Open-type resonator

Abstract

To provide an open-type resonator which can measure the dielectric property of a sample more accurately by removing an unnecessary resonance of a higher mode.SOLUTION: An open-type resonator 100 includes: a first spherical reflection mirror 11 having a first reflection sphere 13; and a second sphere reflection mirror 12 having a second reflection sphere 14 facing the first reflection sphere 13. At least one of the diameters M of opening surfaces exposed in the space between a first reflection sphere 13 and a second reflection sphere 13 of the first reflection sphere 13 and the second reflection sphere 14 is not larger than a half of the distance D between the first reflection sphere 13 and the second reflection sphere 14.SELECTED DRAWING: Figure 1

Description

Technical Field

[0004] , , ,

[0001] The present invention relates to an open resonator suitable for measuring the dielectric properties (real part of the complex relative permittivity (relative permittivity ε') and dielectric tangent (tan δ)) of a dielectric.

Background Art

[0002] In application fields such as automotive radar, optical communication, and high-speed digital devices, millimeter-wave frequencies are used. However, improving the position resolution in radar, increasing the communication speed in optical communication, and speeding up processing in digital devices are essential issues, and it is assumed that the millimeter-wave frequencies used will further increase. Currently, the 75 - 80 GHz band, 50 GHz band, and 40 GHz band are the frequency bands used in state-of-the-art devices, but frequencies exceeding 100 GHz are assumed in the future. Also, in the sixth-generation communication network (6G) following the fifth-generation communication network (5G), discussions have been made assuming the use of up to the 330 GHz band. Along with this, in the measurement of the material properties used in these devices, measurements using higher frequencies have become necessary. Among the material properties, since the energy loss of millimeter waves increases with increasing frequency, the measurement of the dielectric properties of materials has become an essential issue.

[0003] In the measurement of dielectric properties in the millimeter-wave band, since reducing its energy loss is an important development issue, the measurement of the dielectric tangent (loss angle, tan δ) is important. Conventionally, measurement using a resonator has been the mainstream. The split cylinder resonator is a typical device and is used for measuring the dielectric tangent of low-loss materials up to about 60 GHz. However, it has become difficult to accurately measure dielectric properties at higher frequencies with a split cylinder resonator, and an open resonator (Fabry - Perot resonator) is suitable at frequencies above that (Non-Patent Document 1).

[0004] In a Fabry-Perot resonator, a film-like sample is inserted between two spherical mirrors positioned opposite each other. For example, an input signal with a frequency of 100 GHz or higher is applied to perform resonance measurement, obtain the resonant waveform, and measure the dielectric properties of the sample. A network analyzer is often used for resonance measurement. The network analyzer is connected to the Fabry-Perot resonator, and a graph (resonant waveform) is obtained with frequency on the horizontal axis and transmitted signal intensity (transmission coefficient) on the vertical axis, and the resonance characteristics are measured. Here, "resonant characteristics" refer to the center frequency of resonance (resonant frequency) and the Q value (in this specification, the ratio of the center frequency to the 3 dB bandwidth is used). It is common to calculate or simulate the relative permittivity and dielectric loss tangent of the sample from the resonance characteristics with and without the sample.

[0005] Non-patent document 1 discloses an open-type resonator in which the distance D between the two spherical mirrors is 50 to 70 cm, the radius of curvature R between the two spherical mirrors is 127.0 cm, and the aperture diameter (diameter) of the reflective spheres in the two spherical mirrors is 36.8 cm. Furthermore, the Japanese Industrial Standard (JIS R1660-2) provides an example of an open-type resonator in which the aperture diameter of the reflective spheres in the two spherical mirrors is 80 to 205 mm, the radius of curvature R between the two spherical mirrors is the same as the aperture diameter of the reflective spheres, and the distance D between the two spherical mirrors is typically 1.2 times the aperture diameter of the reflective spheres (1.1 to 1.3 times depending on the value of tanδ).

[0006] When measuring the dielectric properties of a sample using a Fabry-Perot resonator, the resonance used for measurement is the TEM00q mode, but it is known that the TEMmnq mode resonance occurs as an unwanted higher-order mode. The order m is the rotational order, and the order n is the radial order. The order q is the z-direction (the direction connecting the centers of the two spherical mirrors) and corresponds to the number of standing waves between the two spherical mirrors (number of standing waves = q + 1). The TEM00q mode resonance can be either a symmetric mode where the antinode of the standing wave is at the center or an antisymmetric mode where the node of the standing wave is at the center. The resonance used for measuring dielectric properties is the symmetric mode, and in that case, the order q is an even number. In a realistic Fabry-Perot resonator, it is rare for the higher-order mode resonance to have an order m other than zero, and the resonance becomes the TEM0nq mode, where the order n is a natural number in the range of 1-5. The resonance of the TEM0nq mode occurs at a slightly higher frequency than the resonance of the TEM00q mode.

[0007] Figure 10 is a conceptual diagram illustrating the resonance modes in a Fabry-Perot resonator. Figure 10(a) shows the resonance of the TEM00q mode, Figure 10(b-1) shows the resonance of the TEM01q mode, which is one of the TEM0nq modes, and Figure 10(b-2) shows the resonance of the TEM02q mode, which is one of the TEM0nq modes. The resonance of the TEM00q mode has a spread approximated by a Gaussian distribution around a central axis connecting the centers of the opposing spherical mirrors 60, as shown in Figure 10(a). In contrast, the resonance of the TEM0nq mode has a larger spread from the central axis compared to the TEM00q mode, as shown in Figures 10(b-1) and (b-2).

