A design method for a highly sensitive micro-optical gyroscope based on high-order non-Hermitian singular characteristics

Abstract

The present invention is a design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics. The present invention belongs to the field of optical gyroscopes. The present invention uses asymmetric coupling between an inverted 8-shaped resonant cavity and a straight waveguide to adjust a second-order PT symmetric system from a second-order non-Hermitian system to a fourth-order non-Hermitian system without increasing the number of control parameters; and uses a highly sensitive π-phase-shifted Bragg grating to cause coupling between back-propagating light modes, thereby realizing nonlinear output of the Sagnac effect. The present invention can ensure that the optical gyroscope has extremely high sensitivity while meeting the requirements of micro volume.

Description

Technical Field

[0001] The invention belongs to the field of optical gyroscopes and is a design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics. Background Art

[0002] Gyroscopes play a key role in inertial navigation systems and have a wide range of applications in both commercial and military fields. The development of consumer smart devices, micro-drones and micro-satellites has highlighted the huge demand for highly accurate, compact and integrated optical gyroscopes, and a large amount of research is currently devoted to the development of chip-scale optical gyroscopes. Resonant micro-optical gyroscopes (RMOGs) feature a small ring resonator or chip-based configuration, and their accuracy is independent of the ring length. Therefore, RMOGs have become the preferred solution for integrated optical gyroscopes. However, in traditional RMOGs, the resonance splitting caused by the Sagnac effect is directly related to the linear size of the device, resulting in unsatisfactory accuracy levels. For example, an RMOG with a radius of 5 mm, a wavelength of 1.55 μm, and a rotation speed of about 1° / h has a Sagnac frequency splitting of about 0.02 Hz, while many practical applications require the measurement of angular velocities in the range of 0.1–100° / h. In a fully integrated optical platform, the area of ​​the loop is usually smaller, which may be several orders of magnitude smaller, so achieving such a sensitivity level in a fully integrated optical platform faces great challenges.

[0003] Since the pioneering work of Bender et al., there has been great interest in singular points (EP) in non-Hermitian systems, especially for sensor applications. Bender et al. demonstrated a special form of non-Hermitian Hamiltonian that exhibits real eigenvalues ​​under the joint manipulation of parity (P) and time (T) operators. The EP is an interesting property of these parity-time (PT) symmetric systems, where the eigenvalues ​​of the system and their corresponding eigenvectors are simultaneously degenerate. The strong spectral response of the eigenvalues ​​near the EP has inspired many research works for sensing applications.

[0004] In a non-Hermitian system of order 2×2 operating at the EP, the splitting of the eigenvalues ​​is proportional to the square root of the applied perturbation, and thus the system shows enhanced sensitivity to small perturbations. In general, higher-order EPs are expected to achieve substantial enhancements in light-matter interactions beyond existing fundamental limits, a feature that makes them particularly attractive. Specifically, for an N-order EP (EP) consisting of N distinct eigenvalues ​​and associated eigenstates, N ), when a disturbance of magnitude ε acts on the system, its response is However, implementing high-order EP in existing schemes is a rather difficult task due to the complexity and sensitivity of manufacturing defects. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics. First, by constructing an inverted 8-shaped resonant cavity, the asymmetric coupling of the resonant cavity is used to expand the second-order non-Hermitian system to a fourth-order system without increasing the difficulty of parameter control; then, by embedding a π-phase-shifted Bragg grating in the inverted 8-shaped resonant cavity, a high-sensitivity Sagnac effect output is achieved. Based on this, the present invention provides a high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics.

