CN114279998B - Liquid enhancement sensing system and method based on quasi-Chinese character 'Hui' type terahertz metamaterial - Google Patents
Liquid enhancement sensing system and method based on quasi-Chinese character 'Hui' type terahertz metamaterial Download PDFInfo
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Abstract
The invention relates to a liquid enhancement sensing system and a liquid enhancement sensing method based on a quasi-return-type terahertz metamaterial, wherein the system comprises a terahertz transmitter, a sensing device, a loading structure, a terahertz detector and a post-processing system, the sensing device consists of a silicon substrate and the quasi-return-type terahertz metamaterial arranged on the silicon substrate, the sensing device is arranged on the loading structure and forms a sample pool for loading a liquid sample to be tested with the sensing device, the terahertz transmitter and the terahertz detector are respectively arranged on the upper side and the lower side of the sensing device, and the terahertz detector is connected with the post-processing system; the measuring method of the system comprises the following steps: and detecting terahertz signals of an empty loading structure, detecting terahertz signals of the quasi-back-shaped terahertz metamaterial without etched grooves when the liquid sample to be tested is not loaded and loaded, and calculating the sensitivity of the quasi-back-shaped terahertz metamaterial without etched grooves. The system has stable performance and high sensing sensitivity, and can support terahertz sensing detection of polar liquids such as water.
Description
Technical Field
The invention belongs to the technical field of terahertz liquid sensing, and particularly relates to a liquid enhancement sensing system and method based on a quasi-Chinese character 'Hui' type terahertz metamaterial.
Background
The metamaterial is used as an artificial engineering material, has unique electromagnetic characteristics, endows terahertz waves with the prospect of becoming a new generation of biological molecular detection technology, supports the generation of local surface plasmon resonance, and realizes the restraint of terahertz electromagnetic fields in frequency and space, so that a remarkable electric field enhancement effect is generated. The characteristic can realize strong interaction between the terahertz wave and the sample, and gets rid of the limitation that the cross section of the biomacromolecule is not matched with the terahertz wave, so that qualitative or quantitative sensing detection can be carried out on the trace sample. Therefore, the terahertz metamaterial sensor has the excellent characteristics of no mark, no damage, high efficiency and high sensitivity, so that the terahertz metamaterial sensor has great application prospect in the field of biochemical detection.
Existing terahertz metamaterial sensors mostly generate divergent electric field distribution based on structural design changes, which cannot maximize the utilization of the excited electric field, so the sensitivity of the sensor is usually limited. Secondly, since the extremely large absorption of terahertz wave energy by water will severely limit the application of terahertz sensors in liquid detection, the current common way is to subject the sample to a dehydration drying process, which will make detection cumbersome and complex. Therefore, how to develop a terahertz metamaterial sensor with high sensitivity and simultaneously can perform sensing detection on liquid becomes a key difficulty in the forward development of the terahertz sensing technology.
Disclosure of Invention
The invention aims to provide a liquid enhancement sensing system and method based on a quasi-return-type terahertz metamaterial, wherein the system is stable in performance and high in sensing sensitivity, and can support terahertz sensing detection of polar liquids such as water.
In order to achieve the above purpose, the invention adopts the following technical scheme: the utility model provides a liquid enhancement sensing system based on class returns style of calligraphy terahertz metamaterial, includes terahertz transmitter, sensing device, loading structure, terahertz detector and aftertreatment system, sensing device comprises silicon substrate and class returns style of calligraphy terahertz metamaterial of locating on it, sensing device installs on loading structure and rather than forming the sample cell that is used for loading the liquid sample that awaits measuring, terahertz transmitter, terahertz detector are located sensing device's upper and lower side respectively to the transmission, receive terahertz signal, terahertz detector is connected with aftertreatment system to handle and show terahertz signal.
Further, the system is provided with two sensing devices, one is composed of a silicon substrate and a quasi-inverted-V-shaped terahertz metamaterial with etched grooves, and the other is composed of the silicon substrate and a quasi-inverted-V-shaped terahertz metamaterial without etched grooves.
