An inclined hollow-core fiber acoustic detection device and method

Through the inclined hollow-core optical fiber acoustic detection device, the temperature cross-interference problem of optical fiber acoustic wave sensor is solved by using metal germanium vibrating film and seamless fusion technology, and acoustic wave detection with high sensitivity and small size is achieved, suitable for military and industrial fields.

CN115931106BActive Publication Date: 2025-07-04YANGTZE DEITA GRADUATE SCHOOI OF BEIJING INST OF TECH (JIAXING) +1
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Patent Information

Application Number
CN202211524269.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-11-30
Publication Date
2025-07-04
Estimated Expiration
2042-11-30

AI Technical Summary

Technical Problem

Existing fiber optic acoustic sensors are affected by temperature cross-interference in practical applications, resulting in reduced sensitivity and signal distortion, limiting their wide application in military and industrial fields.

Method used

The acoustic detection device of inclined hollow core fiber, including a vibrating film, an air core fiber and a dual core fiber, is used as a sensing element, and the external acoustic amplitude and frequency are reduced through an inclined micro-vibration film full fiber acoustic sensor, and the metal vibrating film is prepared in combination with vapor deposition method and backward wet corrosion technology to achieve seamless fusion and temperature self-calibration.

Benefits of technology

It improves the sensitivity and anti-interference ability of the sensor, is suitable for working in strong electromagnetic interference and harsh environments, and is suitable for biomedical and micro-nano structures and other fields.

✦ Generated by Eureka AI based on patent content.

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Abstract

An inclined hollow-core fiber acoustic detection device and method disclosed by the present invention belong to the field of fiber optic sensing. The inclined hollow-core fiber acoustic detection device includes a vibration membrane, a hollow-core fiber, and a dual-core fiber that are connected in sequence. The present invention uses the vibration membrane as the sensing element of the fiber optic acoustic wave sensor to improve the sensitivity of the intensity-type fiber optic acoustic wave sensor. The present invention uses dual-core photonic crystal fibers as the outgoing core and the receiving core respectively to simplify the complexity of the beam transmission fiber; in addition, a pure silicon-core multimode fiber is used as the preparation element of the cavity, enabling seamless fusion splicing of the photonic crystal fiber and the cavity without any connecting devices; meanwhile, a metal vibration membrane is prepared by directly coating using the chemical vapor deposition method, increasing the uniformity of the sensor; the present invention adopts the backside wet etching processing technology to form a metal vibration membrane from the backside of the fiber by using the selective etching of TMAH solution for pure silicon, quartz, and germanium metal, realizing suspended coating of the metal material.
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Description

Technical Field

[0001] The present invention relates to an inclined hollow-core fiber acoustic detection device and method, belonging to the field of fiber optic sensing. Background Art

[0002] An acoustic wave sensor can collect acoustic wave signals in the air, realizing target detection, recognition, and tracking of low-altitude and slow-moving aircraft, and is an effective air defense detection means. The development of acoustic wave sensors can not only make up for the deficiencies of existing infrared detectors that cannot detect under strong electromagnetic interference, but also solve the problem that electromagnetic radars are difficult to effectively detect new "stealth" aircraft. Therefore, the research on acoustic wave sensing technology has very important strategic significance in the field of national security.

