CN112332841B - Rectangular microwave cavity for rubidium frequency standard - Google Patents

Rectangular microwave cavity for rubidium frequency standard Download PDF

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CN112332841B
CN112332841B CN202110010055.0A CN202110010055A CN112332841B CN 112332841 B CN112332841 B CN 112332841B CN 202110010055 A CN202110010055 A CN 202110010055A CN 112332841 B CN112332841 B CN 112332841B
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dielectric block
cavity
rubidium
dielectric
block
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CN112332841A (en
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牛秀梅
王晨
王鹏飞
赵峰
梅刚华
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Institute of Precision Measurement Science and Technology Innovation of CAS
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    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03LAUTOMATIC CONTROL, STARTING, SYNCHRONISATION OR STABILISATION OF GENERATORS OF ELECTRONIC OSCILLATIONS OR PULSES
    • H03L7/00Automatic control of frequency or phase; Synchronisation
    • H03L7/26Automatic control of frequency or phase; Synchronisation using energy levels of molecules, atoms, or subatomic particles as a frequency reference

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Abstract

The invention discloses a rectangular microwave cavity for a rubidium frequency scale, which comprises a cavity, wherein the cavity is internally cuboid, one end face of the cavity is opened to serve as a light outlet, the other end face of the cavity is provided with a light inlet hole, a wire groove is circumferentially arranged on the outer surface of the cavity, a C-field coil is wound in the wire groove, a rubidium atomic bubble is arranged in the cavity, a first dielectric block and a third dielectric block are arranged on two opposite sides of the rubidium atomic bubble, a second dielectric block and a fourth dielectric block are arranged on two opposite sides of the rubidium atomic bubble, and the first dielectric block, the second dielectric block, the third dielectric block, the fourth dielectric block and the fourth dielectric block respectively comprise a dielectric base block and a metal sheet arranged on the dielectric. The method has the advantages of small processing difficulty, easy control of precision to ensure consistency, contribution to excitation of rubidium atoms for clock transition, further obtainment of microwave search signals with high signal-to-noise ratio, and very concise cavity structure.

Description

Rectangular microwave cavity for rubidium frequency standard
Technical Field
The invention belongs to the field of atomic frequency standards, and particularly relates to a rectangular microwave cavity for a rubidium frequency standard, which is mainly applied to a high-performance miniaturized rubidium atomic frequency standard.
Background
The atomic frequency standard (atomic clock) uses stable transition frequency between energy levels in atoms or ions as a measurement reference, provides high-reliability frequency and time instruments and equipment, and greatly improves the accuracy and stability of time frequency measurement. Rubidium atomic clock is the most widely used atomic clock at present due to the characteristics of simple structure, small volume, light weight, low power consumption, good comprehensive performance and the like, and the important progress is made in the aspects of high performance, miniaturization, adaptation to severe environment and the like.
The core of the rubidium frequency standard is a physical system which mainly comprises a rubidium spectrum lamp, a microwave cavity, a rubidium atomic bubble, a photoelectric detector and other components. Wherein, the rubidium atom bubble is positioned in the microwave cavity and is a place where the rubidium atoms generate resonance transition; the microwave cavity is used for storing microwave energy, resonance generates a standing wave field consistent with transition frequency of rubidium atoms, and rubidium atoms in the atom bubbles are excited to generate resonance transition, so that a physical system can provide stable reference frequency. The size and the internal structure of the microwave cavity determine the characteristics of the cavity such as resonant frequency, resonant mode, field pattern distribution and the like, further determine the number of rubidium atoms participating in resonant transition, and influence the performance of a rubidium frequency standard complete machine to a great extent. Meanwhile, as the most main structural component in a physical system, the size of the microwave resonant cavity basically determines how small the physical system can be, that is, the miniaturization and integration degree of the microwave cavity also affect the miniaturization of the rubidium frequency standard complete machine. Therefore, in order to obtain a high-performance miniaturized rubidium frequency standard complete machine, the structural optimization and the miniaturized design of the microwave cavity are important contents of research and design.
