CN111982859A - Refractive index sensor based on Mach-Zehnder structure and detection method thereof - Google Patents
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Abstract
本发明涉及一种基于马赫‑曾德尔结构的折射率传感器及其检测方法，该传感器包括马赫‑曾德尔结构，在其中一个干涉臂上剥离掉一定长度的包层，形成折射率感知区，折射率感知区用于检测液体或气体；当待测液体或气体注入到折射率感知区，会导致折射率感知区中干涉臂的有效折射率变化，进而引起器件输出光谱的中心波长的变化，并且有效折射率的变化与中心波长的变化是线性的，输出光谱的中心波长为输出强度与输入强度比值最大时对应的波长。本发明提供的基于马赫‑曾德尔结构的折射率传感器制作成本低、制备简单、结构坚固，器件中心波长的改变量与待测折射率的改变量呈线性关系，因此可以同时做到超大量程与高灵敏度。The invention relates to a refractive index sensor based on a Mach-Zehnder structure and a detection method thereof. The sensor includes a Mach-Zehnder structure, and a certain length of cladding is peeled off on one of the interference arms to form a refractive index sensing area, and the refraction The rate sensing area is used to detect liquid or gas; when the liquid or gas to be tested is injected into the refractive index sensing area, it will cause the effective refractive index of the interference arm in the refractive index sensing area to change, thereby causing the center wavelength of the output spectrum of the device to change, and The change of the effective refractive index is linear with the change of the center wavelength, and the center wavelength of the output spectrum is the wavelength corresponding to the maximum ratio of the output intensity to the input intensity. The refractive index sensor based on the Mach-Zehnder structure provided by the present invention has the advantages of low production cost, simple preparation and firm structure, and the change of the center wavelength of the device is linearly related to the change of the refractive index to be measured, so it can achieve ultra-large range and High sensitivity.
Description
技术领域technical field
本发明涉及一种基于马赫-曾德尔结构的折射率传感器及其检测方法，属于折射率测量技术领域。The invention relates to a refractive index sensor based on a Mach-Zehnder structure and a detection method thereof, belonging to the technical field of refractive index measurement.
背景技术Background technique
物质折射率是反映物质内部信息的一个重要物理量。物质折射率的测量在基础研究、化学分析、环境污染评估、医疗诊断和食品工业等领域有着广泛的应用。在生产和科学研究中对一些固体、液体和气体折射率的精确测定具有重要的意义。例如：生物分子的相互作用以及溶液中的化学反应引起的分子结构变化都会产生折射率的微小变化，这种微小变化的检测是识别病毒和不同分子的重要手段。尤其是随着我国国民经济的快速发展，人口的不断增加，环境污染已成为严重损害人民健康的重大问题，越来越多的人们开始关注大气中有毒有害气体，以及江河、湖泊和海洋中有机物和重金属离子的水污染。对大气和水中有毒物质浓度(折射率)的精细检测已成为一项十分迫切的课题。The refractive index of a substance is an important physical quantity that reflects the internal information of a substance. The measurement of the refractive index of substances has a wide range of applications in basic research, chemical analysis, environmental pollution assessment, medical diagnosis, and the food industry. The precise determination of the refractive index of some solids, liquids and gases is of great significance in production and scientific research. For example, the interaction of biomolecules and changes in molecular structure caused by chemical reactions in solution can produce small changes in refractive index. The detection of such small changes is an important means to identify viruses and different molecules. Especially with the rapid development of my country's national economy and the continuous increase of population, environmental pollution has become a major problem that seriously damages people's health. and heavy metal ions in water pollution. The precise detection of the concentration (refractive index) of toxic substances in the atmosphere and water has become a very urgent subject.
