CN112697753A - Ultra-compact high-sensitivity double-parameter sensor based on stack type dual-mode photonic crystal nano beam cavity - Google Patents

Ultra-compact high-sensitivity double-parameter sensor based on stack type dual-mode photonic crystal nano beam cavity Download PDF

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CN112697753A
CN112697753A CN202011412685.2A CN202011412685A CN112697753A CN 112697753 A CN112697753 A CN 112697753A CN 202011412685 A CN202011412685 A CN 202011412685A CN 112697753 A CN112697753 A CN 112697753A
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田慧平
杨莹
孙富君
王铮
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Beijing University of Posts and Telecommunications
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Abstract

The invention relates to a double-parameter sensor design based on a stack type photonic crystal nano-beam double-mode cavity, and belongs to the technical field of photonic crystal sensors. The invention can locate the two modes in the same photon crystal nanometer beam cavity, to improve the property of sensor. Specifically, a cuboid silicon block with gradually changed length and width is introduced on a silicon dioxide substrate, the length is linearly increased from the center to two sides, and the width is linearly decreased from the center to two sides, so that a photonic crystal nano beam cavity supporting coexistence of an air mode and a dielectric mode is formed, and the multi-parameter detection capability and the integration capability are improved. Compared with a traditional sensor, the photonic crystal nano-beam cavity is used for sensing temperature and humidity simultaneously for the first time, and the humidity sensitivity is improved by 2-3 times. Compared with other double-parameter sensors, the double-parameter sensor is simpler in structure and device and more beneficial to manufacturing; the size is greatly reduced, and is only 14 mu m multiplied by 0.67 mu m multiplied by 0.22 mu m (length multiplied by width multiplied by height), which is more beneficial to integration. The invention can be used in the field of sensing ambient humidity and temperature.

Description

Ultra-compact high-sensitivity double-parameter sensor based on stack type dual-mode photonic crystal nano beam cavity
Technical Field
The invention relates to a double-parameter sensor based on a one-dimensional stack type photonic crystal nano-beam double-mode cavity, which is characterized by excellent sensing performance, small size, capability of realizing simultaneous detection of temperature and relative humidity and belongs to the technical field of photonic crystal sensors.
Background
Relative humidity is important in various fields such as industrial production, weather forecasting, agriculture, grain storage and medical facilities. The application of electronic humidity sensors is limited by problems of low sensitivity, electromagnetic interference, electrical leakage, etc. Humidity Sensors based on optical fibers are superior to electronic methods, but require complex manufacturing processes (document 1: S.A. Kolpakov, N.T.Gordon, C.Mou, and K.Zhou, "heated a New Generation of Photonic Humidity Sensors," Sensors,14(3),. 3986-. In recent years, the on-chip micro-nano sensor has attracted attention due to the advantages of simple device, stable structure, low cost, mass production and the like. Among other things, photonic crystal nanocavities characterized by high quality factors (Q) and ultra-low effective mode volumes (V) show advantages. This is because a high Q/V ratio represents a strong photo-object interaction, enabling the optical sensor to achieve high resolution and high sensitivity, and the photonic crystal nano-beam cavity is small in size and easy to integrate.