[0008] When a sample is placed in a Fabry-Pero resonator for dielectric properties measurement, the resonance frequencies for each mode change (shift) from the state without the sample. Depending on the sample, the resonance frequency of the TEM00q mode used for measurement may shift, resulting in the TEM00q mode resonance waveform overlapping with the TEM0nq mode resonance waveform, causing measurement errors or making measurement impossible. Therefore, the above JIS recommends inserting an aperture (optical diaphragm) made of polyvinyl chloride (PVC) or the like, with a changeable hole diameter (diaphragm diameter), between the sample stage and one of the spherical reflectors 60 to reduce unwanted TEM0nq mode resonance. Figure 11 is a conceptual diagram illustrating the function of the aperture in a Fabry-Pero resonator. As shown in Figure 11(a), the TEM00q mode resonance has a small spread from the central axis connecting the centers of the opposing spherical reflectors 60, so it is hardly affected by the aperture diaphragm of the aperture 61. In contrast, the resonance of the TEM0nq mode has a radial extension of the spherical reflector 60, as shown in Figure 11(b), and is therefore blocked and suppressed by the aperture 61. [Prior art documents] [Non-patent literature]

[0009] [Non-Patent Document 1] AL CULLEN and PK YU, The accurate measurement of permittivity by means of open resonator, Proc. R. Soc. Lond. A. 325, 493-509 (1971) [Overview of the Initiative] [Problems that the invention aims to solve]

[0010] This invention provides an open-type resonator that allows for more accurate measurement of the dielectric properties of a sample by minimizing the impact on the resonant mode used for measuring dielectric properties (TEM00q mode) while suppressing the resonance of unwanted higher-order modes (especially TEM04q mode), more efficiently than when using an aperture. [Means for solving the problem]

[0011] The open-type resonator of the present disclosure comprises a first spherical mirror having a first reflective spherical surface, and a second spherical mirror having a second reflective spherical surface positioned opposite the first reflective spherical surface. At least one of the diameters of the opening surfaces of the first and second reflective spherical surfaces that are exposed in the space between the first and second reflective spherical surfaces is less than or equal to half the inter-spherical distance between the first and second reflective spherical surfaces. [Effects of the Invention]

[0012] According to the open-type resonator of this disclosure, it is possible to suppress unwanted higher-order mode resonances while minimizing the influence on the resonant modes used for measuring dielectric properties, more efficiently than when using an aperture, and thus measure the dielectric properties of a sample with higher accuracy. [Brief explanation of the drawing]

[0013] [Figure 1] Schematic diagram of a Fabry-Perot resonator according to Embodiment 1 [Figure 2] A schematic diagram showing the aperture diameter M, inter-spherical distance D, and radius of curvature R of the two reflective spherical surfaces of the Fabry-Perot resonator according to Embodiment 1 ((a): Comparative Example 1a, (b): Example 1). [Figure 3] Conceptual diagram illustrating the resonant modes measured in a Fabry-Perot resonator. [Figure 4] The figure shows the resonance waveform measured with the Fabry-Perot resonator according to Embodiment 1 when no sample is attached ((a): Comparative Example 1a, (b): Example 1). [Figure 5]The figure shows the resonance waveform with the measurement sample attached, measured using the Fabry-Perot resonator according to Embodiment 1 ((a): Comparative Example 1a, (b): Example 1). [Figure 6] Figure (a): Comparative Example 1a, (b): Example 1, showing the dielectric loss tangent (tanδ) measured with the Fabry-Perot resonator according to Embodiment 1. [Figure 7] A schematic diagram showing the aperture diameter M, inter-spherical distance D, and radius of curvature R of the two reflective spherical surfaces of the Fabry-Perot resonator according to Embodiment 2 ((a): Comparative Example 2a, (b): Example 2). [Figure 8] Figure (a): Comparative Example 2a, (b): Example 2, showing the resonance waveform measured with the Fabry-Perot resonator according to Embodiment 2 without a sample attached. [Figure 9] This figure summarizes the results of resonance measurements using a Fabry-Perot resonator, as in Embodiment 3. [Figure 10] Conceptual diagram illustrating the resonant modes in a Fabry-Perot resonator ((a): TEM00q mode, (b-1): TEM0nq (TEM01q) mode, (b-2): TEM0nq (TEM02q) mode) [Figure 11] Conceptual diagram illustrating the function of aperture in a Fabry-Perot resonator ((a): TEM00q mode, (b): TEM0nq mode) [Modes for carrying out the invention]

[0014] (Embodiment 1) Figure 1 is a schematic diagram of a Fabry-Perolo resonator according to Embodiment 1. As shown in Figure 1, the Fabry-Perolo resonator 100 according to Embodiment 1 includes a fixed base 10, a first spherical reflector 11, a second spherical reflector 12, a sample stage 20, a position adjustment mechanism 35, and a cover 50. The Fabry-Perolo resonator 100 is an example of an open-type resonator. In the following description, the XYZ Cartesian coordinate system shown in Figure 1 will be used, with the X direction corresponding to the vertical direction, the Y direction to the front-back direction, and the Z direction to the left-right direction.