目前检测大气和水中物质浓度的常用方法有以下几种：阿贝折射仪全反射临界角法、使用分光计的最小偏向角法、迈克耳逊干涉仪等倾干涉法，以及原子吸收法、分光光度法、原子荧光光谱和高效液相色谱等技术等，但这些技术的灵敏度普遍不高、检出限一般都在10-3～10-5之间；有的光路调整复杂，测量过程时间长，不利于实时测量；有的检测量程小，对检测量程大的情况往往一种仪器不够，需采用另一种仪器；或需要大型昂贵的设备，检测成本高，难以推广应用。At present, the commonly used methods for detecting the concentration of substances in the atmosphere and water are as follows: Abbe refractometer total reflection critical angle method, minimum deflection angle method using spectrometer, Michelson interferometer equal dip interferometry, and atomic absorption method, spectroscopic method Photometry, atomic fluorescence spectroscopy and high performance liquid chromatography, etc., but the sensitivity of these technologies is generally not high, and the detection limit is generally between 10 -3 and 10 -5 ; some optical path adjustment is complicated, and the measurement process takes a long time. , which is not conducive to real-time measurement; some detection ranges are small, and when the detection range is large, one instrument is often insufficient, and another instrument is required; or large and expensive equipment is required, and the detection cost is high, making it difficult to popularize and apply.
光学芯片折射率传感器具有传感器本质绝缘、抗电磁干扰、高集成度，高带宽、可复用以及生物化学相容性等特点，在生物分子检测、环境污染治理及化学过程控制等领域具有广泛应用。随着折射率测量要求的提高，光学芯片折射率传感器的灵敏度、分辨率和线性度等性能需要进一步提升。Optical chip refractive index sensors have the characteristics of intrinsic insulation, anti-electromagnetic interference, high integration, high bandwidth, reusability, and biochemical compatibility. They are widely used in the fields of biomolecule detection, environmental pollution control, and chemical process control. . With the improvement of refractive index measurement requirements, the sensitivity, resolution and linearity of optical chip refractive index sensors need to be further improved.
马赫-曾德尔干涉型集成光波导传感器通过采用干涉测量法产生相位调制以便获得较高的灵敏度和分辨率，特别是基于马赫-曾德尔干涉仪的新型光波导传感器具有许多优点，例如插入损耗低，制造方法简单，结构紧凑，成本低。因此，该类型的光波导传感器被用以测量各类参数，其发展前景相当广阔。但是传统的马赫-曾德尔型传感器是基于光强度检测的，待测量与光强之间的关系为正弦余弦曲线，在实际使用中通常采用的方法是仅使用其中线性度较好的一段，因此，其灵敏度与测量范围之间仍然存在一定的矛盾，即测量范围较大的情况下，折射率变化量引起的光强的变化较小。而且由于这种测量方法本身不是线性的，给出厂校准和后期校准带来极大的不便。Mach-Zehnder interferometric integrated optical waveguide sensors use interferometry to generate phase modulation in order to obtain higher sensitivity and resolution, especially the new optical waveguide sensors based on Mach-Zehnder interferometers have many advantages, such as low insertion loss , the manufacturing method is simple, the structure is compact, and the cost is low. Therefore, this type of optical waveguide sensor is used to measure various parameters, and its development prospect is quite broad. However, the traditional Mach-Zehnder sensor is based on light intensity detection, and the relationship between the to-be-measured and light intensity is a sine-cosine curve. In practice, the method usually adopted is to use only the segment with better linearity, so , there is still a certain contradiction between its sensitivity and the measurement range, that is, when the measurement range is large, the change in light intensity caused by the change in refractive index is small. And because this measurement method itself is not linear, it brings great inconvenience to factory calibration and post-calibration.
发明内容SUMMARY OF THE INVENTION
针对现有技术的不足，本发明提供了一种基于马赫-曾德尔结构的折射率传感器，该折射率传感器具有成本低、灵敏度高、抗干扰性能强、制作简单且结构坚固的优点。In view of the deficiencies of the prior art, the present invention provides a refractive index sensor based on a Mach-Zehnder structure, which has the advantages of low cost, high sensitivity, strong anti-interference performance, simple fabrication and firm structure.
