving of strongly coupled photonic dimers to the parity-time symmetric mode selection pumping strategy, highlighting the central role of quantum frequency combs in emerging applications such as quantum computing and communication.

[0004] However, the existing mainstream material platforms (such as silicon nitride) mainly rely on third-order nonlinear effects, which face problems such as high pump threshold and limited quantum efficiency in generating entangled photon pairs. In contrast, lithium niobate exhibits unique advantages due to its significant second-order nonlinear coefficient: through the spontaneous parametric down-conversion (SPDC) process, entangled photon pairs can be efficiently generated, and the required pump threshold is much lower than that of platforms such as silicon nitride; at the same time, lithium niobate supports quantum frequency conversion of single photons between the telecom band and the visible or mid-infrared band, meeting the compatibility requirements of multimode quantum architecture, and its heterogeneous integration technology lays the foundation for the development of multifunctional quantum photonic chips. In addition, the Pockels effect of lithium niobate enables high-speed and low-loss electro-optic modulation, which has important application value in optical communication systems.

[0005] Although lithium niobate microring resonators have shown great potential in the field of quantum frequency combs, existing research still faces many challenges: first, there is a lack of a unified analytical framework for the multi-mode compression characteristics of second-order frequency combs, making it difficult to quantitatively evaluate the quantum correlations and compression distribution between modes; second, the precise control of dispersion and coupling engineering still needs to be broken through, which restricts the realization of ultra-wideband, high-compression multi-mode squeezed states. Summary of the Invention

[0006] In response to the above-mentioned deficiencies in the prior art, this application provides a multi-mode compression analysis method based on the second-order frequency comb of a lithium niobate microring resonator. By optimizing structural design and simulation analysis, efficient second-order frequency comb generation and accurate quantum multi-mode compression characteristic characterization are achieved.

[0007] In one aspect of the present application, a microring resonator is provided, wherein the microring resonator comprises a nonlinear microring resonator made of a lithium niobate crystal film, wherein:

[0008] The nonlinear micro-ring resonance is based on the second-order nonlinear χ (2) , a cascaded second-order nonlinear process occurs in the resonant cavity structure, forming two sets of frequency combs: pump field and semi-harmonic field. There is a quantum multimode compression characteristic between these modes.

[0009] Optionally, the nonlinear microring resonant cavity includes a nonlinear microring and a straight waveguide, and mode coupling occurs between the two in a coupling region. By optimizing the coupling relationship of the nonlinear microring resonant cavity and the nonlinear microring and straight waveguide structures, the dispersion relationship of the nonlinear microring resonant cavity is changed to control the formation of soliton crystals.

[0010] Optionally, the lithium niobate crystal film is a z-cut lithium niobate film, the bottom of which is provided with a substrate consisting of a SiO2 layer, and the top is exposed to the air.

[0011] Optionally, the thickness of the lithium niobate crystal film is H = 0.6 μm, the width W = 2 μm, the etching depth h = 0.41 μm, and the etching angle θ = 75°; the radius of the nonlinear microring is R = 100 μm, the spacing gap between the nonlinear microring and the straight waveguide is gap = 0.49 μm, and the coupling ratio r = 1.222.

[0012] In a second aspect of the present application, a multi-mode compression analysis method based on a second-order frequency comb of a lithium niobate microring resonator is provided, comprising:

[0013] Constructing a second-order frequency comb generation model based on a MATLAB simulation environment for simulating and characterizing the evolution of a second-order frequency comb based on the structure of the microring resonator, wherein the simulation uses a second-order coupled mean-field theory model that includes the interaction between a pump field and a semi-harmonic field;

[0014] The analytical Bloch-Messiah decomposition algorithm is used to calculate the multi-mode compression degree and analyze the distribution of supermode decomposition coefficients of the generated second-order frequency comb, in order to quantitatively evaluate the quantum compression characteristics and mode coupling laws of the frequency comb.