Further, the terahertz metamaterial is composed of an external square-shaped closed square ring and an internal U-shaped split ring, wherein the unit period of the metamaterial is 60 microns, the side length of the external square-shaped closed square ring is 50 microns, the side length of the internal U-shaped split ring is 32 microns, the metal line width of the structure is 3 microns, and the groove depth of etched grooves is 15 microns.
Further, the quasi-reverse terahertz metamaterial is used as a carrier for loading a liquid sample to be detected and exciting local surface plasma resonance, and is processed by combining magnetron sputtering coating, photoetching, IBE ion beam etching and deep silicon etching technologies; firstly, adopting aluminum as a target material, plating a layer of aluminum film with the thickness of 200 nm on a silicon substrate by utilizing a magnetron sputtering coating technology, and then processing the aluminum film into a quasi-rectangular terahertz metamaterial without etching grooves by utilizing photoetching and IBE ion beam etching technologies; on the basis, the quasi-reverse-shaped terahertz metamaterial with the etched grooves is formed by deep silicon etching technology.
Further, the loading structure is composed of a left bracket, a right bracket and a cover plate, wherein the left bracket and the right bracket are clamped on the left side and the right side of the sensing device to support the sensing device and form a sample pool for loading a liquid sample to be tested, the lower part of the cover plate is provided with a convex plane, and the cover plate is covered on the upper side of the sensing device to flatten the upper surface of the liquid sample to be tested between the sensing device and the cover plate.
Further, the loading structure is made of a 4-methylpentene based polymer TPX.
The invention also provides a measuring method of the liquid enhancement sensing system based on the quasi-Chinese character 'Hui' type terahertz metamaterial, which is characterized by comprising the following steps of:
step S1: the method comprises the steps that a silicon substrate without a metamaterial is mounted on a loading structure, the loading structure is fixed between a terahertz transmitter and a terahertz detector, and a terahertz signal obtained by detection of a detection light path is a reference signal r;
step S2: the sensing device loaded with the quasi-square terahertz metamaterial without etching grooves is arranged in a loading structure, and a terahertz signal obtained by detection of a detection light path is a sample signal s1;
step S3: the method comprises the steps of taking a quasi-reverse-shaped terahertz metamaterial without etching grooves as a carrier, loading a liquid sample to be detected into a sample tank, and taking a terahertz signal detected by a detection light path as a sample signal s2;
step S4: transmitting the obtained reference signal r and the sample signals s1 and s2 to a post-processing system, and calculating the sensitivity of the quasi-echo-type terahertz metamaterial without etching the groove;
step S5: and replacing the quasi-back-shaped terahertz metamaterial without the etched groove with the quasi-back-shaped terahertz metamaterial with the etched groove, and repeating the steps S2-S4 to calculate the sensitivity of the quasi-back-shaped terahertz metamaterial with the etched groove.
Further, the method for calculating the sensitivity of the terahertz metamaterial in the shape of the Chinese character 'hui' without etching the groove comprises the following steps:
step S41: converting the terahertz time-domain pulse signal obtained by detection into a terahertz frequency-domain amplitude spectrum signal through Fast Fourier Transform (FFT);
step S42: calculating the transmittance spectrum of the sample signals s1 and s2 by adopting a transmittance spectrum calculation formula so as to obtain the resonance frequency of the samplef s1 Andf s2 i.e. the formant frequencies of the middle lobe of the transmittance spectrum;
step S43: calculating the sensitivity of the quasi-Chinese character 'Hui' type terahertz metamaterial without etching grooves by adopting a sensitivity calculation formula of the metamaterial;
the method for calculating the sensitivity of the terahertz metamaterial like the Chinese character 'hui' with the etched groove comprises the following steps of: and replacing the quasi-back-shaped terahertz metamaterial without the etched groove with the quasi-back-shaped terahertz metamaterial with the etched groove, and repeating the steps S41-S43 to calculate the sensitivity of the quasi-back-shaped terahertz metamaterial with the etched groove.
Further, in the step S42, the transmittance spectrum calculation formula is:
wherein,E s (ω) AndE r (ω) Terahertz frequency domain amplitude spectra of the sample signal and the reference signal respectively.
