Design method of symmetrical quasi-optical cavity for dielectric constant measurement

Abstract

The invention discloses a symmetric quasi-optical cavity design method for dielectric constant measurement, which belongs to the technical field of quasi-optical cavity design and comprises a mirror design method and a coupling design method. The design method of the mirror is as follows: the quasi-optical cavity is composed of a transmission-type spherical mirror with a symmetrical structure, and parameters needing to be designed mainly comprise the curvature radius of the spherical mirror, the aperture radius of the spherical mirror, the distance between the two spherical mirrors and the material of the spherical mirror; factors considered during design comprise intrinsic spectral line purity, stability of an open cavity, an open cavity Q value and a girdling radius; the coupling design method comprises the following step of feeding a signal into and out of the symmetrical quasi-optical cavity by adopting a coupling ring mode. According to the design method of the symmetric quasi-optical cavity, the coupling ring is innovatively placed between the two spherical mirrors for signal feed-in / feed-out, a traditional fixed small hole coupling mode is replaced, the coupling strength of the coupling ring is flexibly adjusted through parameters such as the ring diameter, the wire diameter and the position, and the problems that after small hole coupling machining, adjustment cannot be conducted, and flexibility is poor are solved.

Description

Technical Field

[0001] This invention belongs to the field of quasi-optical cavity design technology, and particularly relates to a symmetrical quasi-optical cavity design method for dielectric constant measurement. Background Technology

[0002] In the centimeter-wave band, closed resonant cavities are widely used to measure the dielectric constant of low-loss materials. However, this method has strict requirements for material processing, is difficult to simulate in abnormal environments, and the quality factor that determines the low-loss measurement capability is hard to exceed 10,000. Quasi-optical cavity methods are widely used in the millimeter-wave band due to their non-destructive nature and suitability for high-precision measurement of low-loss materials.

[0003] The basic principle of the quasi-cavity method is to deduce the dielectric constant and loss tangent by comparing the changes in resonant frequency, cavity length, or quality factor before and after the material under test is placed in the cavity, combined with parameters such as the thickness of the material under test and the initial cavity length. Currently, semi-symmetric quasi-cavities, consisting of a spherical mirror and a plane mirror, are commonly used to test the dielectric constant of materials. This method is simple in structure and easy to align and use, but it is not suitable for high-precision measurements due to factors such as the beam waist being located on the plane mirror surface and non-ideal field distribution. A symmetric quasi-cavity method consists of two spherical mirrors with identical shape, radius of curvature, and mirror width, arranged to form an open resonant cavity. This structure is complex to align and has a higher cost, but the fundamental mode (TEM) is more stable. 00q The waist of the mold is precisely located at the center of the cavity, and the field distribution is symmetrical about the center and very uniform, making it more suitable for high-precision material testing.

[0004] When using a quasi-optical cavity to test the dielectric constant of materials, a pinhole coupling is mainly used to feed the signal into the cavity, thereby generating resonance. Pinhole coupling can be achieved by directly machining a through-hole on the mirror surface, which has the advantages of simple processing, system repeatability, and high stability. However, since the size and position of the pinhole are fixed, they cannot be adjusted after processing, resulting in poor flexibility. When the system is subsequently expanded to multi-band testing or high-power environments, pinhole coupling cannot meet the requirements.

[0005] Therefore, this invention proposes a new coupling method, in which a coupling ring is placed between the two spherical mirrors of a symmetrical quasi-optical cavity for signal feeding. This facilitates subsequent integration with other coupling methods for cross-band dielectric constant testing, wideband tuning, and generating high-power material testing environments, thus providing convenience for expanding material testing scenarios.