[0015] As shown in Fig. 1, on the fixed stage 10, a first spherical mirror 11 having a first reflecting spherical surface 13 and a second spherical mirror 12 having a second reflecting spherical surface 14 are arranged opposite to each other. At this time, the center of the first reflecting spherical surface 13 and the center of the second reflecting spherical surface 14 have a predetermined spherical distance D. At the centers of the first reflecting spherical surface 13 and the second reflecting spherical surface 14, a first waveguide 41 and a second waveguide 42 are respectively arranged. At the tip openings on the spherical side of the first waveguide 41 and the second waveguide 42, a first coupling hole 15 and a second coupling hole 16 having a minute diameter for forming a coupling state to obtain a desired resonance characteristic are respectively formed. The first waveguide 41 of the first spherical mirror 11 is a signal injection part to which an input signal for measuring the dielectric characteristics of the sample is input, and the second waveguide 42 of the second spherical mirror 12 is a signal detection part from which a detection signal is output.

[0016] As shown in Fig. 1, the sample stage 20 has a through hole 24 and is arranged between the first spherical mirror 11 and the second spherical mirror 12 that face each other. A sample 25 to be measured for dielectric characteristics is mounted on the sample stage 20. The sample 25 mounted on the sample stage 20 is exposed from the through hole 24. The diameter of the through hole 24 is set smaller than the opening diameter M of the first and second reflecting spherical surfaces 13, 14.

[0017] As shown in Fig. 1, the position adjustment mechanism 35 has a pedestal 36 and a micrometer 37. The pedestal 36 is installed so as to be movable (slide) in the Z direction with respect to the fixed stage 10 (that is, the first spherical mirror 11 and the second spherical mirror 12). The operator can move the pedestal 36 by operating the micrometer 37. The sample stage 20 is fixed to the pedestal 36. That is, the operator can adjust the position of the sample 25 attached to the sample stage 20 in the Z direction by operating the micrometer 37 to move the sample stage 20 fixed to the pedestal 36 via the pedestal 36.

[0018] The cover 50 is formed in a U-shape and has a front plate, a back plate, and a top plate connecting the front plate and the back plate, all made of transparent acrylic. As shown in Figure 1, when measuring dielectric properties, the front plate, back plate, and top plate of the cover 50 cover the front, back, and top sides of the Fabry-Pero resonator 100, respectively. When the sample 25 is mounted on the sample stage 20, the cover 50 is slid upward and removed from the Fabry-Pero resonator 100, exposing the space between the first spherical mirror 11 and the second spherical mirror 12 (i.e., the space where the sample stage 20 is placed).

[0019] Figure 2 is a schematic diagram showing the relationship between the aperture diameter M, the distance between spheres D, and the radius of curvature R in the two reflective spheres of the Fabry-Perot resonator according to Embodiment 1, where Figure 2(a) shows Comparative Example 1a and Figure 2(b) shows Embodiment 1. In Embodiment 1, as shown in Figures 1 and 2, the entirety of the first reflective spheres 13, 13a and the second reflective spheres 14, 14a are exposed in the space between the first and second reflective spheres, so the diameter of the reflective spheres coincides with the aperture diameter M of the reflective spheres (corresponding to the diameter of the aperture surface).

[0020] The aperture diameter M, inter-spherical distance D, and radius of curvature R of the reflective spheres in Comparative Example 1a and Example 1 shown in Figure 2 are as follows. In the Fabry-Perot resonator 100 according to Embodiment 1, the inter-spherical distance D is set to 80 mm to correspond to an input signal with a relatively high measurement frequency bandwidth (J band: 220-330 GHz). Aperture diameter M of the reflective sphere: 50 mm (Comparative Example 1a), 28 mm (Example 1) Radius of curvature R: 64 mm (Comparative Example 1a and Example 1) Interspherical distance D: 80 mm (Comparative Example 1a and Example 1)

[0021] That is, the aperture diameter M of the reflective sphere in Comparative Example 1a is greater than half the distance between spheres D and greater than half the radius of curvature R. In contrast, the aperture diameter M of the reflective sphere in Example 1 is less than or equal to half the distance between spheres D and less than or equal to half the radius of curvature R. Note that the configuration of the Fabry-Perot resonator in Comparative Example 1a, other than the first and second spherical reflectors 11a, 12a and the first and second reflective spheres 13a, 14a, is the same as that of the Fabry-Perot resonator 100 in Example 1, so a description is omitted.

[0022] (Measurement of dielectric properties) The procedure (steps) for measuring the dielectric properties using the Fabry-Perot resonator 100 is as follows: 1) Connect the Fabry-Perot resonator 100, network analyzer, and controller with cables. 2) Without a sample attached (no sample), measure the resonance characteristics (first resonance characteristics) at the resonance frequency to be measured, and determine the Q value Qempty from the bandwidth of the resonance waveform. 3) Measure five resonant frequencies, including the resonance at the frequency to be measured and the resonances immediately before and after it. From these five resonant frequencies, calculate the inter-spherical distance D between the reflective spheres. 4) After removing the cover 50 and mounting the sample 25 onto the sample stage 20, the space between the first spherical reflecting mirror 11 and the second spherical reflecting mirror 12 is covered with the cover 50. 5) Operate the micrometer 37 to adjust the position of the sample 25 (adjust the position of the sample 25 to the position where the resonant frequency is at its minimum). 6) With the position of sample 25 adjusted (sample present), measure the resonance characteristics (second resonance characteristics) at the resonance frequency to be measured, and determine the center frequency of the resonance (resonance frequency Fsample) and the Q value Qsample that have shifted due to the insertion of sample 25. 7) Calculate the relative permittivity ε' and dielectric loss tangent tanδ of the sample from the thickness t of sample 25, the inter-spherical distance D, the Q value Qempty without the sample, the resonant frequency Fsample with the sample, and the Q value Qsample with the sample. When measuring dielectric properties at multiple frequencies for the same sample 25, after step 1) above, steps 2) and 3) above are performed for all frequencies of the sample to be measured, then steps 4) and 5) above are performed, and then steps 6) and 7) above are performed for all frequencies of the sample to be measured.