Further, in the step S43, the sensitivity calculation formula is:
wherein,f s1 for the resonance frequency of the sample signal s1,f s2 for the resonance frequency of the sample signal s2,nis the refractive index of the sample to be measured.
Compared with the prior art, the invention has the following beneficial effects: the liquid enhancement sensing system uses the quasi-return-type terahertz metamaterial as a carrier, and the electric field is enhanced by etching grooves in the structure, so that interaction between terahertz waves and a sample to be measured is improved, sensing of liquid is enhanced, and sensitivity is greatly improved. Meanwhile, a sample to be detected is loaded by adopting the sample cell integrated terahertz metamaterial, and the sensing detection of the liquid sample is realized by utilizing the dielectric sensitivity of the metamaterial local surface plasma resonance, so that the strong absorption of the polar liquid to the terahertz wave is greatly relieved, and the effective sensing detection of the liquid sample is realized.
Drawings
FIG. 1 is a schematic diagram of a system architecture of an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a sensing device including a terahertz metamaterial in a shape like a Chinese character 'Hui' without etching a groove in an embodiment of the invention;
FIG. 3 is a schematic structural diagram of a sensing device including a terahertz metamaterial shaped like a Chinese character 'Hui' with etched grooves in an embodiment of the invention;
FIG. 4 is a graph of the property test transmittance spectrum in an embodiment of the invention;
FIG. 5 is a graph of sensing sensitivity in an embodiment of the invention.
In the figure: a 1-terahertz transmitter; 2-incident terahertz pulses; 3-cover plate; 4-a bracket; 5-a liquid sample to be measured; 6-class-Chinese character 'Hui' type terahertz metamaterial; 601-a square closed ring in a shape of Chinese character kou; 602-U-shaped split ring; 603-grooves; a 7-silicon substrate; 8-transmitting terahertz pulses; a 9-terahertz detector; 10-aftertreatment system.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
As shown in fig. 1, the embodiment provides a liquid enhancement sensing system based on a terahertz metamaterial shaped like a Chinese character 'hui', which comprises a terahertz transmitter 1, a sensing device, a loading structure, a terahertz detector 9 and a post-processing system 10, wherein the sensing device is composed of a silicon substrate 7 and the terahertz metamaterial shaped like the Chinese character 'hui' 6 arranged on the silicon substrate, the sensing device is arranged on the loading structure and forms a sample pool for loading a liquid sample 5 to be detected with the silicon substrate, the terahertz transmitter and the terahertz detector are respectively arranged on the upper side and the lower side of the sensing device to transmit and receive terahertz signals, and the terahertz detector is connected with the post-processing system to process and display the terahertz signals.
As shown in fig. 2 and 3, in this embodiment, the system is provided with two sensing devices, one is composed of a silicon substrate and a terahertz metamaterial shaped like a Chinese character 'hui' with etched grooves, and the other is composed of a silicon substrate and a terahertz metamaterial shaped like a Chinese character 'hui' without etched grooves.
In this embodiment, the terahertz metamaterial is composed of an external square-shaped closed square ring 601 and an internal U-shaped split ring 602, wherein the unit period of the metamaterial is 60 μm, the side length of the external square-shaped closed square ring is 50 μm, the side length of the internal U-shaped split ring is 32 μm, the metal line width of the structure is 3 μm, and the groove depth with the etched groove 603 is 15 μm.
The quasi-reverse terahertz metamaterial is used as a carrier for loading a liquid sample to be detected and exciting local surface plasma resonance, and is processed by combining magnetron sputtering coating, photoetching, IBE ion beam etching and deep silicon etching technologies; firstly, adopting aluminum as a target material, plating a layer of aluminum film with the thickness of 200 nm on a silicon substrate by utilizing a magnetron sputtering coating technology, and then processing the aluminum film into a quasi-rectangular terahertz metamaterial without etching grooves by utilizing photoetching and IBE ion beam etching technologies; on the basis, the quasi-reverse-shaped terahertz metamaterial with the etched grooves is formed by deep silicon etching technology.