[0006] It should be noted that the above content falls within the inventor's technical knowledge and does not necessarily constitute prior art. Summary of the Invention

[0007] To address the aforementioned issues, the present invention aims to provide a symmetrical quasi-optical cavity design method for dielectric constant measurement. It innovatively proposes placing a coupling ring between two spherical mirrors for signal input / output, replacing the traditional fixed pinhole coupling method. The coupling ring coupling is a type of "magnetic field coupling," and its coupling strength can be flexibly adjusted using parameters such as ring diameter, wire diameter, and position, thus solving the problems of poor flexibility and inability to adjust pinhole coupling after processing.

[0008] To achieve the above objectives, this invention proposes a symmetrical quasi-optical cavity design method for dielectric constant measurement, which includes a mirror design method and a coupling design method.

[0009] The mirror design method is as follows:

[0010] The quasi-optical cavity is an open cavity composed of transmission-type symmetrical spherical mirrors. The main parameters that need to be designed include the radius of curvature of the spherical mirrors, the aperture radius of the spherical mirrors, the distance between the two spherical mirrors, and the material of the spherical mirrors.

[0011] Factors considered in the design include intrinsic spectral purity, open cavity stability, open cavity Q value, and beam waist radius, where Q is the quality factor.

[0012] The coupled design method is as follows:

[0013] The signal is fed into and out of the symmetrical quasi-optical cavity using a coupling loop. The coupling loop achieves energy exchange through "magnetic field coupling". The coupling effect is related to the loop diameter, loop wire diameter, number of turns and position parameters. The design of the coupling loop needs to balance coupling efficiency, impedance matching and mode compatibility requirements.

[0014] Preferably, the specific design method of the face mirror design includes the following steps:

[0015] S11: Based on the stability of the open cavity, the relationship between the cavity length L and the radius of curvature R is initially obtained;

[0016] S12: Based on the purity of intrinsic spectral lines and the stability requirements of open cavities, the relationship between cavity length L and radius of curvature R is derived.

[0017] S13: Estimate the Q-value design target based on the required accuracy of the material loss tangent measurement;

[0018] S14: Based on the open cavity Q value design target and target test frequency, determine the cavity material and the relationship between the coating material and cavity length;

[0019] S15: Determine the aperture radius of the spherical mirror based on the beam radius and cavity length;

[0020] S16: Determine the optimal cavity length based on the Fresnel number.

[0021] The specific design method of the coupled design includes the following steps:

[0022] S21: The range of ring diameter is determined by the coupling strength;

[0023] S22: The loop diameter range is determined by impedance matching and conductor loss;

[0024] S23: Number of turns design;

[0025] S24: The position of the coupling ring is determined by the quasi-optical cavity master mode.

[0026] Preferably, S11 specifically includes:

[0027] Using curvature factor g i Describing the stability of a quasi-optical cavity, when the curvature factor satisfies 0 < g i g i When L / 2 < 1, the resonant cavity reaches stability and satisfies L / 2. <R<L;

[0028] Preferably, S12 is specifically designed as follows:

[0029] Δf1=f 00q -f 11(q-2) =2a-3ab

[0030] Δf2=f' W(q-1) -f Wq =2ab-a

[0031] in

[0032] When choosing b, to maximize both Δf1 and Δf2, the relationship between cavity length L and radius of curvature R is as follows:

[0033]

[0034] Preferably, S13 specifically includes:

[0035] The accuracy of the loss tangent measurement depends on the quality factor, as shown in the formula:

[0036]

[0037] The ability to estimate the loss tangent by using the reciprocal of the quality factor is useful; the loss tangent of common low-loss materials is around 10. -4 The target Q value is 50,000 or higher.

[0038] Preferably, S14 specifically includes:

[0039] The relationship between quality factor and mirror loss is as follows:

[0040] Q = L / 2δ

[0041] In the formula, δ represents the skin depth;

[0042] The formula for calculating the minimum cavity length is:

[0043] L>2δQ;

[0044] Specifically, S15 is:

[0045] The aperture radius A of the spherical mirror is greater than 2.2 times the beam radius at the spherical mirror.