[0003] Fiber optic acoustic wave sensing technology Fiber optic acoustic wave sensors are technologies that use light waves as carriers and optical fibers as media to pick up acoustic wave information. In recent years, fiber optic acoustic wave sensors have not only attracted extensive research, but also made up for the deficiencies of traditional electro-acoustic wave sensors with unique advantages: First, all-fiber sensors are passive devices, so they overcome the disadvantage that traditional electro-acoustic wave sensors cannot work under strong electromagnetic interference and are very suitable for working in harsh interference environments. Second, the multiplexing characteristics of optical fibers make it easy for fiber optic acoustic wave sensors to form large-scale arrays, and multi-point long-distance simultaneous measurements can be achieved without a front-end electronic amplifier, thus solving the problem that electrical sensors are not suitable for long-distance transmission. Finally, compared with electro-electret acoustic sensors (50 mV / Pa), the sensitivity of fiber optic acoustic wave sensors (≥100 mV / Pa) is generally stronger, thus improving the problem of limited ability of electrical sensors to pick up weak acoustic wave signals. Many experts and scholars have pointed out that the research on high-precision photoacoustic sensors combining optical measurement and micro-optical technology is an important development direction to solve the development bottleneck of traditional electro-acceleration sensors. In the military field, currently, countries such as the United States, Sweden, and Israel have carried out air defense early warning using fiber optic acoustic detection technology. Among them, Israel developed the "Search Helicopter" acoustic detection system based on the sound vibration characteristics generated by different models of armed helicopters, which can detect helicopters flying low at a distance of 6 km. In addition to the military field, fiber optic acoustic wave sensors can also be converted into acoustic wave sensors applied to the industrial field, including fields such as building health monitoring, perimeter security monitoring, and biomedical research. At the beginning of 2014, the first domestic fiber optic earthquake and tsunami disaster warning acoustic detection system was deployed at sea near Xiaoqushan, Zhejiang Province. This system monitors the nearby undersea earthquakes, tsunamis, etc. in real time. The important scientific significance and application value of fiber optic acoustic wave sensors are being taken seriously by academia, industry, and military departments in many countries around the world.

[0004] However, the current practical applications of fiber optic acoustic sensors are not very extensive, and the main problem restricting their practical applications is the cross-interference of temperature. Especially for interferometric high-sensitivity fiber optic acoustic sensors, the change in temperature in the actual measurement environment will cause the working point of the sensor to drift, resulting in a series of problems such as a decrease in the sensitivity of the fiber optic acoustic sensor, signal distortion, and a decline in linearity. Therefore, studying the temperature self-calibration mechanism is the key scientific issue to solve the working point drift of fiber optic acoustic sensors and develop their practical applications. This project intends to use the characteristics of the optical wavelength dispersion of diffraction gratings, taking the orthogonal diffraction wavelength as the research object, and deeply study the scientific issue of the temperature self-calibration mechanism in interferometric fiber optic acoustic sensors. The research on this issue can not only solve the problem of temperature interference in fiber optic acoustic sensors, but also provide a research basis for the application of new fiber optic acoustic detection systems in the military and industrial fields. Summary of the Invention

[0005] Traditional electronic acoustic sensors, such as piezoelectric microphones or electret microphones, are difficult to ensure the sensitivity of acoustic wave detection while reducing the size. The main purpose of the present invention is to provide an inclined hollow fiber acoustic detection device and a manufacturing method. Through an inclined micro-vibration membrane all-fiber acoustic wave sensor, the amplitude and frequency of external acoustic waves can be restored, and it has the advantages of high sensitivity, small volume, and low interference.

[0006] The technical solution adopted by the present invention is as follows:

[0007] An inclined hollow fiber acoustic detection device disclosed by the present invention includes a vibration membrane, a hollow fiber, and a dual-core fiber connected in sequence; it is necessary to ensure that one core in the dual-core photonic crystal fiber is directly opposite to the center of the hollow fiber to become the central core; the other core in the dual-core fiber is located below the central core.

[0008] According to an embodiment of the present invention, the dual-core fiber used in the device is a dual-core photonic crystal fiber.

[0009] According to an embodiment of the present invention, the hollow fiber used in the device is a multimode fiber with an etched core.

[0010] According to an embodiment of the present invention, the device uses a metal vibration membrane made of germanium as the sensing element of the fiber optic acoustic sensor, and the light emitted from the dual-core photonic crystal fiber is always reflected at the point with the maximum mechanical displacement of the vibration membrane.

[0011] A manufacturing method of an inclined hollow fiber acoustic detection device disclosed by the present invention includes the following steps:

[0012] Step 1: Process a short cavity on the end face of a pure silicon multimode fiber according to the selective corrosion of the TMAH solution.

[0013] Step 2: Use a fusion splicer to offset-fuse the dual-core photonic crystal fiber and the pure silica multimode fiber.

[0014] Step 3: Grind the end face of the pure silica multimode fiber through a fiber end face grinding device to form an inclined end face, and then deposit a germanium film on the inclined end face by chemical vapor deposition.

