A bragg grating flexible vibration sensing structure

CN117553901BActive Publication Date: 2026-10-16ELECTRIC POWER RES INST OF STATE GRID ZHEJIANG ELECTRIC POWER COMAPNY
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Patent Information

Application Number
CN202311822167.1
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-12-27
Publication Date
2026-10-16
Estimated Expiration
2043-12-27

AI Technical Summary

Technical Problem

[0003]为克服现有技术存在的变形量小、制备流程复杂等不足,本发明的目的在于提供一种可用于振动传感的布拉格光栅柔性振动传感结构,属于一种布拉格体光栅结构,使其具有不受电磁干扰、制备流程简单、成本低的优点,同时不受温度干扰,无需进行温度补偿,且可调整弹性材料的比例来进行形变量程上的设计

Benefits of technology

[0021] The beneficial effects of this invention are as follows: The manufacturing cost is low, and the manufacturing process is not complex. By changing the proportion of the elastic material (such as PDMS), its elastic modulus and Poisson's ratio, as well as the grating duty cycle and coating thickness, can be altered, thereby changing the deformation range and measurable range. Furthermore, the elastic material has a low coefficient of thermal expansion, making it less susceptible to temperature effects, eliminating the need for temperature compensation measurements. The elastic material itself can replace the springs, spring sheets, hinges, and other components found in many existing Bragg grating vibration sensors, ensuring structural simplicity.

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Abstract

The application discloses a Bragg grating flexible vibration sensing structure. The application comprises a first elastic material layer located on an upper layer, a second elastic material layer located on a lower layer, a Bragg grating arranged between the two elastic material layers, an incident light source and a light receiver, wherein the light emitted by the incident light source is parallel to the periodically changing direction of the Bragg grating; the first elastic material layer, the Bragg grating and the second elastic material layer are connected into an integrated whole; a sliding block is arranged below the second elastic material layer, and the sliding block and the second elastic material layer are connected through a linkage member to realize linkage of the two, and deformation of the Bragg grating is realized through movement of the sliding block. Movement of the sliding block can drive the Bragg grating to vibrate, and the deformation caused by the vibration leads to changes of grating period and duty ratio, thereby leading to wavelength displacement of a transmission valley in a collected transmission spectrum or a reflection peak in a reflection spectrum, i.e. displacement of a waveguide resonance wavelength; through real-time changes of the resonance wavelength, vibration signal related parameters can be obtained.
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Description

Technical Field

[0001] This invention relates to the field of Bragg grating technology, and in particular to a flexible vibration sensing structure for Bragg gratings. Background Technology

[0002] There are two main types of commonly used Bragg grating structures: one is the fiber Bragg grating structure, which has advantages such as resistance to electromagnetic interference, small size, dynamic measurement capability, and high sensitivity. However, due to its susceptibility to factors such as temperature, it is difficult to achieve accurate sensing in harsh detection environments, such as high humidity, large temperature differences, or large strain. The other type is the volume Bragg grating, which also has advantages such as resistance to electromagnetic interference, but suffers from problems such as higher manufacturing costs, complex manufacturing processes, and small deformation. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, such as small deformation and complex manufacturing process, the present invention aims to provide a Bragg grating flexible vibration sensing structure that can be used for vibration sensing. It belongs to a Bragg volume grating structure, which has the advantages of being unaffected by electromagnetic interference, having a simple manufacturing process, and low cost. At the same time, it is unaffected by temperature interference, does not require temperature compensation, and the deformation range can be designed by adjusting the proportion of elastic material.

[0004] The present invention adopts the following technical solution: a Bragg grating flexible vibration sensing structure, which includes a first elastic material layer on the upper layer, a second elastic material layer on the lower layer, a Bragg grating containing a high refractive index material coating disposed between the two elastic material layers, an incident light source and a light receiver, wherein the light emitted by the incident light source is parallel to the periodic direction of the Bragg grating.

[0005] The Bragg grating includes an upper grating disposed on the boundary surface of the first elastic material layer, a lower grating disposed on the boundary surface of the second elastic material layer, and a high refractive index material coating located between the upper and lower gratings; the first elastic material layer, the Bragg grating, and the second elastic material layer are integrated into one unit.

