A high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure and a design method thereof

Abstract

The application belongs to the field of optical gyroscopes, and particularly relates to a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure and a design method thereof. The gyroscope is composed of a laser, a ring cavity, an S-shaped waveguide, a coupler and a photodetector. An active S-shaped waveguide and a passive S-shaped waveguide are coupled in the ring cavity. By adjusting the gain / loss value in the active / passive waveguide and the coupling coefficient of the coupler, the system can be adjusted to be near an exceptional point (EP). The gyroscope system at the EP can exhibit extremely high sensitivity to rotation speed. The ring cavity works below the laser threshold, and a power detection technology is used to measure the sensitivity of the gyroscope. Through the technology, the signal-to-noise ratio of the gyroscope can be accurately measured. In addition, by coupling two counter-propagating modes in the same optical resonator, instead of coupling two coupled modes in the double-resonator in the traditional scheme, the area can be reduced by 3 / 4, and the non-reciprocity error caused by the influence of different disturbance sources on the two resonant cavities in the general PT symmetric gyroscope can be suppressed.

Description

Technical Field

[0001] This invention belongs to the field of optical gyroscopes, specifically relating to a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure and its design method. Background Technology

[0002] Optical gyroscopes based on the Sagnac effect are central to inertial navigation systems and are widely used in commercial and military fields. Driven by smart devices, micro-drones, and microsatellites, high-precision, miniaturized, and integrated gyroscopes have received considerable attention. Since the advent of integrated optics for communication, resonant micro-optical gyroscopes (RMOGs) with small ring resonators or even chip resonators have been identified as the preferred solution. Currently, RMOGs have become ideal candidates for next-generation optical gyroscopes because their accuracy is independent of the ring cavity length. However, traditional RMOGs are sensitive to optical noise, and the frequency shift caused by the Sagnac effect is linearly proportional to the rotational speed, which prevents the desired accuracy from being achieved.

[0003] Singularities (EPs) based on parity-time (PT) symmetry in non-Hermitian systems show significant potential for improving sensitivity to external perturbations. At an EP, two or more eigenvalues ​​and their corresponding eigenstates merge and degenerate simultaneously. Theoretical and experimental studies on various non-Hermitian platforms have demonstrated superior physical properties in classical and quantum systems near EPs, particularly enhanced eigenfrequency splitting to small perturbations. However, recent studies have shown that the signal-to-noise ratio (SNR) of EP-based sensors is not improved. Currently, EP-based micro-optical laser gyroscopes detect angular velocity by measuring laser beat frequency signals, but excessive quantum noise generated by the non-orthogonality of laser modes causes the laser linewidth broadening to precisely compensate for the frequency splitting, thus failing to improve the SNR of the micro-optical laser gyroscope. Summary of the Invention

[0004] This invention provides a high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure and its design method, which improves the sensitivity and detection accuracy of the optical gyroscope and suppresses the non-dissimilarity error caused by the two resonant cavities being affected by different differential disturbance sources in a general PT-symmetric gyroscope.

[0005] This invention is achieved through the following technical solution:

[0006] A design method for a high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, the design method comprising the following steps:

[0007] Step 1: Construct a PT-symmetric system;

[0008] Step 2: Adjust the system from Step 1 to point EP and write the dynamic equations of the system;

[0009] Step 3: Solve for the characteristic frequencies of the system based on the dynamic equations from Step 2;

[0010] Step 4: Based on the characteristic frequencies of the system in Step 3, find the power transfer spectrum of the PT-symmetric single-ring resonator;

[0011] Step 5: Evaluate the performance of the EP sensor based on the power transfer spectrum obtained in Step 4.

[0012] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 1 specifically involves connecting an S-shaped active waveguide Sa to the ring cavity 2 via couplers C1 and C3, and an S-shaped passive waveguide S... b A PT-symmetric system is constructed by connecting it to the annular cavity 2 via couplers C2 and C4.