本发明还提供了上述基于马赫-曾德尔结构的折射率传感器的检测方法。The present invention also provides the above-mentioned detection method of the refractive index sensor based on the Mach-Zehnder structure.
本发明的技术方案为：The technical scheme of the present invention is:
一种基于马赫-曾德尔结构的折射率传感器，所述传感器包括马赫-曾德尔结构，所述马赫-曾德尔结构包括输入分束器、长度不等的两个干涉臂、输出合束器，输入分束器的两个输出端分别与两个干涉臂的一端相连接，两个干涉臂的另一端分别与输出合束器的两个输入端口相连接；在其中一个干涉臂上剥离掉部分包层，形成折射率感知区，折射率感知区用于检测液体或气体；当待测液体或气体注入到折射率感知区，会导致折射率感知区中干涉臂的有效折射率改变，进而引起器件输出光谱的中心波长的变化，并且折射率感知区中干涉臂的有效折射率的改变量与中心波长的变化量是线性的，所述输出光谱的中心波长为输出强度与输入强度比值最大时对应的波长。A refractive index sensor based on a Mach-Zehnder structure, the sensor comprising a Mach-Zehnder structure, the Mach-Zehnder structure comprising an input beam splitter, two interference arms of unequal lengths, and an output beam combiner, The two output ends of the input beam splitter are respectively connected with one end of the two interference arms, and the other ends of the two interference arms are respectively connected with the two input ports of the output beam combiner; part is peeled off on one of the interference arms The cladding layer forms the refractive index sensing area, which is used to detect liquids or gases; when the liquid or gas to be tested is injected into the refractive index sensing area, the effective refractive index of the interference arm in the refractive index sensing area will change, which in turn causes The change of the center wavelength of the output spectrum of the device, and the change of the effective refractive index of the interference arm in the refractive index sensing region is linear with the change of the center wavelength, and the center wavelength of the output spectrum is the maximum ratio of the output intensity to the input intensity. the corresponding wavelength.
根据本发明优选的，在干涉臂上剥离掉长度为1000-106μm的包层,形成折射率感知区。折射率感知区包含的波导长度越长，测量灵敏度越高。Preferably according to the present invention, a cladding layer with a length of 1000-10 6 μm is peeled off on the interference arm to form a refractive index sensing region. The longer the waveguide length contained in the refractive index sensing region, the higher the measurement sensitivity.
根据本发明优选的，两个干涉臂之间的长度差为1～500μm。长度差越大，感知的量程越小，在该量程内，检测效果最好。Preferably according to the present invention, the length difference between the two interference arms is 1˜500 μm. The larger the length difference, the smaller the perceived range, and within this range, the detection effect is the best.
根据本发明优选的，两个干涉臂的横截面宽度均为1-10μm，横截面厚度均为1-10μm。Preferably according to the present invention, the width of the cross-section of the two interference arms is both 1-10 μm, and the thickness of the cross-section is both 1-10 μm.
根据本发明优选的，所述干涉臂包括芯层和包层，所述包层包围在所述芯层的外侧。Preferably according to the present invention, the interference arm includes a core layer and a cladding layer, and the cladding layer surrounds the outer side of the core layer.
根据本发明优选的，芯层的折射率为1.45-1.51，包层的折射率为1.40-1.45，进一步优选的，芯层的折射率为1.4746，包层的折射率为1.4448。According to the preferred embodiment of the present invention, the refractive index of the core layer is 1.45-1.51, and the refractive index of the cladding layer is 1.40-1.45. Further preferably, the refractive index of the core layer is 1.4746 and the refractive index of the cladding layer is 1.4448.