[0046] Preferably, S16 specifically includes:

[0047] The relationship between the cavity length of a symmetrical collimator and the Fresnel number and the aperture radius of the spherical mirror is as follows:

[0048]

[0049] If it is a confocal cavity, then it is:

[0050]

[0051] The range of values ​​for the cavity length and radius of curvature of the spherical mirror is as follows: When using a confocal cavity, R = L, where A is related to both L and R, to obtain the optimal cavity length L, and then obtain the corresponding radius of curvature R and the spherical mirror aperture radius A.

[0052] Preferably, S21 specifically means that the ring diameter r needs to match the effective range of the magnetic field inside the cavity, and is taken as 0.1λ≤r≤0.3λ.

[0053] Specifically, S22 involves performing impedance matching to obtain the wire diameter d range, where 0.05λ≤d≤0.1λ is taken.

[0054] Specifically, S23 refers to the use of a single-turn ring.

[0055] Specifically, S24 involves placing the coupling loop at the point of strongest magnetic field, and the quasi-optical cavity used for measuring the dielectric constant of materials operating in the TEM. 00q The mode has a maximum magnetic field strength located radially at the axis and axially at the center of a symmetrical quasi-optical cavity.

[0056] Preferably, in S24, the coupling ring is located between the two spherical mirrors of the symmetrical quasi-optical cavity, at the radial center.

[0057] Preferably, the range of values ​​for the ring diameter and wire diameter is related to the frequency. Parameter scanning simulation is performed within the range using simulation software to obtain the optimal values ​​that meet the usage scenario.

[0058] The symmetrical quasi-optical cavity design method for dielectric constant measurement proposed in this invention can bring the following beneficial effects:

[0059] 1. The symmetrical quasi-optical cavity design method of this invention innovatively proposes to place a coupling ring between two spherical mirrors for signal input / output, replacing the traditional fixed pinhole coupling method. The coupling ring coupling belongs to "magnetic field coupling", and its coupling strength can be flexibly adjusted by parameters such as ring diameter, wire diameter, and position, solving the problem of pinhole coupling being unable to be adjusted and having poor flexibility after processing.

[0060] 2. The symmetrical quasi-optical cavity design method of this invention adopts a symmetrical quasi-optical cavity structure, in which the beam waist of the fundamental mode is precisely located at the center of the cavity, resulting in a symmetrical and uniform field distribution, thus avoiding the disadvantage of uneven field distribution in semi-symmetrical quasi-optical cavities. Through a systematic mirror design method, cavity parameters can be optimized to ensure high mode purity and low diffraction loss, thereby providing a structural foundation for achieving high-precision dielectric constant measurement of low-loss materials. The designed Q-value target is significantly better than that of traditional closed resonant cavities, greatly improving low-loss measurement capabilities. This design facilitates subsequent integration with other coupling methods such as waveguides and probes, laying the foundation for system functional expansion.

[0061] 3. The symmetrical quasi-optical cavity design method of this invention has a clear coupling ring design method and a clear parameter range. Through simulation optimization, it can be quickly adapted to different frequency bands and scenarios. This adjustable coupling mechanism makes the quasi-optical cavity system easy to extend to higher frequency bands such as millimeter waves and terahertz, or to environments that require high-power testing. It overcomes the limitation that small hole coupling is prone to breakdown or nonlinear effects under high power, and significantly broadens the application scenarios of material testing.

[0062] 4. The symmetrical quasi-optical cavity design method of this invention: Although the alignment requirements of a symmetrical quasi-optical cavity are higher than those of a semi-symmetrical cavity, this invention reduces the difficulty of engineering implementation through clear design specifications. The coupling ring structure is relatively simple and easy to manufacture, and through parameter optimization, it can well balance coupling efficiency, impedance matching, and mode purity, improving system flexibility while ensuring measurement repeatability and stability. Attached Figure Description

[0063] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0064] Figure 1 This is a schematic diagram of the design parameters for the spherical mirror of the present invention.

[0065] Figure 2 This is a schematic diagram of the coupling ring design parameters for this invention.