[0015] Step 4: Use a femtosecond laser to process a rectangular groove in the upper half of the photonic crystal fiber, and then fill all the air holes of the photonic crystal fiber with TMAH solution. In this way, the TMAH solution in the upper half of the photonic crystal fiber flows out through the groove, while the TMAH solution in the lower half of the photonic crystal fiber fills the short cavity of the pure silica multimode fiber for etching. The residual air in the air holes also flows out from the upper half of the photonic crystal fiber on the other side of the groove, so that a suspended and inclined metal germanium vibration film is plated on the surface of the cavity.

[0016] Step 5: Use a pump to suck out the TMAH solution, and then fill the air holes and the cavity with distilled water for cleaning in the same way. Cut off one side of the photonic crystal fiber with the groove processed, and the fabrication of the inclined hollow fiber acoustic detection device is completed.

[0017] A working method of an inclined hollow fiber acoustic detection device disclosed by the present invention includes the following steps:

[0018] Step 1: Inject laser light into the central core, and after being reflected by the vibration film, couple it into the other core and emit it. The emitted optical power P is:

[0019] P≈I0 exp(ω l 2 )·πrR

[0020] wherein, I0 is the light intensity of the light beam, the mode field diameter of the light beam ω l =ω o [1+(θ A l / ω o ) 2 1 / 2 , ω o is the mode field diameter of the photonic crystal fiber, θ A is the divergence angle of the photonic crystal fiber, l is the light beam propagation distance, l = Y(1 + 1 / cos2θ), Y is the vibration film displacement distance, θ is the incident angle of the vibration film and the inclination angle of the vibration film, R is the distance between the midpoint of the reflected light and the center, R = d - Ltanθ, d is the dual-core spacing of the photonic crystal fiber, L is the cavity length, Y is the vibration film displacement distance, and r is the radius from the center point in polar coordinates.

[0021] Step 2: The displacement distance of the diaphragm, that is, the deformation Y of the diaphragm, can be obtained by using the coupled optical power P:

[0022] ​

[0023] Step 3: Solve the deformation Y and forced frequency response f of the diaphragm according to the theory of small deflection bending of the vibrating membrane mn for the equation:

[0024]

[0025] where r is the radius from the center point in polar coordinates, P is the acting pressure, D is the flexural rigidity of the vibrating membrane, φ mn is a constant related to the vibration mode of the vibrating membrane, ρ is a constant related to the vibration mode of the vibrating membrane, and h is the thickness of the vibrating membrane. All parameters are obtained by referring to the relevant literature of germanium metal.

[0026] Step 4: The sound source intensity of the sound wave is equal to the acting pressure P:

[0027]

[0028] The vibration frequency of the sound wave is the forced frequency response f:

[0029]

[0030] Beneficial effects:

[0031] 1. For an inclined hollow-core fiber acoustic detection device and method disclosed in the present invention, the inclined vibrating membrane structure will cause dynamic changes in the beam coupling efficiency. The sensing mechanism has a simple structure and high sensitivity, and can overcome the disadvantage of low sensitivity of traditional intensity-type fiber acoustic wave sensors. In addition, a vibrating membrane is used as the sensing element of the fiber acoustic wave sensor, replacing the method of changing the physical quantity of the fiber itself in the traditional intensity-type fiber acoustic wave sensor, to improve the sensitivity of the intensity-type fiber acoustic wave sensor. At the same time, the finite element method is used to analyze the mechanical displacement characteristics of the vibrating membrane, and the sensitivity of the sensor is further optimized by offset splicing the optical fiber.

[0032] 2. For an inclined hollow-core fiber acoustic detection device and method disclosed in the present invention, two cores of a dual-core photonic crystal fiber are respectively used as the outgoing core and the receiving core, simplifying the complexity of the beam transmission optical fiber. In addition, the sensor uses a pure silica-core multimode optical fiber as the preparation element of the cavity, enabling seamless fusion splicing of the photonic crystal fiber and the cavity without any connecting devices, improving the integrity of the sensor. At the same time, a metal vibrating membrane is prepared by directly coating using the vapor deposition method, increasing the unity of the sensor. The entire sensor is composed entirely of quartz optical fibers, and its size is the cross-sectional size of the optical fiber. Therefore, the present invention can break through the structural limitations of traditional fiber acoustic wave sensors and make the present invention suitable for applications in fields such as biomedicine and micro-nano structures.