Relative humidity is defined as the ratio of the partial pressure of water vapor to the saturated vapor pressure of water at a given temperature. Thus, only given a given temperature, an accurate humidity sensing can be achieved. Previous humidity sensors (G.Yan, Y.Liang, E.H Lee, and S.He, "Novel Knob-integrated fiber Bragg grating sensor with a polyvinyl alcohol coating for a simultaneous dependent humidity and temperature measurement," Opt.express 23(12),15624-15634 (2015)) generally required a separate temperature sensor to obtain temperature information, which made the device complicated. In addition, conventional humidity sensors usually only sense a variable of humidity. However, as the research goes into, we find that the influence of the temperature in the external environment cannot be ignored due to the thermo-optic effect when sensing the humidity. Therefore, designing a dual parameter sensor capable of detecting humidity) and temperature at the same time has been a research focus (document 4: ding, P.Liu, J.Chen, D.Dai, and Y.Shi, "On-chip linked present sensing of hustling and temperature with a dual-polarization silicon microring reactor," opt.express 27(20),28649-28659 (2019); document 5: s.pevec and d.donlagic, "minor all-silica fiber-optical sensor for a immunological measure of relative humidity and temperature," opt.lett.40(23), 5646-; document 6: jin, y.liu, y.zhang, a.li, p.song, z.wu, y.zhang, and w.pen, "high Sensitive FBG-FP sensor for Simultaneous Measurement of husband and Temperature," in 26th International Conference Optical Fiber Sensors, OSA Technical Digest (Optical Society of America,2018), paper wf79; document 7: zhang, X.Dong, T.Li, C.C.Chan, and P.Shumd, "Simulanous resources measurement of relative humidity and temperature with PCF-MZI masked by fiber Bragg rating," opt.communications 303(15),42-45 (2013.). In recent years, some photonic crystal nano-beam sensing structures capable of simultaneously detecting refractive index (humidity change is essentially refractive index change) and temperature are reported in succession. For example, a Photonic Crystal nano-beam dual-parameter Sensor in cascade of an air mode and a dielectric mode (document 8: P.Liu and Y.Shi, "discrete antenna measurement of passive Index and thermal use of modulated side-coupled Photonic nano-beam sensors," Opti.Express 25(23), "28398-, "Opt.express 27(19)," 26471- "26482 (2019). However, these structures require the integration of two or more resonators, which increases the size and difficulty of fabrication.
Therefore, on the basis of ensuring the sensing performance, the ultra-compact dual-parameter sensor based on the single photonic crystal nano beam cavity is provided for the first time. By linearly modulating the length and width of the cuboid silicon block, it is ensured that both air and dielectric modes are present in a single photonic crystal nanobeam cavity. Only one nanobeam cavity is needed to achieve simultaneous detection of both humidity and temperature parameters. Wherein, the humidity sensitivity reaches-764.3 pm/% RH, the temperature sensitivity reaches 58.9pm/° C, and the sensor has excellent sensing performance. In addition, the structure has the size of only 14 microns multiplied by 0.67 microns multiplied by 0.22 microns (length multiplied by width multiplied by height), which is beneficial to large-scale on-chip integration.
Disclosure of Invention
1. Technical problem to be solved
The invention aims to overcome the defects of the existing photonic crystal sensing technology: firstly, the traditional humidity optical sensor only considers one sensing index of humidity, and recent researches show that the thermo-optic effect cannot be ignored and the influence of the environmental temperature on the detection result needs to be considered; secondly, for the reported micro-nano sensor capable of detecting humidity and temperature at the same time, the humidity sensitivity is low, and the sensitivity needs to be further improved; finally, the existing photonic crystal double-parameter sensing structure needs to multiplex at least 2 resonant cavities, so that the structure size and the manufacturing difficulty are greatly increased.
2. The technical scheme is as follows:
in order to achieve the above object, the technical solution adopted by the present invention is specifically as follows:
(1) first, the present invention is on Silica (SiO)2) A rectangular silicon (Si) block with fixed thickness and linearly-changed length and width is placed on a substrate. The lattice constant of these silicon blocks is constant and the overall structure is symmetric about the center. Finally, a layer of water-absorbing material, polyvinyl chloride (PVA), is coated on the surface of the film to sense the change of humidity in the environment. The formed stack type photonic crystal nano-beam cavity supports coexistence of an air mode and a medium mode, and resonance peaks corresponding to the air mode and the medium mode can be observed in a transmission spectrum.
(2) In the above scheme, SiO2The refractive index of (a) was 1.45, the refractive index of the Si block was 3.46, and the refractive index of the dried PVA was 1.49. The thicknesses of the PVA clad layer, the Si core layer, and the SiO2 layer were set to 2 μm, 220nm, and 2 μm, respectively.
(3) In the above scheme, the lattice constant a (silicon)Block spacing) is constant at 400nm, a cuboid stack structure which is symmetrical about the center and has gradually changed width and length is etched to form a Gaussian attenuation mirror image, and a one-dimensional photonic crystal nano beam cavity with an air mode and a dielectric mode coexisting is designed. The ith silicon block on one side of the structure is represented by i, imaxRepresenting the number of silicon blocks on one side of the structure. The width (x direction) of the silicon block is linearly reduced from the center to the left and right sides, and the calculation formula is lx(i)=lx(1)-(i-1)·[lx(1)-lx(imax)]/imax,i∈[1,imax]Wherein l isx(1)=320nm,lx(imax)=200nm,lx(i) Represents the width of the ith silicon block; the length (y direction) of the silicon block is linearly increased from the center to the left and right sides, and the calculation formula is ly(i)=ly(1)+(i-1)·[ly(imax)-lx(1)]/imax,i∈[1,imax]Wherein l isy(1)=430nm,ly(imax)=670nm,ly(i) Indicating the length of the ith silicon block.