[0066] Figure 3 This is a simulation model diagram of the symmetrical quasi-optical cavity of the present invention.

[0067] Figure 4 For the present invention S 11 Simulation results diagram. Detailed Implementation

[0068] To more clearly illustrate the overall concept of the present invention, a detailed description will be provided below with reference to the accompanying drawings and examples.

[0069] The embodiments of the present invention propose a symmetric quasi-optical cavity design method for dielectric constant measurement, which includes a mirror design method and a coupling design method.

[0070] The mirror design method is as follows:

[0071] The quasi-optical cavity is an open cavity composed of transmission-type symmetrical spherical mirrors. The main parameters that need to be designed include the radius of curvature of the spherical mirrors, the aperture radius of the spherical mirrors, the distance between the two spherical mirrors (i.e., the cavity length), and the material of the spherical mirrors.

[0072] The main factors considered in the design include intrinsic spectral purity, open cavity stability, open cavity Q-value, and beam waist radius, where Q is the quality factor. The specific design method includes the following steps:

[0073] S11: Based on the stability of the open cavity, the relationship between the cavity length L and the radius of curvature R is initially obtained;

[0074] Using curvature factor g i Describing the stability of a quasi-optical cavity, when the curvature factor satisfies 0 < g i g i When <1, the resonant cavity reaches stability. For example... Figure 1 As shown, since the quasi-optical cavity used in this invention is a symmetrical quasi-optical cavity, it satisfies... therefore L / 2 can be derived <R<L。

[0075] S12: Based on the purity of intrinsic spectral lines and the stability requirements of open cavities, the relationship between cavity length L and radius of curvature R is derived.

[0076] Unlike semi-symmetric quasi-optical cavities, symmetric quasi-optical cavities (TEMs) 00q The two adjacent higher-order modes of the mode are TEM. 11(q-2) and TEM 10(q-1) It is necessary to design the quasi-cavity size appropriately so that the TEM 00q The frequency spacing between the mode and the two adjacent higher-order modes is large enough to avoid degeneracy or interference between the modes, as designed below:

[0077] Δf1=f 00q -f 11(q-2) =2a-3ab

[0078] Δf2=f 10(q-1) -f 00q =2ab-a

[0079] in

[0080] f 00q It is TEM 00q The frequency of the mode, f 11(q-2) It is TEM 00q The frequency of the higher-order modes on the left side of the mode, f 10(q-1) It is TEM 00q The frequency of the higher-order modes on the right side of the mode.

[0081] Δf1 is TEM 00q The frequency difference between the TEM mode and the higher-order mode on the left, Δf2 is the TEM frequency difference. 00q The frequency difference between the mode and the higher-order mode on the right.

[0082] We should choose b appropriately to maximize both Δf1 and Δf2, and then we can obtain...

[0083]

[0084] Considering the stability requirements of the open cavity, the final relationship between the cavity length L and the radius of curvature R is obtained as follows:

[0085]

[0086] S13: Estimate the Q-value design target based on the required accuracy of the material loss tangent measurement;

[0087] The measurement accuracy of the loss tangent mainly depends on the quality factor, as shown in the formula:

[0088]

[0089] Where, n is the refractive index of the sample to be tested;

[0090] k — wave number;

[0091] t — half the sample thickness;

[0092] d' = Dt;

[0093]

[0094] The measurement capability of the loss tangent can be estimated by taking the reciprocal of the quality factor. The loss tangent of common low-loss materials is around 10. -4 The Q value of the open cavity is approximately 10,000. Considering factors such as imperfect processing, the general design target for the Q value is 50,000 or higher.

[0095] S14: Based on the open cavity Q value design target and target test frequency, determine the cavity material and the relationship between the coating material and cavity length;

[0096] The Q value is mainly determined by the mirror loss, which in turn depends on the skin depth of the material used in the collimator. The simplified relationship between the quality factor and the mirror loss is as follows:

[0097] Q = L / 2δ

[0098] In the formula, δ represents the skin depth.