[0033] 3. An inclined hollow-core fiber acoustic detection device and method disclosed by the present invention adopt a backside wet etching processing technique. By using the selective etching theory of TMAH solution for pure silicon, quartz, and germanium metal, a metal vibration film is formed from the backside of the optical fiber to achieve suspended metal coating. In addition, the method of fiber microfabrication technology can solve the problem of air flow inside the optical fiber. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0035] Figure 1 It is a schematic diagram of the geometric structure of the inclined hollow-core fiber acoustic detection device according to an embodiment of the present invention;

[0036] Figure 2 It is a flowchart of the preparation method of the inclined hollow-core fiber acoustic detection device according to an embodiment of the present invention; wherein Fig. a is a schematic diagram of an etched multimode optical fiber, Fig. b is a schematic diagram of the fusion splicing process, Fig. c is a schematic diagram of metal coating, Figs. d1, 2, and 3 are flowcharts of the backside wet etching processing technique, and Fig. e is a schematic diagram of the final processed product.

[0037] Figure 3 It is a schematic diagram of the acoustic wave sensing principle in the inclined hollow-core fiber acoustic detection device according to an embodiment of the present invention; wherein Fig. a is an optical path diagram without acoustic waves, and Figs. b and c are optical path diagrams under the influence of sound source vibration. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0039] Figure 1 It is a schematic diagram of the geometric structure of the inclined hollow-core fiber acoustic detection device according to an embodiment of the present invention.

[0040] As Figure 1 shown, an inclined hollow-core fiber acoustic detection device disclosed in this embodiment includes a dual-core photonic crystal fiber, a cavity (prepared from a silicon-core optical fiber), and a vibration film plated on the end face of the cavity.

[0041] Specifically, since there is a certain angle between the end face of the cavity and the axis of the optical fiber, the vibration membrane is inclined. After the optical signal is transmitted through the dual-core photonic crystal fiber, it exits from the optical fiber core A and enters the cavity. Then, when the optical signal propagates to the vibration membrane, reflection occurs. Due to the existence of the inclination angle, the optical signal is reflected into the optical fiber core B.

[0042] In one embodiment of the present invention, the photonic crystal fiber used in the device is a dual-core photonic crystal fiber, and the distance between the two cores is 20 micrometers.

[0043] In one embodiment of the present invention, the cavity used in the device is prepared from a silica-core fiber, which is a multimode fiber with an etched core, and the cavity length is 5 millimeters.

[0044] In one embodiment of the present invention, the sensing element of the fiber optic acoustic wave sensor used in the device is a germanium metal vibration membrane, and the thickness of the membrane is 30 micrometers.

[0045] In one embodiment of the present invention, there is a certain angle θ = 10° between the end face of the cavity used in the device and the axis of the optical fiber, so the vibration membrane is inclined.

[0046] Specifically, since there is a certain angle between the end face of the cavity and the axis of the optical fiber, the vibration membrane is inclined. After the optical signal is transmitted through the dual-core photonic crystal fiber, it exits from the optical fiber core A and enters the cavity. Then, when the optical signal propagates to the vibration membrane, reflection occurs. Due to the existence of the inclination angle, the optical signal is reflected into the optical fiber core B. When the vibration membrane undergoes mechanical displacement due to the acoustic wave, the coupling efficiency of the reflected light incident on the optical fiber core B will change. Thus, the external acoustic wave information can be measured by detecting the reflected light in the photonic crystal fiber.

[0047] Figure 2 It is a flowchart of the preparation method of the inclined hollow-core fiber acoustic detection device according to the embodiment of the present invention;

[0048] In one embodiment of the present invention, according to the selective corrosion theory, a backside wet etching process technology is designed to process the suspended inclined metal vibration membrane.