[0013] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 2 specifically involves adjusting the S-shaped active waveguide S based on the constructed PT-symmetric system. a The gain value and the coupling coefficients of couplers C1, C2, C3, and C4 will adjust the system to the EP point;

[0014] Or, based on the constructed PT-symmetric system, by adjusting the S-shaped passive waveguide S... b The loss value and the coupling coefficients of couplers C1, C2, C3, and C4 will adjust the system to the EP point;

[0015] The dynamic equations of the system can be derived using coupled-mode theory.

[0016]

[0017] da ccw / dt=(-iω0-γ2)a ccw -iκ2a cw (2)

[0018] Where γ2=(l+γ c +u1+u3-g) / 2,γ2=(l+γ c +u1+u3-g) / 2, ω0 is the resonant frequency, l is the inherent loss of the ring cavity, γ c μ1 is the coupling coefficient between the ring cavity and coupler C0, μ2 is the coupling coefficient of coupler C1, μ3 is the coupling coefficient of coupler C3, μ4 is the coupling coefficient of coupler C4, g is the equivalent gain of the active S-shaped waveguide, and κ1 and κ2 are two clockwise and counterclockwise modes a. cw and a ccw The mutual coupling coefficient between them.

[0019] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 3 specifically involves determining the characteristic frequency of the system.

[0020]

[0021] Where γ d =(γ1+γ2) / 2,κ1=κ2=κ,κ EP = (γ1-γ2) / 2, when the resonator rotates at an Ω rotational speed, the CW and CCW modes experience opposite Sagnac frequency shifts, Δω s =ωRΩ / cn eff Where R is the radius of the ring, n eff ω is the refractive index, and ω is the operating frequency of the laser.

[0022] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, for a system initially operating at the EP point, exhibits the following frequency splitting due to rotation:

[0023]

[0024] Further, the sensitivity improvement ratio between the EP-based micro-optical gyroscope and the conventional RMOG with the same radius was determined:

[0025]

[0026] Where Δω DP =2Δω s This is the frequency difference caused by traditional RMOG.

[0027] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 4 specifically involves: laser 1 being coupled into the ring cavity via coupler C0; the output optical power being converted into an electrical signal after passing through photodetector 3; the characteristic frequency splitting caused by rotation is extracted from the transmission spectrum; and the power transfer spectrum of the PT-symmetric single-ring resonator is found by solving the linear coupling ordinary differential equation through Laplace transform.

[0028]

[0029] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 5 specifically involves determining the minimum detectable rotational speed under noise constraints, where the minimum detectable rotational speed refers to the change in power dP that causes the rotation. out Equal to the total noise power P in the sensor detection system noise Minimum rotational speed Ω min , represented as:

[0030] Ω min =P noise / SPin，

[0031] in This refers to the sensitivity of an optical gyroscope based on a PT-symmetric structure. Ω min It is a quantity that should be minimized in an optical gyroscope.

[0032] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein the noise sources in the EP structure include detector noise, shot noise, relative intensity noise of the laser, laser frequency noise, and excessive noise of the gain medium.

[0033] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure is proposed. Most noise sources can be eliminated through balanced detection techniques and high-Q resonant cavities, while shot noise and detector noise cannot, as shown below:

[0034]

[0035] in, For shot noise, For detector noise, It is the photon energy, the minimum detectable rotational speed Ω. min Represented as:

[0036]

[0037] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure is disclosed. The high-sensitivity optical gyroscope is obtained using the design method described in claim 1. The high-sensitivity optical gyroscope includes a laser 1, a ring cavity 2, and an S-shaped active waveguide S. a S-type passive waveguide S b Coupler C0, coupler C1, coupler C2, coupler C3, coupler C4 and photodetector 3;

[0038] The laser 1 is connected to the photodetector 3 and the ring cavity 2 via coupler C0, and the ring cavity 2 is connected to the S-shaped active waveguide S via couplers C1 and C3. a The annular cavity 2 is connected to the S-shaped passive waveguide S via couplers C2 and C4. b Connected.

[0039] The beneficial effects of this invention are:

[0040] This invention achieves the construction of a PT-symmetric system in a single microcavity by coupling an active and a passive S-shaped waveguide in a ring cavity.

[0041] This invention enables optical gyroscopes to achieve high sensitivity and high signal-to-noise ratio while meeting the requirements of small size.