[0099] Considering the difficulty and cost of manufacturing, brass is commonly used as the material for cavity fabrication, with a plating of silver or gold. Therefore, once the spherical mirror material and Q-value design target are determined, the minimum cavity length can be obtained based on the conductivity of different materials, as follows:

[0100] L>2δQ.

[0101] S15: Determine the aperture radius of the spherical mirror based on the beam radius and cavity length;

[0102] Theoretical analysis reveals the beam radius w s The value increases with increasing cavity length L, and increases as the resonant frequency decreases. s The larger the value, the more likely it is to satisfy L = 2D. Therefore, the beam radius w at the spherical mirror is obtained. s The calculation formula is as follows:

[0103]

[0104] Wherein, λ represents the wavelength;

[0105] ω0 — Waist radius.

[0106] Therefore, the aperture radius A of the spherical mirror should be greater than 2.2 times the beam radius at the spherical mirror. This effectively limits the generation of higher-order modes while ensuring the operation of the quasi-cavity TEM. 00q The pattern is given by the formula, where D is the half-cavity length.

[0107] S16: Determine the optimal cavity length based on the Fresnel number;

[0108] The Fresnel number N represents the maximum number of round trips the signal makes between the two reflecting mirrors of the quasi-optical cavity. A larger N indicates lower diffraction loss and a higher system quality factor. In practical designs, a Fresnel number greater than 4 is generally required. Therefore, the relationship between the cavity length of a symmetrical quasi-optical cavity and the Fresnel number and the aperture radius of the spherical mirror is as follows:

[0109]

[0110] g = 1 - L / R;

[0111] If it is a confocal cavity, then it is:

[0112]

[0113] Based on the above steps, the range of values ​​for the cavity length and radius of curvature of the spherical mirror is as follows: (If a confocal cavity is used, then R = L), where A is related to both L and R. Therefore, the optimal cavity length L can be obtained, and then the corresponding radius of curvature R, spherical mirror aperture radius A and other parameters can be obtained.

[0114] The coupled design method is as follows:

[0115] This invention proposes using a coupling loop to feed signals into and out of a symmetrical quasi-optical cavity. The coupling loop achieves energy exchange through "magnetic field coupling," meaning that when the alternating magnetic field within the quasi-optical cavity passes through the coupling loop, an alternating current is induced within the loop, and the energy is then output through the transmission line. The coupling effect is related to parameters such as the loop diameter, loop wire diameter, number of turns, and position. The coupling loop design needs to balance coupling efficiency, impedance matching, and mode compatibility requirements. The specific design method includes the following steps:

[0116] S21: The range of ring diameter is determined by the coupling strength;

[0117] like Figure 2 As shown, the dielectric constant of the material requires a high Q-value testing system, resulting in weak coupling. The larger the ring diameter, the more it overlaps with the magnetic field inside the cavity, leading to stronger coupling. Therefore, the ring diameter r needs to match the effective range of the magnetic field inside the cavity, and is chosen to be 0.1λ ≤ r ≤ 0.3λ.

[0118] S22: The loop diameter range is determined by impedance matching and conductor loss;

[0119] Since the coupling loop needs to be connected to the external transmission line, impedance matching is required; otherwise, reflections will occur, reducing efficiency and interfering with cavity stability. However, if the wire diameter d is too small, conductor losses will increase, while if d is too large, impedance matching will be difficult. Therefore, a value of 0.05λ≤d≤0.1λ is chosen.

[0120] S23: Number of turns design;

[0121] Since more turns increase volume and losses, a single-turn ring can meet most testing scenarios.

[0122] S24: The position of the coupling loop is determined by the quasi-optical cavity master mode;

[0123] The position of the coupling loop directly affects the coupling strength and mode purity; it must be placed where the magnetic field is strongest. The quasi-optical cavity used for measuring the dielectric constant of materials operates in a TEM. 00q The maximum magnetic field strength of this mode is located radially at the axis and axially at the center of the symmetrical quasi-optical cavity. Therefore, the coupling ring should be located between the two spherical mirrors of the symmetrical quasi-optical cavity, at the radial center.