[0049] The manufacturing method of an inclined hollow-core fiber acoustic detection device disclosed in this embodiment is as follows: (a) First, a short cavity is processed on the end face of a pure silica multimode fiber according to the selective corrosiveness of the TMAH (tetramethylammonium hydroxide) solution, as shown in Figure 2 (a). (b) Second, the dual-core photonic crystal fiber and the pure silica multimode fiber are offset welded by a fusion splicer, as shown in Figure 2 (b). (c) Then, the end face of the pure silica multimode fiber is ground by a fiber end face grinding device to form an inclined end face, and a germanium film is deposited on the inclined end face by chemical vapor deposition, as shown in Figure 2(c). Subsequently, a rectangular groove is machined on the upper half of the photonic crystal fiber using a femtosecond laser, and then the TMAH solution is filled into all the air holes of the photonic crystal fiber, as shown in Figure 2 (d1). The TMAH solution on the upper half of the photonic crystal fiber flows out through the groove, while the TMAH solution on the lower half of the photonic crystal fiber is filled into the short cavity of the pure silica multimode fiber for etching. The residual air in the air holes also flows out from the upper half of the photonic crystal fiber on the other side of the groove, as shown in Figure 2 (d2). In this way, the suspended and inclined germanium metal vibration membrane is plated on the surface of the cavity, as shown in Figure 2 (d3). (e) Finally, the TMAH solution is sucked out using a pump, and then distilled water is filled into the air holes and the cavity in the same way for cleaning. Then, one side of the photonic crystal fiber with the groove is cut off, as shown in Figure 2 (e). In this way, the preparation process of the suspended and inclined metal vibration membrane is realized.

[0050] In an embodiment of the present invention, a working method of an inclined hollow fiber acoustic detection device disclosed in this embodiment is as follows: The method includes the following steps:

[0051] Step 1: Laser with an intensity of 10 millicandelas is injected into the central core, reflected by the vibration membrane, and then coupled into another core and emitted. The emitted optical power P is:

[0052]

[0053] where I0 is the optical intensity of the light beam, the mode field diameter ω of the light beam l = ω o [1+(θ A l / ω o ) 2 1 / 2 , ω o is the mode field diameter of the photonic crystal fiber, θ A is the divergence angle of the photonic crystal fiber, l is the light beam propagation distance, l = Y(1 + 1 / cos2θ), Y is the vibration membrane displacement distance, θ is the incident angle of the vibration membrane and the inclination angle of the vibration membrane, R is the distance between the midpoint of the reflected light and the center, R = d - Ltanθ, d is the distance between the two cores of the photonic crystal fiber, L is the cavity length, Y is the vibration membrane displacement distance, and r is the radius from the center point in polar coordinates.

[0054] Step 2: The displacement distance of the vibration membrane, that is, the deformation Y of the diaphragm, can be obtained using the coupled optical power P:

[0055]

[0056] Step 3: According to the theory of small deflection bending of the vibration membrane, the deformation Y of the diaphragm and the forced frequency response f of the membrane​mn Solve the equation:

[0057]

[0058] Where r is the radius from the center point in polar coordinates, P is the applied pressure, D is the bending stiffness of the vibrating membrane, φ mn is a constant related to the vibration mode of the vibration film, ρ is a constant related to the vibration mode of the vibration film, and h is the thickness of the vibration film. All parameters can be obtained by consulting the relevant literature on metal germanium.

[0059] Step 4: Substituting the parameters of the device into the following formula, it can be calculated that the sound source intensity of the sound wave is equal to the applied pressure P:

[0060]

[0061] The vibration frequency of the sound wave is the forced frequency response f:

[0062]

[0063] The sound wave pressure measured by the standard acoustic sensor is 0.2 Pa, and the difference between the measured result and the standard result is 0.01 Pa, which is within the acceptable error range. The sound wave vibration frequency measured is 110 Hz, and the difference between the measured result and the standard result is 6 Hz, which is also within the acceptable error range.

[0064] Through step one, the relationship between the mechanical displacement of the vibrating diaphragm and the coupling of the reflected light intensity is obtained. Then, through step two, the relationship between the mechanical displacement of the vibrating diaphragm and the acoustic vibration is obtained. Based on the independent analysis of the above two parts of the model, the two parts are combined to establish the overall model of the sensor. The coupling rate of the light beam in the sensor will be modulated with the mechanical displacement of the vibrating diaphragm caused by the acoustic wave, thereby realizing tilted hollow-core optical fiber acoustic detection.

[0065] The method for manufacturing the tilted hollow-core optical fiber acoustic detection device of the embodiment of the present invention manufactures a small-sized tilted hollow-core optical fiber acoustic detection device, which can realize the direction detection of the sound source signal and has the advantage of small size, and can realize remote detection or sound signal frequency detection in a strong electromagnetic interference environment.