根据本发明优选的，输入分束器为Y分支型或1分2型输入分束器，输出合束器为Y分支或2合1型输出合束器。在Y分支型输入分束器中，光从Y分支型的单波导部分输入，从Y分支型的两个分支输出光；在Y分支型输出合束器中，光从Y分支从Y分支型的两个分支输入，从单波导部分输出。Preferably according to the present invention, the input beam splitter is a Y-branch type or a 1-in-2 type input beam splitter, and the output beam combiner is a Y-branch or a 2-in-1 type output beam combiner. In the Y-branch type input beam splitter, light is input from the single-waveguide part of the Y-branch type, and light is output from the two branches of the Y-branch type; in the Y-branch type output beam combiner, light from the Y branch type Two branch inputs of , and outputs from a single waveguide section.
上述基于马赫-曾德尔结构的折射率传感器的检测方法，包括步骤如下：The above-mentioned detection method of the refractive index sensor based on the Mach-Zehnder structure includes the following steps:
(1)将宽谱光输入到所述基于马赫-曾德尔结构的折射率传感器，并使用光谱仪检测基于马赫-曾德尔结构的折射率传感器的输出光谱，得到待测气体为空气，折射率为n0时，对应的器件的输出光谱的中心波长λ0；(1) Input the broad-spectrum light into the refractive index sensor based on the Mach-Zehnder structure, and use a spectrometer to detect the output spectrum of the refractive index sensor based on the Mach-Zehnder structure, and obtain that the gas to be measured is air, and the refractive index is When n is 0 , the center wavelength λ 0 of the output spectrum of the corresponding device;
(2)将所述折射率感知区放入已知折射率为n1的液体或气体中，将宽谱光通过基于马赫-曾德尔结构的折射率传感器，通过光谱仪检测折射率传感器的输出光谱，得到当前液体或气体下器件输出光谱的中心波长λ1，从而完成器件的校准；(2) Put the refractive index sensing region into a liquid or gas with a known refractive index of n 1 , pass the broad-spectrum light through the refractive index sensor based on the Mach-Zehnder structure, and detect the output spectrum of the refractive index sensor by a spectrometer , obtain the center wavelength λ 1 of the output spectrum of the device under the current liquid or gas, so as to complete the calibration of the device;
(3)将折射率感知区放入待测折射率为n2的液体或气体中，将宽谱光输入到所述折射率传感器中，通过光谱仪检测所述折射率传感器的输出光谱，得到待测液体或气体对应折射率下器件的输出光谱中心波长λ2；由式(V)计算得出待测折射率n2，式(V)为：(3) Put the refractive index sensing area into a liquid or gas with a refractive index of n 2 to be measured, input broad-spectrum light into the refractive index sensor, and detect the output spectrum of the refractive index sensor by a spectrometer to obtain the refractive index sensor to be measured. The center wavelength λ 2 of the output spectrum of the device under the corresponding refractive index of the liquid or gas is measured; the refractive index n 2 to be measured is calculated from the formula (V), and the formula (V) is:
本发明提供基于马赫-曾德尔结构的折射率传感器的检测方法基于以下原理：The present invention provides a method for detecting a refractive index sensor based on a Mach-Zehnder structure based on the following principles:
根据非对称马赫-曾德尔干涉器的基本干涉原理得出：According to the basic interference principle of the asymmetric Mach-Zehnder interferometer:
式(I)中，ne为两个干涉臂波导的有效折射率，L1为短干涉臂的长度，Ls+L′为长干涉臂的长度，Ls为折射率感知区中干涉臂的长度，λ0为未检测气体或液体下，衍射级数为M时的器件输出光谱的中心波长；M为衍射级数，M＝int(nΔL/λ0)，int(·)表示向下舍入取整实数，λ0为折射率感知区未检测气体或液体时，器件输出光谱的中心波长；ΔL为长干涉臂和短干涉臂的长度差；In formula (I), ne is the effective refractive index of the two interference arm waveguides, L 1 is the length of the short interference arm, L s + L′ is the length of the long interference arm, and L s is the interference arm in the refractive index sensing region. The length of λ 0 is the center wavelength of the output spectrum of the device when the diffraction order is M when the gas or liquid is not detected; M is the diffraction order, M=int(nΔL/λ 0 ), int(·) means downward Rounded to a real number, λ 0 is the center wavelength of the output spectrum of the device when no gas or liquid is detected in the refractive index sensing region; ΔL is the length difference between the long and short interference arms;