(4) In the above scheme, the number of silicon blocks on both sides is 14, and the structure size is only 14 μm × 0.67 μm × 0.22 μm (length × width × height).
(5) In the above scheme, the sensitivities of the air mode-based mode and the dielectric mode-based mode to humidity and temperature form a 2 × 2 sensing matrix in consideration of the thermo-optic effects of the waveguide material and the detection solution. By detecting the respective shift in the resonance wavelength in the transmission spectrum, the respective amounts of change in humidity and temperature can be calculated.
3. Has the advantages that:
compared with the prior art, the beneficial effects of the invention are summarized as follows:
(1) the invention realizes the simultaneous sensing of two parameters of humidity and temperature.
(2) The cuboid stack type nano beam structure designed by the invention adopts a width and length gradual change type design, has constant lattice constant, does not need to change the mutual position, only needs to adjust the length and the width of the silicon block, and is simpler to manufacture.
(3) Compared with the conventional photonic crystal double-parameter sensing structure, the nano beam cavity designed by the invention supports coexistence of an air mode and a medium mode, and can realize sensing of two parameters only by one resonant cavity. On the basis of not sacrificing the sensing performance, the size of the structure is greatly reduced, and the manufacturing of devices and on-chip integration are facilitated.
(4) Compared with the existing double-parameter optical sensing structure for simultaneously detecting the relative humidity and the temperature, the double-mode photonic crystal nano-beam cavity designed by the invention has the advantages that the relative humidity sensitivity is improved by 2-3 times, and the temperature sensitivity is higher.
(5) The nano-beam sensor designed by the invention has the structure size of only 14 mu m multiplied by 0.67 mu m multiplied by 0.22 mu m (length multiplied by width multiplied by height), and is beneficial to large-scale on-chip integration.
Drawings
Fig. 1 is a schematic structural diagram of a stacked one-dimensional photonic crystal nano-beam dual-parameter sensor according to an embodiment of the present invention. The photonic crystal nano-beam cavity consists of a cuboid silicon block with linearly modulated width and length, and supports simultaneous existence of an air mode and a medium mode. SiO22The refractive index of the substrate was 1.45, the refractive index of the Si bulk was 3.46, and the refractive index of the dried PVA cladding was 1.49. SiO22The thicknesses of the layer, the Si core layer and the PVA clad layer were set to 2 μm, 220nm and 2 μm, respectively. The lattice constant was 400nm and the background refractive index was 1.330.
FIG. 2 is a graph of the relationship between the width, length and mirror image intensity of a silicon block calculated according to the mirror image intensity formula.
FIG. 3 shows the values of l obtained by the plane wave expansion method (PWE)x=320nm,ly430nm and lx(imax)=200nm,ly(imax) Band diagram of a single cell at 670 nm.
Fig. 4(a) is an electric field distribution diagram of a nano beam cavity air mode fundamental mode at a resonance wavelength, which is obtained by simulation using a three-dimensional time domain finite difference method (3D-FDTD).
Fig. 4(b) is a graph of the electric field energy density profile of the air mode fundamental mode of the nanobeam cavity along the x-axis. The electric field energy of the air mode is concentrated in the PVA gap between the silicon blocks.
Fig. 4(c) is an electric field distribution diagram of the nano beam cavity dielectric mode fundamental mode at the resonance wavelength, which is obtained by simulation using a three-dimensional time domain finite difference method (3D-FDTD).
Fig. 4(d) is the electric field energy density profile along the x-axis for the dielectric mode fundamental mode of the nanobeam cavity.
Fig. 4(e) is the electric field energy density profile of the nanobeam cavity dielectric mode fundamental mode along the y-direction axis of symmetry of the middle silicon block. Referring to fig. 4(d), the electric field energy of the dielectric mode is concentrated in the bulk silicon.