In this embodiment, the loading structure is composed of a left bracket 4, a right bracket 4 and a cover plate 3, wherein the left bracket 4 and the right bracket are clamped on the left side and the right side of the sensing device to support the sensing device and form a sample pool for loading a liquid sample to be tested therewith, the lower part of the cover plate 3 is provided with a convex plane, and the cover plate 3 is covered on the upper side of the sensing device to flatten the upper surface of the liquid sample to be tested between the sensing device and the cover plate. The loading structure is made of a 4-methylpentene based polymer TPX.
When the liquid sample is sensed and detected, the quasi-reverse terahertz metamaterial 6 is used as a carrier and is integrated in a sensing device loading structure formed by the cover plate 3 and the bracket 4. Then fixing the terahertz wave on the space between the terahertz emitter 1 to be started and the terahertz detector 9, then starting the terahertz emitter 1 and the terahertz detector 9, transmitting incident terahertz pulse 2, enabling terahertz waves to react on the surface of the quasi-inverted-V-shaped terahertz metamaterial 6 in a transmission mode, then emitting out through the silicon substrate 7, finally transmitting detected transmission terahertz pulse 8 sample signals to the terahertz signal post-processing system 10 to obtain sample signals 1, loading a liquid sample 5 to be detected on the surface of the integrated quasi-inverted-V-shaped terahertz metamaterial of the sample cell, repeating the process to obtain sample signals 2, and finally calculating the sensitivity of the metamaterial. The above process is respectively carried out on the quasi-reverse-character terahertz metamaterial without etched grooves and with etched grooves. The measuring method of the system specifically comprises the following steps:
step S1: and mounting the silicon substrate without the processed metamaterial on a loading structure, and fixing the loading structure between the terahertz transmitter and the terahertz detector, wherein the terahertz signal detected by the detection light path is a reference signal r.
Step S2: and installing the sensing device loaded with the quasi-reverse-shaped terahertz metamaterial without etching the groove in a loading structure, wherein the terahertz signal detected by the detection light path is a sample signal s1.
Step S3: and loading the liquid sample to be detected into a sample cell by taking the terahertz metamaterial like the Chinese character 'Hui' shape without etching the groove as a carrier, wherein the terahertz signal detected by the detection light path is a sample signal s2.
Step S4: and transmitting the obtained reference signal r and the sample signals s1 and s2 to a post-processing system, and calculating the sensitivity of the quasi-echo-type terahertz metamaterial without etching the groove.
Step S5: and replacing the quasi-back-shaped terahertz metamaterial without the etched groove with the quasi-back-shaped terahertz metamaterial with the etched groove, and repeating the steps S2-S4 to calculate the sensitivity of the quasi-back-shaped terahertz metamaterial with the etched groove.
The method for calculating the sensitivity of the quasi-Chinese character 'Hui' type terahertz metamaterial without etching the groove comprises the following steps of:
step S41: and converting the terahertz time-domain pulse signal obtained by detection into a terahertz frequency-domain amplitude spectrum signal through fast Fourier transform FFT.
Step S42: calculating the transmittance spectrum of the sample signals s1 and s2 by adopting a transmittance spectrum calculation formula so as to obtain the resonance frequency of the samplef s1 Andf s2 i.e. the formant frequencies of the middle lobe of the transmittance spectrum.
The transmittance spectrum calculation formula is as follows:
wherein,E s (ω) AndE r (ω) Terahertz frequency domain amplitude spectra of the sample signal and the reference signal respectively.
Step S43: and calculating the sensitivity of the quasi-Chinese character 'Hui' type terahertz metamaterial without etching the groove by adopting a sensitivity calculation formula of the metamaterial.
The sensitivity calculation formula is as follows:
wherein,f s1 for the resonance frequency of the sample signal s1,f s2 for the resonance frequency of the sample signal s2,nis the refractive index of the sample to be measured.
The method for calculating the sensitivity of the terahertz metamaterial like the Chinese character 'hui' with the etched groove comprises the following steps of: and replacing the quasi-back-shaped terahertz metamaterial without the etched groove with the quasi-back-shaped terahertz metamaterial with the etched groove, and repeating the steps S41-S43 to calculate the sensitivity of the quasi-back-shaped terahertz metamaterial with the etched groove.