[0066] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A manufacturing method of an inclined hollow-core fiber acoustic detection device, characterized in that: The following steps are included: Step 1: Processing a short cavity on the end face of a pure silicon multimode optical fiber according to the selective corrosiveness of the TMAH solution; Step 2: Use a fusion splicer to perform offset fusion splicing of the dual-core photonic crystal fiber and the pure silica multimode fiber; Step 3: Grind the end face of the pure silicon multimode optical fiber to form an inclined end face by using an optical fiber end face grinding device, and then coat a layer of germanium film on the inclined end face by using a vapor deposition method; Step 4: Use a femtosecond laser to process a rectangular groove in the upper half of the photonic crystal fiber, and then fill all the air holes of the photonic crystal fiber with TMAH solution; in this way, the TMAH solution in the upper half of the photonic crystal fiber flows out from the groove, and the TMAH solution in the lower half of the photonic crystal fiber is filled into the short cavity of the pure silicon multimode fiber for corrosion; the residual air in the air hole will also flow out from the upper half of the photonic crystal fiber on the other side of the groove; so that the suspended inclined metal germanium vibration film is plated on the surface of the cavity; Step 5: Use a pump to suck out the TMAH solution, and then use the same method to fill distilled water into the air holes and cavities for cleaning; then cut off one side of the photonic crystal fiber with the grooves.

2. An inclined hollow-core fiber acoustic detection device is fabricated by using the fabrication method of an inclined hollow-core fiber acoustic detection device as described in claim 1, and is characterized in that: It includes a vibration membrane, a hollow-core optical fiber and a dual-core optical fiber connected in sequence; it is necessary to ensure that one core of the dual-core photonic crystal optical fiber is directly facing the center of the hollow-core optical fiber to become the central core; and the other core of the dual-core optical fiber is located below the central core.

3. The tiltable hollow-core fiber acoustic detection device according to claim 2, characterized in that: The dual-core optical fiber used is a dual-core photonic crystal fiber.

4. The inclined hollow-core fiber acoustic detection device according to claim 2, wherein: The hollow core optical fiber used is a multimode optical fiber with an etched core.

5. The tiltable hollow-core fiber acoustic detection device according to claim 2, wherein: A metal vibration membrane made of germanium is used as the sensing element of the optical fiber acoustic wave sensor, and the output light of the double-core photonic crystal fiber is always located at the maximum point of mechanical displacement of the vibration membrane for reflection.

6. The method for measuring the acoustic wave frequency of the inclined hollow-core fiber acoustic detection device according to claim 2, 3 or 4, characterized in that: The following steps are included: Step 1: The laser is injected from the central core, and after being reflected by the vibrating membrane, it is coupled to another core and emitted. The emitted optical power P is: where, I0 is the light intensity of the light beam, and the mode field diameter of the light beam is ω l = ω o [1 + (θ A l / ω o ) 2 1 / 2 , ω o is the mode field diameter of the photonic crystal fiber, θ A is the divergence angle of the photonic crystal fiber, l is the propagation distance of the light beam, l = Y(1 + 1 / cos2θ), Y is the displacement distance of the vibrating membrane, θ is the incident angle and the inclination angle of the vibrating membrane, R is the distance between the midpoint of the reflected light and the center, R = d - Ltanθ, d is the distance between the two cores of the photonic crystal fiber, L is the cavity length, and r is the radius from the center point in polar coordinates;​ Step 2: The displacement distance of the diaphragm can be obtained by using the coupled optical power P, which is the deformation Y of the diaphragm: Step 3: Solve the equations for the deformation Y and the forced frequency response f of the diaphragm according to the theory of small deflection bending of the vibrating membrane mn as follows: where r is the radius from the center point in polar coordinates, P is the acting pressure, D is the flexural rigidity of the diaphragm, φ mn is a constant related to the vibration mode of the diaphragm, ρ is a constant related to the vibration mode of the diaphragm, and h is the thickness of the diaphragm; Step 4: The sound source intensity of the sound wave is equal to the applied pressure P: The vibration frequency of the sound wave is the forced frequency response f:

Citation Information

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