High-quality factor frequency-tunable planar open resonator and its implementation method

Abstract

This invention relates to the field of electromagnetic resonator design. Planar resonators have weak electromagnetic wave confinement capabilities and require high parallelism of end-face mirrors. Although concave resonators can solve the problems of planar cavities, the introduction of curved surfaces makes them difficult to integrate into planar optical paths. This invention discloses a planar open-face resonator with a high quality factor and adjustable frequency, and its implementation method. By filling the planar open-face resonator with dielectric blocks of different sizes arranged in a specific manner, a strong electromagnetic wave confinement capability similar to that of a concave resonator is achieved, while reducing the parallelism requirements of the end-face mirrors, thus improving its quality factor by nearly 10 times compared to ordinary planar resonators.

Description

Technical Field

[0001] This invention relates to a high-quality factor rectangular open resonant cavity, and more specifically, to a frequency-tunable planar open resonant cavity with a high-quality factor and a method for implementing it. Background Technology

[0002] Traditional open-face resonators are fundamental devices in physics, commonly found in applications such as radiation and sensing. They consist of either plane or concave mirrors. Fabry-Pérot resonators, composed of two plane mirrors, offer advantages in integration and fabrication. However, they require extremely high parallelism between the mirrors; low parallelism weakens the resonator's electromagnetic wave containment, resulting in a lower quality factor. In contrast, plano-concave resonators offer a higher quality factor and lower parallelism requirements. However, non-planar mirrors pose challenges to their integration and fabrication. While existing work has achieved similar effects to plano-concave resonators using metasurfaces, these metasurfaces utilize materials with relatively high refractive indices. Since high-refractive-index materials are relatively difficult to obtain in high-frequency bands, there is currently no effective solution to this problem. Summary of the Invention

[0003] In view of the problems described in the background art, the purpose of this invention is to provide a planar open resonant cavity with high quality factor frequency adjustable and its implementation method. This invention can take into account the shape advantages of planar cavities and the stability advantages of concave cavities, and the required materials are readily available from microwave band to optical band.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A planar open-type resonant cavity with a high quality factor is characterized in that: the cavity structure includes two sets of parallel planes, the two ends of the cavity are open, and the cavity is filled with a graded refractive index medium, the graded refractive index distribution of which is as follows:

[0006]

[0007] Where u and v are the coordinates of the original concave resonant cavity and x and y are the coordinates of the planar open resonant cavity.

[0008] Furthermore, the equivalent refractive index distribution range of the graded refractive index medium is 1 to 1.3. The graded refractive index medium includes several dielectric blocks placed inside the cavity of the resonant cavity. The dielectric blocks are made of acrylic material in the microwave band and silicon dioxide material in the optical band.

[0009] Furthermore, the formula for calculating the side length of the dielectric block is as follows:

[0010]

[0011] Where p is the period of the equivalent dielectric element, and ε is the equivalent dielectric constant. eff =n 2 (x,y) represents the square of the refractive index calculated by formula (1), ε d is the dielectric constant of dielectric block (2).

[0012] Furthermore, the two sets of parallel planes are made of metal in the microwave band and use Bragg gratings in the optical band.

[0013] A method for realizing a planar open-face resonant cavity with a high quality factor is provided. Based on the aforementioned planar open-face resonant cavity, the cavity body of the planar open-face resonant cavity is obtained by conformal transformation of a concave resonant cavity without material filling. The operating frequency of the planar open-face resonant cavity is adjusted by regulating the spacing of the parallel planes. The gradient refractive index distribution of the gradient refractive index medium is calculated according to the following formula:

[0014]

[0015] u and v are the coordinates of the original concave resonant cavity, and x and y are the coordinates of the planar open resonant cavity;

[0016] Based on the equivalent medium theory, the obtained gradient refractive index distribution is discretized to form discrete equivalent medium units. The equivalent medium units are realized by medium blocks with different side lengths. The medium blocks and the air in the cavity form equivalent medium units. Different refractive indices of the equivalent medium units are obtained by adjusting the size parameters of the medium blocks in each equivalent medium unit.

[0017] In summary, the present invention has the following beneficial effects:

[0018] (1) The boundary of the resonant cavity of the present invention is a plane, which is easy to integrate and has the high stability of a concave cavity. The present invention is a novel resonant cavity that combines the shape advantages of a planar cavity and the stability advantages of a concave cavity.

[0019] (2) The present invention is filled with dielectric blocks of different sizes arranged in a specific manner. The material is simple and easy to obtain in various wavebands. It achieves a strong ability to confine electromagnetic waves similar to a concave resonant cavity, while reducing the parallelism requirements of the end face mirror, making its quality factor nearly 10 times higher than that of a common planar resonant cavity.