[0015] Optionally, in the second-order coupled mean field theory model, the second-order coupled mean field equation is expressed as:

[0016]

[0017] Where a and b represent the time domain fields of semi-harmonic and pump, respectively, Δ represents detuning, Γ represents total loss, γ represents external loss, g0 represents the second-order nonlinear coefficient, and v f represents the free spectral range, L represents the cavity length, and B in represents the input pump amplitude, represents the partial derivative formula, i is the imaginary unit, * represents the conjugate of the complex number, k"1 and k"2 represent the group velocity dispersion of the semi-harmonic field and the pump field respectively, B in represents the input pump amplitude, and Δk′ represents the walkoff.

[0018] Optionally, the second-order coupled mean field equation is solved using the split-step Fourier method, including: using the split-step Fourier method for time domain simulation, setting the initial excitation to Gaussian white noise, and simulating the evolution process of the second-order frequency comb by uniformly scanning the detuning amount.

[0019] Optionally, the analytical Bloch-Messiah decomposition algorithm includes: performing similarity transformation and matrix decomposition on the system transmission matrix to obtain key parameters characterizing the quantum characteristics of the system, wherein the key parameters include the phase and amplitude distribution of the supermode decomposition coefficients and the compression degree information of the multimode compression.

[0020] Optionally, the analytical Bloch-Messiah decomposition algorithm, wherein: the time domain numerical values ​​corresponding to the evolution process of the second-order frequency comb are substituted into the decomposition program of the analytical Bloch-Messiah decomposition algorithm to characterize the supermode decomposition coefficient distribution and multimode compression spectrum at different times, as well as the change curve of the multimode compression degree at zero Fourier frequency during the entire evolution process.

[0021] Optionally, the quantitative evaluation of the quantum compression characteristics of the frequency comb includes: recording the time-domain pulse morphology and spectral distribution of the frequency comb under different detuning conditions, observing the change in multi-mode compression at zero Fourier frequency during the evolution of the frequency comb, and thus evaluating the quantum compression characteristics.

[0022] Compared with the prior art, this application has at least one of the following beneficial effects:

[0023] The micro-ring resonator provided by the embodiment of the application adopts a lithium niobate thin film structure design, and high-efficiency second-order frequency comb generation can be realized by combining parameter optimization.

[0024] The multimode compression analysis method of the second-order frequency comb based on the lithium niobate micro-ring resonator cavity provided by the embodiment of the application realizes effective regulation of two groups of frequency combs of pump fields and half-harmonic fields by optimizing the dispersion relationship of the resonant cavity and the formation of soliton crystals, and can realize precise regulation of dispersion and coupling engineering; the quantum multimode compression characteristics are excavated based on the analytical Bloch-Messiah decomposition algorithm, the problem that the multimode compression characteristics of the second-order frequency comb are difficult to quantitatively evaluate the quantum correlation and compression degree distribution between modes is solved, and a new technical means is provided for quantum communication and precision measurement.

[0025] Other technical effects brought by the additional features will be further described in the corresponding embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0026] Other features, objects and advantages of the application will become more apparent from the following detailed description of non-limiting embodiments with reference to the following drawings:

[0027] Figure 1 The figure is a schematic diagram of the micro-ring resonator cavity design and the coupling relationship and cross-sectional structure in a preferred embodiment of the application;

[0028] Figure 2 The figure is a dispersion curve simulated by COMSOL Multiphysics in a preferred embodiment of the application, and the values of the integrated dispersion D of each mode are given; int

[0029] Figure 3 The figure is the evolution process of the second-order frequency comb and the time-domain waveform of the soliton crystal at one time in a preferred embodiment of the application;

[0030] Figure 4 The figure is the second-order frequency comb and the distribution of the amplitude of the supermode decomposition coefficient under different detunings in a preferred embodiment of the application;

[0031] Figure 5 The figure is the change of the maximum compression degree of the multimode compression of the evolution process of the second-order frequency comb and the multimode compression spectrum under different detunings in a preferred embodiment of the application. DETAILED DESCRIPTION

[0032] ​The application will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the application, but in no way limit the application. It should be pointed out that those skilled in the art can make several modifications and improvements without departing from the concept of the application. These all belong to the protection scope of the application. The parts not described in detail in the following examples can be implemented with reference to the prior art.