[0006] A slider is provided below the second elastic material layer. The slider and the second elastic material layer are connected by a linkage to realize the linkage between the two. The movement of the slider realizes the deformation of the first elastic material layer, the second elastic material layer and the Bragg grating.

[0007] According to the principle of Bragg grating, the output transmitted light after the input light passes through the Bragg grating will show obvious transmission valleys or the output reflected light will have obvious reflection peaks. The first and second elastic materials have good tensile and springback effects. When used for vibration sensing, the movement of the slider can drive the Bragg grating to vibrate. The deformation caused by the vibration leads to changes in the grating period and duty cycle, which in turn causes the wavelength of the transmission valley or reflection peak to shift. By observing the real-time change of the resonant wavelength (wavelength of the transmission valley or reflection peak), the relevant parameters of the vibration signal, such as frequency and amplitude, can be obtained.

[0008] The amplitude and frequency response range of the vibration sensor can be adjusted by adjusting the mass of the slider.

[0009] One specific implementation of the above technical solution is as follows:

[0010] Furthermore, there is one linkage and one slider. One side of the second elastic material layer is fixedly connected to the first side plate, and the other side is a movable side, which is connected to the slider through the linkage.

[0011] Furthermore, the Bragg grating flexible vibration sensing structure also includes a bracket located outside the first side plate, on which a collimating lens and the incident light source are mounted, and the incident light source is connected to an incident optical fiber.

[0012] Furthermore, the Bragg grating flexible vibration sensing structure also includes a second side plate on which the optical receiver is mounted. A space for Bragg grating deformation is formed between the second side plate and the other side of the second elastic material layer. The optical receiver is connected to the outgoing optical fiber.

[0013] Furthermore, the slider is fitted onto a sliding rod, and the two ends of the sliding rod are fixedly connected to the first side plate and the second side plate, respectively.

[0014] Another specific implementation of the above technical solution is as follows:

[0015] Furthermore, there are two sliders and two linkages. Both sides of the second elastic material layer are connected to the corresponding sliders via linkages. A first side plate is provided on one side of the second elastic material layer, and a sensing spring is provided between the first side plate and its corresponding linkage. The natural vibration frequency and amplitude are further adjusted by the sensing spring.

[0016] Furthermore, a collimating lens and an incident light source are mounted on the first side plate, and the incident light source is connected to an incident optical fiber.

[0017] Furthermore, the Bragg grating flexible vibration sensing structure also includes a second side plate on which the optical receiver is mounted. A space for Bragg grating deformation is provided between the second side plate and the other side of the second elastic material layer. The optical receiver is connected to the outgoing optical fiber.

[0018] Furthermore, the two sliders are fitted onto a sliding rod, the two ends of which are fixedly connected to the first side plate and the second side plate, respectively.

[0019] Furthermore, the method for manufacturing the Bragg grating is as follows:

[0020] Deep silicon etching is performed on a silicon substrate, or photolithography is performed on a glass substrate to obtain a silicon grating or a glass substrate grating structure with an aspect ratio ≥ 1. A nickel grating is obtained by transferring the grating structure onto a nickel plate using a nickel plate fabrication method. A lower grating with an aspect ratio ≥ 1 is obtained by casting an elastic material onto the nickel grating. A high refractive index material is deposited on the lower grating to obtain a lower grating wrapped with a high refractive index material. The gaps in the lower grating are then filled with an elastic material and covered with a high refractive index material coating to form an upper grating, thereby obtaining a Bragg grating.

[0021] The beneficial effects of this invention are as follows: The manufacturing cost is low, and the manufacturing process is not complex. By changing the proportion of the elastic material (such as PDMS), its elastic modulus and Poisson's ratio, as well as the grating duty cycle and coating thickness, can be altered, thereby changing the deformation range and measurable range. Furthermore, the elastic material has a low coefficient of thermal expansion, making it less susceptible to temperature effects, eliminating the need for temperature compensation measurements. The elastic material itself can replace the springs, spring sheets, hinges, and other components found in many existing Bragg grating vibration sensors, ensuring structural simplicity. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the Bragg grating flexible vibration sensing structure of Embodiment 1 of the present invention;

[0023] Figure 2 The first and second elastic material layers of Embodiment 1 of the present invention have the same refractive index, and the simulated broadband transmittance and reflectance curves are compared with the coating with a higher refractive index.