[0006] The present invention provides a design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics. The present invention provides the following technical solutions:

[0007] A high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that the high-sensitivity micro-optical gyroscope comprises: a laser, an active inverted 8-shaped resonant cavity, a passive inverted 8-shaped resonant cavity, a first coupler, a second coupler, a straight waveguide, a π-phase-shifted Bragg grating, and a photodetector;

[0008] The laser is coupled to the left lobe of the active inverted 8-shaped resonant cavity through a straight waveguide via a first coupler, and then coupled to the right lobe of the active inverted 8-shaped resonant cavity through a second coupler;

[0009] The passive inverted 8-shaped resonant cavity is directly coupled to the active inverted 8-shaped resonant cavity;

[0010] The photoelectric detector is connected to the active inverted 8-shaped resonant cavity through a straight waveguide.

[0011] A design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics comprises the following steps:

[0012] Step 1: Construct a parity-time PT symmetric system;

[0013] Step 2: Based on the parity-time PT symmetric system, use a straight waveguide to adjust the second-order system to a fourth-order system;

[0014] Step 3: By adjusting the gain / loss value of the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity and the coupling coefficient between the two, the imaginary part of their eigenvalues ​​is degenerated, thereby adjusting the system in step 2 to the EP point in the non-Hermitian system;

[0015] Step 4: embed the π-phase-shifted Bragg grating into the active inverted 8-shaped resonant cavity to achieve the nonlinear output of the gyro Sagnac effect;

[0016] Step 5: Calculate the sensitivity improvement factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics compared with the traditional gyroscope.

[0017] Preferably, the step 1 is specifically:

[0018] The active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity have exactly the same shape, and both are composed of two asymmetric lobes connected together by cross-connection. A PT symmetric system is constructed by direct coupling between the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity.

[0019] Preferably, the step 2 is specifically:

[0020] Both lobes of the active inverted 8-shaped resonator are coupled to the straight waveguide, and the two coupling ratios between the lobe and the straight waveguide are μ L and μ R , through the two coupling excitations with the straight waveguide, there are four transmission modes in the two coupled resonant cavities. In the case of only two resonant cavities, the second-order system is adjusted to a fourth-order system by utilizing the two couplings between the straight waveguide and the inverted 8-shaped resonant cavity.

[0021] Preferably, the step 3 is specifically:

[0022] The dynamic equation of the system is obtained through time coupling theory:

[0023]

[0024] Among them, ω0 is the resonant frequency of the two inverted 8-shaped resonant cavities, κ0 is the direct coupling rate of the two inverted 8-shaped resonant cavities, and γ G is the gain rate of the active inverted 8-shaped resonant cavity, γ L is the loss rate of the passive inverted 8-shaped resonant cavity, It represents the phase obtained when the optical mode propagates between the two lobes of the active inverted 8-shaped resonant cavity.

[0025] The characteristic frequency of the system can be obtained from formula (1), which is expressed as:

[0026]

[0027] Among them, γ1=(γ G +μ R +μ L ) / 2,γ2=γ L / 2, κ EP =(γ2-γ1) / 2 represents the coupling coefficient that adjusts the system to the EP. At the EP, all four eigenfrequencies and their corresponding eigenvectors are degenerate simultaneously.

[0028] Preferably, the step 4 is specifically:

[0029] When an angular velocity Ω acts on the system in the CW direction, the π-phase-shifted Bragg grating will cause mutual coupling between the counter-propagating modes in the resonant cavity, and its perturbation Hamiltonian H Ω It can be expressed as:

[0030]

[0031] Among them, Δω s is the Sagnac phase shift related to the rotation speed, so the reverse mode coupling coefficient ε(Δω) caused by the π-phase-shifted Bragg grating s ) is a coefficient related to the rotation speed;

[0032] When the angular velocity Ω is small enough, that is, Δω s <<ε(Δω s ), then the eigenfrequency splitting can be expressed as Δω EP =2e -iπ / 4 κ1 1 / 4 κ EP 1 / 2 ε(Δω s ) 1 / 4 , showing the fourth root relationship between frequency splitting and rotation speed.

