High-precision air pressure sensor based on composite optical fiber microcavity and detection method

Abstract

The invention discloses a high-precision gas pressure sensor based on a composite optical fiber microcavity and a detection method, and relates to the technical field of gas pressure measurement. A plurality of radial air holes are formed in the side wall of a first hollow optical fiber, external air is communicated with the interior of the first hollow optical fiber through the air holes, and the interior of a second hollow optical fiber is filled with air; the welding surface of the first single-mode optical fiber and the first hollow optical fiber is a first reflecting surface, the welding surface of the first hollow optical fiber and the second single-mode optical fiber is a second reflecting surface, the welding surface of the second single-mode optical fiber and the second hollow optical fiber is a third reflecting surface, and the critical surface of air in the second hollow optical fiber and the UV film is a fourth reflecting surface. The device meets the requirements of the field of high-precision air pressure detection, and has the effects of high integration level, high precision, high sensitivity, stable structure and low temperature crosstalk.

Description

Technical Field

[0001] The present invention relates to the technical field of gas pressure measurement, and in particular to a high-precision gas pressure sensor based on a composite optical fiber microcavity and a detection method. Background Art

[0002] Gas pressure is an important physical parameter in the fields of biomedicine, environmental monitoring, aerospace, etc., and accurate detection of air pressure changes is crucial to the above fields. Compared with traditional electronic barometers, fiber optic Fabry-Perot microcavity air pressure sensors have attracted much attention from researchers due to their compact structure, resistance to electromagnetic interference, and ability to achieve remote and accurate measurement in extreme environments, and have developed rapidly in recent years. In the process of gas pressure detection, fiber optic Fabry-Perot microcavity air pressure sensors are widely used. The detection sensitivity of common fiber optic Fabry-Perot microcavity air pressure sensors can only reach a few nanometers per megapascal, which is difficult to meet the needs of some high-precision air pressure detection fields.

[0003] Therefore, it is necessary to provide a high-sensitivity and high-precision trace air pressure sensor. Summary of the invention

[0004] In view of the above-mentioned defects of the prior art, the present invention provides a high-precision air pressure sensor and detection method based on a composite optical fiber microcavity, which meets the needs of the field of high-precision air pressure detection and has the effects of high integration, high precision, high sensitivity, stable structure and low temperature crosstalk.

[0005] The present invention provides a high-precision air pressure sensor based on a composite optical fiber microcavity, comprising a broadband light source, an optical fiber circulator, a spectrum analyzer and a sensor head;

[0006] The sensor head includes a first single-mode optical fiber, a first hollow-core optical fiber, a second single-mode optical fiber, a second hollow-core optical fiber and a UV film which are fused in sequence. A plurality of radial air holes are provided on the side wall of the first hollow-core optical fiber, and the air holes connect the outside air with the interior of the first hollow-core optical fiber. The interior of the second hollow-core optical fiber is filled with air. The fusion surface of the first single-mode optical fiber and the first hollow-core optical fiber is a first reflection surface, the fusion surface of the first hollow-core optical fiber and the second single-mode optical fiber is a second reflection surface, the fusion surface of the second single-mode optical fiber and the second hollow-core optical fiber is a third reflection surface, and the critical surface of the air and the UV film in the second hollow-core optical fiber is a fourth reflection surface.

[0007] Furthermore, the inner diameter of the first single-mode optical fiber is in the range of 8 to 9 microns, and the inner diameter of the second single-mode optical fiber is in the range of 8 to 9 microns.

[0008] Furthermore, the inner diameter of the first hollow-core optical fiber is in the range of 50 to 70 microns, and the inner diameter of the second hollow-core optical fiber is in the range of 50 to 70 microns.

[0009] Furthermore, the length difference between the first hollow-core optical fiber and the second hollow-core optical fiber ranges from 1 to 50 microns.

[0010] Furthermore, the diameter of the pores ranges from 15 to 20 micrometers, and the density of the pores ranges from 15 to 20 per millimeter.

[0011] Furthermore, the thickness of the UV film ranges from 10 to 20 microns.