FIG. 5 is a graph of resonant transmission spectra when the relative humidity of the environment is changed. The relative humidity was increased from 0% RH to 90% RH in steps of 10% RH while the ambient temperature was kept constant at 300K.
Fig. 6 is a graph of the amount of shift in resonance wavelength versus relative humidity, and the straight line is a linear fit calculated between the two.
Fig. 7 is a resonance transmission spectrum when the ambient temperature is changed. The relative humidity was kept constant at 50% and the temperature was increased from 300K to 340K in 10K steps. Considering the influence of thermo-optic effect, the thermo-optic coefficient of silicon is 1.8 × 10-4RIU/K,SiO2Thermo-optic coefficient of (1X 10)-5RIU/K。
Fig. 8 is a graph of the amount of shift in resonance wavelength versus temperature, and the straight line is a linear fit calculated between the two.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the following will further explain the dual parameter sensing principle, specific structure and sensing performance of the present invention with reference to the accompanying drawings:
firstly, the invention defines the realization principle of double-parameter sensing by using the air mode and the medium mode of a single nano beam cavity: humidity sensitivity (S) by air mode fundamental mode for dual mode nanobeam structuresRH,a) Air mold base mold temperature sensitivity (S)T,a) Dielectric mold base mold humidity sensitivity (S)RH,d) Temperature sensitivity of dielectric mold base mold (S)T,d) Can form a sensing matrix
Figure BDA0002814856440000041
Thereby constructing a system of linear equations
Figure BDA0002814856440000042
Wherein, Δ λaAnd Δ λdRespectively, the shift amounts of the resonance wavelengths of the air mode fundamental mode and the dielectric mode fundamental mode, and Δ RH and Δ T respectively represent the change amounts of humidity and temperature. When the matrix is full rank, the system of linear equations in two dimensions has a unique solution. By measuring the transmission spectrumaAnd Δ λdThe equations can be solved to calculate Δ RH and Δ T.
The invention provides a dual-parameter sensor based on a one-dimensional stack type dual-mode photonic crystal nano beam cavity, and the structural schematic diagram of the dual-parameter sensor is shown in figure 1. The stack type photonic crystal nano-beam cavity formed by the cuboid Si blocks with linearly-changed lengths and widths is arranged in SiO2A layer of water-absorbing material PVA is coated on the surface of the substrate to sense the change of humidity in the environment. SiO22The refractive index of (a) was 1.45, the refractive index of the Si block was 3.46, and the refractive index of the dried PVA was 1.49. PVA clad layer, Si core layer and SiO2The thicknesses of the layers were set to 2 μm, 220nm, and 2 μm, respectively.
In this structure, the lattice constant a of 400nm and the thickness h of the silicon block of 220nm are kept constant, and the width and length of the rectangular parallelepiped silicon block are linearly tapered from the middle to both sides to form a stack structure. In order to enable an air mode and a medium mode to coexist in a single cavity, the parameters of the stack type dual-mode nano-beam cavity dual-parameter sensor provided by the invention are mainly researched to select the variation range and the gradual change mode of the width and the length of a silicon block. Since the resonance peak is around 1550nm, we choose lx=320nm,ly430nm as the length and width of the silicon block at the center. FIG. 2 shows the formula using the mirror image intensity
Figure BDA0002814856440000051
And calculating the corresponding relation graph among the length, the width and the mirror image intensity of the silicon block, wherein omega1And ω2At the edge frequency of the upper and lower sidebands, omegaresIs a central hole unit cell dielectric moldFrequency of (a), omegam=(ω12) And/2 is the middle band frequency. It can be seen that whenx=200nm,lyAt 670nm, the maximum specular intensity is obtained. FIG. 3 is a band diagram with lattice constants of 394nm and 330nm obtained by a Plane Wave Expansion (PWE) method. The ith silicon block on one side of the structure is represented by i, imaxRepresenting the number of silicon blocks on one side of the structure. The width (x direction) of the silicon block is linearly reduced from the center to the left and right sides, and the calculation formula is lx(i)=lx(1)-(i-1)·[lx(1)-lx(imax)]/imax,i∈[1,imax]Wherein l isx(1)=320nm,lx(imax)=200nm,lx(i) Represents the width of the ith silicon block; the length (y direction) of the silicon block is linearly increased from the center to the left and right sides, and the calculation formula is ly(i)=ly(1)+(i-1)·[ly(imax)-lx(1)]/imax,i∈[1,imax]Where ly (1) is 430nm, ly(imax)=670nm,ly(i) Indicating the length of the ith silicon block. The light source is input from the left side of the waveguide, and the detector is positioned at the right side of the waveguide and is used for monitoring the transmission spectrum of the structure. And simulating to obtain the electric field distribution condition of the nano beam cavity in different modes by a three-dimensional time domain finite difference method (3D-FDTD). The electric field distribution of the air mode fundamental mode of the dual-mode nanobeam cavity is shown in fig. 4 (a). Fig. 4(b) shows the electric field energy density distribution of the air mode along the x-axis, and it can be seen that the electric field energy of the air mode is concentrated in the gap between the silicon blocks. The electric field distribution of the air mode fundamental mode of the dual-mode nanobeam cavity is shown in fig. 4 (c). FIG. 4(d) shows the electric field energy distribution of the dielectric mode along the x-axis; fig. 4(e) shows the electric field energy density distribution of the dielectric mode along the y-direction symmetrical center line of the central silicon block, and it can be seen that the electric field energy of the dielectric mode is concentrated and distributed in the silicon block.