[0033] Preferably, the step 5 is specifically:

[0034] The Sagnac scale factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics is expressed as follows:

[0035]

[0036] Among them, 2πR / (n eff λ) is the Sagnac scale factor of the conventional gyroscope, and the Sagnac scale factor of a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singularity is enhanced by a factor of 2e -iπ / 4 κ EP 1 / 2 κ1 1 / 4 [c / (n eff l)] 1 / 4 r g -3 / 4 Depends on the coupling ratio κ1 and the reflection amplitude r of the π-phase-shifted Bragg grating g , reflection amplitude r g Determined by the structural parameters of the π-phase-shifted Bragg grating.

[0037] Preferably, the sensitivity of the micro-optical gyroscope based on high-order non-Hermitian singular characteristics can be improved by several orders of magnitude by using a high-sensitivity π-phase-shifted Bragg grating.

[0038] A computer-readable storage medium stores a computer program, which is executed by a processor to implement a design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics.

[0039] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics is implemented.

[0040] The present invention has the following beneficial effects:

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] The present invention utilizes the asymmetric coupling of the inverted 8-shaped resonant cavity and the straight waveguide to adjust the second-order PT symmetric system from a second-order non-Hermitian system to a fourth-order non-Hermitian system without increasing the number of control parameters; and uses a highly sensitive π-phase-shifted Bragg grating to induce coupling between back-propagating light modes, thereby realizing the nonlinear output of the Sagnac effect. The present invention can ensure that the optical gyroscope has extremely high sensitivity while meeting the requirements of micro volume. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0044] Figure 1 It is a schematic diagram of the structure of the micro-optical gyroscope of the present invention;

[0045] Figure 2 is a schematic diagram of a π-phase-shifted Bragg grating used for angular velocity detection;

[0046] Figure 3 This is a graph showing the sensitivity improvement compared to traditional gyroscopes. DETAILED DESCRIPTION

[0047] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying 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 limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0049] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" 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 it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0050] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0051] The present invention is described in detail below in conjunction with specific embodiments. Specific embodiment one:

[0053] according to Figures 1 to 3 As shown, the specific optimization technical solution adopted by the present invention to solve the above technical problems is: the present invention relates to a design method of a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics.

[0054] A high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that the high-sensitivity micro-optical gyroscope comprises: a laser, an active inverted 8-shaped resonant cavity 1, a passive inverted 8-shaped resonant cavity 2, a first coupler 3, a second coupler 4, a straight waveguide 6, a π-phase-shifted Bragg grating 5, and a photodetector;

[0055] The laser is coupled to the left lobe of the active inverted 8-shaped resonant cavity 1 through the straight waveguide 6 via the first coupler 3, and then coupled to the right lobe of the active inverted 8-shaped resonant cavity 1 through the second coupler 4;

[0056] The passive inverted 8-shaped resonant cavity 2 is directly coupled to the active inverted 8-shaped resonant cavity 1;

[0057] The photodetector is connected to the active inverted-8-shaped resonant cavity 1 via a straight waveguide 6 .

[0058] The present invention is composed of a laser, an active inverted 8-shaped resonant cavity, a passive inverted 8-shaped resonant cavity, a straight waveguide, a coupler, a π-phase-shifted Bragg grating, and a photodetector. By designing the resonant cavity into an inverted 8-shaped structure and coupling it twice to a bus straight waveguide, a second-order non-Hermitian system can be modulated into a fourth-order non-Hermitian system without increasing the difficulty of system manufacturing; by adjusting the gain / loss values ​​of two inverted 8-shaped resonant cavities and the coupling coefficient between the two resonant cavities, the fourth-order non-Hermitian system can be adjusted to the vicinity of a singular point (EP), and a sensor at the EP can show extremely high sensitivity to external disturbances, and the higher the system order, the greater the sensitivity enhancement; by embedding a π-phase-shifted Bragg grating in an inverted 8-shaped resonant cavity, the nonlinear output of the system to angular velocity can be achieved, and high-sensitivity detection of a gyroscope can be achieved. Specific embodiment 2:

[0060] The difference between the second embodiment of the present invention and the first embodiment is that:

[0061] The present invention provides a design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, comprising the following steps:

[0062] Step 1: Construct a parity-time PT symmetric system;

[0063] Step 2: Based on the parity-time PT symmetric system, use a straight waveguide to adjust the second-order system to a fourth-order system;

[0064] Step 3: By adjusting the gain / loss value of the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity and the coupling coefficient between the two, the imaginary part of their eigenvalues ​​is degenerated, thereby adjusting the system in step 2 to the EP point in the non-Hermitian system;

[0065] Step 4: embed the π-phase-shifted Bragg grating into the active inverted 8-shaped resonant cavity to achieve the nonlinear output of the gyro Sagnac effect;

[0066] Step 5: Calculate the sensitivity improvement factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics compared with the traditional gyroscope. Specific embodiment three:

[0068] The difference between the third embodiment of the present invention and the second embodiment is that:

[0069] The step 1 is specifically as follows:

[0070] The active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity have exactly the same shape, and both are composed of two asymmetric lobes connected together by cross-connection. A PT symmetric system is constructed by direct coupling between the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity. Specific embodiment four:

[0072] The difference between the fourth embodiment of the present invention and the third embodiment is that:

[0073] The step 2 is specifically as follows:

[0074] Both lobes of the active inverted 8-shaped resonator are coupled to the straight waveguide, and the two coupling ratios between the lobe and the straight waveguide are μ L and μ R , through the two coupling excitations with the straight waveguide, there are four transmission modes in the two coupled resonant cavities. In the case of only two resonant cavities, the second-order system is adjusted to a fourth-order system by utilizing the two couplings between the straight waveguide and the inverted 8-shaped resonant cavity. Specific embodiment five:

[0076] The difference between the fifth embodiment of the present invention and the fourth embodiment is that:

[0077] Preferably, the step 3 is specifically:

[0078] The dynamic equation of the system is obtained through time coupling theory:

[0079]

[0080]

[0081]

[0082]

[0083] Among them, ω0 is the resonance frequency of the two inverted 8-shaped resonant cavities, κ0 is the direct coupling rate of the two inverted 8-shaped resonant cavities, γG is the gain rate of the active inverted 8-shaped resonant cavity, γL is the loss rate of the passive inverted 8-shaped resonant cavity, and φ represents the phase obtained by the optical mode propagating between the two lobes of the active inverted 8-shaped resonant cavity.

[0084] The characteristic frequency of the system can be obtained from formula (1), which is expressed as:

[0085]

[0086] Among them, γ1=(γ G +μ R +μ L ) / 2,γ2=γ L / 2, κ EP =(γ2-γ1) / 2 represents the coupling coefficient that adjusts the system to the EP. At the EP, all four eigenfrequencies and their corresponding eigenvectors are degenerate simultaneously. Specific embodiment six:

[0088] The difference between the sixth embodiment of the present invention and the fifth embodiment is that:

[0089] The step 4 is specifically as follows:

[0090] When an angular velocity Ω acts on the system in the CW direction, the π-phase-shifted Bragg grating will cause mutual coupling between the counter-propagating modes in the resonant cavity, and its perturbation Hamiltonian H Ω It can be expressed as:

[0091]

[0092] Among them, Δω s is the Sagnac phase shift related to the rotation speed, so the reverse mode coupling coefficient ε(Δω) caused by the π-phase-shifted Bragg grating s ) is a coefficient related to the rotation speed;

[0093] When the angular velocity Ω is small enough, that is, Δω s <<ε(Δω s ), then the eigenfrequency splitting can be expressed as Δω EP =2e -iπ / 4 κ1 1 / 4 κ EP 1 / 2 ε(Δω s ) 1 / 4 , showing the fourth root relationship between frequency splitting and rotation speed. Specific embodiment seven:

[0095] The difference between the seventh embodiment of the present invention and the sixth embodiment is that:

[0096] The step 5 is specifically as follows:

[0097] The Sagnac scale factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics is expressed as follows:

[0098]

[0099] Among them, 2πR / (n eff λ) is the Sagnac scale factor of the conventional gyroscope, and the Sagnac scale factor of a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singularity is enhanced by a factor of 2e -iπ / 4 κ EP 1 / 2 κ1 1 / 4 [c / (n eff l)] 1 / 4 r g -3 / 4 Depends on the coupling ratio κ1 and the reflection amplitude r of the π-phase-shifted Bragg grating g , reflection amplitude r g Determined by the structural parameters of the π-phase-shifted Bragg grating. Specific embodiment eight:

[0101] The difference between the eighth embodiment of the present invention and the seventh embodiment is that:

[0102] The sensitivity of micro-optical gyroscopes based on high-order non-Hermitian singular properties can be improved by several orders of magnitude by using highly sensitive π-phase-shifted Bragg gratings. Specific embodiment nine:

[0104] The difference between the ninth embodiment of the present invention and the eighth embodiment is that:

[0105] The present invention provides a computer-readable storage medium on which a computer program is stored. The program is executed by a processor to implement a design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics.

[0106] A design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics comprises the following steps:

[0107] Step 1: Construct a parity-time PT symmetric system;

[0108] Step 2: Based on the parity-time PT symmetric system, use a straight waveguide to adjust the second-order system to a fourth-order system;

[0109] Step 3: By adjusting the gain / loss value of the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity and the coupling coefficient between the two, the imaginary part of their eigenvalues ​​is degenerated, thereby adjusting the system in step 2 to the EP point in the non-Hermitian system;

[0110] Step 4: embed the π-phase-shifted Bragg grating into the active inverted 8-shaped resonant cavity to achieve the nonlinear output of the gyro Sagnac effect;

[0111] Step 5: Calculate the sensitivity improvement factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics compared with the traditional gyroscope. Specific embodiment ten:

[0113] The difference between the tenth embodiment of the present invention and the ninth embodiment is that:

[0114] The present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics is implemented.

[0115] A design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics comprises the following steps:

[0116] Step 1: Construct a parity-time PT symmetric system;

[0117] Step 2: Based on the parity-time PT symmetric system, use a straight waveguide to adjust the second-order system to a fourth-order system;

[0118] Step 3: By adjusting the gain / loss value of the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity and the coupling coefficient between the two, the imaginary part of their eigenvalues ​​is degenerated, thereby adjusting the system in step 2 to the EP point in the non-Hermitian system;

[0119] Step 4: embed the π-phase-shifted Bragg grating into the active inverted 8-shaped resonant cavity to achieve the nonlinear output of the gyro Sagnac effect;

[0120] Step 5: Calculate the sensitivity improvement factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics compared with the traditional gyroscope. Specific embodiment eleven:

[0122] A high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics The high-sensitivity micro-optical gyroscope comprises: a laser, an active inverted 8-shaped resonant cavity, a passive inverted 8-shaped resonant cavity, a coupler, a coupler, a straight waveguide, a π-phase-shifted Bragg grating, and a photodetector;

[0123] The laser is coupled to the left lobe of the active inverted 8-shaped resonant cavity through a straight waveguide via a coupler, and then coupled to the right lobe of the active inverted 8-shaped resonant cavity through a coupler;

[0124] The passive inverted 8-shaped resonant cavity is directly coupled to the active inverted 8-shaped resonant cavity;

[0125] The photoelectric detector is connected to the active inverted 8-shaped resonant cavity through a straight waveguide.