[0012] The second aspect of the present invention provides a high-precision air pressure detection method based on a composite optical fiber microcavity, which is implemented based on the high-precision air pressure sensor based on the composite optical fiber microcavity, and includes the following steps:

[0013] S1, the detection light enters the first hollow-core optical fiber through the first single-mode optical fiber, and forms the first reflected light and the second reflected light at the first reflecting surface and the second reflecting surface. When the air pressure changes, the refractive index of the gas inside the first hollow-core optical fiber changes, so that the refractive index of the medium in the cavity of the first hollow-core optical fiber changes, and the reflection spectrum of the first hollow-core optical fiber moves;

[0014] S2, the second single-mode optical fiber enters the second hollow-core optical fiber, and forms a third reflected light and a fourth reflected light at the third reflecting surface and the fourth reflecting surface. When the air pressure changes, the UV film at the end of the second hollow-core optical fiber is deformed by force, so that the cavity length of the second hollow-core optical fiber changes, and the reflection spectrum of the second hollow-core optical fiber moves;

[0015] S3, the reflection spectrum envelope formed by the superposition of the first reflected light, the second reflected light, the third reflected light and the fourth reflected light moves, and the measurement of the ambient air pressure is achieved by detecting the spectrum envelope response.

[0016] Furthermore, the translation amount Δλ of the reflection spectrum envelope is Envelope for:

[0017] Δλ Envelope =M(Δλ FP2 -Δλ FP1 );

[0018] Where M is the amplification factor of the envelope, Δλ FP1 is the wavelength shift of the first hollow-core optical fiber reflection spectrum, which is: λ is the incident wavelength of the detection light, n 1 is the refractive index of the medium in the first hollow-core fiber cavity, Δn 1 is the change in refraction of the medium in the first hollow-core fiber, Δλ FP2 is the wavelength shift of the second hollow-core fiber reflection spectrum, L 2 The cavity length of the first hollow-core fiber, ΔL 2 is the change in the second hollow-core fiber cavity length.

[0019] Furthermore, the envelope amplification factor M is:

[0020]

[0021] Among them, FSR FP1 is the free spectral range of the first hollow-core fiber, which is: FSR FP1 =λ 2 / 2n 1 L 1 ; L 1 is the cavity length of the first hollow-core fiber; FSR FP2 is the free spectral range of the second hollow-core fiber, which is: FSR FP2 =λ 2 / 2n 2 L 2 , n 2 is the refractive index of the medium in the second hollow-core optical fiber cavity.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] The present invention forms a high-precision air pressure sensor based on a composite optical fiber microcavity by combining a single-mode optical fiber, two hollow-core optical fibers and UV glue, and realizes an optical fiber microcavity cascade structure through fusion, hole opening, coating and other technologies; a plurality of air holes are opened on the side wall of the first hollow-core optical fiber, an open Fabry-Perot cavity is formed between the first reflection surface and the second reflection surface, a UV film is arranged at the end of the second hollow-core optical fiber, and a closed Fabry-Perot cavity is formed between the third reflection surface and the fourth reflection surface; when the air pressure changes, the refractive index of the gas in the first hollow-core optical fiber changes, thereby changing the refractive index of the medium in the open Fabry-Perot cavity, and the spectrum of the open Fabry-Perot cavity moves accordingly; at the same time, the air pressure When the pressure changes, the UV film at the end is deformed by force, thereby changing the cavity length of the closed Fabry-Perot cavity, and the spectrum of the closed Fabry-Perot cavity moves accordingly, causing the total reflected light envelope obtained by the sensor to move, thereby realizing the detection of changes in ambient air pressure; in this process, the open Fabry-Perot cavity and the closed Fabry-Perot cavity serve as sensor references for each other when the air pressure changes, and the vernier effect sensitivity is realized by adjusting the parameters of the two optical fiber Fabry-Perot cavities; the open Fabry-Perot cavity and the closed Fabry-Perot cavity show opposite air pressure responses to realize enhanced vernier effect, thereby realizing secondary sensitivity based on traditional vernier effect sensitivity, and improving the sensor sensitivity by two to three orders of magnitude. The optical fiber air pressure sensor provided by the present invention has high integration, high precision, high sensitivity, stable structure, and low temperature crosstalk, and can be used for high-precision air pressure detection.