At present, the resonant cavities applied to the miniaturized rubidium frequency standard are mainly as follows. Standard TE111The cylindrical cavity is a miniaturized rubidium frequency scale microwave cavity which is most widely applied, but the cylindrical cavity is large in size, small in Q value and uneven in-cavity field distribution. TE adopted in FE-5680A type rubidium frequency standard produced by FEI company101The modular standard rectangular cavity structure can effectively reduce the volume of the microwave cavity, and is realized by filling a dielectric plate with certain thickness in the direction parallel to the Z axis, but the part with uniform microwave magnetic field is limited. Another commonly used rectangular structure resonant cavity is the coaxial TEM cavity designed by j. dun et al, described by document CN 1452798A. The microwave cavity is a nonstandard cavity based on the principle of a coaxial oscillator, a lumped L-C structure formed by a conducting rod extending into the cavity and a gap between the rod and the cavity wall generates resonance, the cavity frequency is mainly determined by the geometric dimension of the conducting rod and the distance between the conducting rod and the cavity wall, the microwave cavity is basically not limited by the size and the shape of the cavity, and the microwave cavity with a very small volume can be manufactured in principle. However, the resonance mode is a TEM mode, the microwave field distribution in the cavity is not uniform, which is not beneficial to obtaining high-strength atomic transition signals and is not suitable for developing high-performance miniaturized rubidium frequency standard. In order to obtain better intra-cavity pattern distribution, Rong Feng et al developed a rectangular microwave cavity based on a slotted tube cavity structure in document CN110504963A, which is also a non-standard cavity, wherein a metal pole piece is fixed on the inner wall of a rectangular cavity tube, and a narrow slot between the metal pole piece and the pole piece is used for formingThe cavity frequency of the lumped L-C structure is mainly determined by the size of the pole piece and the pole piece gap. The microwave magnetic field pattern is similar to TE011The mode and the field distribution are very uniform, which is beneficial to exciting atoms to generate transition signals. However, the microwave cavity frequency is very sensitive to the change of the physical dimensions of the pole piece and the narrow groove, so that the precision required for manufacturing the structural member is very high, and the mass production of the miniaturized rubidium frequency standard is difficult to realize.
Disclosure of Invention
The invention provides a rectangular microwave cavity for rubidium frequency standard, aiming at overcoming the defects of the prior art and enabling the designed microwave cavity to simultaneously meet the specific standard TE111The cylindrical cavity has small volume compared with TE101The standard rectangular cavity and the coaxial TEM cavity of the mode have good field pattern distribution and are TE-like011The microwave cavity of the grooved tube has the advantages of simple structure and low processing difficulty, and is suitable for mass production of high-performance miniaturized rubidium frequency standard.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the utility model provides a rectangle structure microwave cavity for rubidium frequency scale, which comprises a cavity, the interior sky of cavity is the cuboid, cavity one terminal surface is opened as the light-emitting window, another terminal surface of cavity is opened there is the unthreaded hole, cavity surface circumference is equipped with the wire casing, the coiling of C field coil is in the wire casing, rubidium atomic bubble sets up in the cavity, first dielectric block and third dielectric block set up in the relative both sides of rubidium atomic bubble, second dielectric block and fourth dielectric block set up in the other relative both sides of rubidium atomic bubble, first dielectric block, second dielectric block, third dielectric block and fourth dielectric block all include dielectric base block and set up the sheetmetal on dielectric base block, the top cap sets up in the light-emitting window department of cavity, be fixed with photoelectric detector on the top cap internal surface.
The dielectric substrate is Al as described above2O3Ceramic or FR-4 board.
The rubidium atomic bubble has a bubble tail extending along the optical axis direction on one end of the bubble surface, and the root of the bubble tail is located at a position close to the edge of the bubble surface.
The two opposite side walls of the cavity close to the end part of the light outlet are provided with a coupling probe mounting hole and a tuning threaded hole which are opposite in position, and the tuning threaded hole is connected with a tuning screw rod.
The second dielectric block as described above includes the second dielectric block a and the second dielectric block B of the same shape, the second dielectric block a and the second dielectric block B being distributed in parallel on the rubidium atom bubble side; the fourth dielectric block includes a fourth dielectric block a and a fourth dielectric block B of the same shape, which are distributed on the other opposite sides of the rubidium atomic bubble.
Compared with the prior art, the invention has the following advantages:
1. the cavity is a rectangular metal box body, one surface of the cavity is open, the cavity is a cuboid with a regular shape, the processing difficulty is small, and the precision is easy to control so as to ensure the consistency.