[0024] Figure 3 This is a simulated transmittance and reflectance curve of two elastic materials with the same refractive index and close to the refractive index of the coating in Embodiment 1 of the present invention.

[0025] Figure 4 This is a simulated transmittance and reflectance curve of two elastic materials with different refractive indices and a coating with a higher refractive index, as shown in Embodiment 1 of the present invention.

[0026] Figure 5This is a simulated transmittance and reflectance curve of two elastic materials with different refractive indices and a coating with a low refractive index, as shown in Embodiment 1 of the present invention.

[0027] Figure 6 The simulated reflectance diagram of the two elastic materials with the same refractive index in Embodiment 1 of the present invention under the periodic variation of the Bragg grating;

[0028] Figure 7 The simulated reflectance diagram for the two elastic materials of Embodiment 1 of the present invention have different refractive indices, under the condition of changing coating refractive index;

[0029] Figure 8 This is a schematic diagram of the Bragg grating flexible vibration sensing structure of Embodiment 2 of the present invention;

[0030] In the figure, 1-first elastic material layer, 2-second elastic material layer, 3-Bragg grating, 4-incident fiber, 5-outgoing fiber, 6-collimating lens, 7-incident light source, 8-light receiver, 9-slider, 10-slider, 11-first side plate, 12-second side plate, 13-linkage component, 14-support, 15-sensing spring, 16-high refractive index material coating. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Example 1

[0033] This embodiment describes a Bragg grating flexible vibration sensing structure, such as... Figure 1 As shown, it consists of a first elastic material layer 1 on the upper layer, a second elastic material layer 2 on the lower layer, a Bragg grating 3 containing a high refractive index material coating 16, an incident light source 7, a collimating lens 6, an incident optical fiber 4, an outgoing optical fiber 5, a light receiver 8, a slider 9, and a slider 10.

[0034] The Bragg grating 3 is disposed between two elastic material layers, and the first elastic material layer 1, the Bragg grating 3, and the second elastic material layer 2 are integrated. The Bragg grating consists of an upper grating disposed on the boundary surface of the first elastic material layer 1, a lower grating disposed on the boundary surface of the second elastic material layer 2, and a high refractive index material coating 16 located between the upper and lower gratings. The light emitted from the incident light source 7 is parallel to the periodic direction of the Bragg grating 3.

[0035] The material of the upper grating can be the same as the first elastic material, so that the upper grating and the first elastic material layer are integrally formed; other elastic materials can also be used, and the upper grating and the first elastic material layer can be connected into one piece by means of bonding or other methods.

[0036] The material of the lower grating can be the same as the second elastic material, so that the lower grating and the second elastic material layer are integrally formed; or other elastic materials can be used, and the lower grating and the second elastic material layer can be connected into one piece by means of bonding or other methods.

[0037] The Bragg grating 3 has a first side plate 11 and a second side plate 12 on its two sides respectively.

[0038] A slider 10 is provided below the second elastic material layer 2. The slider 10 is connected to the second elastic material layer 2 by an L-shaped linkage 13, realizing the linkage between the two. The movement of the slider 10 realizes the deformation of the first elastic material layer 1, the second elastic material layer 2, and the Bragg grating 3. The slider 10 is mounted on a slide rod 9, and the two ends of the slide rod 9 are fixedly connected to the first side plate 11 and the second side plate 12, respectively.

[0039] One side of the second elastic material layer 2 is fixedly connected to the first side plate 11, and the other side is a movable side, which is connected to the slider 10 through the linkage 13.

[0040] A bracket 14 is provided on the outer side of the first side plate 11. A collimating lens 6 and an incident light source 7 are mounted on the bracket 14. The incident light source 7 is connected to the incident optical fiber 4.