[0024] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1It is a structural schematic diagram of a high-precision air pressure sensor based on a composite optical fiber microcavity in a specific embodiment of the present invention;

[0026] Figure 2 It is a structural schematic diagram of a sensor head in a specific embodiment of the present invention;

[0027] Figure 3 is a spectrum envelope diagram of a sensor head in a specific embodiment of the present invention;

[0028] Figure 4 This is a diagram showing how the spectrum changes with the ambient air pressure in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0029] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0030] It should be noted that the illustrations provided in the following embodiments are only used to illustrate the basic concept of the present invention in a schematic manner, and thus the illustrations only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0031] While some exemplary embodiments of the present invention have been described for the purpose of illustration, it should be understood that the present invention may be implemented in other ways not specifically shown in the drawings.

[0032] like Figure 1 As shown, in a specific embodiment, a high-precision air pressure sensor based on a composite optical fiber microcavity is provided, including a broadband light source, an optical fiber circulator, a spectrum analyzer and a sensor head.

[0033] The fiber optic circulator is provided with a first port, a second port and a third port in sequence along the circumferential direction, the broadband light source is connected to the first port, the sensor head is connected to the second port, and the spectrum analyzer is connected to the third port. The detection light is emitted by the broadband light source, enters the fiber optic circulator through the first port, enters the sensor head from the second port after passing through the fiber optic circulator, and the reflected light reflected by the sensor head returns to the fiber optic circulator through the second port again, and enters the spectrum analyzer through the third port. The spectrum emitted by the broadband light source is used as the detection light, the sensor head detects the change of the ambient air pressure, and the spectrum analyzer receives and displays the spectrum of the sensor head to obtain the specific air pressure value.

[0034] like Figure 2 As shown, the sensor head includes a first single-mode optical fiber 1, a first hollow-core optical fiber 2, a second single-mode optical fiber 3, a second hollow-core optical fiber 4 and a UV film 5. The first single-mode optical fiber 1 is connected to the second port, the other end of the first single-mode optical fiber 1 is fused to one end of the first hollow-core optical fiber 2, the other end of the first hollow-core optical fiber 2 is fused to one end of the second single-mode optical fiber 3, the other end of the second single-mode optical fiber 3 is fused to one end of the second hollow-core optical fiber 4, and the other end of the second hollow-core optical fiber 4 is not provided with a UV film 5. In this embodiment, the first single-mode optical fiber 1 is mainly used to transmit optical signals, and its length can be theoretically extended indefinitely to achieve remote measurement. Therefore, in actual application, the length of the first single-mode optical fiber 1 is set according to the measurement needs; the second single-mode optical fiber 3 is mainly used to connect two optical fiber Fabry-Perot cavities, and the length ranges from 1 to 2 mm; the inner diameter range of the first single-mode optical fiber 1 and the second single-mode optical fiber 3 is 8 to 9 microns, and the outer diameter is 125 microns.

[0035] A plurality of radial air holes 6 are provided on the side wall of the first hollow-core optical fiber 2, and the air holes 6 connect the outside air with the inside of the first hollow-core optical fiber 2. The fusion surface of the first single-mode optical fiber 1 and the first hollow-core optical fiber 2 is the first reflection surface M1, and the fusion surface of the first hollow-core optical fiber 2 and the second single-mode optical fiber 3 is the second reflection surface M2. An open Fabry-Perot cavity is formed between the first reflection surface M1 and the second reflection surface M2. In this embodiment, the inner diameter of the first hollow-core optical fiber 2 is in the range of 50 to 70 microns, the outer diameter is 125 microns, and the length of the first hollow-core optical fiber 2 is in the range of 100 to 300 microns; the diameter of the air holes 6 is in the range of 15 to 20 microns, and the density of the air holes 6 is in the range of 15 to 20 per millimeter.