2. The dielectric substrate of the metal dielectric block may be made of Al2O3Common high dielectric constant materials such as ceramics, epoxy resin plates, epoxy glass cloth laminates, polytetrafluoroethylene resins (Rogers plates), and the like; the metal sheet can be copper or gold foil, the thickness is generally not more than dozens of micrometers, and the shape is a single rectangle or a plurality of rectangles with consistent shapes and fixed intervals. In example 1, 4 pieces of metal dielectric blocks are opposite to each other in pairs and are symmetrical to each other, and in example 2, six pieces of metal dielectric blocks are opposite to each other in pairs and are symmetrical to each other to form a structure similar to a pole piece and a narrow groove, the width and the length of rectangular metal sheets, and the gaps among a plurality of metal sheets determine the resonant frequency of a cavity. The process of loading the metal foil on the dielectric substrate usually adopts a printing plate process, and the processing precision and consistency can be well ensured.
3. The metal sheets loaded on the dielectric substrate block are symmetrically distributed in the cavity to form a pole piece and narrow slot structure similar to those in a microwave cavity of a slotted tube, and an atomic resonance transition region is generated in a rubidium atomic bubble, and the microwave magnetic field type is similar to TE011In the mode, magnetic lines of force are distributed very uniformly, which is very favorable for exciting rubidium atoms to generate clock transition so as to obtain microwave searching signals with high signal-to-noise ratio, and the method is beneficial to the research of high-performance ultra-small rubidium frequency standard.
4. Rubidium atom bubble is the cuboid glass bubble, and the bubble tail stretches out along the optical axis direction, and its root is located the position that one end bubble face is close to the edge, can not shelter from the light path, has avoided additionally increasing the structure of installation bubble tail on the cavity simultaneously for the structure of cavity is very succinct.
5. And the tuning screw arranged on the side wall of the cavity can realize fine tuning of the cavity frequency. In the actual operation process, the length of the tuning screw rod extending into the cavity can be changed by slowly screwing the screw, so that the resonance frequency can be finely adjusted.
Drawings
FIG. 1(a) is a longitudinal sectional view of a microwave cavity of a rectangular structure for rubidium frequency standard in example 1; fig. 1(b) is a transverse cross-sectional view of a rectangular microwave cavity for rubidium frequency standard in example 1.
Fig. 2 is a cavity structure diagram of a rectangular microwave cavity for rubidium frequency standard in embodiment 1.
Fig. 3(a) is a first dielectric block pattern of a rectangular-structured microwave cavity for a rubidium frequency scale in example 1, and fig. 3(b) is a second dielectric block pattern of a rectangular-structured microwave cavity for a rubidium frequency scale in example 1.
Fig. 4 is a diagram showing the assembly effect of the dielectric block of the microwave cavity with a rectangular structure for rubidium frequency standard in example 1.
Fig. 5(a) is a microwave field pattern distribution diagram along the optical axis direction and parallel to the first and third dielectric block planes in the microwave cavity of example 1; fig. 5(b) is a microwave field pattern distribution diagram along the optical axis direction and perpendicular to the first and third dielectric block planes in the microwave cavity in example 1.
FIG. 6(a) is a longitudinal sectional view of a microwave cavity of a rectangular structure for rubidium frequency standard in example 2; fig. 6(b) is a transverse cross-sectional view of a rectangular microwave cavity for rubidium frequency standard in example 2.
Fig. 7 is a cavity structure diagram of a rectangular microwave cavity for rubidium frequency standard in embodiment 2.
Fig. 8(a) is a first dielectric block pattern of a rectangular structure microwave cavity for rubidium frequency scale in example 2;
FIG. 8(b) is a diagram showing the construction of a second dielectric block A of a rectangular-structured microwave cavity for a rubidium frequency scale in example 2;
fig. 8(c) is a structural view of a fourth dielectric block a of a rectangular microwave cavity for a rubidium frequency scale in example 2.
FIG. 9(a) is a diagram showing a microwave field pattern distribution along the optical axis direction and parallel to the planes of the first and third dielectric blocks in the microwave cavity in example 2,
fig. 9(b) is a distribution diagram of microwave field patterns along the optical axis direction and perpendicular to the planes of the first and third dielectric blocks in the microwave cavity of example 2.