[0124] The number of turns and position of the coupling ring can be determined by the above steps. The range of values ​​for the ring diameter and wire diameter is related to the frequency. Simulation software such as HFSS / CST can be used to perform parameter scanning simulation within this range to obtain the optimal values ​​that meet the usage scenario.

[0125] Specific implementation steps for the symmetrical quasi-optical cavity design for using the X-band for dielectric constant measurement:

[0126] The target Q-value for the symmetrical quasi-optical cavity is 50,000. In this embodiment, brass is to be used for machining, with a skin depth δ = (1.14~1.4) μm, resulting in a cavity length L > 140 mm. Based on the main mode frequency interval, Fresnel number, and spherical mirror aperture radius requirements, the X-band spherical mirror curvature radius is determined to be 207 mm, the aperture diameter to be 280 mm, and the cavity length to be 300 mm.

[0127] According to the above coupling ring design process, the ring diameter is 3mm ≤ r ≤ 9mm, the wire diameter is 1.5mm ≤ d ≤ 3mm, the number of turns is 1, and it is located in the middle of the quasi-optical cavity. CST software is used to perform scanning simulations on the ring diameter and wire diameter parameters. The simulation model is shown below. Figure 3 Based on simulation results, this embodiment uses a ring diameter of 5mm and a wire diameter of 2.88mm. The X-band quasi-optical cavity design is now complete.

[0128] In the CST software, the number of scan points is set to 1001, and the above model is simulated using the time-domain solver to obtain the cavity S. 11 As a result, Figure 4 As shown, the quasi-optical cavity designed according to the method proposed in this embodiment can effectively resonate in the X-band.

[0129] A quartz sample with a thickness of 4 mm and a diameter of 100 mm was added to the simulation model. Its theoretical dielectric constant is 3.75, and it can resonate effectively. Substituting the two resonant frequencies into the algorithm, the measured dielectric constants were found to be 3.82, 3.79, 3.84, and 3.86, respectively. The center value of the measured dielectric constant interval is 3.82, which agrees well with the standard value of quartz input into the simulation model. Therefore, the quasi-optical cavity designed according to the method proposed in this invention can perform dielectric constant testing in the X-band.

[0130] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A symmetrical quasi-optical cavity design method for dielectric constant measurement, characterized in that, The symmetrical quasi-optical cavity design method includes a mirror design method and a coupling design method; The mirror design method is as follows: The quasi-optical cavity is an open cavity composed of transmission-type symmetrical spherical mirrors. The main parameters that need to be designed include the radius of curvature of the spherical mirrors, the aperture radius of the spherical mirrors, the distance between the two spherical mirrors, and the material of the spherical mirrors. Factors considered in the design include intrinsic spectral purity, open cavity stability, open cavity Q value, and beam waist radius, where Q is the quality factor. The coupling design method is as follows: The signal is fed into and out of the symmetrical quasi-optical cavity using a coupling loop. The coupling loop achieves energy exchange through "magnetic field coupling". The coupling effect is related to the loop diameter, loop wire diameter, number of turns and position parameters. The design of the coupling loop needs to balance coupling efficiency, impedance matching and mode compatibility requirements.

2. The symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 1, characterized in that, The specific design method for the face mirror design includes the following steps: S11: Based on the stability of the open cavity, the relationship between the cavity length L and the radius of curvature R is initially obtained; S12: Based on the purity of intrinsic spectral lines and the stability requirements of open cavities, the relationship between cavity length L and radius of curvature R is derived. S13: Estimate the Q-value design target based on the required accuracy of the material loss tangent measurement; S14: Based on the open cavity Q value design target and target test frequency, determine the cavity material and the relationship between the coating material and cavity length; S15: Determine the aperture radius of the spherical mirror based on the beam radius and cavity length; S16: Determine the optimal cavity length based on the Fresnel number; The specific design method of the coupled design includes the following steps: S21: The range of ring diameter is determined by the coupling strength; S22: The loop diameter range is determined by impedance matching and conductor loss; S23: Turns design; S24: The position of the coupling ring is determined by the quasi-optical cavity master mode.