[0023] Next, we will explain the resonance modes excited in the Fabry-Perot resonator. Figure 3 is a conceptual diagram illustrating the resonance modes excited in the Fabry-Perot resonator. Figure 3 shows the resonance waveform measured when the resonance characteristics are measured without the sample in step 2) above, along with the corresponding resonance modes. The arrows in Figure 3 indicate the direction of shift in the resonance frequency of each resonance mode and the amount of change (shift) when the resonance characteristics are measured with the sample in step 6) above.

[0024] The resonance used for measuring dielectric properties is the TEM00q mode. Below the resonance frequency of the TEM00q mode, the resonance of the TEM00(q-1) mode is observed, and above the resonance of the TEM00(q+1) mode is observed. The TEM00q, TEM00(q-1), and TEM00(q+1) modes are resonances in which the signal intensity spreads in a Gaussian distribution around a central axis connecting the centers of two opposing reflective spheres. In the TEM00q mode, the antinode of the standing wave is located at the center of its central axis, while in the TEM00(q-1) and TEM00(q+1) modes, the nodes of the standing wave are located at the center of their central axis. Resonances of the TEM0n(q-1) mode and TEM0nq mode appear at frequencies between the TEM00q and TEM00(q-1) modes, and between the TEM00q and TEM00(q+1) modes, respectively. Figure 3 shows the resonances of the TEM0n(q-1) mode and TEM0nq mode when the order n is 1 to 4.

[0025] When sample 25 is mounted in step 6) above and positioned at the antinode (center of the resonator) of the TEM00q mode resonance, the measured shift in resonance frequency alternates between resonance modes with relatively large and small shifts, as shown by the arrows in Figure 3. In Figure 3, the resonance modes with large shifts are those where the antinode is at the center of the resonator where the sample is located, and the resonance modes with small shifts are those where the node is at the center. Since the TEM00q mode resonance is used to measure dielectric properties, sample 25 is positioned at the antinode (center of the resonator) of that resonance, and the shift in its resonance frequency is relatively large. This shift differs depending on the type and thickness t of sample 25. For example, comparing modified polyimide (MPI) with a thickness t of 50 μm and polycarbonate (PC) with a thickness t of 98 μm as sample 25, the shift in the resonance frequency of polycarbonate is larger. When the resonant frequency shift of the TEM00q mode, which is used to measure dielectric properties, becomes large, the resonant frequency shift of the TEM04(q-1) mode, which is located on the lower frequency side of the TEM00q mode, is relatively small. Therefore, when measuring the resonant properties with sample 25 attached, the resonant waveform of the TEM00q mode is superimposed on the resonant waveform of the TEM04(q-1) mode, causing distortion in the TEM00q mode's resonant waveform, which can make it impossible to accurately measure the dielectric properties of sample 25. In a realistically designed Fabry-Perot resonator, resonances of the TEM0n(q-1) mode with an order n of 5 or higher rarely occur. Furthermore, as shown in Figure 3, the resonant frequency of the TEM03(q-1) mode shifts in the same direction and to the same extent as the TEM00q mode, and the resonant frequency of the TEM02(q-1) mode is far removed from the TEM00q mode, so it does not affect actual measurements. Therefore, in order to more accurately measure the dielectric properties of sample 25, it is necessary to sufficiently reduce the resonance of the TEM04(q-1) mode.

[0026] The amplitude (intensity) of each resonance, such as the TEM00q mode and TEM04(q-1) mode, tends to be relatively larger on the high-frequency side of the measurement frequency bandwidth (220-330 GHz in Embodiment 1) and smaller on the low-frequency side. On the high-frequency side, the input signal wavelength is short, so the input signal easily passes through the coupling hole, and the spreading due to diffraction is small, making it difficult to reduce the aperture diameter M of the reflective sphere (or reduce the aperture diameter if aperture 61 is used), resulting in larger amplitudes for each resonance mode. On the low-frequency side, the input signal wavelength is long, so the input signal is difficult to pass through the coupling hole, and the spreading due to diffraction is large, making it easier to reduce the aperture diameter M of the reflective sphere (or reduce the aperture diameter if aperture 61 is used), resulting in smaller amplitudes for each resonance and a deterioration in the Q factor. Therefore, in order to more accurately measure the dielectric properties of sample 25, it is necessary to sufficiently reduce the resonance of the TEM04(q-1) mode, which has a large amplitude at high frequencies, and to ensure sufficient amplitude and Q value for the resonance of the TEM00q mode, which has a small amplitude and degraded Q value at low frequencies.