[0042] This invention not only solves the stringent requirement that the two resonant cavities of a PT-symmetric system have the same resonant frequency, but also suppresses the non-dissimilarity error caused by different differential disturbance sources affecting the two resonant cavities in a typical PT-symmetric gyroscope. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the structure of the present invention.

[0044] Figure 2 This is a schematic diagram of the Sagnac frequency splitting enhancement of the present invention, wherein (a) shows the relationship between the frequency splitting enhancement factor and the rotational speed, and (b) shows the relationship between frequency splitting and rotational speed under different normalized gain rates at the same coupling rate.

[0045] Figure 3 This is a transmission spectrum diagram of the present invention at different detuning frequencies.

[0046] Figure 4 This is a schematic diagram of the minimum detectable accuracy of the present invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] A high-precision gyroscope symmetric to parity-time (PT) is constructed by coupling gain and loss waveguides in a single micro-ring cavity.

[0049] An active S-shaped waveguide and a passive S-shaped waveguide are coupled inside the ring cavity. By appropriately adjusting the gain / loss values ​​within the active / passive waveguides and the coupling coefficient of the coupler, the system can be tuned to near the singularity (EP). A gyroscope system at the EP exhibits extremely high sensitivity to rotational speed. The ring cavity operates below the laser threshold, and power detection technology is used to measure the gyroscope's sensitivity, allowing for precise measurement of the gyroscope's signal-to-noise ratio. Furthermore, by coupling two backpropagation modes in the same optical resonator, rather than coupling two modes in different resonators, not only is the area reduced by 3 / 4, but the sensor is also protected from differential perturbation sources applied to the two different resonators.

[0050] A design method for a high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, the design method comprising the following steps:

[0051] Step 1: Construct a PT-symmetric system;

[0052] Step 2: Adjust the system from Step 1 to point EP and write the dynamic equations of the system;

[0053] Step 3: Solve for the characteristic frequency of the system based on the dynamic equations in Step 2. The sensitivity is obtained by solving for the reciprocal of the frequency detuning Δ = ω - ω0 of the power transmission spectrum. The detuning frequency at the position of maximum sensitivity is taken as the frequency of the input laser.

[0054] Step 4: Based on the characteristic frequencies of the system in Step 3, find the power transfer spectrum of the PT-symmetric single-ring resonator;

[0055] Step 5: Evaluate the performance of the EP sensor based on the power transfer spectrum obtained in Step 4.

[0056] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 1 of constructing the PT-symmetric system specifically involves using an S-shaped active waveguide S in the circulator 1. a The S-shaped passive waveguide S is connected to the ring cavity via couplers C1 and C3. b A PT-symmetric system is constructed by connecting it to the annular cavity 2 via couplers C2 and C4.

[0057] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 2 adjusts the system to the EP point, and the dynamic equation of the system is obtained. Specifically, based on the constructed PT-symmetric system, the S-shaped active waveguide S is adjusted... a The gain value and the coupling coefficients of couplers C1, C2, C3, and C4 will adjust the system to the EP point;

[0058] Or, based on the constructed PT-symmetric system, by adjusting the S-shaped passive waveguide S... b The loss value and the coupling coefficients of couplers C1, C2, C3, and C4 will adjust the system to the EP point;

[0059] The dynamic equations of the system can be derived using coupled-mode theory.

[0060]

[0061] da ccw / dt=(-iω0-γ2)a ccw -iκ2a cw (2)

[0062] Where γ2=(l+γ c +u1+u3-g) / 2,γ2=(l+γ c +u1+u3-g) / 2, ω0 is the resonant frequency, l is the inherent loss of the ring cavity, γ cμ1 is the coupling coefficient between the ring cavity and coupler C0, μ2 is the coupling coefficient of coupler C1, μ3 is the coupling coefficient of coupler C3, μ4 is the coupling coefficient of coupler C4, g is the equivalent gain of the active S-shaped waveguide, and κ1 and κ2 are two clockwise and counterclockwise modes a. cw and a ccw The mutual coupling coefficient between them.