Wherein: 1-cavity, 2-first dielectric block, 3-second dielectric block, 4-third dielectric block, 5-fourth dielectric block, 6-rubidium atom bubble, 7-coupling probe, 8-tuning screw, 9-photodetector, 10-top cap, 11-C field coil, 301-second dielectric block a, 302-second dielectric block B, 501-fourth dielectric block a, 502-fourth dielectric block B, 601-bubble tail.
Detailed Description
The present invention will be described in further detail with reference to examples for the purpose of facilitating understanding and practice of the invention by those of ordinary skill in the art, and it is to be understood that the present invention has been described in the illustrative embodiments and is not to be construed as limited thereto.
Example 1:
a microwave cavity with a rectangular structure for a rubidium frequency standard mainly comprises a cavity body 1, a first dielectric block 2, a second dielectric block 3, a third dielectric block 4, a fourth dielectric block 5, a rubidium atom bubble 6, a coupling probe 7, a tuning screw 8, a photoelectric detector 9, a top cover 10 and a C field coil 11. The concrete solution is as follows:
the cavity 1 is made of aluminum alloy materials, the overall dimension of the cavity is a rectangular box body with the size of 16mm multiplied by 8mm multiplied by 23mm, the cavity is a cuboid with a regular shape, and the dimension is 11.4mm multiplied by 6.4mm multiplied by 22.5 mm. One end face of the cavity 1 is opened to be used as a light outlet, the other end face of the cavity 1 is provided with a light inlet hole, and a wire groove is formed in the circumferential direction of the outer surface of the cavity 1. The diameter of the C-field coil 11 is 0.27mm, the C-field coil is densely wound in the wire slot and is used for generating a stable static magnetic field parallel to the optical axis direction, and the direction from the end face of the cavity 1 provided with the light inlet to the open end face is the optical axis direction and provides a quantization axis for atomic transition;
the dielectric block comprises a dielectric base block made of Al and a metal foil provided on the dielectric base block2O3The dielectric block is made of ceramic and has a thickness of 0.5mm, and in this embodiment, the dielectric block includes a first dielectric block 2, a second dielectric block 3, a third dielectric block 4, and a fourth dielectric block 5 disposed around a rubidium atom bubble 6. The first dielectric block 2 and the third dielectric block 4 are disposed on opposite sides of the rubidium atom bubble 6, the second dielectric block 3 and the fourth dielectric block 5 are disposed on opposite sides of the rubidium atom bubble 6, and the rubidium atom bubble 6 is disposed in the cavity 1.
The dimensions of the first dielectric block 2 and the third dielectric block 4 are 10mm × 18mm, and the metal sheets provided on the first dielectric block 2 and the third dielectric block 4 are copper foils each having a thickness of 12 μm. The dimensions of the metal sheets provided on the first dielectric block 2 and the third dielectric block 4 were 7mm × 16 mm.
The dimensions of the second dielectric block 3 and the fourth dielectric block 5 are each 6mm × 18mm, the metal sheets provided on the second dielectric block 3 and the fourth dielectric block 5 are also copper foils 12 μm thick, and the dimensions of the metal sheets provided on the second dielectric block 3 and the fourth dielectric block 5 are 3mm × 16 mm.