[0041] A light receiver 8 is installed on the second side plate 12. A space for the deformation of the Bragg grating 3 is formed between the second side plate 12 and the other side of the second elastic material layer 2. The light receiver 8 is connected to the outgoing optical fiber 5.

[0042] The first and second elastic material layers are made of materials such as PDMS, TPU, silicone, and gel that are transparent to the working wavelength; the materials can be the same or different. The refractive index of the first and second elastic material layers can be adjusted by doping or other methods to obtain the desired spectral properties.

[0043] The Bragg grating period, duty cycle, and refractive index are designed based on the operating wavelength so that the resonant wavelength occurring within the deformation range falls within the operating band. The spectrum corresponding to the resonant wavelength is either a transmission valley or a reflection peak.

[0044] When this invention is used for vibration sensing, it is installed on the surface of a vibration source. When vibration occurs, the Bragg grating deforms, causing a change in the wavelength of its output resonant spectrum. The initial state of the Bragg grating is: unloaded, under tension, or under compression.

[0045] The elastic material (including the first and second elastic materials) can have its Young's modulus and stiffness coefficient adjusted by changing different proportions, that is, its resonant frequency can be adjusted. Similarly, the resonant frequency can be adjusted by appropriately adjusting the mass of the slider, the overall mass of the elastic material, etc., so as to achieve the vibration requirements at different amplitudes or frequencies.

[0046] The deformation range is designed by adjusting the proportion of elastic material.

[0047] Design principle: When the phase matching condition is met, light passing through a Bragg grating will generate a transmission valley or reflection peak, the center wavelength of which is λ. B =2N eff Λ.

[0048] In the formula, λ B N is the center wavelength of the Bragg grating; eff The effective refractive index of the Bragg grating is related to its duty cycle and transverse cross-sectional dimensions, while Λ represents the grating period. The stress-induced deformation of the Bragg grating affects both the period Λ and the equivalent refractive index N. eff Simultaneous change, thereby causing the center wavelength λ B The center wavelength of the Bragg grating is affected by factors such as displacement strain ε and Poisson's ratio, i.e., stress and strain are the main parameters, which can be expressed as:

[0049] Δλ B =2ΛΔN eff +2N eff ΔΛ.

[0050] The method for manufacturing the Bragg grating is as follows:

[0051] Deep silicon etching is performed on a silicon substrate, or photolithography is performed on a glass substrate to obtain a micro / nano silicon grating or glass grating structure with an aspect ratio ≥ 1. A nickel grating is obtained by transferring the grating structure onto a nickel plate using a nickel plate fabrication method. A lower grating with an aspect ratio ≥ 1 is obtained by casting an elastic material onto the nickel grating. A high refractive index material is deposited on the lower grating to obtain a lower grating wrapped with a high refractive index material. The gaps in the lower grating are then filled with an elastic material and covered with a high refractive index material coating to form an upper grating, thereby obtaining a Bragg grating.

[0052] When the material of the lower grating is the same as the material of the second elastic material layer, the second elastic material layer integrally formed with the lower grating can be obtained at the same time as the lower grating; when the material of the upper grating is the same as the material of the first elastic material layer, the first elastic material layer integrally formed with the upper grating can be obtained at the same time as the upper grating.

[0053] In this embodiment, a grating period of 400 nm and a grating height of 400 nm were used. The refractive indices of the first and second elastic materials (PDMS) were 1.5, and the refractive index of the magnetron sputtered high-refractive-index coating material TiO2 was 2.7. COMSOL Multiphysics simulation was performed, and the results were as follows: Figure 2 The results show that, under ideal conditions, the transmittance is in a rectangular band-stop filter state, while the reflectance is in a band-pass filter state. The simulation results of this Bragg grating flexible vibration sensing structure are consistent with the theoretical results of the Bragg grating, proving the theoretical correctness and feasibility of the structure.

[0054] Furthermore, it was optimized so that when the refractive index of the first elastic material and the second elastic material (PDMS) was 1.44, and the refractive index of the high refractive index material coating was 1.55, the following was obtained: Figure 3 The simulation results show that by optimizing the refractive index contrast, the desired spectral properties can be obtained to meet the required sensing effect.