[0063] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 3, based on the dynamic equations of step 2, solves for the characteristic frequency of the system, specifically as follows: the characteristic frequency of the system is...

[0064]

[0065] Where γ d =(γ1+γ2) / 2,κ1=κ2=κ,κ EP = (γ1-γ2) / 2, when the resonator rotates at an Ω rotational speed, the CW and CCW modes experience opposite Sagnac frequency shifts, Δω s =ωRΩ / cn eff Where R is the radius of the ring, n eff ω is the refractive index, and ω is the operating frequency of the laser.

[0066] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, for a system initially operating at the EP point, exhibits the following frequency splitting due to rotation:

[0067]

[0068] Further, the sensitivity improvement ratio between the gyroscope and a conventional RMOG with the same radius was determined:

[0069]

[0070] Where Δω DP =2Δω s This refers to the sensitivity of the RMOG.

[0071] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 4, based on the characteristic frequency of the system in step 3, finds the power transfer spectrum of the PT-symmetric single-ring resonator. Specifically, the laser (1) is coupled into the ring cavity through coupler C0, and the output optical power is converted into an electrical signal after passing through a photodetector (3); the characteristic frequency splitting caused by rotation is extracted from the transmission spectrum, and the power transfer spectrum of the PT-symmetric single-ring resonator is found by solving the linear coupling ordinary differential equation through Laplace transform.

[0072]

[0073] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, wherein step 5 evaluates the performance of the EP sensor based on the power transfer spectrum of step 4, specifically by determining the minimum detectable rotational speed under noise constraints. The minimum detectable rotational speed refers to the change in power dP that causes this rotation. out Equal to the total noise power P in the sensor detection system noise Minimum rotational speed Ω min , represented as:

[0074] Ω min =P noise / SP in

[0075] Represented as: Ω min =P noise / SP in .in This refers to the sensitivity of an optical gyroscope based on a PT-symmetric structure. Ω min These are quantities that should be minimized in an optical gyroscope (long-term drift and scaling factor stability).

[0076] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure is disclosed. The noise sources in the EP structure include detector noise, shot noise, relative intensity noise of the laser, laser frequency noise, and excessive noise from the gain medium. Since these noise sources are uncorrelated, the total noise power is obtained by adding them squared.

[0077] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure is proposed. Most noise sources can be eliminated through balanced detection techniques and high-Q resonant cavities, while shot noise and detector noise cannot, as shown below:

[0078]

[0079] in, For shot noise, For detector noise, It is the photon energy, the minimum detectable rotational speed Ω. min Represented as:

[0080]

[0081] A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure is disclosed. The high-sensitivity optical gyroscope is obtained using the design method described in claim 1. The high-sensitivity optical gyroscope includes a laser 1, a ring cavity 2, and an S-shaped active waveguide S. a S-type passive waveguide S b Coupler C0, coupler C1, coupler C2, coupler C3, coupler C4 and photodetector 3;

[0082] The laser 4 is connected to the photodetector 3 and the ring cavity 2 via coupler C0. The ring cavity 2 is connected to the S-shaped active waveguide Sa via coupler C1 and coupler C3. The ring cavity 2 is connected to the S-shaped passive waveguide Sb via coupler C2 and coupler C4.

Claims

1. A design method for a high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, characterized in that, The design method includes the following steps: Step 1: Construct a PT-symmetric system; Step 2: Adjust the system from Step 1 to the EP point to obtain the system's dynamic equations; Step 3: Solve for the characteristic frequencies of the system based on the dynamic equations from Step 2; Step 4: Based on the characteristic frequencies of the system in Step 3, find the power transfer spectrum of the PT-symmetric single-ring resonator; Step 5: Evaluate the performance of the EP sensor based on the power transfer spectrum obtained in Step 4; Step 1 specifically involves connecting an S-shaped active waveguide Sa to the annular cavity (2) via couplers C1 and C3, and an S-shaped passive waveguide S... b A PT-symmetric system is constructed by connecting the system to the annular cavity (2) via couplers C2 and C4.