Performance evaluation of a terahertz metamaterial sensing system:
the performance evaluation of the developed liquid enhancement sensing system based on the quasi-back-shaped terahertz metamaterial is carried out by respectively loading nitrogen and purified water on the surface of the sample cell integrated type quasi-back-shaped terahertz metamaterial without etching grooves and with etching grooves, and then fixing the surface at a specified detection position.
According to the frequency shift delta of the resonance point frequency of the transmissivity spectrum calculated by the terahertz frequency domain amplitude spectrum of the liquid sample to be measured under different frequenciesfDelta with the change of the refractive index of the liquid sample to be measurednAnd carrying out sensing characterization. Sensing sensitivity for performance of terahertz metamaterial sensing systemS n The representation is:whereinS n1 Representing a metamaterial without etching a trench,S n2 representing metamaterial with etched trenches, deltaf = f s1 - f s2 , Δn = n-1。
Performance evaluation was performed on the terahertz subsurface sensing system, and the performance test results of the embodiment of the present invention are shown in fig. 4 below. As can be seen from the experimental transmittance spectrum, compared with nitrogen, the water has higher refractive index and loss, so that the transmittance spectrum of the terahertz metamaterial has obvious red shift and stretching and strength weakening of formants, the groove-like terahertz metamaterial is not etched, the formants are red-shifted from original 0.662 THz to 0.626 THz, and after the groove is etched, the formants are red-shifted from original 1.132 THz to 0.8THz. These remarkable changes confirm that the localized surface plasmon resonance supported by the terahertz metamaterial shaped like a Chinese character 'hui' is extremely sensitive to the change of the surrounding dielectric environment, and the sensing sensitivity calculation according to the embodiment of the invention is shown in fig. 5, and the sensing sensitivity calculation is obtainedS n1 = 0.032 THz/RIU，S n2 The comparison found that the sensing sensitivity was improved by 9.4 times after etching the trench, which is an effective method of enhancing sensing, =0.302 THz/RIU. Meanwhile, the obvious transmittance spectrum profile caused by water also shows that the system can effectively relieve the strong absorption of the polar liquid to the terahertz waves, thereby realizing the refractive index sensing detection of the liquid sample.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the invention in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (7)
1. The liquid enhancement sensing system based on the quasi-return-type terahertz metamaterial is characterized by comprising a terahertz transmitter, a sensing device, a loading structure, a terahertz detector and a post-processing system, wherein the sensing device consists of a silicon substrate and the quasi-return-type terahertz metamaterial arranged on the silicon substrate, the sensing device is arranged on the loading structure and forms a sample pool for loading a liquid sample to be tested with the loading structure, the terahertz transmitter and the terahertz detector are respectively arranged on the upper side and the lower side of the sensing device to transmit and receive terahertz signals, and the terahertz detector is connected with the post-processing system to process and display the terahertz signals;
the liquid enhancement sensing system based on the quasi-back-shaped terahertz metamaterial is provided with two sensing devices, wherein one sensing device consists of a silicon substrate and the quasi-back-shaped terahertz metamaterial with etched grooves, and the other sensing device consists of the silicon substrate and the quasi-back-shaped terahertz metamaterial without etched grooves; the quasi-Chinese character 'Hui' type terahertz metamaterial consists of an external square closed ring and an internal U-shaped split ring;
the loading structure consists of a left bracket, a right bracket and a cover plate, wherein the left bracket and the right bracket are clamped on the left side and the right side of the sensing device to support the sensing device and form a sample pool for loading a liquid sample to be tested, the lower part of the cover plate is provided with a convex plane, and the cover plate is covered on the upper side of the sensing device to flatten the upper surface of the liquid sample to be tested between the sensing device and the cover plate;
the measuring method of the liquid enhanced sensing system based on the quasi-return terahertz metamaterial comprises the following steps of:
step S1: the method comprises the steps that a silicon substrate without a metamaterial is mounted on a loading structure, the loading structure is fixed between a terahertz transmitter and a terahertz detector, and a terahertz signal obtained by detection of a detection light path is a reference signal r;
step S2: the sensing device loaded with the quasi-square terahertz metamaterial without etching grooves is arranged in a loading structure, and a terahertz signal obtained by detection of a detection light path is a sample signal s1;
step S3: the method comprises the steps of taking a quasi-reverse-shaped terahertz metamaterial without etching grooves as a carrier, loading a liquid sample to be detected into a sample tank, and taking a terahertz signal detected by a detection light path as a sample signal s2;
step S4: transmitting the obtained reference signal r and the sample signals s1 and s2 to a post-processing system, and calculating the sensitivity of the quasi-echo-type terahertz metamaterial without etching the groove;
step S5: and replacing the quasi-back-shaped terahertz metamaterial without the etched groove with the quasi-back-shaped terahertz metamaterial with the etched groove, and repeating the steps S2-S4 to calculate the sensitivity of the quasi-back-shaped terahertz metamaterial with the etched groove.