[0126] A high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics, the design method comprising the following steps:

[0127] Step 1: Construct a parity-time (PT) symmetric system;

[0128] Step 2: Based on step 1, use a straight waveguide to adjust the second-order system to a fourth-order system;

[0129] Step 3: By adjusting the gain / loss value of the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity and the coupling coefficient between the two, the imaginary part of their eigenvalues ​​is degenerated, thereby adjusting the system in step 2 to the EP point in the non-Hermitian system;

[0130] Step 4: Based on the system structure of step 3, the π-phase-shifted Bragg grating is embedded in the active inverted 8-shaped resonant cavity to realize the nonlinear output of the gyro Sagnac effect;

[0131] Step 5: Based on step 4, calculate the sensitivity improvement factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics compared with the traditional gyroscope;

[0132] A method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that the step 1 is specifically as follows: Figure 1 As shown in the figure, the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity have exactly the same shape, and are both connected by two asymmetric lobes through a cross. The cross is ideal, and the light mode can only pass through it in a straight line, and no other modes are excited in the cross waveguide. The PT symmetric system is constructed by direct coupling between the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity.

[0133] A method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that the step 2 is specifically as shown in step 1, both lobes of the active inverted 8-shaped resonant cavity are coupled to a straight waveguide, and the two coupling rates between the lobes and the straight waveguide are μL and μR respectively. Like the traditional ring resonator, the inverted 8-shaped resonant cavity also supports two counter-propagating optical modes α and β. The characteristic of α is that whenever it passes near the area coupled with the straight waveguide, it points to the center of the resonant cavity, that is, to the intersection of the two lobes, while the latter propagation mode β passes through the inverted 8-shaped resonant cavity in the opposite direction. The two modes interact differently with the straight waveguide. When the optical signal is coupled to the straight waveguide, α is excited first, and then β is excited, and it is independent of the excitation direction. Only α can transfer energy to β through the straight waveguide. When α is coupled to the straight waveguide, it propagates to another coupling area and excites β; on the contrary, when β is coupled to the straight waveguide, it can only propagate outward from the inverted 8-shaped resonant cavity. Therefore, the coupling coefficient connecting α to β is not equal to zero, while the coupling coefficient connecting β to α is equal to zero. Through the two coupling excitations with the straight waveguide, there are four transmission modes in the two coupled resonant cavities. Therefore, in the case of only two resonant cavities, the second-order system is adjusted to a fourth-order system by utilizing the two couplings between the straight waveguide and the inverted 8-shaped resonant cavity.

[0134] A high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics, characterized in that the step 3 specifically comprises obtaining the dynamic equation of the system through time coupling theory:

[0135]

[0136]

[0137]

[0138]

[0139] Where ω0 is the resonance frequency of the two inverted-8-shaped resonant cavities, κ0 is the direct coupling rate of the two inverted-8-shaped resonant cavities, γG is the gain rate of the active inverted-8-shaped resonant cavity, γL is the loss rate of the passive inverted-8-shaped resonant cavity, and φ represents the phase obtained by the optical mode propagating between the two lobes of the active inverted-8-shaped resonant cavity.

[0140] The characteristic frequency of the system can be obtained from formula (1), which is expressed as:

[0141]

[0142] Where γ1=(γ G +μ R +μ L ) / 2,γ2=γ L / 2, κ EP =(γ2-γ1) / 2 represents the coupling coefficient that adjusts the system to the EP. At the EP, all four eigenfrequencies and their corresponding eigenvectors are degenerate simultaneously.

[0143] A method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that the step 4 is specifically as follows: Figure 2 As shown in the figure, the π-phase-shifted Bragg grating is embedded in the active inverted 8-shaped resonant cavity. When the angular velocity Ω (CW direction) acts on the system, the π-phase-shifted Bragg grating will cause mutual coupling of the counter-propagating modes in the resonant cavity, and its perturbation Hamiltonian HΩ can be expressed as:

[0144]

[0145] Where Δωs is the Sagnac phase shift related to the rotation speed, so the reverse mode coupling coefficient ε(Δωs) caused by the π-phase-shifted Bragg grating is a coefficient related to the rotation speed. Assuming that the angular velocity Ω is small enough, that is, Δωs<<ε(Δωs), the eigenfrequency splitting can be expressed as Δω EP =2e -iπ / 4 κ1 1 / 4 κ EP 1 / 2 ε(Δω s ) 1 / 4 , showing the fourth root relationship between frequency splitting and rotation speed.