[0036] The fusion surface of the second single-mode optical fiber 3 and the second hollow-core optical fiber 4 is the third reflection surface M3, the critical surface of the air in the second hollow-core optical fiber 4 and the UV film 5 is the fourth reflection surface M4, the third reflection surface M3 and the fourth flip surface form a closed Fabry-Perot cavity, and the second hollow-core optical fiber 4 is filled with air. In this embodiment, the thickness of the UV film 5 ranges from 10 to 20 microns, and the UV glue is preferably purchased from Norland, and the preferred model is NOA 68TH; the inner diameter of the second hollow-core optical fiber 4 ranges from 50 to 70 microns, and the outer diameter is 125 microns; the length of the second hollow-core optical fiber 4 ranges from 100 to 300 microns. In order to improve the sensitivity of the sensor head, there is a difference in the length of the first hollow-core optical fiber 2 and the second hollow-core optical fiber 4, and the length difference ranges from 1 to 50 microns.

[0037] During operation, the detection light enters the first hollow-core optical fiber 2, the second single-mode optical fiber 3 and the second hollow-core optical fiber 4 in sequence through the first single-mode optical fiber 1, and is reflected at the first reflection surface M1, the second reflection surface M2, the third reflection surface M3 and the fourth reflection surface M4 respectively; the four beams of reflected light are transmitted through the single-mode optical fiber and superimposed in the first single-mode optical fiber 1 to form the total reflected light. The reflected light of the two optical fiber Fabry-Perot cavities is superimposed to form the reflection spectrum of the sensor head, and the measurement of the ambient air pressure is achieved by detecting the spectral envelope response of the sensor head.

[0038] Based on the above-mentioned high-precision air pressure sensor based on the composite optical fiber microcavity, in a specific embodiment, a high-precision air pressure detection method based on the composite optical fiber microcavity is provided, comprising the following steps:

[0039] S1, the detection light enters the first hollow-core optical fiber 2 through the first single-mode optical fiber 1, and forms the first reflected light and the second reflected light at the first reflection surface M1 and the second reflection surface M2. The first reflection surface M1 and the second reflection surface M2 constitute an open Fabry-Perot cavity, and the reflection spectrum function of the open Fabry-Perot cavity is:

[0040] I FP1 =A 2 +B 2 +2ABcos(4πn 1 L 1 / λ);

[0041] Where A = R 1 1 / 2 ; B = (1-a 1 )(1-R 1 )R 2 1 / 2 ;n 1 is the refractive index of the inner medium of the open Fabry-Perot cavity; L 1 is the cavity length of the open Fabry-Perot cavity; λ is the incident wavelength of the probe light; a 1is the transmission loss of the detection light in the open Fabry-Perot cavity; R 1 and R 2 are the reflection coefficients of the first reflection surface M1 and the second reflection surface M2 respectively.

[0042] When the gas pressure changes, the refractive index of the gas in the open Fabry-Perot cavity changes, causing the refractive index of the medium in the open Fabry-Perot cavity to change, causing the reflection spectrum in the open Fabry-Perot cavity to shift. The shift amount Δλ of the open Fabry-Perot cavity is FP1 for:

[0043]

[0044] Among them, Δn 1 is the refraction change of the medium in the open Fabry-Perot cavity.

[0045] S2, the second single-mode optical fiber 3 enters the second hollow optical fiber 4, and forms a third reflected light and a fourth reflected light at the third reflection surface M3 and the fourth reflection surface M4; the third reflection surface M3 and the fourth reflection surface M4 constitute a closed Fabry-Perot cavity, and the reflection spectrum function of the closed Fabry-Perot cavity is:

[0046] I FP2 =C 2 +D 2 +2CDcos(4πn 2 L 2 / λ);

[0047] Where C = R 3 1 / 2 ; D = (1-a 2 )(1-R 3 )R 4 1 / 2 ;n 2 is the refractive index of the medium in the closed Fabry-Perot cavity; L 2 is the length of the closed Fabry-Perot cavity; a 2 is the transmission loss of the detection light in the closed Fabry-Perot cavity; R 3 and R 4 are the reflection coefficients of the third reflection surface M3 and the fourth reflection surface M4 respectively.