[0033] Referring to Figure 1 As shown, the micro-ring resonator cavity related design based on lithium niobate (LiNbO3, LN for short) material is displayed, including a structural schematic diagram (a), a coupling relationship model (b), and a cross-sectional parameter diagram (c).

[0034] Lithium niobate has second-order nonlinear optical properties, and thus the micro-ring resonator cavity prepared by the lithium niobate crystal film can enhance the interaction between the optical field and the material and improve the efficiency of the nonlinear optical process. Figure 1 As shown in (a), the micro-ring resonator cavity in the embodiment includes a nonlinear micro-ring resonator cavity prepared by a lithium niobate crystal film. The nonlinear micro-ring resonator is based on the second-order nonlinear χ (2) In the resonator structure, a cascade second-order nonlinear process occurs, forming two groups of frequency combs of pump fields and semi-harmonic fields, and there is a quantum multimode compression characteristic between these modes. Specifically, pump photons generate two semi-harmonic photons through down-conversion, and the semi-harmonic photons generate pump photons in reverse through sum-frequency process, thereby forming two groups of frequency combs of pump fields and semi-harmonic fields that are coupled with each other, and there is a quantum multimode compression characteristic between these modes.

[0035] As Figure 1 As shown in (b), the nonlinear micro-ring resonator cavity includes a nonlinear micro-ring and a straight waveguide, and the two are mode-coupled in the coupling region. By optimizing the coupling relationship of the nonlinear micro-ring resonator cavity and the structure of the nonlinear micro-ring and the straight waveguide, the dispersion relationship of the nonlinear micro-ring resonator cavity is changed, and the formation of the soliton crystal is controlled. In (b), "Ring" (micro-ring waveguide, i.e., nonlinear micro-ring) and "Bus" (straight waveguide) are included, and the two are mode-coupled in the "Coupling region". The micro-ring waveguide can confine the optical field in the ring to circulate and resonate, and the straight waveguide is used for inputting and outputting optical signals.

[0036] For the straight waveguide, the input signal is represented by a1, the output signal is a2, and the parameter t1 describes the transmission of light in the straight waveguide itself (including transmission loss, phase change, and other linear transmission characteristics).

[0037] For the micro-ring waveguide (nonlinear micro-ring), the signals in the ring along the clockwise and counterclockwise directions are represented by b1 and b2 respectively, and the transmission characteristics of the micro-ring waveguide itself are represented by t1 *etc. parameter description.

[0038] The coupling between the straight waveguide and the microring waveguide is through t2, -t2 * t2 represents the coupling coefficient between the two modes, including information such as coupling efficiency and phase matching. The negative sign indicates that the mode propagation direction or phase relationship is related. γ is the external loss, which originates from the coupling between the microring and the straight waveguide. μ is the intrinsic loss, which refers to the inevitable energy loss when light propagates within the microring and is unrelated to external coupling. It mainly includes loss paths such as material absorption loss, scattering loss, radiation loss, and mode leakage.

[0039] In the figure, n0 and n e Represents the refractive index of light, related to the birefringence characteristics of LN crystal. LN is a uniaxial crystal, n o is the refractive index of ordinary light (o light), n e It is the refractive index of extraordinary light (e-light). The relationship between the polarization state of light and the crystal axis (x, y, z directions) will affect the refractive index, thereby changing the propagation mode and coupling characteristics of light.

[0040] like Figure 1 As shown in (a), the lithium niobate crystal film is a z-cut lithium niobate film, the bottom of which is provided with a substrate composed of a SiO2 layer and the top is exposed to the air.