The first dielectric block 2 and the third dielectric block 4 are bonded to the inner surfaces of a pair of side walls with a large area of the cavity 1 in a manner of being opposite to each other by using silica gel, the second dielectric block 3 and the fourth dielectric block 5 are bonded to the inner surfaces of a pair of side walls with a small area of the cavity 1 in a manner of being opposite to each other, and the metal sheets of the first dielectric block 2, the second dielectric block 3, the third dielectric block 4 and the fourth dielectric block 5 face the hollow area in the cavity 1, so that a 'fence' type structure similar to a magnetron cavity is formed as shown in fig. 4;
the rubidium atomic bubble 6 is a sealed transparent cuboid glass bubble, and working atomic rubidium metal steam and buffer gas with set air pressure are filled in the rubidium atomic bubble 6. And a bubble tail extending out along the optical axis direction is arranged on one end bubble surface and used for storing liquid metal rubidium. The tail root of the bulb is positioned at a position close to the edge of the bulb surface, so that the light path is prevented from being blocked. The size of the cuboid glass bubble in the embodiment is 10mm multiplied by 5mm multiplied by 17mm, the diameter of the glass tail bubble is 2.5mm, the length of the glass tail bubble is 4mm, the glass tail bubble is positioned on the end face facing the light outlet, and the root part of the glass tail bubble is positioned on the edge close to one side of the coupling probe 7;
the two opposite side walls of the cavity 1 close to the end part of the light outlet are provided with a coupling probe mounting hole and a tuning threaded hole which are opposite in position, the tuning threaded hole is connected with a tuning screw 8, the tuning screw 8 is a threaded metal round rod, and the length of the tuning screw 8 extending into the cavity 1 can be changed by slowly screwing the tuning screw 8, so that the resonant frequency of the microwave cavity is finely adjusted;
the top cover 10 is made of aluminum alloy material, is positioned at the light outlet of the cavity 1, and is fixed at the light outlet of the cavity 1 through two M1.6 screws to form a metal closed cavity; a photoelectric detector 9 is fixed on the inner surface of the top cover 10 and used for detecting optical signals;
fig. 5(a) and 5(b) show microwave field patterns of two planes in the optical axis direction in the cavity in this embodiment. As can be seen from the figure, since the 4 dielectric blocks form a pole piece and narrow slot structure in a microwave cavity similar to a slotted tube, the microwave magnetic field obtained by excitation is similar to TE011In the mode, in the region where atomic resonance transition occurs in the rubidium atomic bubble 6, magnetic lines of force are distributed along the axial direction, the uniformity is very good, rubidium atoms are very favorably excited to perform clock transition, and then microwave search signals with high signal-to-noise ratio are obtained, so that the method is beneficial to the research of high-performance ultra-small rubidium atomic frequency standard. In fact, by adopting the design scheme in the embodiment, the ultra-small rubidium atomic frequency standard sample machine with the height of less than 1cm can be prepared, and the short-term frequency stability of the ultra-small rubidium atomic frequency standard sample machine can be better than that of the ultra-small rubidium atomic frequency standard sample machine
Figure 574161DEST_PATH_IMAGE001
The level of (a) of (b),
Figure 107911DEST_PATH_IMAGE002
to measure time.
Example 2:
a microwave cavity with a rectangular structure for a rubidium frequency standard is characterized in that a cavity body 1 is made of an aluminum alloy material, the outer dimension of the cavity body is a rectangular box body with the size of 18mm x 15mm x 23mm, the inner cavity is a cube with a square cross section, and the size of the inner cavity is 12.6mm x 22.5 mm. One end face of the cavity 1 is opened to be used as a light outlet, the other end face of the cavity 1 is provided with a light inlet hole, and a wire groove is formed in the circumferential direction of the outer surface of the cavity 1. The diameter of the C-field coil 11 is 0.27mm, the C-field coil is densely wound in the wire slot and is used for generating a stable static magnetic field parallel to the optical axis direction, and the direction from the end face of the cavity 1 provided with the light inlet to the open end face is the optical axis direction and provides a quantization axis for atomic transition;
the dielectric block comprises a dielectric base block and a metal sheet arranged on the dielectric base block, in the embodiment, the dielectric base block is an FR-4 plate, the FR-4 is an epoxy glass fiber board, the thickness of the dielectric base block is 1.2mm, and the dielectric block comprises a first dielectric block, a second dielectric block, a third dielectric block and a fourth dielectric block which are sequentially arranged around the rubidium atomic bubble 6. The first dielectric block and the second dielectric block are disposed on opposite sides of the rubidium atomic bubble 6, and the third dielectric block and the fourth dielectric block are disposed on the other opposite sides of the rubidium atomic bubble 6.
The first dielectric block and the third dielectric block are both 12.6mm by 18mm in size, the metal sheet is a copper foil with the thickness of 12 microns, and the size of the metal sheet is 9mm by 16 mm;
the second dielectric block comprises a second dielectric block A and a second dielectric block B which are identical in shape and are distributed on one side of the rubidium atomic bubble 6 in parallel; the fourth dielectric block includes a fourth dielectric block a and a fourth dielectric block B of the same shape, which are distributed on the other opposite sides of the rubidium atomic bubble 6, wherein the second dielectric block a is opposed to the fourth dielectric block a, and the second dielectric block B is opposed to the fourth dielectric block B.
