A micro atomic optical filter based on faraday anomalous dispersion and its implementation method

Abstract

This invention discloses a miniature Faraday atom filter based on Faraday anomalous dispersion and its implementation method, comprising: an alkali metal atom gas cell with antireflection films coated on both sides of the light-passing holes corresponding to the wavelengths of the alkali metal atom absorption lines, and filled with a buffer gas; a permanent magnet or coil surrounding the alkali metal atom gas cell to generate a uniform strong magnetic field parallel to the direction of light propagation; first and second polarizers located on both sides of the alkali metal atom gas cell and facing it directly; the polarization directions of the two polarizers are perpendicular to each other; and a temperature control system that heats and maintains the temperature of the alkali metal atom gas cell, and detects and controls the temperature. This invention reduces the size of the Faraday atom filter to 1 / 1000 of the mainstream size, improves mechanical stability, expands its applicability, and is expected to achieve plug-and-play functionality, greatly broadening the application of Faraday atom filters in fields such as space communication, laser technology, quantum information, and metrology.

Description

Technical Field

[0001] This invention relates to the fields of atomic filtering technology and laser technology, and in particular to a micro atomic filter based on Faraday anomalous dispersion and its implementation method. Background Technology

[0002] Faraday atom filters based on the Faraday anomalous dispersion effect have the advantages of narrow bandwidth, high transmittance, high signal-to-noise ratio, long-term stable operation, and insensitivity to external temperature. They are suitable for use in harsh environments with drastic temperature changes, such as outdoor environments.

[0003] However, existing Faraday atom filters are relatively large, with most gas cells having a volume greater than 5.3 cm³. 3 It is impossible to generate a magnetic field with sufficient intensity and uniformity to meet the requirements of Faraday rotation. Taking a currently mainstream cylindrical glass gas cell with a length of 30mm and a diameter of 15mm as an example, to generate a magnetic field of 1000Gs along its central axis of symmetry, the volume of the magnet and its fixing structure would need to be greater than 0.5dm. 3 This is the main factor limiting the size reduction of atomic filters, and in this scheme, the magnetic field inhomogeneity exceeds 20%, which also has a significant impact on the optical rotation performance of the atomic filters.

[0004] Besides the limitations imposed by the magnetic field, the larger the volume of the gas chamber, the more difficult it is to control its temperature. On one hand, large-volume atomic filters are prone to atomic condensation at the light-transmitting surfaces at both ends of the gas chamber, causing them to malfunction. This necessitates a more complex insulation structure design to prevent atomic condensation, further increasing the volume of the atomic filter, sometimes exceeding 1 dm². 3 On the other hand, large-volume atomic filters require higher heating power and longer heating time, which increases the startup time and power consumption during normal operation, which is not conducive to engineering applications. Summary of the Invention

[0005] This invention provides a miniature atomic filter based on Faraday anomalous dispersion and its implementation method. This invention overcomes the problem of large size in existing Faraday atomic filter technology, and provides a method for realizing a miniature Faraday atomic filter using a miniature atomic gas cell and its corresponding magnet (or spiral coil), temperature control device, and polarization element, as well as a method for filtering light using this atomic filter, as detailed below:

[0006] A miniature Faraday atom filter based on Faraday anomalous dispersion, the Faraday atom filter comprising:

[0007] The alkali metal atom gas cell has light-transmitting holes on both sides coated with anti-reflection films corresponding to the wavelengths of the alkali metal atom absorption lines, and is filled with buffer gas.

[0008] A permanent magnet or coil is wrapped around an alkali metal atom gas cell to generate a uniform strong magnetic field parallel to the direction of light propagation.

[0009] The first and second polarizers are located on both sides of the alkali metal atom gas cell and are directly opposite the alkali metal atom gas cell; the polarization directions of the two polarizers are perpendicular to each other.

[0010] The temperature control system heats and maintains the temperature of the alkali metal atom gas chamber, and detects and controls the temperature.

[0011] The temperature control system includes:

[0012] The heating module is used to heat the alkali metal atom gas chamber, and the heat is kept by insulation material;

[0013] Thermistors or thermocouples are used for temperature detection;

[0014] Temperature feedback control circuit, used for temperature control, with a temperature control accuracy of more than 0.01 degrees.