[0020] (3) The present invention can adjust the resonant frequency by adjusting the cavity length alone, without redesigning the internal filling material. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the resonant cavity structure of the present invention.

[0022] Figure 2 This is a side view of the present invention.

[0023] Figure 3 The electromagnetic simulation results are for the microwave resonant cavity, with acrylic as the dielectric block.

[0024] Figure 4 The results are electromagnetic simulations of the optical resonant cavity, with silicon dioxide as the dielectric block.

[0025] Figure 5 This is a schematic diagram of cavity length adjustment, where the cavity length is changed by moving the lower flat plate.

[0026] Figure 6 The curves show the changes in the resonant frequency and Q value of the resonant cavity as the cavity length changes.

[0027] In the diagram, 1 is the plane of the resonant cavity structure, 2 is the dielectric block, and 3 is the air. Detailed Implementation

[0028] The present invention will now be described in further detail with reference to the accompanying drawings.

[0029] It should be noted that, for ease of description, the descriptions of direction in the following text are consistent with the directions in the accompanying drawings, but they do not limit the structure of the present invention.

[0030] like Figures 1-4 As shown, this invention discloses a planar open-type resonant cavity with a high quality factor. The cavity structure includes two sets of parallel planes. The two sets of parallel planes are made of metal in the microwave band and a Bragg grating in the optical band. The cavity is open at both ends, and the cavity is filled with a graded refractive index medium. The graded refractive index distribution of the graded refractive index medium is as follows:

[0031]

[0032] Where u and v are the coordinates of the original concave resonant cavity and the coordinates of the planar open resonant cavity, respectively. The equivalent refractive index distribution range of the graded refractive index medium is 1 to 1.3. The graded refractive index medium includes several dielectric blocks 2 placed inside the cavity of the resonant cavity. Dielectric blocks 2 are made of acrylic material in the microwave band and silicon dioxide material in the optical band. The formula for calculating the side length of dielectric block 2 is as follows:

[0033]

[0034] Where p is the period of the equivalent medium element, ε eff =n 2(x, y) is the dielectric constant calculated by formula (1), ε d is the dielectric constant of dielectric block 2.

[0035] This invention also discloses a method for realizing a planar open-face resonant cavity with a high quality factor. Based on the aforementioned planar open-face resonant cavity, this invention has a planar resonant cavity shape and can achieve the same high quality factor as a concave resonant cavity. The cavity of the planar open-face resonant cavity is obtained by conformal transformation of a concave resonant cavity without material filling. The operating frequency of the planar open-face resonant cavity is adjusted by regulating the spacing of parallel planes. For a highly stable concave resonant cavity, coordinate transformation is performed to transform it into a planar resonant cavity. Simultaneously with the boundary change, the internal material also changes. To ensure that the material remains isotropic after the transformation, a conformal transformation method is used, and the internal refractive index distribution after the transformation is shown in formula (1). The gradient refractive index distribution of the gradient refractive index medium is calculated according to formula (1). Based on the equivalent medium theory, the obtained gradient refractive index distribution is discretized to form discrete equivalent medium units. The equivalent medium units are realized by medium blocks 2 with different side lengths. The medium blocks and the air in the cavity form equivalent medium units. Different refractive indices of the equivalent medium units are obtained by adjusting the size parameters of the medium blocks 2 in each equivalent medium unit. The side length of the medium blocks 2 is calculated using formula (2).

[0036] Implementation Example 1:

[0037] This example illustrates the implementation of the planar open-type resonant cavity of this invention in the microwave band using the method of this invention: First, a copper cavity with dimensions of 400mm (length), 100mm (width), and 10mm (height) is fabricated, as follows... Figure 1 As shown, the cavity has openings on both sides (along the x-direction), forming a typical open-planar resonant cavity. An acrylic dielectric block 2, designed using formula (1) and equivalent dielectric theory, is placed at the corresponding position inside the copper cavity, as shown... Figure 1 As shown, the side length a of dielectric block 2 is calculated using formula (2). The size of the resonant cavity can be adjusted according to actual requirements. After determining the size of the resonant cavity, calculate the material parameters, the size and position of the dielectric block. If the size of the resonant cavity changes, the size of the dielectric block needs to be recalculated. If only the cavity length is changed, no recalculation is required.