[0041] Specifically, Figure 1 In (a), from bottom to top, the substrate is a silicon dioxide (SiO2) layer, the middle layer is a LN layer, or z-cut lithium niobate thin film, and the top layer is exposed to the air environment. This layered structure utilizes the optical properties of different materials. The SiO2 serves as a substrate, providing support and optical isolation, the LN layer is the core functional layer for achieving nonlinear optical effects, and the air layer forms the optical boundary condition. The "Pump mode" and "Signal / Idler mode" in the figure represent the resonant cavity structure used in the nonlinear process of parametric down-conversion, where the pump light excites the signal and idler light in the structure. "Z-cut" indicates the cutting direction of the LN crystal. For LN crystals cut along the z-axis, the utilization of its nonlinear optical coefficients is related to the crystal orientation. The x, y, and z coordinates are the spatial rectangular coordinates that define the directional relationship between light propagation and the crystal axes.

[0042] Reference Figure 1 The cross-sectional structure of the microring resonator shown in (c), and Figure 1(a) corresponds to the cross-section in the xz plane. From bottom to top, it shows the SiO2 substrate, the LN layer (z-cut lithium niobate thin film), and the air layer. Embedded within the LN layer are the "Bus" (straight waveguide) and the "Ring" (microring waveguide). Both are ridge waveguide structures that guide light by confining the light field to the waveguide core (the ridges of the Bus and Ring).

[0043] The waveguide size parameters shown in the figure: W B is the width of the straight waveguide ridge, W R is the width of the micro-ring waveguide ridge; H is the thickness of the lithium niobate crystal film, h is the etching depth, that is, the height of the waveguide ridge relative to the LN layer plane (the height of the ridge waveguide protrusion); "gap" is the gap between the straight waveguide and the micro-ring waveguide ridge, which affects the mode coupling strength between the two. The smaller the gap, the stronger the coupling. θ is the etching angle, that is, the inclination angle of the micro-ring waveguide ridge and other geometric parameters, which affects the mode distribution and light field confinement ability of the micro-ring waveguide; the refractive index n e (extraordinary refractive index) and n o (ordinary light refractive index) reflects the birefringence characteristics of the LN crystal. The propagation refractive index of light in different polarization states and different waveguide structures is different, which will change the effective mode refractive index of the light, thereby affecting the resonance conditions and coupling efficiency.

[0044] In the coupling region, the straight waveguide and the microring waveguide achieve optical field coupling and energy exchange through mode overlap. Linear transmission parameters (such as t1 and t1*) describe the propagation loss and phase change of light in the waveguide, while coupling parameters (such as t2) describe the energy coupling ratio between the two. At the same time, the second-order nonlinear characteristics of the LN crystal and the crystal birefringence jointly determine the transmission, resonance, and nonlinear interaction process of the pump light, signal light, and idler light in the microring resonator structure. Analyzing this specific process can be used to construct nonlinear optical devices (such as optical parametric oscillators and nonlinear frequency converters), and utilize the resonance enhancement effect of the microring resonator to improve the efficiency of nonlinear optical processes.

[0045] Figure 2 The dispersion curves simulated by COMSOL Multiphysics in a preferred embodiment of this application are given as follows: int The lithium niobate microring resonator provided in the embodiment achieves dispersion flattening within a certain range by optimizing the cross-sectional structure and coupling relationship of the resonator, reducing the influence of phase mismatch and providing a basis for the preparation of multi-mode compression resources. p is 2.41406×10 15 rad / s, and the center frequency ω0 of the semi-harmonic field resonance peak is 1.20688×10 15rad / s, with the left part being the signal field (Signal) and the right part being the idler field (Idler). Marking the central mode number l of the semi-harmonic field as 0, the central mode number of the pump field is 959. This dispersion engineering not only significantly improves the energy conversion efficiency of the optical parametric oscillator process, but also provides phase matching conditions for the stable generation of the second-order frequency comb, and can stably prepare soliton crystals, that is, coherent states composed of periodically arranged soliton pulses. The second-order frequency comb supported by soliton crystals can provide a large number of entangled mode pairs with quantum multimode compression characteristics, providing high-density quantum resources for scenarios such as parallel quantum computing and multi-channel quantum key distribution.