[0055] Furthermore, different refractive index settings were applied to the first and second elastic materials, with the refractive index of the first elastic material set to 2.6, the refractive index of the second elastic material set to 1.4, and the refractive index of the high-refractive-index coating set to 2.0. This further optimized the simulation results, yielding... Figure 4 The results show that when the first elastic material and the second elastic material are set to be different materials or have different refractive indices, multiple transmission valleys / reflection peaks will be generated. The presence of multiple transmission valleys / reflection peaks can improve the working range of the sensing, and the existence of multiple sensing regions can also increase the number of parameters that can be sensed.

[0056] Further optimization will be carried out. Figure 4 Based on this, the refractive index of the high refractive index material coating was changed to 1.5, resulting in... Figure 5 The result shows two transmission valleys or two reflection peaks, with operating wavelengths of 500-600 nm and 800-900 nm, respectively. Figure 4 and Figure 5 This provides ample justification for increasing the operating frequency band.

[0057] Furthermore, in Figure 3 Based on this, optimization simulations were performed for different period variations, ranging from 350 to 900 nm, with the first and second elastic materials having the same refractive index. Specifically, the refractive index of both the first and second elastic materials was 1.44, while the refractive index of the high-refractive-index coating was 1.55. Figure 6 The results show that, under periodic variations, the changes in resonance valleys or resonance peaks are linear with the period, consistent with the formula.

[0058] ΔλB =2N eff ΔΛ

[0059] The results show a consistent pattern. When the period varies from 400 to 560 nm, which means the deformation rate is 40%, the result shows only one transmission valley, which can accurately reflect the change in vibration amplitude.

[0060] Furthermore, simulations were conducted on the refractive index variation of the high-refractive-index material coating, with the first and second elastic materials having different refractive indices (the first elastic material has a refractive index of 2.6, the second elastic material has a refractive index of 1.44), and the refractive index of the high-refractive-index material coating varies from 1.6 to 3. The results were... Figure 7 The results show two distinct black areas, representing the operating band. This indicates that the operating band has been expanded, resulting in a wider sensing range, which is highly feasible.

[0061] Example 2

[0062] This embodiment describes a Bragg grating flexible vibration sensing structure, such as... Figure 8 As shown, it consists of a first elastic material layer 1 located on the upper layer, a second elastic material layer 2 located on the lower layer, a Bragg grating 3, an incident light source 7, a collimating lens 6, an incident optical fiber 4, an outgoing optical fiber 5, a light receiver 8, a slider 9, and a slider 10.

[0063] The Bragg grating 3 is disposed between two elastic material layers, and the first elastic material layer 1, the Bragg grating 3, and the second elastic material layer 2 are integrated. The Bragg grating consists of an upper grating disposed on the boundary surface of the first elastic material layer 1, a lower grating disposed on the boundary surface of the second elastic material layer 2, and a high refractive index material coating 16 located between the upper and lower gratings. The light emitted from the incident light source 7 is parallel to the periodic direction of the Bragg grating 3.

[0064] The Bragg grating 3 has a first side plate 11 and a second side plate 12 on its two sides respectively.

[0065] Two sliders 10 are provided below the second elastic material layer 2. Both sides of the second elastic material layer 2 are connected to the corresponding sliders 10 through L-shaped linkages 13. A first side plate 11 is provided on one side of the second elastic material layer 2. A sensing spring 15 is provided between the first side plate 11 and its corresponding linkage 13.

[0066] A collimating lens 6 and an incident light source 7 are installed on the first side plate 11, and the incident light source 7 is connected to the incident optical fiber 4.

[0067] A light receiver 8 is installed on the second side plate 12. A space for the Bragg grating 3 to deform is provided between the second side plate 12 and the other side of the second elastic material layer 2. The light receiver 8 is connected to the outgoing optical fiber 5.

[0068] The two sliders 10 are mounted on the slide rod 9, and the two ends of the slide rod 9 are fixedly connected to the first side plate 11 and the second side plate 12, respectively.

[0069] In this embodiment, the natural vibration frequency and amplitude can be further adjusted using a sensing spring.