The double-parameter sensor based on the dual-mode stack type nano beam cavity with the gradually changed width and length has 14 silicon blocks on two sides respectively, and the structural size is only 14 microns multiplied by 0.67 microns multiplied by 0.22 microns (length multiplied by width multiplied by height). At this time, the fundamental mode of the air mode is located at 1498.93nm, and the Q value is about 3.7X 105Mode volume of 0.1(λ)a/nPVA)3(ii) a The dielectric mode fundamental mode is located at 1598.45nm, and the Q value is about 6.3 × 104Mode volume of 1.8(λ)d/nSi)3And can be applied to the sensing field.
Based on the definite double-parameter sensing mechanism, the relative humidity sensing and the temperature sensing are respectively analyzed on the structure by using a 3D-FDTD method. FIG. 5 is a resonance transmission spectrum when the ambient humidity is changed, when the ambient temperature is maintained at 300K and the humidity is increased from 0% RH to 90% RH in steps of 10% RH. Fig. 6 is a graph showing the relationship between the amount of resonant wavelength shift and the amount of humidity change. As can be seen from fig. 5 and 6, when the relative humidity is increased from 40% RH to 90% RH, the wavelength is linearly blue-shifted with the increase of the relative humidity, and the humidity sensitivity S of the fundamental mode of the air mode is increasedRH,aHumidity sensitivity of dielectric mode-basis mode S-386.6 pm/% RHRH,d=-764.3pm/%RH。
Next, taking into account the influence of the thermo-optic effect, the thermo-optic coefficient of Si is 1.8X 10-4RIU/K,SiO2Thermo-optic coefficient of (1X 10)-5RIU/K. Fig. 7 is a resonance transmission spectrum when the ambient temperature is changed, the ambient humidity is kept constant at 50% RH, and the temperatures are set to 300K, 310K, 320K, 330K, and 340K, respectively. FIG. 8 is a linear fit of the amount of resonant wavelength shift versus temperature. It can be seen from fig. 7 and 8 that when the temperature changes, the resonance wavelengths of the air mode fundamental mode and the dielectric mode fundamental mode are linearly shifted to the right, and the sensitivity S of the air mode fundamental mode to the temperatureT,aSensitivity of dielectric mode base mode to temperature S58.9 pm/KT,d=47.6pm/K。
In summary, in the multimode nanobeam structure, the structure is represented by SRH,a,SRH,d,ST,aAnd ST,dFormed sensing matrix
Figure BDA0002814856440000061
Figure BDA0002814856440000062
Satisfy the condition of full rank, binaryThe system of equations has a unique solution. Therefore, in practical applications, the respective variations of the relative humidity and the temperature can be calculated by detecting the shift of the resonance wavelength corresponding to the fundamental mode of the air mode and the fundamental mode of the dielectric mode in the transmission spectrum. In order to make the objects, technical solutions and advantages of the present invention clearer, the following will further explain the detailed structure, principles and sensing characteristics of the present invention with reference to the accompanying drawings.