[0046] For example, in a specific embodiment, the regulation of dispersion and coupling engineering can be achieved by traversing different parameters to find a dispersion relation that is more suitable for the dispersion flatness of the frequency comb.

[0047] In a preferred embodiment of the present application, the cross-sections of the nonlinear microring and straight waveguide are trapezoidal. The dispersion relation of the resonant cavity is modified by optimizing the waveguide cross-sectional structure and coupling relationship. Of course, the cross-sectional shape is not limited to a trapezoid. Generally, the cross-sectional structure includes the thickness H, width W, etching depth h, etching angle θ of the lithium niobate crystal film, and the gap between the microring and waveguide. The dispersion relation curve is obtained by setting these parameters and performing software simulation.

[0048] like Figure 1 As shown in (c), in a specific embodiment, the waveguide structure is fabricated on a z-cut lithium niobate film with a thickness of H = 0.6 μm, the substrate is a SiO2 layer, and the top is exposed to air. The preferred width W of the ring waveguide and the straight waveguide is R =W B =2μm, preferably the etching depth h=0.4μm, preferably the etching angle θ=75°, and preferably the gap=0.49μm.

[0049] In another embodiment, specifically based on the parameters of a lithium niobate microring resonator: the lithium niobate crystal film has a thickness of H = 0.6 μm, a width of W = 2 μm, an etch depth of h = 0.41 μm, and an etch angle of θ = 75°; the radius of the nonlinear microring is R = 100 μm, the gap between the nonlinear microring and the straight waveguide is GAP = 0.49 μm, and the coupling ratio r = 1.222. This overcoupled resonator facilitates parametric down-conversion of pump photons, enabling the efficient generation of quantum multimode squeezed states.

[0050] In the above embodiments of the present application, a lithium niobate microring resonator adapted for second-order frequency comb generation is designed, and by optimizing geometric parameters and material properties, an efficient nonlinear optical response is given to it.

[0051] In the above embodiment, a multi-mode compression analysis method based on the second-order frequency comb of the lithium niobate microring resonator is provided. In another embodiment of the present application, the multi-mode compression analysis method based on the second-order frequency comb of the lithium niobate microring resonator is provided, which specifically includes the following steps:

[0052] S1. Construct a second-order frequency comb generation model based on the MATLAB simulation environment. This model is used to simulate the microring resonator structure and characterize the evolution of the second-order frequency comb. The simulation uses a second-order coupled mean-field theory model that includes the interaction between the pump field and the semi-harmonic field.

[0053] S2. Using the analytical Bloch-Messiah decomposition algorithm, the multi-mode compression degree of the generated second-order frequency comb is calculated and the supermode decomposition coefficient distribution is analyzed to quantitatively evaluate the quantum compression characteristics and mode coupling laws of the frequency comb.

[0054] In the above embodiments of the present application, relying on the designed lithium niobate microring resonant cavity structure, the generation and evolution of the second-order frequency comb are simulated, and then the analytical Bloch-Messiah decomposition method is used to perform multi-mode compression calculation and supermode decomposition coefficient distribution analysis on the generated second-order frequency comb, so as to quantitatively evaluate its quantum compression characteristics and achieve efficient second-order frequency comb generation and accurate quantum multi-mode compression characteristic characterization.

[0055] In some embodiments of the present application, the second-order coupled mean field theoretical model in step S1 above, wherein the second-order coupled mean field equation is expressed as:

[0056]

[0057] Where a and b represent the time domain fields of semi-harmonic and pump, respectively, Δ represents detuning, Γ represents total loss, γ represents external loss, g0 represents the second-order nonlinear coefficient, and v f represents the free spectral range, L represents the cavity length, and B in represents the input pump amplitude, represents the partial derivative formula, i is the imaginary unit, * represents the conjugate of the complex number, k"1 and k"2 represent the group velocity dispersion of the semi-harmonic field and the pump field respectively, and Δk′ represents the walk-off. in represents the input pump amplitude.