[0015] Furthermore, the first and second polarizers are used for polarization initiation and polarization detection, respectively.

[0016] The permanent magnet is a hollow cylinder, and a uniform strong magnetic field with a length adapted to the length of the bubble filled with buffer gas is generated at the center of the cylinder.

[0017] Furthermore, the Faraday atom filter also includes: a housing for fixing an alkali metal atom gas chamber, a permanent magnet or coil, first and second polarizers, and a temperature control system.

[0018] The outer shell is filled with polyurethane foam insulation material and the outer material is polytetrafluoroethylene.

[0019] Secondly, a method for implementing light filtering using a miniature Faraday atom filter based on Faraday anomalous dispersion, the method comprising:

[0020] Using a pre-designed shell, a cesium atom gas chamber filled with buffer gas, a permanent magnet, and the first and second polarizers are assembled together. The heating element and thermistor on the surface of the atom gas chamber are connected to an external temperature control module.

[0021] Adjust the polarization directions of the first and second polarizers so that they are orthogonal to each other;

[0022] When the temperature is increased, the absorption lines of cesium atoms in the gas chamber split into two under the influence of the magnetic field. This causes a path difference between the left-handed and right-handed circularly polarized light in the incident light after passing through the cesium atom gas chamber. The polarization direction of the linearly polarized light superimposed by the left-handed and right-handed circularly polarized light rotates, thus achieving optical rotation.

[0023] Adjust the temperature to select the most suitable operating point.

[0024] The beneficial effects of the technical solution provided by this invention are:

[0025] 1. This invention reduces the size of the Faraday atom filter to 1 / 1000 of the mainstream size, resulting in stronger mechanical stability and a wider range of applications. It is expected to achieve plug-and-play functionality, greatly expanding the application of Faraday atom filters in fields such as space communication, laser technology, quantum information, and metrology.

[0026] 2. The miniature Faraday atom filter designed in this invention is more likely to generate a uniform strong magnetic field within the alkali metal atom gas cell, thereby improving the optical rotation performance of the atom filter;

[0027] 3. Due to the small volume of the alkali metal atom gas chamber in the micro atomic filter, it is easier to design a temperature control system with better temperature control effect, which reduces power consumption and enhances the atomic filter's anti-interference ability to external temperature changes. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of a miniature Faraday atom filter.

[0029] The components are: 1. First polarizer; 2. Permanent magnet or coil; 3. Alkali metal atom gas cell; 4. Second polarizer; 5. Temperature control system. The arrows indicate the direction of light transmission, and the direction of B indicates the direction of the magnetic field.

[0030] Figure 2 This is a schematic diagram of the magnetic field distribution within a 3mm gas cell in this miniature Faraday atom filter;

[0031] Figure 3 Flowchart for filtering light using a miniature Faraday atom filter;

[0032] Figure 4 This is a schematic diagram illustrating the effect of a miniature Faraday atom filter.

[0033] The magnetic field strength was 1000 Gs, the buffer gas pressure was 5 Torr, and the curves are the transmission spectra of the atomic filter at different temperatures. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0035] Example 1

[0036] A miniature Faraday atom filter, see [link / reference] Figure 1 The Faraday atom filter includes:

[0037] A miniature alkali metal atom gas chamber 3, made of quartz or glass, has light-transmitting holes on both sides coated with anti-reflection films corresponding to the wavelengths of alkali metal atom absorption lines, and the interior of the alkali metal atom gas chamber 3 is filled with buffer gas.

[0038] A permanent magnet or coil 2 is wrapped around an alkali metal atom gas cell 3 to generate a uniform strong magnetic field parallel to the direction of light propagation.

[0039] The first polarizer 1 and the second polarizer 4 are located on both sides of the alkali metal atom gas cell 3 and are directly opposite the alkali metal atom gas cell; the polarization directions of the two polarizers (1 and 4) are perpendicular to each other.

[0040] A temperature control system 5 uses an internal heating module to heat the alkali metal atom gas chamber 3, which is insulated by a thermal conductivity material with a thermal conductivity of less than 0.05 W / (m*K). The temperature control system 5 uses an internal thermistor or thermocouple for temperature detection and its own temperature feedback control circuit for temperature control, with a temperature control accuracy of more than 0.01 degrees.