[0048] When the air pressure changes, the UV film 5 at the end of the second hollow-core optical fiber is deformed by force, so that the cavity length of the second hollow-core optical fiber 4 changes, and the reflection spectrum of the second hollow-core optical fiber 4 shifts. The translation amount Δλ of the closed Fabry-Perot cavity is FP2 for;

[0049]

[0050] Where, ΔL 2 is the change in length of the closed Fabry-Perot cavity.

[0051] S3, the reflection spectrum envelope formed by the superposition of the first reflected light, the second reflected light, the third reflected light and the fourth reflected light moves, and the measurement of the ambient air pressure is achieved by detecting the spectrum envelope response.

[0052] When the free spectral ranges of the two fiber Fabry-Perot cavities are close but not equal, due to the double filtering of the two fiber Fabry-Perot cavities, the sensor head reflection spectrum produces periodic vernier interference fringes, thereby producing a periodic envelope. In this embodiment, the sensor head reflection spectrum envelope is as follows: Figure 3 As shown, the free spectral range (FSR) of the sensor head reflectance spectrum envelope is Envelope for:

[0053]

[0054] Among them, M is the enveloping magnification factor, and its value range is 5 to 40. The magnification factor M is obtained by transforming the above formula:

[0055]

[0056] When the ambient air pressure changes, the spectral envelope of the sensor head moves with the air pressure response of the open Fabry-Perot cavity and the closed Fabry-Perot cavity; the translation amount Δλ of the reflected spectrum envelope of the sensor head Envelope for:

[0057]

[0058] It can be seen from the above formula that the open Fabry-Perot cavity and the closed Fabry-Perot cavity show opposite air pressure responses, thereby achieving secondary sensitivity enhancement based on the traditional Vernier effect sensitivity enhancement, and improving the sensitivity of the sensor by two to three orders of magnitude.

[0059] In a specific embodiment, Figure 4 This is a graph showing how the spectrum changes with ambient air pressure. It can be seen from the figure that when the ambient air pressure changes, the reflection spectrum of the open Fabry-Perot cavity redshifts, while the reflection spectrum of the closed Fabry-Perot cavity blueshifts. The two fiber Fabry-Perot cavities show opposite pressure responses. The spectral envelope of the sensor head moves with the pressure responses of the two fiber Fabry-Perot cavities, blueshifts, and the translation of the spectral envelope of the sensor head is M times the difference in the spectral translations of the two fiber Fabry-Perot cavities.

[0060] In summary, when the ambient air pressure changes, both fiber Fabry-Perot cavities are used for air pressure detection, and the two fiber Fabry-Perot cavities serve as sensing references for each other; for the open Fabry-Perot cavity, the refractive index of the gas inside the first hollow-core optical fiber 2 changes, thereby changing the refractive index of the medium in the open Fabry-Perot cavity, and the spectrum of the open Fabry-Perot cavity moves accordingly; for the closed Fabry-Perot cavity, the UV film 5 at the end of the second hollow-core optical fiber 4 is deformed by force, thereby changing the cavity length of the closed Fabry-Perot cavity, and the spectrum of the closed Fabry-Perot cavity moves accordingly; the spectral envelope of the sensor head moves with the air pressure response of the open Fabry-Perot cavity and the closed Fabry-Perot cavity; the open Fabry-Perot cavity and the closed Fabry-Perot cavity show opposite air pressure responses, thereby achieving secondary sensitization based on the traditional vernier effect sensitization, and improving the sensitivity of the sensor by two to three orders of magnitude.

[0061] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A high-precision air pressure sensor based on a composite optical fiber microcavity, characterized in that: It includes broadband light source, fiber optic circulator, spectrum analyzer and sensor head; The sensor head includes a first single-mode optical fiber, a first hollow-core optical fiber, a second single-mode optical fiber, a second hollow-core optical fiber and a UV film which are fused in sequence. A plurality of radial air holes are provided on the side wall of the first hollow-core optical fiber, and the air holes connect the outside air with the interior of the first hollow-core optical fiber. The interior of the second hollow-core optical fiber is filled with air. The fusion surface of the first single-mode optical fiber and the first hollow-core optical fiber is a first reflection surface, the fusion surface of the first hollow-core optical fiber and the second single-mode optical fiber is a second reflection surface, the fusion surface of the second single-mode optical fiber and the second hollow-core optical fiber is a third reflection surface, and the critical surface of the air and the UV film in the second hollow-core optical fiber is a fourth reflection surface.