[0058] In a preferred embodiment of the present application, the parameters of the second-order coupled mean field equation are set as follows: external loss γ = 4×10 8 rad / s, intrinsic loss μ=3.27×10 8 rad / s, group velocity dispersion k"1 of semi-harmonic field 1560nm and pump field 780nm = -0.0219ps 2 / m, k"2=0.3624ps 2 / m, walk-off Δk′=205.7ps / m, free spectral range vf =201.976GHz, the pump wavelength is 780nm, and the input pump amplitude is B in =1.9×10 8 V / m.

[0059] The second-order coupled mean field equation in the above embodiments of the present application can be solved by the split-step Fourier method, including: using the split-step Fourier method (solving the linear part of the equation in the frequency domain and the nonlinear part in the time domain) to perform time domain simulation, the initial excitation is set to Gaussian white noise, and the evolution process of the second-order frequency comb is simulated by uniformly scanning the detuning amount.

[0060] Specifically, in a preferred embodiment of the present application, the coupled equations are solved using the split-step Fourier method: the time evolution process is decomposed into two stages: linear propagation (including dispersion and loss) and nonlinear interaction. The iteration step size is set to 0.1 ps for each step, and the total evolution time is 700 ns. Gaussian white noise is used as the initial excitation to simulate the initial perturbation of spontaneous parametric down-conversion; by uniformly sweeping the detuning amount Δ (range -1×10 10 rad / s to 2.6×10 10 rad / s), record the time domain pulse shape and spectral distribution of the frequency comb under given detuning conditions (considering a total of 800×2 modes of pump and semi-harmonic fields). At this time, the time domain waveform is a periodically arranged soliton pulse, such as Figure 3 shown.

[0061] In some embodiments of the present application, the analytical Bloch-Messiah decomposition algorithm includes: performing similarity transformation and matrix decomposition on the system transmission matrix to obtain key parameters that characterize the quantum characteristics of the system, wherein the key parameters include the phase and amplitude distribution of the supermode decomposition coefficients and the compression degree information of the multimode compression. Specifically, the analytical Bloch-Messiah decomposition algorithm is used to transform the transmission matrix S after similarity transformation into x (ω) decomposes into , where U(ω) contains the phase and amplitude information of the supermode decomposition coefficients, and D(ω) contains the multimode compression degree information.

[0062] On the basis of the above, the time-domain numerical values ​​corresponding to the evolution process of the second-order frequency comb are substituted into the decomposition procedure of the analytical Bloch-Messiah decomposition algorithm to characterize the supermode decomposition coefficient distribution and multimode compression spectrum at different times, as well as the change curve of the multimode compression degree at zero Fourier frequency during the entire evolution process. According to the change of this curve, the multimode compression characteristics of the second-order frequency comb can be analyzed, and the quantum correlation and compression degree distribution between modes can be further quantitatively evaluated.

[0063] Figure 4The spectral distribution and supermode decomposition coefficients of the Turing mode and soliton crystal state of the second-order frequency comb were analyzed. The results show that both states exhibit strong multimode compression: the compression of the Turing mode reaches 21.01 dB, and the compression of the soliton crystal state reaches 37.06 dB. The supermode decomposition coefficient is primarily concentrated in the semi-harmonic field mode, and after the soliton crystal is formed, the maximum supermode decomposition coefficient shifts to the central semi-harmonic mode, reflecting the enhanced localization of the compression characteristics of this mode. To verify the collective nature of the multimode compression (i.e., the need to include all modes within the spectral band to avoid quantum correlation loss due to inter-mode coupling), the semi-harmonic field and the pump field are analyzed separately. Considering only the semi-harmonic field, significant compression is observed, even exceeding the global compression level in some scenarios. No significant compression is observed with the pump field alone. This is because the pump field, as a classical drive, cannot independently generate quantum compression, and ignoring the modes involved in the frequency doubling or sum frequency conversion would destroy the quantum nonlinear coupling required to maintain multimode entanglement.