[0041] Furthermore, the miniature Faraday atom filter also includes a housing for securing the aforementioned components (components numbered 1-5) and for enhanced insulation.

[0042] Example 2

[0043] The following is combined Figure 2 and Figure 3 The solution in Example 1 will be further described below:

[0044] Figure 1 This is a schematic diagram of the structure of a miniature Faraday atom filter designed for an embodiment of the present invention. The atom filter consists of: a first polarizer 1, a permanent magnet or coil 2, atomic gas bubbles 3 filled with inert gas inside an atomic gas chamber 3, a second polarizer 4, and a temperature control system 5.

[0045] The first polarizer 1 is a polarization element; laser light can only pass through when its polarization direction is the same as that of the first polarizer 1. The splitting ratio of the first polarizer 1 within its operating wavelength range is greater than 1000:1. The polarization directions of the first and second polarizers 1 and 4 are as follows: Figure 1As shown by the white arrows (one horizontal and one vertical), the two arrows are orthogonal to each other. The first and second polarizers 1 and 4 are placed at both ends of the atomic gas cell 3, parallel to the two end faces of the atomic gas cell 3, to serve as polarizers and detectors.

[0046] In this embodiment of the invention, the alkali metal atom gas chamber 3 is illustrated using cesium atom bubbles filled with inert gas as an example. In specific implementation, other types of atom bubbles can also be selected, and this embodiment of the invention does not limit this.

[0047] Before the temperature control system 5 heats up, the incident light will be unable to pass through the second polarizer 4 after passing through the first polarizer 1. Since the permanent magnet 2 is a hollow cylinder, a uniform and strong magnetic field with a length adapted to the length of the cesium atom bubble can be generated at the center of the cylinder. Compared with the magnetic field generating devices in the prior art, the permanent magnet 2 has a small structure volume, generates a large magnetic field strength, and has good uniformity, which is of great significance for improving the optical rotation performance of the Faraday atom filter.

[0048] In this system, a cesium atom bubble 3 filled with inert gas is positioned at the center of the permanent magnet 2. The laser beam enters the hollow permanent magnet 2 through the first polarizer 1, passes through the cesium atom bubble 3, and finally exits through the second polarizer 4. The temperature control system 5, with its built-in heating module and temperature sensor, is attached to the surface of the cesium atom bubble and connected to its own temperature feedback control circuit to achieve temperature control of the cesium atom bubble 3.

[0049] In the above embodiments, the first and second polarizers 1 and 4 are preferably circular thin-film polarizers, which are much smaller in volume than other polarizing elements. They can also be replaced by polarizing beam splitters or Glan Taylor prisms with higher beam splitting ratios.

[0050] Furthermore, the atomic bubble 3 is preferably made of quartz, which has a higher transmittance than ordinary glass. The inert gas is argon or xenon, and the gas pressure is preferably 0.1 to 50 Torr. The heating module is preferably a heating wire or a heating film, and the temperature sensor is preferably a thermistor or a thermocouple. Since the bubble length in the miniature Faraday atomic filter is reduced to one-tenth of that in previous atomic filters, in order to achieve the same optical rotation effect, it is necessary to increase the atomic density in the gas chamber by increasing the temperature of the gas chamber. Therefore, the preferred operating temperature range of the atomic gas chamber 3 is 60-150 degrees Celsius.

[0051] In the above example, a uniform strong magnetic field with a length of 3 mm can be generated at the center of the cylinder using the permanent magnet 2. The magnetic field strength is preferably 100 to 1200 Gs, and the magnetic field strength can be varied by changing the inner and outer diameters of the permanent magnet 2. For a permanent magnet with a magnetic field strength of 1000 Gs, its inner diameter is 4 mm, its outer diameter is 28 mm, and its cylinder length is 8 mm. The uniformity of the magnetic field is greater than 95%. Within the atomic gas cell, the magnetic field distribution along the direction of light propagation is as follows: Figure 2 As shown.

[0052] Example 3

[0053] To address the problems of existing Faraday atom filters being large, difficult to generate a uniform and strong magnetic field, and having high power consumption, this invention proposes a miniature alkali metal atom gas chamber 3. This chamber is a cylinder 3mm long and 3mm in diameter, with a volume of 21.2mm². 3 It is used in atomic filters.