[0146] A method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that the step 5 is specifically that the scale factor of the gyroscope is related to its sensitivity. By convention, it is defined as the derivative of the intrinsic frequency splitting with respect to the rotation rate Ω. Therefore, the Sagnac scale factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics can be expressed as:

[0147]

[0148] Where 2πR / (neffλ) is the Sagnac scale factor of the conventional gyroscope. Therefore, compared with the conventional resonant gyroscope, the Sagnac scale factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics is enhanced by a factor of 2e -iπ / 4 κ EP 1 / 2 κ1 1 / 4 [c / (n eff l)] 1 / 4 r g -3 / 4 It depends on the coupling rate κ1 and the reflection amplitude rg of the π-phase-shifted Bragg grating, which is determined by the structural parameters of the π-phase-shifted Bragg grating. Figure 3 As shown, the sensitivity of the micro-optical gyroscope based on high-order non-Hermitian singular characteristics can be improved by 8 orders of magnitude by using a highly sensitive π-phase-shifted Bragg grating.

[0149] In the description of this specification, the description of reference terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples without contradiction. In addition, the terms "first" and "second" are used only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" can explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined. Any process or method description in the flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code including one or more executable instructions for implementing the steps of a custom logic function or process, and the scope of the preferred embodiment of the present invention includes other implementations, in which the functions may not be performed in the order shown or discussed, including in a substantially simultaneous manner or in a reverse order according to the functions involved, which should be understood by a person skilled in the art of the art to which the embodiments of the present invention belong. The logic and / or steps represented in the flowchart or otherwise described herein, for example, may be considered as a sequenced list of executable instructions for implementing the logic function, and may be specifically implemented in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" may be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection having one or N wirings (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM).In addition, the computer readable medium can even be paper or other suitable medium on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, then editing, interpreting or processing in other suitable ways as necessary, and then storing it in a computer memory. It should be understood that the various parts of the present invention can be implemented with hardware, software, firmware, or a combination thereof. In the above-mentioned embodiment, N steps or methods can be implemented with software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented with hardware, as in another embodiment, any one of the following technologies known in the art or their combination can be used to implement: a discrete logic circuit with a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit with a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0150] The above is only a preferred implementation of a high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics. The protection scope of a high-sensitivity micro-optical gyroscope design method based on high-order non-Hermitian singular characteristics is not limited to the above embodiments. All technical solutions under this idea belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, several improvements and changes without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that: The high-sensitivity micro-optical gyroscope comprises: a laser, an active inverted 8-shaped resonant cavity, a passive inverted 8-shaped resonant cavity, a first coupler, a second coupler, a straight waveguide, a π-phase-shifted Bragg grating, and a photodetector; The laser is coupled to the left lobe of the active inverted 8-shaped resonant cavity through a straight waveguide via a first coupler, and then coupled to the right lobe of the active inverted 8-shaped resonant cavity through a second coupler; The passive inverted 8-shaped resonant cavity is directly coupled to the active inverted 8-shaped resonant cavity; The photoelectric detector is connected to the active inverted 8-shaped resonant cavity through a straight waveguide.

2. A design method for a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics, characterized in that: The following steps are involved: Step 1: Construct a parity-time PT symmetric system; Step 2: Based on the parity-time PT symmetric system, use a straight waveguide to adjust the second-order system to a fourth-order system; Step 3: By adjusting the gain and loss values ​​of the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity and the coupling coefficient between the two, the imaginary parts of their eigenvalues ​​are degenerated, thereby adjusting the system in step 2 to the EP point in the non-Hermitian system; Step 4: embed the π-phase-shifted Bragg grating into the active inverted 8-shaped resonant cavity to achieve the nonlinear output of the gyro Sagnac effect; Step 5: Calculate the sensitivity improvement factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics compared with the traditional gyroscope.