[0027] Next, we will explain the results of resonance measurements performed using Fabry-Perot resonators with aperture diameter M, inter-spherical distance D, and radius of curvature R shown in Comparative Example 1a and Example 1 in Figure 2. Figure 4 shows the resonance waveform measured without a sample being attached, with Figure 4(a) showing Comparative Example 1a and Figure 4(b) showing Example 1. In Comparative Example 1a shown in Figure 4(a), a polyvinyl chloride aperture 61 was inserted between the sample stage 20 and the second reflective sphere 14a, and the aperture diameter of the aperture 61 was adjusted to minimize the unwanted higher-order TEM04(q-1) mode resonance within a range that does not significantly affect the TEM00q mode resonance necessary for measurement. In Example 1 shown in Figure 4(b), no aperture was used.

[0028] As shown in Figure 4, in both Comparative Example 1a and Example 1, an input signal of 299 GHz was used as the measurement frequency, and resonance of the TEM00q mode, which is used for measuring dielectric properties, was observed around 299 GHz. In addition, in Comparative Example 1a, as shown in Figure 4(a), resonance of the higher-order mode, TEM04(q-1) mode, was observed around a frequency of 298.3 GHz. That is, in Comparative Example 1a, even if the aperture diameter of aperture 61 is optimized, if the amplitude and Q value of the TEM00q mode resonance are to be maintained to the extent necessary for measurement, the resonance of the TEM04(q-1) mode, which interferes with the measurement, inevitably remains. In contrast, in Example 1, as shown in Figure 4(b), no resonance was observed around a frequency of 298.3 GHz. In other words, in the Fabry-Perot resonator 100 of Example 1, the aperture diameter M (28 mm) of the reflecting sphere is set smaller than the aperture diameter M (50 mm) in Comparative Example 1a. Therefore, the resonance of the TEM04(q-1) mode, which interferes with measurements, is efficiently eliminated without significantly affecting the resonance of the TEM00q mode.

[0029] Figure 5 shows the resonance waveform measured with the measurement sample attached. Figure 5(a) shows Comparative Example 1a, and Figure 5(b) shows Example 1. A polycarbonate with a thickness t of 98 μm was used as sample 25. In Comparative Example 1a shown in Figure 5(a), the measurement was performed with an aperture 61 inserted, similar to Comparative Example 1a shown in Figure 4(a), while in Example 1 shown in Figure 5(b), no aperture was used.

[0030] As shown in Figure 5, in both Comparative Example 1a and Example 1, the insertion of sample 25 shifts the resonance frequency of the TEM00q mode to a lower frequency, and resonance of the TEM00q mode is observed around 298.45 GHz. In Comparative Example 1a, as shown in Figure 5(a), the resonance of the higher-order mode, TEM04(q-1) mode, is observed around 298.3 GHz when sample 25 is inserted. Furthermore, as explained using Figure 3, generally the amount of shift in the resonance frequency of the TEM04(q-1) mode to a lower frequency due to the insertion of sample 25 is smaller than that of the TEM00q mode. However, in this embodiment, when polycarbonate with a thickness t of 98 μm is used as sample 25, it can be seen that the resonance frequency of the TEM04(q-1) mode hardly shifts. In contrast, in Example 1, as shown in Figure 5(b), resonance is not observed around 298.3 GHz. In other words, in the Fabry-Perot resonator 100 of Example 1, the aperture diameter M (28 mm) of the reflective sphere is set to less than half the inter-sphere distance D (80 mm), so it is thought that the resonance of the higher-order mode, TEM04(q-1) mode, is eliminated. As shown in Comparative Example 1a in Figure 5(a), if a resonance of a higher-order mode having a resonance frequency near the resonance frequency of the TEM00q mode used for measuring dielectric properties appears, it will cause distortion in the resonance waveform of the TEM00q mode. When distortion occurs in the resonance waveform of the TEM00q mode, an error occurs in the 3 dB bandwidth, and the Q value (i.e., tanδ) cannot be measured accurately.

[0031] Furthermore, comparing the case without a sample in Figure 4(a) of Comparative Example 1a with the case with a sample in Figure 5(a), the amplitude of the TEM00q mode resonance, which is used for measuring dielectric properties, is reduced due to the dielectric loss of the sample. However, the resonance of the TEM04(q-1) mode, which is detrimental to the measurement, is less affected by the sample, and its amplitude is not reduced. Therefore, if the resonance of the unnecessary higher-order mode, TEM04(q-1) mode, is not sufficiently reduced and remains, the amplitude of the TEM04(q-1) mode resonance becomes relatively larger compared to the TEM00q mode, and its impact on the measurement of dielectric properties becomes greater.

[0032] Figure 6 shows the dielectric loss tangent (tanδ) measured in the Fabry-Perot resonators of Comparative Example 1a and Example 1. Figure 6(a) shows Comparative Example 1a, and Figure 6(b) shows Example 1. The sample 25 measured is polycarbonate with a thickness t of 98 μm. In Comparative Example 1a shown in Figure 6(a), the measurement was performed with an aperture 61 inserted, similar to Comparative Example 1a shown in Figure 4(a), while in Example 1 shown in Figure 6(b), no aperture was used.