3. The symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 2, characterized in that, Specifically, S11 is: Using curvature factor g i Describing the stability of a quasi-optical cavity, when the curvature factor satisfies 0 < g i g i When L / 2 < 1, the resonant cavity reaches stability and satisfies L / 2 <R<L。 4. The symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 3, characterized in that, The specific design of S12 is as follows: Δf1=f 00q -f 11(q-2) =2a-3ab; Δf2=f 10(q-1) -f 00q =2ab-a; f 00q It is TEM 00q The frequency of the mode, f 11(q-2) It is TEM 00q The frequency of the higher-order modes on the left side of the mode, f 10(q-1) It is TEM 00q The frequencies of the higher-order modes on the right side of the mode, Δf1 is the TEM frequency. 00q The frequency difference between the TEM mode and the higher-order mode on the left, Δf2 is the TEM frequency difference. 00q The frequency difference between the mode and the higher-order mode on the right; When choosing b, to maximize both Δf1 and Δf2, the relationship between cavity length L and radius of curvature R is as follows:

5. A symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 4, characterized in that, Specifically, S13 is: The accuracy of the loss tangent measurement depends on the quality factor, as shown in the formula: n is the refractive index of the sample; k is the wavenumber; t is half the sample thickness; d' = Dt; D = L / 2; The ability to estimate the loss tangent by using the reciprocal of the quality factor is useful; the loss tangent of common low-loss materials is around 10. -4 The target Q value is 50,000 or higher.

6. The symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 5, characterized in that, Specifically, S14 is: The relationship between quality factor and mirror loss is as follows: Q = L / 2δ In the formula, δ represents the skin depth; The formula for calculating the minimum cavity length is: L>2δQ; Specifically, S15 is: Beam radius w at the spherical mirror s The calculation formula is as follows: λ is the wavelength; ω0 is the beam waist radius; The aperture radius A of the spherical mirror is greater than 2.2 times the beam radius at the spherical mirror.

7. A symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 6, characterized in that, Specifically, S16 is: The relationship between the cavity length of a symmetrical collimator and the Fresnel number and the aperture radius of the spherical mirror is as follows: N is the Fresnel number, and g = 1 - L / R; If it is a confocal cavity, then it is: The range of values ​​for the cavity length and radius of curvature of the spherical mirror is as follows: When using a confocal cavity, R = L, where A is related to both L and R, to obtain the optimal cavity length L, and then obtain the corresponding radius of curvature R and the spherical mirror aperture radius A.

8. A symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 7, characterized in that, Specifically, S21 means that the ring diameter r needs to match the effective range of the magnetic field inside the cavity, and the value is 0.1λ≤r≤0.3λ. Specifically, S22 involves performing impedance matching to obtain the wire diameter d range, where 0.05λ≤d≤0.1λ is taken. Specifically, S23 refers to the use of a single-turn ring; Specifically, S24 involves placing the coupling loop at the point of strongest magnetic field, and the quasi-optical cavity used for measuring the dielectric constant of materials operating in the TEM. 00q The mode has a maximum magnetic field strength located radially at the axis and axially at the center of a symmetrical quasi-optical cavity.

9. A symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 8, characterized in that, In S24, the coupling ring is located between the two spherical mirrors of the symmetrical quasi-optical cavity, at the radial center.

10. A symmetrical quasi-optical cavity design method for dielectric constant measurement according to claim 9, characterized in that, The range of values ​​for the ring diameter and wire diameter is related to the frequency. Parameter scanning simulation is performed within the range using simulation software to obtain the optimal values ​​that meet the usage scenario.

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