[0054] Based on this alkali metal atom gas cell 3, a matching magnetic field device was designed, with a volume of 0.98 cm³. 3 The magnetic field strength is 1000 Gs within a 3 mm range, and the magnetic field uniformity is greater than 95%. Compared with the previous mainstream magnetic field schemes, this scheme generates a larger and more uniform magnetic field in a smaller volume.

[0055] The volume of the air chamber has been reduced by 250 times (from the mainstream 5.3 cm). 3 Reduced to 21.2mm 3 After that, the phenomenon of atomic condensation on the end face of the gas chamber can be well avoided, and the heat preservation structure is also simpler, which can further reduce the volume of the atomic filter. The heating power required for the gas chamber to heat up is also greatly reduced, which greatly reduces the power consumption of the system.

[0056] Meanwhile, by replacing the 25.4mm cube-shaped polarizing beam splitter and Glan Taylor prism in mainstream Faraday atom filters with a 12.7mm diameter, 0.55mm thick circular thin-film polarizer, the size of the atom filter can be compressed to its limit. Through comprehensive design, the total volume of the miniature Faraday atom filter is 1.1cm². 3 It is 1 / 1000 the size of a mainstream Faraday atom filter. Furthermore, it has fast startup, low power consumption, a more stable mechanical structure, and stronger anti-interference capabilities, making it a promising plug-and-play Faraday filter.

[0057] Example 4

[0058] A method for implementing light filtering using the aforementioned miniature Faraday atom filter, the method comprising the following steps:

[0059] The atomic filter is designed to enclose the atomic gas chamber using polyurethane foam insulation material as the internal filling and polytetrafluoroethylene material as the outer shell. A miniature coated alkali metal atomic bubble 3 filled with buffer gas, a miniature ring permanent magnet 2, a temperature control system 5, and two circular thin-film polarizers (1 and 4) are then assembled into the aforementioned atomic filter.

[0060] Adjust the first and second polarizers (1 and 4) at both ends of the atomic bubble to be orthogonal to each other;

[0061] The temperature of the atomic bubble is increased by using temperature control system 5. At this time, the incident light rotates due to the Faraday effect of alkali metal atoms in a uniform magnetic field, and a transmission spectrum is obtained.

[0062] The temperature of the atomic bubbles is controlled by the temperature control system 5, so that the combined transmittance and linewidth of the transmission spectrum are optimized.

[0063] This invention utilizes the Faraday rotation effect of alkali metal gas on incident laser light under a strong magnetic field to achieve light filtering, with a volume only 1 / 200th that of traditional Faraday atom filters. A uniform, strong magnetic field of 3 mm length is generated at the center of a ring-shaped permanent magnet with an inner diameter of 10.5 mm, an outer diameter of 12.5 mm, and a thickness of 8 mm, along the direction of light propagation. Under the influence of this strong magnetic field, the absorption lines of alkali metal atoms split into two lines due to the Zeeman effect, corresponding to the absorption lines of right-handed and left-handed circularly polarized light, respectively, with slightly different frequencies. At this point, the left-handed and right-handed circularly polarized light in the incident laser exhibit different dispersion curves as they pass through the alkali metal atom gas. This results in a phase difference after they pass through the atom gas cell, manifesting as a change in the polarization direction of the linearly polarized light formed by their superposition.

[0064] Two orthogonal thin-film polarizers, 1 and 4, are used to select the frequency of the incident laser, ensuring that only incident light with frequencies near the atomic absorption lines can exit under the influence of optical rotation. A temperature control system 5 precisely controls the temperature of the atomic bubble, ensuring it operates at its optimal temperature. The outer casing designed in this way serves two purposes: securing all components and providing insulation, thus enhancing the micro Faraday atom filter's resistance to environmental temperature interference.