当检测气体或液体时，长度为Ls的折射率感知区中干涉臂的有效折射率改变量为Δn，此时的干涉方程为：When detecting gas or liquid, the effective refractive index change of the interference arm in the refractive index sensing region of length L s is Δn, and the interference equation at this time is:
将两式两边分别同乘以λ0和λ3，然后相减，化简得：Multiply both sides of the two equations by λ 0 and λ 3 respectively, and then subtract them to simplify:
M(λ0-λ3)＝Δn·LS (III)M(λ 0 -λ 3 )=Δn·L S (III)
令Δλ＝λ0-λ3可得(I)式：Set Δλ=λ 0 -λ 3 to obtain formula (I):
Δλ＝Δn·Ls/M (IV)Δλ=Δn·L s /M (IV)
由式(IV)可以得出，折射率感知区中干涉臂的有效折射率改变量Δn与输出光谱中心波长的变化量Δλ成线性关系；在光学器件制作及计算的过程中存在误差，通过步骤(1)、(2)确定施加在折射率感知区的折射率n与输出光谱的中心波长的变化Δλ之间的具体线性关系。From formula (IV), it can be concluded that the effective refractive index change Δn of the interference arm in the refractive index sensing region has a linear relationship with the change Δλ of the central wavelength of the output spectrum; there are errors in the process of optical device fabrication and calculation, through the steps (1), (2) Determine the specific linear relationship between the refractive index n imposed on the refractive index sensing region and the change Δλ of the central wavelength of the output spectrum.
根据本发明优选的，宽谱光输出光谱的谱宽为40nm。Preferably according to the present invention, the spectral width of the broad-spectrum light output spectrum is 40 nm.
本发明的有益效果为：The beneficial effects of the present invention are:
1.本发明提供的折射率传感器在马赫曾德尔干涉仪上进行特殊设计，将其中一个干涉臂的包层剥离，使得其波导芯层与外界空气/液体相通，外界物质折射率的变化，引起干涉效应的变化，进而可以推算外界折射率，由于干涉臂可以增加至几十厘米，因此具有高灵敏度，最高灵敏度可检测10-6的折射率变化。1. The refractive index sensor provided by the present invention is specially designed on the Mach-Zehnder interferometer, and the cladding of one of the interference arms is peeled off, so that the core layer of the waveguide is communicated with the external air/liquid, and the change of the refractive index of the external material causes The change of the interference effect can then calculate the external refractive index. Since the interference arm can be increased to several tens of centimeters, it has high sensitivity, and the highest sensitivity can detect the refractive index change of 10 -6 .
2.本发明提供的基于马赫-曾德尔结构的折射率传感器制作成本低、制备简单、结构坚固，器件中心波长的改变量与待测折射率的改变量呈线性关系，因此可以同时做到超大量程与高灵敏度,测量折射率变化的量程可高达0.01。2. The refractive index sensor based on the Mach-Zehnder structure provided by the present invention has the advantages of low production cost, simple preparation and firm structure, and the change of the central wavelength of the device is linearly related to the change of the refractive index to be measured, so it can achieve ultra-large at the same time. Range and high sensitivity, the measurement range of refractive index changes can be as high as 0.01.
3.本发明提供的基于马赫-曾德尔结构的折射率传感器基于半导体光波导的器件，结构紧凑，尺寸小。3. The refractive index sensor based on the Mach-Zehnder structure provided by the present invention is a device based on a semiconductor optical waveguide, which is compact in structure and small in size.