[0064] Figure 5 Analysis of the evolution of multimode compression at zero Fourier frequency during a full detuning sweep reveals that, as shown in Figure (a) (detuning-compression characteristic distribution) and Figure (b) (frequency-compression response), in the Turing mode region, the compression exhibits an oscillation with detuning, consistent with the variation of intracavity power with detuning. When the detuning is excessive, the multimode compression disappears completely, indicating a disintegration of the soliton crystal structure. The multimode compression spectrum, extracted by analyzing the Bloch-Messiah decomposition, is characterized by two dominant peaks whose positions are sensitive to detuning. As the detuning increases, only a single isolated compression peak remains near zero Fourier frequency, a characteristic that differs significantly from the phenomenon in which the compression peak position remains essentially unchanged when the pump power is tuned.

[0065] The existing multi-mode compression characteristics of second-order frequency combs lack a unified analytical framework, making it difficult to quantify and evaluate the quantum correlation and compression distribution between modes. In addition, the control technology of dispersion and coupling engineering restricts the realization of ultra-wideband, high-compression multi-mode compressed states. This application solves these technical problems well. Figure 4 、 5 It can be seen that the quantum correlation distribution is Figure 4 The distribution of supermode decomposition coefficients of multimode compression is shown, and the quantization of quantum compression degree is Figure 5 In addition, through the dispersion coupling engineering of this application, ultra-wideband (i.e., compression of 1600 modes across the pump field and semi-harmonic field, 1560nm to 780nm) and high compression (over 30dB) are achieved.

[0066] The second-order frequency comb and multi-mode characteristic analysis method based on the lithium niobate microring resonator in the above-mentioned embodiment of this application is committed to providing a technical solution for efficiently generating a second-order frequency comb and accurately analyzing its multi-mode compression characteristics. The core of this method is to design a lithium niobate microring resonator that is suitable for the generation of a second-order frequency comb, and to give it an efficient nonlinear optical response by optimizing geometric parameters and material properties; relying on the resonant cavity structure, the generation and evolution of the second-order frequency comb is simulated; and then the analytical Bloch-Messiah decomposition method is used to perform multi-mode compression calculation and supermode decomposition coefficient distribution analysis on the generated second-order frequency comb, so as to quantitatively evaluate its quantum compression characteristics. This application lays a key technical foundation for the application of lithium niobate microring resonators in the fields of quantum optics, optical communications, etc.

[0067] In the description of the embodiments of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "bottom", "inside", "outside", "clockwise", "counterclockwise", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application.

[0068] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or to implicitly indicate the quantity of the technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features.

[0069] In the description of the embodiments of the present application, the meaning of "multiple" is two or more, unless otherwise clearly specified and specifically defined. In the present application, unless otherwise clearly specified and defined, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be a communication between the internal parts of two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to the specific circumstances.

[0070] In the embodiments of the present application, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to the process, method, product, or apparatus.

[0071] The above describes the specific embodiments of the present application. It should be understood that the present application is not limited to the specific embodiments described above, and those skilled in the art may make various modifications or variations within the scope of the claims, which do not affect the substantive content of the present application. The above preferred features may be used in any combination as long as they do not conflict with each other.

Claims

1. A microring resonator, characterized in that: The microring resonator comprises a nonlinear microring resonator made of a lithium niobate crystal film, wherein: The nonlinear microring resonance is based on the second-order nonlinear χ (2) , a cascaded second-order nonlinear process occurs in the resonant cavity structure, forming two sets of frequency combs: pump field and semi-harmonic field. There is a quantum multimode compression characteristic between these modes.

2. The microring resonator according to claim 1, characterized in that: The nonlinear microring resonator includes a nonlinear microring and a straight waveguide, and mode coupling occurs between the two in a coupling region. By optimizing the coupling relationship of the nonlinear microring resonator and the structures of the nonlinear microring and the straight waveguide, the dispersion relationship of the nonlinear microring resonator is changed, and the formation of soliton crystals is controlled.