[0038] The rest of the copper cavity is filled with air. Figure 3 (a) shows the resonant mode distribution in the electromagnetic simulation, with a resonant frequency of 3.7 GHz. Figure 3 (b) shows the mode distribution of a standard open-plane resonant cavity (without filler material), with a resonant frequency of 4.5 GHz. Figure 3As can be seen from the comparison, the electromagnetic field distribution is more scattered when there is no dielectric block 2 in the resonant cavity, while after adding dielectric block 2, the electromagnetic field is obviously localized in the center of the resonant cavity. Simulation shows that the quality factor of the resonant cavity is increased by 5 times after adding dielectric block.

[0039] Implementation Example 2:

[0040] This embodiment will verify the performance of the high-quality factor resonator achieved by the present invention in the optical band. In the optical band, a Bragg grating is used instead of the copper cavity in Embodiment 1, and a silicon dioxide block is used instead of the acrylic block as dielectric block 2. The Bragg grating is achieved by alternating silicon dioxide and air in a 1:1 ratio with a period of 316 nm. The size of the silicon dioxide is calculated using formula (2), where ε... d It should be the dielectric constant of silicon dioxide. Figure 4 (a) shows the resonant mode distribution in the electromagnetic simulation, with a resonant wavelength of 804 nm. Figure 4 (b) shows the mode distribution of a normal open-plane resonant cavity (without filling material) with a resonant wavelength of 731 nm. It can be seen that after adding the designed silicon dioxide block, the electromagnetic field is obviously localized in the center of the resonant cavity. Simulation shows that the quality factor of the resonant cavity is increased by 5 times after adding the silicon dioxide block.

[0041] Implementation Example 3:

[0042] This invention enables adjustment of the resonant frequency simply by adjusting the cavity length. Based on Example 1, the cavity length is increased (see...). Figure 5 At this point, the resonant frequency of the resonant cavity will change accordingly, but it will still maintain a high Q value, see... Figure 6 The resonant frequency can be continuously adjusted by continuously changing the cavity length of the resonant cavity. Figure 6 The graph shows the changes in resonant frequency and Q value as the cavity length varies from 100mm to 150mm. It can be seen that the resonant frequency changes approximately linearly with the cavity length, while the Q value, although fluctuating, still remains at a relatively high value.

[0043] The planar open resonant cavity of the present invention combines the shape advantages of a planar cavity with the stability advantages of a concave cavity, enabling continuous frequency adjustment. The cavity structure and the internal dielectric block are made of readily available materials. The resonant frequency can be adjusted by adjusting the cavity length without replacing the internal dielectric block.

[0044] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A planar open-cell resonator with a high quality factor, characterized in that: The resonant cavity structure includes two sets of parallel planes, with openings at both ends. The cavity is filled with a graded refractive index medium, and the graded refractive index distribution of the medium is as follows: Where u and v are the coordinates of the original concave resonant cavity, and x and y are the coordinates of the planar open resonant cavity; The gradient refractive index medium includes several medium blocks (2) placed inside the cavity of the resonant cavity. The cavity of the resonant cavity is filled with medium blocks (2) of different sizes arranged in a specific manner to achieve a strong confinement capability of electromagnetic waves similar to that of a concave resonant cavity. The resonant frequency can be continuously adjusted by continuously changing the cavity length of the resonant cavity.

2. The planar open-type resonant cavity according to claim 1, characterized in that: The equivalent refractive index distribution range of the gradient refractive index medium is 1~1.

3. The medium block (2) is made of acrylic material in the microwave band and silicon dioxide material in the optical band.

3. The planar open resonant cavity according to claim 2, characterized in that: The formula for calculating the side length of the medium block (2) is as follows: Where p is the period of the equivalent dielectric unit and the equivalent dielectric constant is... ε eff = n 2 ( x,y () is the square of the graded refractive index. ε d is the dielectric constant of dielectric block (2).

4. The planar open-type resonant cavity according to claim 1, characterized in that: The two sets of parallel planes are made of metal in the microwave band and Bragg gratings in the optical band.

5. A method for realizing a planar open-cell resonator with a high quality factor, based on the planar open-cell resonator according to any one of claims 1 to 4, characterized in that: A planar open-type resonant cavity is obtained by conformal transformation of a concave resonant cavity without material filling. The operating frequency of the planar open-type resonant cavity is adjusted by regulating the spacing of the parallel planes. The gradient refractive index distribution of the gradient refractive index medium is calculated according to the following formula: u and v are the coordinates of the original concave resonant cavity, and x and y are the coordinates of the planar open resonant cavity; Based on the equivalent medium theory, the obtained gradient refractive index distribution is discretized to form discrete equivalent medium units. The equivalent medium units are realized by medium blocks (2) with different side lengths. The medium blocks and the air in the cavity form equivalent medium units. Different refractive indices of the equivalent medium units are obtained by adjusting the size parameters of the medium blocks (2) in each equivalent medium unit.

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