附图说明Description of drawings
图1为实施例1提供的一种基于马赫-曾德尔结构的折射率传感器的结构示意图；1 is a schematic structural diagram of a refractive index sensor based on a Mach-Zehnder structure provided in
图2为实施例1中未设置折射率感知区的短干涉臂的横截面结构图；2 is a cross-sectional structural diagram of a short interference arm without a refractive index sensing region in Example 1;
图3为实施例1中设置折射率感知区的干涉臂横截面结构图；3 is a cross-sectional structural diagram of an interference arm with a refractive index sensing region set in
1、输入分束器，2、长干涉臂，3、短干涉臂，4、折射率感知区，5、输出合束器，6、包层，7、芯层，8、待测液体或气体。1. Input beam splitter, 2. Long interference arm, 3. Short interference arm, 4. Refractive index sensing area, 5. Output beam combiner, 6. Cladding layer, 7. Core layer, 8. Liquid or gas to be measured .
具体实施方式Detailed ways
下面结合实施例和说明书附图对本发明做进一步说明，但不限于此。The present invention will be further described below with reference to the embodiments and accompanying drawings of the specification, but is not limited thereto.
实施例1Example 1
一种基于马赫-曾德尔结构的折射率传感器，如图1所示，传感器包括宽谱光源、马赫-曾德尔结构和光谱仪，马赫-曾德尔结构包括输入分束器1、长度不等的两个干涉臂、输出合束器5，输入分束器1的两个输出端分别与两个干涉臂的一端相连接，两个干涉臂的另一端分别与输出合束器5的两个输入端口相连接；在其中一个干涉臂上剥离掉部分包层6，形成折射率感知区4，折射率感知区4用于检测液体或气体；当待测液体或气体8注入到折射率感知区4，会导致折射率感知区4中干涉臂的有效折射率改变，进而引起器件输出光谱的中心波长的变化，并且折射率感知区4中干涉臂的有效折射率的改变量与中心波长的变化量是线性的，输出光谱的中心波长为输出强度与输入强度比值最大时对应的波长。A refractive index sensor based on a Mach-Zehnder structure, as shown in Figure 1, the sensor includes a broad-spectrum light source, a Mach-Zehnder structure, and a spectrometer. The Mach-Zehnder structure includes an
长度不等的两个干涉臂分别为长干涉臂2和短干涉臂3，在长干涉臂2上设置折射率感知区4；未设置折射率感知区4的短干涉臂3的横截面结构图如图2所示。The two interfering arms with unequal lengths are the long interfering
如图3所示，设置折射率感知区4的长干涉臂2的横截面结构图，并将待测液体注入到长干涉臂2的折射率感知区4。As shown in FIG. 3 , a cross-sectional structure diagram of the
本实施例中，光波导芯片马赫-曾德尔结构的总长度为30mm，长干涉臂2长度为22144μm，短干涉臂3长度为22000μm，两个干涉臂之间的长度差为144μm。In this embodiment, the total length of the Mach-Zehnder structure of the optical waveguide chip is 30 mm, the length of the
本实施例中,在长干涉臂2上开设折射率感知区4，图1中虚线框出的区域为折射率感知区4。折射率感知区4中干涉臂的长度为1000μm。In this embodiment, a refractive
长干涉臂2和短干涉臂3横截面的尺寸为4μmx4μm。The dimensions of the cross section of the
包层6为低折射率二氧化硅，且低折射率二氧化硅的折射率为1.4448，芯层7为高折射率二氧化硅，且高折射率二氧化硅的折射率为1.4746。The
器件的中心波长为1.55μm。The center wavelength of the device is 1.55 μm.