3. The microring resonator according to claim 1, wherein: The lithium niobate crystal film is a z-cut lithium niobate film, the bottom of which is provided with a substrate consisting of a SiO2 layer, and the top is exposed to the air.

4. The microring resonator according to claim 3, characterized in that: The thickness of the lithium niobate crystal film is H = 0.6 μm, the width is W = 2 μm, the etching depth is h = 0.41 μm, and the etching angle is θ = 75°; the radius of the nonlinear microring is R = 100 μm, the spacing between the nonlinear microring and the straight waveguide is gap = 0.49 μm, and the coupling ratio is r = 1.

222.

5. A multimode compression analysis method based on the second-order frequency comb of lithium niobate microring resonator, characterized in that: include: Constructing a second-order frequency comb generation model based on a MATLAB simulation environment for simulating and characterizing the evolution of a second-order frequency comb based on the structure of the microring resonator according to any one of claims 1 to 4, wherein the simulation uses a second-order coupled mean-field theory model including the interaction between a pump field and a semi-harmonic field; The analytical Bloch-Messiah decomposition algorithm is used to calculate the multi-mode compression degree and analyze the distribution of supermode decomposition coefficients of the generated second-order frequency comb, in order to quantitatively evaluate the quantum compression characteristics and mode coupling laws of the frequency comb.

6. The multi-mode compression analysis method based on the second-order frequency comb of the lithium niobate microring resonator according to claim 5 is characterized in that: The second-order coupled mean field theoretical model, wherein the second-order coupled mean field equation is expressed as: Where a and b represent the time domain fields of semi-harmonic and pump, respectively, Δ represents detuning, Γ represents total loss, γ represents external loss, g0 represents the second-order nonlinear coefficient, and v f represents the free spectral range, L represents the cavity length, and B in represents the input pump amplitude, represents the partial derivative formula, i is the imaginary unit, * represents the conjugate of the complex number, k"1 and k"2 represent the group velocity dispersion of the semi-harmonic field and the pump field respectively, B in represents the input pump amplitude, and Δk′ represents the walkoff.

7. The multi-mode compression analysis method based on the second-order frequency comb of the lithium niobate microring resonator according to claim 6 is characterized in that: The second-order coupled mean-field equation is solved using the split-step Fourier method, including: The time domain simulation is performed using the split-step Fourier method. The initial excitation is set to Gaussian white noise. The evolution of the second-order frequency comb is simulated by uniformly sweeping the detuning amount.

8. The multi-mode compression analysis method based on the second-order frequency comb of the lithium niobate microring resonator according to claim 5 is characterized in that: The analytical Bloch-Messiah decomposition algorithm comprises: The system transmission matrix is ​​subjected to similarity transformation and matrix decomposition to obtain key parameters characterizing the quantum characteristics of the system, including the phase and amplitude distribution of the supermode decomposition coefficients and the compression degree information of the multimode compression.

9. The multi-mode compression analysis method based on the second-order frequency comb of the lithium niobate microring resonator according to claim 8, characterized in that: The analytic Bloch-Messiah decomposition algorithm, wherein: The time-domain numerical values ​​corresponding to the evolution process of the second-order frequency comb are substituted into the decomposition procedure of the analytical Bloch-Messiah decomposition algorithm to characterize the supermode decomposition coefficient distribution and multimode compression spectrum at different times, as well as the change curve of the multimode compression degree at zero Fourier frequency during the entire evolution process.

10. The multi-mode compression analysis method based on the second-order frequency comb of lithium niobate microring resonator according to claim 5, characterized in that: The quantitative evaluation of the quantum compression properties of the frequency comb includes: The time-domain pulse morphology and spectral distribution of the frequency comb under different detuning conditions are recorded, and the changes in the multi-mode compression degree at zero Fourier frequency during the evolution of the frequency comb are observed to evaluate the quantum compression characteristics.

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