[0065] The miniature Faraday atom filter designed in this invention significantly reduces the size of the Faraday atom filter, achieves a more uniform and strong magnetic field, reduces power consumption, and possesses stronger mechanical stability. It is insensitive to external mechanical vibrations and temperature changes, making it suitable for various harsh environments with large vibrations and temperature variations, such as outdoor or vehicle-mounted environments. It is expected to achieve plug-and-play functionality for Faraday atom filters (since the Faraday atom filter does not change the direction of light propagation, it can be directly placed in the optical path to achieve plug-and-play functionality), which is of great significance for scientific research and industrial applications related to atomic filtering.

[0066] Example 5

[0067] The following is combined Figure 3 and Figure 4 The method steps in Example 4 will be further described below:

[0068] Step 101: Using the designed shell, assemble the cesium atom gas chamber 3 filled with buffer gas, the permanent magnet 2, and the first and second thin-film polarizers 1 and 4 together. The heating element and thermistor on the surface of the atom gas chamber 3 are connected to an external temperature control module.

[0069] Step 102: Adjust the polarization directions of the first and second thin-film polarizers 1 and 4 so that they are orthogonal to each other. At this time, since the temperature has not been increased, the Faraday rotation effect is weak, and the incident light cannot be emitted from the second thin-film polarizer 4.

[0070] Step 103: Increase the temperature. Under the influence of the magnetic field, the absorption lines of cesium atoms in the gas chamber split into two lines. This causes a path difference between the left-handed and right-handed circularly polarized light in the incident light after passing through the cesium atom gas chamber 3. The polarization direction of the linearly polarized light superimposed by the left-handed and right-handed circularly polarized light rotates, thus achieving optical rotation.

[0071] In practice, as the temperature rises, the cesium atom absorption line splits into two under the influence of a magnetic field, corresponding to the absorption lines of left-handed and right-handed circularly polarized light, respectively, with slightly different frequencies. Furthermore, the left-handed and right-handed circularly polarized light have different dispersion curves. Since their refractive indices differ when passing through the atomic gas cell, an optical path difference is generated. This optical path difference alters the phase difference of the light after exiting the gas cell relative to the phase difference before entering the gas cell.

[0072] When left-handed and right-handed circularly polarized light are superimposed to form linearly polarized light, the polarization direction of the linearly polarized light is directly related to the phase difference between the left-handed and right-handed circularly polarized light. When the phase difference changes, the polarization direction of the linearly polarized light will rotate, which is the Faraday rotation effect. The Faraday rotation effect is a well-known physical phenomenon in the art, and will not be described in detail in this embodiment of the invention.

[0073] In this process, incident light near the atomic absorption peak frequency undergoes optical rotation and can exit through the second thin-film polarizer 4, while incident light with frequencies far from the absorption peak cannot exit, thus achieving frequency selection of the incident light.

[0074] Step 104: Adjust the temperature to select the most suitable operating point.

[0075] When the temperature changes, the rotation angle of the polarization direction of the incident light changes, and the absorption of cesium atoms also changes. The final transmission spectrum is determined by these two factors. Therefore, it is necessary to select the optimal temperature to maximize the transmittance.

[0076] For example, when the buffer gas pressure is 5 Torr and the magnetic field strength is 1000 Gauss, the optimal temperature is 75.5 degrees Celsius, at which point the transmittance is highest.

[0077] The miniature Faraday atom filter in the above embodiment, by designing a miniature atomic gas cell 3 and a corresponding annular permanent magnet 2, and by replacing the polarizing beam splitter and Glan Taylor prism with first and second thin-film polarizers 1 and 4, greatly reduces the size of the Faraday atom filter, improves the anti-interference ability of the atom filter against mechanical vibration, and greatly reduces the power consumption of the atom filter.

[0078] This invention employs a novel magnetic field generation scheme, utilizing a smaller permanent magnet 3 to achieve a more uniform and stronger magnetic field, thereby improving the optical rotation performance of the atomic filter. Through improved insulation measures and a feedback control circuit with higher temperature control precision, the stability of the temperature control system 5 is enhanced, while simultaneously improving the atomic filter's resistance to external temperature changes.