2. The liquid enhancement sensing system based on the quasi-back-shaped terahertz metamaterial according to claim 1, wherein the metamaterial unit period in the quasi-back-shaped terahertz metamaterial is 60 microns, the outer square-shaped closed square ring side length is 50 microns, the inner U-shaped split ring side length is 32 microns, the metal line width of the structure is 3 microns, and the groove depth with etched grooves is 15 microns.
3. The liquid enhanced sensing system based on the quasi-gyratory terahertz metamaterial according to claim 1, wherein the quasi-gyratory terahertz metamaterial is processed by combining magnetron sputtering coating, photoetching, IBE ion beam etching and deep silicon etching technologies and is used as a carrier for loading a liquid sample to be detected and exciting local surface plasma resonance; firstly, adopting aluminum as a target material, plating a layer of aluminum film with the thickness of 200 nm on a silicon substrate by utilizing a magnetron sputtering coating technology, and then processing the aluminum film into a quasi-rectangular terahertz metamaterial without etching grooves by utilizing photoetching and IBE ion beam etching technologies; on the basis, the quasi-reverse-shaped terahertz metamaterial with the etched grooves is formed by deep silicon etching technology.
4. The gyroid-shaped terahertz metamaterial-based liquid enhancement sensing system according to claim 1, wherein the loading structure is made of a polymer TPX based on 4-methylpentene.
5. The liquid enhancement sensing system based on the quasi-back-shaped terahertz metamaterial according to claim 1, wherein the method for calculating the sensitivity of the quasi-back-shaped terahertz metamaterial without etching the groove is as follows:
step S41: converting the terahertz time-domain pulse signal obtained by detection into a terahertz frequency-domain amplitude spectrum signal through Fast Fourier Transform (FFT);
step S42: calculating the transmittance spectrum of the sample signals s1 and s2 by adopting a transmittance spectrum calculation formula so as to obtain the resonance frequency of the samplef s1 Andf s2 i.e. the formant frequencies of the middle lobe of the transmittance spectrum;
step S43: calculating the sensitivity of the quasi-Chinese character 'Hui' type terahertz metamaterial without etching grooves by adopting a sensitivity calculation formula of the metamaterial;
the method for calculating the sensitivity of the terahertz metamaterial like the Chinese character 'hui' with the etched groove comprises the following steps of: and replacing the quasi-back-shaped terahertz metamaterial without the etched groove with the quasi-back-shaped terahertz metamaterial with the etched groove, and repeating the steps S41-S43 to calculate the sensitivity of the quasi-back-shaped terahertz metamaterial with the etched groove.
6. The liquid enhancement sensing system based on the terahertz metamaterial shaped like a Chinese character 'hui' according to claim 5, wherein in the step S42, a transmittance spectrum calculation formula is as follows:；
wherein,T(ω) In order to obtain a transmittance spectrum,E s (ω) AndE r (ω) Terahertz frequency domain amplitude spectra of the sample signal and the reference signal respectively.
7. The liquid enhancement sensing system based on the terahertz metamaterial shaped like a Chinese character 'hui' according to claim 5, wherein in the step S43, a sensitivity calculation formula is as follows:；
wherein,S n in order to be sensitive to this,f s1 for the resonance frequency of the sample signal s1,f s2 for the resonance frequency of the sample signal s2,nis the refractive index of the sample to be measured.
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