[0070] The method for manufacturing the Bragg grating is the same as in Example 1.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions and implementation methods of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A flexible vibration sensing structure using a Bragg grating, characterized in that, It includes a first elastic material layer (1) located on the upper layer, a second elastic material layer (2) located on the lower layer, a Bragg grating (3) disposed between the two elastic material layers, an incident light source (7) and a light receiver (8), and the light emitted by the incident light source (7) is parallel to the periodic direction of the Bragg grating (3); The Bragg grating (3) includes an upper grating disposed on the boundary surface of the first elastic material layer (1), a lower grating disposed on the boundary surface of the second elastic material layer (2), and a high refractive index material coating (16) located between the upper and lower gratings; the first elastic material layer (1), the Bragg grating (3), and the second elastic material layer (2) are integrated into one unit; A slider (10) is provided below the second elastic material layer (2). The slider (10) is connected to the second elastic material layer (2) through a linkage (13) to realize the linkage between the two. The movement of the slider (10) realizes the deformation of the first elastic material layer (1), the second elastic material layer (2) and the Bragg grating (3).

2. The Bragg grating flexible vibration sensing structure according to claim 1, characterized in that, The linkage (13) and the slider (10) are both one. One side of the second elastic material layer (2) is fixedly connected to the first side plate (11), and the other side is the movable side, which is connected to the slider (10) through the linkage (13).

3. The Bragg grating flexible vibration sensing structure according to claim 2, characterized in that, It also includes a bracket (14) located outside the first side plate (11), on which a collimating lens (6) and the incident light source (7) are mounted, and the incident light source (7) is connected to the incident optical fiber (4).

4. The Bragg grating flexible vibration sensing structure according to claim 2, characterized in that, It also includes a second side plate (12) on which the optical receiver (8) is mounted. The second side plate (12) and the other side of the second elastic material layer (2) form a space for the Bragg grating (3) to deform. The optical receiver (8) is connected to the outgoing optical fiber (5).

5. The Bragg grating flexible vibration sensing structure according to claim 4, characterized in that, The slider (10) is fitted onto a slide rod (9), and the two ends of the slide rod (9) are fixedly connected to the first side plate (11) and the second side plate (12) respectively.

6. The Bragg grating flexible vibration sensing structure according to claim 1, characterized in that, There are two sliders (10) and two linkages (13). Both sides of the second elastic material layer (2) are connected to the corresponding sliders (10) through linkages (13). A first side plate (11) is provided on one side of the second elastic material layer (2). A sensing spring (15) is provided between the first side plate (11) and the corresponding linkage (13).

7. The Bragg grating flexible vibration sensing structure according to claim 6, characterized in that, The collimating lens (6) and the incident light source (7) are installed on the first side plate (11), and the incident light source (7) is connected to the incident optical fiber (4).

8. The Bragg grating flexible vibration sensing structure according to claim 6, characterized in that, It also includes a second side plate (12), on which the optical receiver (8) is mounted. A space for the Bragg grating (3) to deform is provided between the second side plate (12) and the other side of the second elastic material layer (2). The optical receiver (8) is connected to the outgoing optical fiber (5).

9. The Bragg grating flexible vibration sensing structure according to claim 8, characterized in that, The two sliders (10) are fitted onto a slide rod (9), and the two ends of the slide rod (9) are fixedly connected to the first side plate (11) and the second side plate (12) respectively.

10. The Bragg grating flexible vibration sensing structure according to any one of claims 1-9, characterized in that, The method for manufacturing the Bragg grating is as follows: Deep silicon etching is performed on a silicon substrate, or photolithography is performed on a glass substrate to obtain a silicon grating or a glass substrate grating structure with an aspect ratio ≥ 1. A nickel grating is obtained by transferring the grating structure onto a nickel plate using a nickel plate fabrication method. A lower grating with an aspect ratio ≥ 1 is obtained by casting an elastic material onto the nickel grating. A high refractive index material is deposited on the lower grating to obtain a lower grating wrapped with a high refractive index material. The gaps in the lower grating are then filled with an elastic material and covered with a high refractive index material coating to form an upper grating, thereby obtaining a Bragg grating.

Citation Information

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