[0033] As shown in Figure 6, the measured value of tanδ in Comparative Example 1a shown in Figure 6(a) shows greater variation compared to Example 1 shown in Figure 6(b). This is because, in the Fabry-Perot resonator of Comparative Example 1a, the aperture diameter M of the first and second reflective spheres 13a and 14a is greater than half the inter-sphere distance D, so the resonance of higher-order modes is not sufficiently reduced. As a result, the resonance waveform of the higher-order mode, TEM04(q-1), is superimposed on the resonance waveform of the TEM00q mode used for measuring dielectric properties, causing distortion in the resonance waveform of the TEM00q mode.

[0034] (Embodiment 2) Figure 7 is a schematic diagram showing the relationship between the aperture diameter M, the distance between spheres D, and the radius of curvature R in the two reflective spheres of the Fabry-Perot resonator according to Embodiment 2, where Figure 7(a) shows Comparative Example 2a and Figure 7(b) shows Embodiment 2.

[0035] The aperture diameter M, inter-spherical distance D, and radius of curvature R of the reflective spheres in Comparative Example 2a and Example 2 shown in Figure 7 are as follows. In the Fabry-Perot resonator according to Embodiment 2, the inter-spherical distance D is set to 120 mm to correspond to an input signal with a lower measurement frequency bandwidth (D-band: 110-170 GHz) than that of the Fabry-Perot resonator according to Embodiment 1. Aperture diameter M of the reflective spherical surface: 61 mm (Comparative Example 2a), 45 mm (Example 2) Radius of curvature R: 96 mm (Comparative Example 2a and Example 2) Interspherical distance D: 120 mm (Comparative Example 2a and Example 2)

[0036] That is, the aperture diameter M of the reflective sphere in Comparative Example 2a is greater than half the distance between spheres D and greater than half the radius of curvature R. In contrast, the aperture diameter M of the reflective sphere in Example 2 is less than or equal to half the distance between spheres D and less than or equal to half the radius of curvature R. Note that the configurations of the Fabry-Perot resonators in Comparative Example 2a and Example 2, other than the first spherical mirrors 111a, 111, the second spherical mirrors 112a, 112, the first reflective spheres 113a, 113 and the second reflective spheres 114a, 114, are the same as those of the Fabry-Perot resonator 100 in Embodiment 1 (Example 1), so their description is omitted.

[0037] Next, we will explain the results of resonance measurements performed using Fabry-Perot resonators having aperture diameter M, inter-spherical distance D, and radius of curvature R as shown in Comparative Example 2a and Example 2 in Figure 7. Figure 8 shows the resonance waveform measured without a sample being attached, with Figure 8(a) showing Comparative Example 2a and Figure 8(b) showing Example 2. In Comparative Example 2a shown in Figure 8(a), an aperture 61 was inserted between the sample stage 20 and the second reflective sphere 114a, and the aperture diameter of the aperture 61 was adjusted to minimize the unwanted higher-order TEM0nq mode resonance within a range that does not affect the TEM00q mode resonance necessary for measurement. In Example 2 shown in Figure 8(b), no aperture was used.

[0038] As shown in Figure 8, in both Comparative Example 2a and Example 2, an input signal of 167 GHz was used as the measurement frequency, and resonance of the TEM00q mode, which is used for measuring dielectric properties, was observed around 167 GHz. In addition, in Comparative Example 2a, as shown in Figure 8(a), resonance of the higher-order mode, TEM04(q-1) mode, was observed around a frequency of 166.6 GHz. In contrast, in Example 2, as shown in Figure 8(b), no resonance was observed around a frequency of 166.6 GHz. That is, in the Fabry-Perot resonator of Example 2, the aperture diameter M (45 mm) of the reflecting sphere was set smaller than the aperture diameter M (61 mm) in Comparative Example 2a, so it is thought that the resonance of the higher-order mode, TEM04(q-1) mode, was eliminated.

[0039] (Embodiment 3) Next, the relationship between the aperture diameter M of the reflective sphere and the measurement frequency (i.e., the corresponding wavelength λ) will be explained. In Comparative Examples 1a and 2a of Embodiments 1 and 2, the aperture diameter 61 was adjusted to minimize the unwanted higher-order TEM04(q-1) mode resonance within a range that does not substantially affect the TEM00q mode resonance used for resonance measurement, and the measurement results are shown. Embodiment 3 shows the low-frequency and high-frequency measurement results for Examples 1 and 2 of Embodiments 1 and 2, Comparative Examples 1a and 2a (large aperture diameter) in which the aperture 61 was adjusted to minimize the TEM04(q-1) mode resonance within a range that does not affect the TEM00q mode resonance, and Comparative Examples 1b and 2b (small aperture diameter) in which the aperture 61 was further narrowed to the extent that the TEM04(q-1) mode resonance could be eliminated compared to Comparative Examples 1a and 2a. Figure 9 is a summary of these resonance measurement results. Figure 9 shows the wavelength λ corresponding to the measurement frequency range and the ratio M / λ of the aperture diameter of the reflecting sphere to the wavelength λ, along with whether the TEM04(q-1) mode resonance that interferes with the measurement has been sufficiently removed, and whether the amplitude and Q value of the TEM00q mode resonance used for the measurement are sufficient. In Figure 9, the "○" mark indicates that the TEM04(q-1) mode resonance has been sufficiently removed or the amplitude and Q value of the TEM00q mode resonance are sufficient, while the "×" mark indicates that the TEM04(q-1) mode resonance has not been sufficiently removed or the amplitude or Q value of the TEM00q mode resonance is insufficient.