2. According to claim 1, a high-precision air pressure sensor based on a composite optical fiber microcavity is characterized in that: The inner diameter of the first single-mode optical fiber is in the range of 8 to 9 microns, and the inner diameter of the second single-mode optical fiber is in the range of 8 to 9 microns.

3. According to claim 1, a high-precision air pressure sensor based on a composite optical fiber microcavity is characterized in that: The inner diameter of the first hollow-core optical fiber is in the range of 50 to 70 microns, and the inner diameter of the second hollow-core optical fiber is in the range of 50 to 70 microns.

4. According to claim 1, a high-precision air pressure sensor based on a composite optical fiber microcavity is characterized in that: The length difference between the first hollow core optical fiber and the second hollow core optical fiber is in the range of 1 to 50 microns.

5. The high-precision air pressure sensor based on a composite optical fiber microcavity according to claim 1, characterized in that: The diameter of the pores ranges from 15 to 20 micrometers, and the density of the pores ranges from 15 to 20 per millimeter.

6. The high-precision air pressure sensor based on a composite optical fiber microcavity according to claim 1, characterized in that: The thickness of the UV film ranges from 10 to 20 microns.

7. A high-precision air pressure detection method based on a composite optical fiber microcavity, characterized in that: The high-precision air pressure sensor based on the composite optical fiber microcavity according to any one of claims 1 to 6 is implemented, comprising the following steps: S1, the detection light enters the first hollow-core optical fiber through the first single-mode optical fiber, and forms the first reflected light and the second reflected light at the first reflecting surface and the second reflecting surface. When the air pressure changes, the refractive index of the gas inside the first hollow-core optical fiber changes, so that the refractive index of the medium in the cavity of the first hollow-core optical fiber changes, and the reflection spectrum of the first hollow-core optical fiber moves; S2, the second single-mode optical fiber enters the second hollow-core optical fiber, and forms a third reflected light and a fourth reflected light at the third reflecting surface and the fourth reflecting surface. When the air pressure changes, the UV film at the end of the second hollow-core optical fiber is deformed by force, so that the cavity length of the second hollow-core optical fiber changes, and the reflection spectrum of the second hollow-core optical fiber moves; S3, the reflection spectrum envelope formed by the superposition of the first reflected light, the second reflected light, the third reflected light and the fourth reflected light moves, and the measurement of the ambient air pressure is achieved by detecting the spectrum envelope response.

8. A high-precision air pressure detection method based on a composite optical fiber microcavity according to claim 7, characterized in that: The shift Δλ of the reflection spectrum envelope Envelope for: Dl E envelope=M·(Dλ FP2 -Dl FP1 ); Where M is the amplification factor of the envelope, Δλ FP1 is the wavelength shift of the first hollow-core optical fiber reflection spectrum, which is: λ is the incident wavelength of the probe light, n1 is the refractive index of the medium in the first hollow-core fiber cavity, Δn1 is the refractive index change of the medium in the first hollow-core fiber, Δλ FP2 is the wavelength shift of the second hollow-core fiber reflection spectrum, L2 is the cavity length of the first hollow-core fiber, and ΔL2 is the change in the cavity length of the second hollow-core fiber.

9. A high-precision air pressure detection method based on a composite optical fiber microcavity according to claim 8, characterized in that: The envelope amplification factor M is: Among them, FSR FP1 is the free spectral range of the first hollow-core fiber, which is: FSR FP1 =λ 2 / 2n1L1; L1 is the cavity length of the first hollow-core fiber; FSR FP2 is the free spectral range of the second hollow-core fiber, which is: FSR FP2 =λ 2 / 2n2L2, n2 is the refractive index of the medium in the second hollow-core optical fiber cavity.

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