2. The design method for a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure according to claim 1, characterized in that, Step 2 specifically involves adjusting the S-shaped active waveguide S based on the constructed PT-symmetric system. a The gain value and the coupling coefficients of couplers C1, C2, C3, and C4 will adjust the system to the EP point; Or, based on the constructed PT-symmetric system, by adjusting the S-shaped passive waveguide S... b The loss value and the coupling coefficients of couplers C1, C2, C3, and C4 will adjust the system to the EP point; The dynamic equations of the system can be derived using coupled-mode theory. yes ccw / dt=(-iω0-γ2)a ccw -iκ2a cw (2) Where γ2=(l+γ c +u1+u3-g) / 2,γ2=(l+γ c +u2+u4-g) / 2, ω0 is the resonant frequency, l is the inherent loss of the ring cavity, γ c κ1 is the coupling coefficient between the ring cavity and coupler C0, u1 is the coupling coefficient of coupler C1, u2 is the coupling coefficient of coupler C2, u3 is the coupling coefficient of coupler C3, u4 is the coupling coefficient of coupler C4, g is the equivalent gain of the active S-shaped waveguide, and κ1 and κ2 are two clockwise and counterclockwise modes a. cw and a ccw The mutual coupling coefficient between them.

3. The design method for a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure according to claim 2, characterized in that, Specifically, step 3 involves determining the system's characteristic frequency as follows: Where γ d =(γ1+γ2) / 2,κ1=κ2=κ,κ EP = (γ1-γ2) / 2, when the resonator rotates at an Ω rotational speed, the CW and CCW modes experience opposite Sagnac frequency shifts, Δω s =ωRΩ / cn eff Where R is the radius of the ring, n eff ω is the refractive index, and ω is the operating frequency of the laser.

4. The design method for a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure according to claim 3, characterized in that, For a system initially operating at point EP, the frequency splitting caused by rotation is: Sensitivity improvement ratio between EP-based micro-optical gyroscopes and conventional RMOGs with the same radius: Where Δω DP =2Δω s This refers to the sensitivity of the RMOG.

5. The design method for a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure according to claim 4, characterized in that, Specifically, step 4 involves the laser (1) being coupled into the ring cavity via coupler C0, and the output optical power being converted into an electrical signal after passing through a photodetector (3). The characteristic frequency splitting caused by rotation is extracted from the transmission spectrum, and the power transfer spectrum of the PT-symmetric single-ring resonator is found by solving the linear coupling ordinary differential equation through Laplace transform.

6. The design method of a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure according to claim 1, characterized in that, Step 5 specifically involves determining the minimum detectable rotational rate under noise constraints. The minimum detectable rotational rate refers to the rate that causes a change in power dP. out Equal to the total noise power P in the sensor detection system noise Minimum rotational speed Ω min , is represented as: Ω min =P noise / SP in in The sensitivity of an optical gyroscope based on a PT-symmetric structure, Ω min It is a quantity that should be minimized in an optical gyroscope.

7. The design method for a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure according to claim 6, characterized in that, Noise sources in EP sensors include detector noise, shot noise, relative intensity noise of the laser, laser frequency noise, and excessive noise from the gain medium.

8. The design method of a high-sensitivity optical gyroscope based on a single-cavity PT symmetric structure according to claim 7, characterized in that, Most noise sources can be eliminated through balanced detection techniques and high-Q resonant cavities, while shot noise and detector noise cannot, as shown below: in, For shot noise, For detector noise, It is the photon energy, the minimum detectable rotational speed Ω. min Represented as:

9. A high-sensitivity optical gyroscope based on a single-cavity PT-symmetric structure, characterized in that, The high-sensitivity optical gyroscope is obtained using the design method described in claim 1. The high-sensitivity optical gyroscope includes a laser (1), a ring cavity (2), and an S-shaped active waveguide S. a S-type passive waveguide S b Coupler C0, coupler C1, coupler C2, coupler C3, coupler C4 and photodetector (3); The laser (1) is connected to the photodetector (3) and the ring cavity (2) via coupler C0, respectively. The ring cavity (2) is connected to the S-shaped active waveguide S via couplers C1 and C3. a The annular cavity (2) is connected to the S-shaped passive waveguide S via couplers C2 and C4. b Connected.

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