[0040] In resonance measurements, as described above, the amplitude of each resonance mode is larger at higher frequencies than at lower frequencies in the bandwidth of the measurement frequency. As described above, the amplitude reduction when a sample is attached is greater for the TEM00q mode resonance used for measurement than for the TEM04(q-1) mode which interferes with the measurement. Therefore, at higher frequencies, in resonance measurements without a sample, the amplitude of the TEM04(q-1) mode resonance must be sufficiently reduced. As shown in Figure 9, in the Fabry-Perot resonator of Example 1, the amplitude of the TEM04(q-1) mode resonance was sufficiently reduced at both the high-frequency and low-frequency 220 GHz measurement frequencies, and in the Fabry-Perot resonator of Example 2, the amplitude of the TEM04(q-1) mode resonance was sufficiently reduced at both the high-frequency 170 GHz and low-frequency 110 GHz measurement frequencies, confirming that the amplitude and Q value of the TEM00q mode resonance were sufficient.

[0041] In contrast, the Fabry-Pero resonator of Comparative Example 1a did not sufficiently reduce the TEM04(q-1) mode resonance at the high-frequency end of 330 GHz, and the Fabry-Pero resonator of Comparative Example 2a did not sufficiently reduce the TEM04(q-1) mode resonance at the high-frequency end of 170 GHz. In Comparative Example 1b, where the aperture 61 diameter was reduced to sufficiently reduce the TEM04(q-1) mode resonance at the high-frequency end of 330 GHz, and in Comparative Example 2b, where the aperture 61 diameter was reduced to sufficiently reduce the TEM04(q-1) mode resonance at the high-frequency end of 170 GHz, the TEM00q mode resonance resonance amplitude or Q value was not sufficient. In other words, in each comparative example, even when adjusting the aperture diameter of aperture 61, it is difficult to achieve both sufficient reduction of the TEM04(q-1) mode resonance and sufficient amplitude and Q value of the TEM00q mode resonance across the entire bandwidth of the measurement frequency.

[0042] Furthermore, as mentioned above, at lower frequencies within the bandwidth of the measurement frequency, the amplitude and Q value of the resonance of each resonance mode become relatively smaller. If the amplitude and Q value of the TEM00q mode used for measuring dielectric properties become too small, it becomes difficult to measure the resonance properties. In particular, with samples that have high dielectric loss, the amplitude and Q value of the TEM00q mode resonance become too small, making it difficult to distinguish from noise and making it difficult to obtain accurate resonance measurement results. In resonance measurements using polycarbonate (PC) with a thickness t of 98 μm, which has relatively high dielectric loss, the Fabry-Perot resonator in Example 1, even at a low measurement frequency of 220 GHz, and the Fabry-Perot resonator in Example 2, even at a low measurement frequency of 110 GHz, were able to obtain the amplitude and Q value necessary for resonance measurement without the amplitude and Q value of the TEM00q mode itself becoming too small. Furthermore, when the aperture diameter M of the reflective spherical surface of the Fabry-Perot resonators in Examples 1 and 2 was further reduced, a tendency for the resonance characteristics of the TEM00q mode to deteriorate was observed, particularly at low frequencies. From the above results, it is necessary to set the aperture diameter M of the reflective spherical surface to 15 times or more the wavelength of the measurement frequency at measurement frequencies of 100 GHz or higher, and 20 times or more the wavelength of the measurement frequency at measurement frequencies of 220 GHz or higher, in order to accurately measure the resonance.

[0043] (Effects, etc.) As described above, the Fabry-Perot resonators of Examples 1 and 2 include first spherical mirrors 11 and 111 having first reflective spherical surfaces 13 and 113, and second spherical mirrors 12 and 112 having second reflective spherical surfaces 14 and 114 positioned opposite the first reflective spherical surfaces 13 and 113. The aperture diameter M of the first reflective spherical surfaces 13 and 113 and the second reflective spherical surfaces 14 and 114 is less than or equal to half the inter-spherical distance D between the first reflective spherical surfaces 13 and 113 and the second reflective spherical surfaces 14 and 114.

[0044] This allows the Fabry-Perot resonator to measure the dielectric properties of a sample with greater accuracy by eliminating unwanted higher-order mode resonances without substantially affecting the resonance of the TEM00q mode used for measurement.

[0045] Furthermore, in the Fabry-Perot resonators according to Examples 1 and 2, the aperture diameter M of the first reflective spherical surfaces 13, 113 and the second reflective spherical surfaces 14, 114 is less than or equal to half the radius of curvature R of the first reflective spherical surfaces 13, 113 and the second reflective spherical surfaces 14, 114. As a result, the Fabry-Perot resonator can more effectively reduce unwanted higher-order mode resonances.

[0046] Furthermore, it is desirable to set the aperture diameter M of the reflective sphere to 15 times or more the wavelength of the measurement frequency. This allows the Fabry-Perot resonator to measure the resonance of the TEM00q mode used for measurement with a sufficiently large amplitude and Q value.

[0047] Furthermore, in the Fabry-Perot resonators according to Embodiments 1 and 2, the diameter of the through-hole 24 in the sample stage 20 is smaller than the aperture diameter M of the first reflective spheres 13 and 113 and the second reflective spheres 14 and 114. As a result, the Fabry-Perot resonator can more effectively reduce unwanted higher-order mode resonances.