3. The method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics according to claim 2, characterized in that: The step 1 is specifically as follows: The active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity have exactly the same shape, and both are composed of two asymmetric lobes connected together by cross-connection. A PT symmetric system is constructed by direct coupling between the active inverted 8-shaped resonant cavity and the passive inverted 8-shaped resonant cavity.

4. The method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics according to claim 3, characterized in that: The step 2 is specifically as follows: Both lobes of the active inverted 8-shaped resonator are coupled to the straight waveguide, and the two coupling ratios between the lobe and the straight waveguide are μ L and μ R , through the two coupling excitations with the straight waveguide, there are four transmission modes in the two coupled resonant cavities. In the case of only two resonant cavities, the second-order system is adjusted to a fourth-order system by utilizing the two couplings between the straight waveguide and the inverted 8-shaped resonant cavity.

5. The method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics according to claim 4, characterized in that: The step 3 is specifically as follows: The dynamic equation of the system is obtained through time coupling theory: Among them, ω0 is the resonant frequency of the two inverted 8-shaped resonant cavities, κ0 is the direct coupling rate of the two inverted 8-shaped resonant cavities, and γ G is the gain rate of the active inverted 8-shaped resonant cavity, γ L is the loss rate of the passive inverted 8-shaped resonant cavity, represents the phase obtained by the optical mode propagating between the two lobes of the active inverted 8-shaped resonant cavity; The characteristic frequency of the system can be obtained from formula (1), which is expressed as: Among them, γ1=(γ G +μ R +μ L ) / 2,γ2=γ L / 2 represents the coupling coefficient that adjusts the system to the EP, where all four eigenfrequencies and their corresponding eigenvectors degenerate simultaneously.

6. The method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics according to claim 5, characterized in that: The step 4 is specifically as follows: When an angular velocity Ω acts on the system in the CW direction, the π-phase-shifted Bragg grating will cause mutual coupling between the counter-propagating modes in the resonant cavity, and its perturbation Hamiltonian H Ω It can be expressed as: Among them, Δω s is the Sagnac phase shift related to the rotation speed, so the reverse mode coupling coefficient ε(Δω) caused by the π-phase-shifted Bragg grating s ) is a coefficient related to the rotation speed; When the angular velocity Ω is small enough, that is, Δω s <<ε(Δω s ), then the eigenfrequency splitting can be expressed as Δω EP =2e -iπ / 4 κ1 1 / 4 κ EP 1 / 2 ε(Δω s ) 1 / 4 , showing the relationship between frequency splitting and the fourth root of rotation speed, κ EP =(γ2-γ1) / 2.

7. The method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics according to claim 6, characterized in that: The step 5 is specifically as follows: The Sagnac scale factor of the high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics is expressed as follows: Among them, 2πR / (n eff λ) is the Sagnac scale factor of the conventional gyroscope, an enhancement factor of the Sagnac scale factor of a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singularity 2e -iπ / 4 κ EP 1 / 2 κ1 1 / 4 [c / (n eff l)] 1 / 4 r g -3 / 4 Depends on the coupling ratio κ1 and the reflection amplitude r of the π-phase-shifted Bragg grating g , reflection amplitude r g Determined by the structural parameters of the π-phase-shifted Bragg grating.

8. The method for designing a high-sensitivity micro-optical gyroscope based on high-order non-Hermitian singular characteristics according to claim 7, characterized in that: The sensitivity of micro-optical gyroscopes based on high-order non-Hermitian singular properties can be improved by several orders of magnitude by using highly sensitive π-phase-shifted Bragg gratings.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the method according to claims 2-8.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method of claims 2-8 is implemented.

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