Claims (5)

1. Provides a stack type one-dimensional photonic crystal nano-beam dual-parameter sensor supporting coexistence of an air mode and a medium mode, which is applied to silicon dioxide (SiO)2) On the substrate, a rectangular silicon (Si) block with fixed thickness and linearly gradually changed length and width is placed; the lattice constant of the silicon blocks is 400nm, and the whole structure is symmetrical about the center; finally, a layer of water-absorbing material, namely polyvinyl chloride (PVA), is coated on the surface of the film to sense the change of the humidity in the environment; SiO22The refractive index of the substrate was 1.45, the refractive index of the Si core layer was 3.46, and the refractive index of the dried PVA cladding layer was 1.49; SiO22The thicknesses of the substrate, the Si core layer, and the PVA clad layer were set to 2 μm, 220nm, and 2 μm, respectively.
2. A method for realizing dual-parameter sensing by using a dual-mode photonic crystal nano beam cavity is provided: because the electric field energy distribution of the air mode and the medium mode is different, the sensitivity to the change of the external environment is different; a binary linear equation set can be constructed by using a sensing matrix formed by the temperature sensitivity and the humidity sensitivity of the air mode and the medium mode and detecting the resonance wavelength offset of the transmission spectrum air mode and the medium mode, and the variation of the temperature and the refractive index can be calculated.
3. A dual-mode stack-type one-dimensional photonic crystal nano-beam cavity dual-parameter sensor according to claims 1 and 2, characterized in that: and supporting the coexistence of an air mode and a dielectric mode in a single one-dimensional photonic crystal nano-beam cavity. The lattice constant a (silicon block pitch) is constant at 400nm, the length and width of the cuboid stack varies linearly from the center of the structure to both sides to form a gaussian attenuation mirror image, and the overall structure is symmetric about the center. By generation iThe ith silicon block on one side of the watch structure, usingmaxRepresenting the number of silicon blocks on one side of the structure. The width (x direction) of the silicon block is linearly reduced from the center to the left and right sides, and the calculation formula is lx(i)=lx(1)-(i-1)·[lx(1)-lx(imax)]/imax,i∈[1,imax]Wherein l isx(1)=320nm,lx(imax)=200nm,lx(i) Represents the width of the ith silicon block; the length (y direction) of the silicon block is linearly increased from the center to the left and right sides, and the calculation formula is ly(i)=ly(1)+(i-1)·[ly(imax)-lx(1)]/imax,i∈[1,imax]Wherein l isy(1)=430nm,ly(imax)=670nm,ly(i) Indicating the length of the ith silicon block. The number of silicon blocks on both sides was 14, and the structure size was only 14 μm × 0.67 μm × 0.22 μm (length × width × height).
4. The dual-mode stacked one-dimensional photonic crystal nano-beam dual-parameter sensor according to claims 1 and 2, wherein: the structure is placed in an air environment, and the excited air mode and the excited medium mode respectively show different sensitivities to the temperature change and the relative humidity change of the surrounding environment; the temperature sensitivity of the air mode was 58.9pm/K, the relative humidity sensitivity was-386.6 pm/% RH, the temperature sensitivity of the media mode was 47.6pm/K, and the relative humidity sensitivity was-764.3 pm/% RH; the sensing matrix formed by the two linear equations has full rank, the system of the first-order binary equations has unique solution, the change quantity of temperature and relative humidity can be calculated, and double-parameter simultaneous sensing is realized.
5. The dual-mode stacked one-dimensional photonic crystal nano-beam dual-parameter sensor according to claims 1 and 2, wherein: the number of the silicon blocks on two sides is 14, the mode volume is small, the structure size is only 14 mu m multiplied by 0.67 mu m multiplied by 0.22 mu m (length multiplied by width multiplied by height), and the device miniaturization and the on-chip integration are facilitated.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113899717A (en) * 2021-10-11 2022-01-07 南京信息工程大学 Air humidity measurement method based on one-dimensional photonic crystal defect mode characteristics

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* Cited by examiner, † Cited by third party
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CN113899717A (en) * 2021-10-11 2022-01-07 南京信息工程大学 Air humidity measurement method based on one-dimensional photonic crystal defect mode characteristics
CN113899717B (en) * 2021-10-11 2023-06-13 南京信息工程大学 Air humidity measurement method based on one-dimensional photonic crystal defect mode characteristics

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