[0048] (Other embodiments) In Embodiments 1 to 3, a Fabry-Pero resonator was described in which the aperture diameters M of the first reflective spheres 13 and 113 and the second reflective spheres 14 and 114 were the same. Since the measured resonance characteristics depend on the smaller aperture diameter, if the aperture diameter M of at least one of the first and second reflective spheres is less than or equal to half the distance D between the spheres, then, as in Embodiments 1 to 3, the resonance of higher-order modes that are unnecessary for measuring dielectric properties can be sufficiently reduced. For example, in a Fabry-Pero resonator using the first spherical reflector 11a (aperture diameter M of the first reflective sphere 13a: 50 mm) of Comparative Example 1a of Embodiment 1 and the second spherical reflector 12 (aperture diameter M of the second reflective sphere 14: 28 mm) of Example 1, the resonance of unwanted higher-order modes can also be sufficiently reduced.

[0049] In embodiments 1 to 3, a Fabry-Perot resonator was described in which the entirety of the first reflective spherical surfaces 13, 113 and the second reflective spherical surfaces 14, 114 are exposed in the space between the first and second reflective spherical surfaces, and the diameter of the reflective spherical surface is the same as the aperture diameter M of the reflective spherical surface. Instead of reducing the diameter of the reflective spherical surface itself, a limiter (for example, a plate made of aluminum or resin) having a circular opening smaller than the diameter of the reflective spherical surface may be attached to the reflective spherical surface so that the centers of the reflective spherical surface and the circular opening are coaxial, thereby substantially reducing the aperture diameter M of the reflective spherical surface. In this case as well, if the diameter of the aperture surface of the reflective spherical surface that contributes to the measured resonance characteristics (aperture diameter M) is half or less of the inter-spherical distance D, then, as in embodiments 1 to 3, resonance of higher-order modes that are unnecessary for measuring dielectric properties can be sufficiently reduced. For example, in the Fabry-Perot resonator of Comparative Example 1a of Embodiment 1, if a limiter having a circular opening (diameter: 28 mm) is attached to the first spherical reflector 11a (aperture diameter M of the first reflecting spherical surface 13a: 50 mm), the aperture diameter M of the first reflecting spherical surface 13a becomes substantially 28 mm, so unwanted higher-order mode resonances can be sufficiently reduced.

[0050] In the Fabry-Perot resonators of Embodiments 1 to 3, an example was described in which the diameter of the through-hole 24 of the sample stage 20 is smaller than the aperture diameter M of the first reflective spheres 13, 113 and the second reflective spheres 14, 114. If the aperture diameter M is less than or equal to half the inter-sphere distance D, it is possible to sufficiently reduce the resonance of higher-order modes that are unnecessary for measuring dielectric properties, so the diameter of the through-hole 24 may be set larger than the aperture diameter M. However, setting the diameter of the through-hole 24 smaller than the aperture diameter M can further reduce the resonance of higher-order modes.

[0051] In the Fabry-Perot resonators of Embodiments 1 to 3, a first waveguide 41 and a second waveguide 42 were used in the signal injection section and the signal detection section, respectively. Depending on the measurement frequency, a coaxial cable with a loop antenna at its end can also be used instead of the first waveguide 41 and the second waveguide 42. [Industrial applicability]

[0052] The open-type resonator of the present invention is suitable for measuring the dielectric properties of a sample with higher precision by eliminating unwanted higher-order mode resonances in the millimeter-wave frequency band exceeding 100 GHz. [Explanation of symbols]

[0053] 10 Fixed base 11, 11a, 111, 111a First spherical reflector 12, 12a, 112, 112a Second spherical reflector 13, 13a, 113, 113a First reflecting sphere 14, 14a, 114, 114a Second reflecting sphere 15 First bonding pore 16 Second bonding pore 20 Sample stage 24 Through holes 25 samples 35 Position adjustment mechanism 36 Pedestal 37 micrometers 41 The first waveguide 42 The second waveguide 50 Cover 60 Spherical reflector 61 Aperture 100 Fabry-Perot resonators D: Distance between spheres M Opening diameter R radius of curvature λ wavelength

Claims

1. a first spherical reflector having a first reflective spherical surface; a second spherical reflecting mirror having a second reflecting spherical surface disposed opposite to the first reflecting spherical surface, the open resonator being used for measuring dielectric characteristics of a dielectric material at a measurement frequency of 100 GHz or more, At least one of the opening diameter of the first reflecting spherical surface and the opening diameter of the second reflecting spherical surface is equal to or less than half the inter-spherical distance between the first reflecting spherical surface and the second reflecting spherical surface, and is equal to or less than half the radius of curvature of the first reflecting spherical surface and the second reflecting spherical surface. Open resonator.

2. At least one of the opening diameter of the first reflecting spherical surface and the opening diameter of the second reflecting spherical surface is 15 times or more the wavelength of the measurement frequency.

2. The open resonator according to claim 1.

3. a sample stage disposed between the first and second reflecting spherical surfaces and having a through hole for exposing a sample; The diameter of the through hole is smaller than at least one of the opening diameter of the first reflecting spherical surface and the opening diameter of the second reflecting spherical surface.

3. The open resonator according to claim 1 or 2.

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