[0079] Figure 4 This is a diagram illustrating the implementation effect of the miniature Faraday atom filter in the above embodiments. The magnetic field strength is 1000 Gauss, the buffer gas pressure is 5 Torr, the horizontal axis represents the measured laser frequency, and the zero point of the horizontal axis corresponds to cesium atoms. 2 S 1 / 2 F = 4 to 6 2 P 3 / 2 The transition frequency is F=3. The vertical axis represents the absolute transmittance of the miniature Faraday atom filter. Different colored curves correspond to the transmission spectra at different temperatures. Figure 4 The dataset on the right shows the maximum transmittance and full width at half maximum (FWHM) of the transmission spectrum of this atomic filter at different temperatures.

[0080] The above embodiments are merely for illustrating the principle of the present invention. The volume of the atomic gas chamber 3 and the magnetic field strength of the permanent magnet 2 in the atomic filter can be replaced, and the invention is not limited to the embodiments described above. For example, the volume of the atomic gas chamber 3 can be changed to 30 mm. 3 Or 15mm 3The magnetic field strength becomes 800 Gs or 1200 Gs.

[0081] Unless otherwise specified, the model numbers of the various devices in this embodiment of the invention are not limited, and any device that can perform the above functions is acceptable.

[0082] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A miniature Faraday atomic optical filter based on Faraday anomalous dispersion, characterized in that, The Faraday atomic optical filter comprises: an alkali metal atom cell, both sides of which are coated with an anti-reflection film corresponding to the wavelength of the absorption line of the alkali metal atom, and which is filled with buffer gas; a permanent magnet or a coil wrapped around the alkali metal atom cell to generate a uniform magnetic field parallel to the direction of light propagation; first and second polarizers respectively located on both sides of the alkali metal atom cell and facing the alkali metal atom cell, the polarization directions of the two polarizers being perpendicular to each other; a temperature control system for heating and temperature maintaining the alkali metal atom cell, detecting and controlling the temperature, the magnetic field strength being 100 to 1200 Gs; the temperature control system comprises: a heating module for heating the alkali metal atom cell and maintaining the temperature by a heat-insulating material; a thermistor or thermocouple for temperature detection; a temperature feedback control circuit for temperature control, the temperature control accuracy being higher than 0.01 degree; the atomic filter has a transmission spectral bandwidth of 3-5 GHz, and the maximum absolute transmittance reaches 0.7, depending on the set magnetic field and cell temperature; the first and second polarizers are respectively used for polarization and detection, a miniature atom cell with a length and diameter of only 3 mm is used, and the heating module and the permanent magnet are in close contact with the miniature atom cell.

2. A miniature Faraday atomic optical filter based on Faraday anomalous dispersion as claimed in claim 1, wherein, The permanent magnet is a hollow cylinder, and a uniform magnetic field with a length adapted to the length of the bubble filled with buffer gas is generated in the center of the cylinder.

3. A miniature Faraday atomic optical filter based on Faraday anomalous dispersion as claimed in claim 1, wherein, The Faraday atomic optical filter further comprises a shell for fixing the alkali metal atom cell, the permanent magnet or coil, the first and second polarizers, and the temperature control system; the maximum transmission spectral bandwidth of the atomic filter can reach 5.2 GHz, depending on the temperature and magnetic field strength of the atomic filter.

4. A miniature Faraday atomic optical filter based on Faraday anomalous dispersion as claimed in claim 3, wherein, The shell is internally filled with polyurethane foam heat-insulating material and externally made of polytetrafluoroethylene material.

5. A method for filtering based on a miniature Faraday atomic filter with Faraday anomalous dispersion, the filter being as claimed in claim 1, characterized in that, The method comprises: assembling the cesium atom cell filled with buffer gas, the permanent magnet, the first and second polarizers together by using the designed shell, and externally connecting the temperature control module to the heating sheet and the thermistor on the surface of the atom cell; adjusting the polarization directions of the first and second polarizers so that they are perpendicular to each other; increasing the temperature, the cesium atom absorption line in the cell splits into two under the action of the magnetic field, so that the left-handed circularly polarized light and the right-handed circularly polarized light in the incident light have a path difference after passing through the cesium atom cell, the polarization direction of the linearly polarized light obtained by superimposing the left-handed circularly polarized light and the right-handed circularly polarized light is rotated, and optical rotation is realized; adjusting the temperature to select the most suitable working point; and making the transmittance of the atomic filter higher while ensuring that the transmission spectral bandwidth of the atomic filter is as large as possible and the transmission peak top is relatively flat.

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