当待测液体或气体8注入到折射率感知区4，会导致折射率感知区4中干涉臂的有效折射率变化，进而引起器件输出光谱的中心波长的变化，并且有效折射率的变化与中心波长的变化是线性的，输出光谱的中心波长为输出强度与输入强度比值最大时对应的波长。When the liquid or
本实施例提供的折射率传感器可感知待测液体或气体8的10-6折射率变化。The refractive index sensor provided in this embodiment can sense the 10 −6 refractive index change of the liquid or
实施例2Example 2
实施例1提供的基于马赫-曾德尔结构的折射率传感器的检测方法，包括步骤如下：The detection method of the refractive index sensor based on the Mach-Zehnder structure provided by
(1)将宽谱光输入到基于马赫-曾德尔结构的折射率传感器，并使用光谱仪检测基于马赫-曾德尔结构的折射率传感器的输出光谱，得到待测气体为空气，折射率为n0时，对应的器件的输出光谱的中心波长λ0；(1) Input the broad-spectrum light into the refractive index sensor based on the Mach-Zehnder structure, and use a spectrometer to detect the output spectrum of the refractive index sensor based on the Mach-Zehnder structure, and obtain that the gas to be measured is air, and the refractive index is n 0 When , the center wavelength λ 0 of the output spectrum of the corresponding device;
本实施例中，宽谱光的谱宽为40nm。折射率传感器的输出光谱由光谱仪或者波长解调仪测出。In this embodiment, the spectral width of the broad-spectrum light is 40 nm. The output spectrum of the refractive index sensor is measured by a spectrometer or a wavelength demodulator.
(2)将折射率感知区4放入已知折射率为n1的液体或气体中，将宽谱光通过基于马赫-曾德尔结构的折射率传感器，通过光谱仪检测折射率传感器的输出光谱，得到当前液体或气体下器件输出光谱的中心波长λ1，从而完成器件的校准；(2) Put the refractive
(3)将折射率感知区4放入待测折射率为n2的液体或气体中，将宽谱光输入到折射率传感器中，通过光谱仪检测折射率传感器的输出光谱，得到待测液体或气体8对应折射率下器件的输出光谱中心波长λ2；由式(V)计算得出待测折射率n2，式(V)为：(3) Put the refractive
本发明提供基于马赫-曾德尔结构的折射率传感器的检测方法基于以下原理：The present invention provides a method for detecting a refractive index sensor based on a Mach-Zehnder structure based on the following principles:
根据非对称马赫-曾德尔干涉器的基本干涉原理得出：According to the basic interference principle of the asymmetric Mach-Zehnder interferometer:
式(I)中，ne为两个干涉臂波导的有效折射率，L1为短干涉臂3的长度，Ls+L′为长干涉臂2的长度，Ls为折射率感知区4中干涉臂的长度，λ0为未检测气体或液体下，衍射级数为M时的器件输出光谱的中心波长；M为衍射级数，M＝int(nΔL/λ0)，int(·)表示向下舍入取整实数，λ0为折射率感知区4未检测气体或液体时，器件输出光谱的中心波长；ΔL为长干涉臂2和短干涉臂3的长度差；In formula (I), ne is the effective refractive index of the two interference arm waveguides, L 1 is the length of the
当检测气体或液体时，长度为Ls的折射率感知区4中干涉臂的有效折射率改变量为Δn，此时得到的输出光谱的中心波长λ3，此时的干涉方程为：When detecting gas or liquid, the effective refractive index change of the interference arm in the refractive
将两式两边分别同乘以λ0和λ3，然后相减，化简得：Multiply both sides of the two equations by λ 0 and λ 3 respectively, and then subtract them to simplify:
M(λ0-λ3)＝Δn·LS (III)M(λ 0 -λ 3 )=Δn·L S (III)
令Δλ＝λ0-λ3可得(I)式：Set Δλ=λ 0 -λ 3 to obtain formula (I):
Δλ＝Δn·Ls/M (IV)；Δλ=Δn·L s /M (IV);
由式(IV)可以得出，折射率感知区4中干涉臂的有效折射率改变量Δn与输出光谱中心波长的变化量Δλ成线性关系；在光学器件制作及计算的过程中存在误差，通过步骤(1)、(2)确定施加在折射率感知区4的折射率n与输出光谱的中心波长的变化Δλ之间的具体线性关系。From formula (IV), it can be concluded that the effective refractive index change Δn of the interference arm in the refractive
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