The sizes of the second dielectric block A and the second dielectric block B are both 5 mm-18 mm, the metal sheets on the second dielectric block A and the second dielectric block B are copper foils with the thickness of 12 mu m, and the size of the copper foils is 4 mm-16 mm;
the dimensions of the fourth dielectric block a and the fourth dielectric block B are both 5mm × 18mm, and the metal foils on the fourth dielectric block a and the fourth dielectric block B are also copper foils with a thickness of 12 μm, and the dimensions of the copper foils are 4mm × 16 mm.
The rubidium atomic bubbles 6 had a size of 10mm by 17 mm. The diameter of the bulb tail is 2.5mm, and the length is 4 mm.
The other part of the structure is the same as that of embodiment 1.
Fig. 9(a) and 9(b) show microwave field patterns of both surfaces in the optical axis direction in the cavity in this embodiment. As can be seen from the figure, since the 6 dielectric blocks form a pole piece and narrow slot structure in a microwave cavity similar to a slotted tube, the excited microwave magnetic field is similar to TE011In the mode, in the region where atomic resonance transition occurs in the rubidium atomic bubble 6, magnetic lines of force are distributed along the axial direction, the uniformity is very good, rubidium atoms are very favorably excited to perform clock transition, and then microwave search signals with high signal-to-noise ratio are obtained, so that the method is beneficial to the research of high-performance ultra-small rubidium atomic frequency standard. By adopting the design scheme in the embodiment, a small rubidium atom frequency standard sample machine with the height of less than 18mm can be prepared, and the short-term frequency stability of the sample machine is expected to be superior to that of the sample machine
Figure 162455DEST_PATH_IMAGE001
The level of (a) of (b),
Figure 857878DEST_PATH_IMAGE002
to measure time.
It should be noted that the specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (5)

1. A microwave cavity with a rectangular structure for rubidium frequency scale comprises a cavity (1) and is characterized in that the cavity (1) is internally hollow and is a cuboid, the top surface of the cavity (1) is opened to serve as a light outlet, a light inlet hole is formed in the bottom surface of the cavity (1), a line slot is formed in the side surface of the cavity (1), a C-field coil is wound in the line slot, a rubidium atom bubble (6) is arranged in the cavity (1), a first dielectric block (2) and a third dielectric block (4) are arranged on two opposite sides of the rubidium atom bubble (6), a second dielectric block (3) and a fourth dielectric block (5) are arranged on two opposite other sides of the rubidium atom bubble (6), the first dielectric block (2), the second dielectric block (3), the third dielectric block (4) and the fourth dielectric block (5) respectively comprise a base block and a metal sheet arranged on the dielectric base block, a top cover (10) is arranged at the light outlet of the cavity (1), a photoelectric detector (9) is fixed on the inner surface of the top cover (10).
2. The rectangular microwave cavity for rubidium frequency standard according to claim 1, wherein the dielectric substrate is Al2O3Ceramic or FR-4 board.
3. The rectangular microwave cavity for the rubidium frequency standard according to the claim 1, wherein a bulb tail extending out along the optical axis direction is arranged on a bulb surface at one end of the rubidium atom bulb (6), and a bulb tail root is located at a position close to the edge of the bulb surface.
4. The microwave cavity with the rectangular structure for the rubidium frequency standard according to the claim 1, wherein the two opposite side walls of the cavity (1) near the end part of the light outlet are provided with a coupling probe mounting hole and a tuning threaded hole which are opposite in position, and the tuning threaded hole is connected with a tuning screw rod (8).
5. The microwave cavity with a rectangular structure for rubidium frequency standard according to claim 1, characterized in that the second dielectric block (3) comprises a second dielectric block A and a second dielectric block B which are same in shape and are distributed in parallel on one side of the rubidium atomic bubble (6); the fourth dielectric block (5) comprises a fourth dielectric block A and a fourth dielectric block B which are identical in shape, and the fourth dielectric block A and the fourth dielectric block B are distributed on the other opposite sides of the rubidium atom bubble (6).
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