FDTD Analysis of a High-Sensitivity Refractive Index Sensing Based on Fano Resonances in A Plasmonic Planar Split-Ring Resonators
Subject Areas : Journal of Optoelectronical Nanostructures
Mohsen Nasrolahi
1
,
Ali Farmani
2
,
Ashkan Horri
3
,
Hossein Hatami
4
1 -
2 -
3 -
4 -
Keywords: Ring resonator, Plasmonics sensor, FDTD,
Abstract :
A tunable label-free refractive index biosensor based on plasmonic planar split-ring resonators is proposed. The effects of Fano resonances are studied to harness the transmission spectra in near-infrared region. In the structure, dual hexagonal ring resonators are utilized to realize the Fano resonances with the advantages of high sensitivity, large figure of merit, narrow full wave at half-maximum (FWHM), and extremely large Q-factor. Analytical and numerical outcomes display that, by slight variation of the refractive index and geometrical modes resonances can be manipulated. A high sensitivity of 1160 nm/RIU with a FoM as large as 33 is achieved. Besides, the proposed biosensor shows a relatively narrow FWHM of 50 nm, which introduces a high Q-factor of 31. Such this moderately high Q-factor ensures that the structure exhibits extreme low resonance losses that can be advantageous for high resolution detections with acceptable accuracy. Nano Fano resonance sensing is a technique used in nanophotonics for highly sensitive detection of bioanalytes. It leverages the Fano resonance effect, which arises from interference between a discrete state and a broadband continuum of states. This can lead to sharp asymmetric peaks in the absorption or scattering spectrum.
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Islamic Azad University
| Journal of
Summer 2024 / Vol. 9, No. 3 |
|
Research Paper
| |
FDTD Analysis of a High-Sensitivity Refractive Index Sensing Based on Fano Resonances in A Plasmonic Planar Split-Ring Resonators | |
Mohsen Nasrolahi 1, Ali Farmani*2, Ashkan Horri1 , Hossein Hatami2 1 Department of Electrical Engineering, Islamic Azad University, Arak, Iran 2 Department of Electrical Engineering, Lorestan University, Khoramabad, Iran
| |
Received: 19 Feb. 2024 Revised: 20 Mar. 2024 Accepted: 1 Jun. 2024 Published: 15 Sep. 2024 | Abstract A tunable label-free refractive index biosensor based on plasmonic planar split-ring resonators is proposed. The effects of Fano resonances are studied to harness the transmission spectra in near-infrared region. In the structure, dual hexagonal ring resonators are utilized to realize the Fano resonances with the advantages of high sensitivity, large figure of merit, narrow full wave at half-maximum (FWHM), and extremely large Q-factor. Analytical and numerical outcomes display that, by slight variation of the refractive index and geometrical modes resonances can be manipulated. A high sensitivity of 1160 nm/RIU with a FoM as large as 33 is achieved. Besides, the proposed biosensor shows a relatively narrow FWHM of 50 nm, which introduces a high Q-factor of 31. Such this moderately high Q-factor ensures that the structure exhibits extreme low resonance losses that can be advantageous for high resolution detections with acceptable accuracy. Nano Fano resonance sensing is a technique used in nanophotonics for highly sensitive detection of bioanalytes. It leverages the Fano resonance effect, which arises from interference between a discrete state and a broadband continuum of states. This can lead to sharp asymmetric peaks in the absorption or scattering spectrum. |
| |
Keywords: Ring resonator, Plasmonics sensor, FDTD | |
1. INTRODUCTION
Numerous studies have explored various advancements in different types of biosensors, including unstable wave fluorescence sensors, photonic crystals, and surface plasmon resonance (SPR) sensors, with some of these studies focusing on specific applications. Optical biosensors have been highly welcomed by scientists in the last few years due to their fast response, small dimensions, low cost, timely detection ability, and ability to adapt to biological analytes with excellent s (sensitivity) and QF (quality factor). Taken in optical biosensors, a converter that converts the light change received from the source into measurable parameters is used to investigate the properties of the biological analyte for detection [1-6]. Usually, the measured parameters of the molecule are converted into measurable parameters such as intensity or wavelength resonance by a transducer [7-16]. The sensitivity value of the sensor is related to the architecture of the transducer and the waveguide structure used for measurement [16-23]. Optical biosensors have attracted the attention of researchers due to their small size and ability to be integrated, the cost of manufacturing and proper operation, and the detection of biological analyte without the need of any label [24-30]. Biosensors with resonator ring structure have smaller volume, better sensitivity and higher quality factor than photonic sensors such as photonic crystal, disk resonator sensors, MZI (Mach-Zehnder Interferometer) based sensors, PCF (photonic crystal fiber) sensors. [31-36]. Most plasmonic devices use metal-insulator-metal (MIM) waveguides for propagation [37-41], because MIM has the advantages of high sensitivity, ease of design, simple fabrication, and small dimensions. The most common metals used in these devices are the noble metals gold and silver, which have little losses in terms of ohmic [42-48]. However, they have a large optical wavelength penalty due to the energy required for interband transfer, intraband transfer, and scattered wave [49, 50]. Diffusion losses due to metallic nature are high and can cause errors in analyte detection. The response of the sensors that use the Kericthman configuration is good, but they are very expensive [51-54].
These elements may include antibodies, enzymes, proteins, and similar substances. Measurements are typically conducted by a transducer, followed by data analysis [55-60]. Optical biosensors are unique due to their use of optical measurement methods. These sensors utilize optical transducers to perform measurements, with the optical transducer closely integrated with the biosensing element.
For this reason, the classification of optical biosensors based on the type of transducers is of great importance. One common approach in this classification is to divide them into two categories: labeled and unlabeled. In labeled biosensors, fluorescent or chromogenic markers are used, where the intensity of fluorescence or color change is analyzed for the identification of analytes [60-64].
Here, with Finite-Difference Time-Domain (FDTD) a novel biosensor is suggested.
Taken together, the proposed plasmonic biosensor might pave the way towards the related limitations of biosensing, detection, and imaging.
2. Theory of Schottky Junction
Ring resonators have many uses due to their ability to be integrated and have been noticed and have emerged in integrated optics. Integrated ring resonators do not need a periodic surface under the wave or a mirror and a prism or grating surface for optical feedback. As a result, their structure is small and can be integrated. be made with other components. In the design of ring resonators, their structure can be customized and coupled in different ways. Thus, plasmonic biosensors constructed with label-free ring resonators that operate based on changes in the refractive index parameter can be widely used in medical applications, imaging, disease diagnosis, and pathogens in various foods. be placed.
The basic design includes a one-way resonator ring, we show the ring radius with r and the width of the waveguide with a that in one direction, the coupling and excitation mode is created in the resonator, in this case the loss is very small and we consider it as zero. The polarization has been investigated individually so that the coupling between the ring and the waveguide of different polarizations does not occur. Different losses occur along the propagation path. Resonance mode occurs at a specific wavelength and frequency, and the coupling of light occurs in the ring (see Figure 1.).
Fig. 1 2D-configuration of biosensor
A part of the structure illustrates in the following figure.
Fig. 2 Fano resonance structure
For analysis, we can express the relationship between input and output by considering the attenuation coefficient of the light path as follows:
(1) |
|
For the simplicity of the analysis of mixed modes, we normalize E, in this case, the absolute value of their square is equal to the modal power. We represent the path length attenuation coefficient with t and the coupling attenuation coefficient with k. With this interpretation, we have:
(2) |
|
To simplify the analysis model, we consider 
equal to 1. Therefore, the circular path is defined by the following relation:
(3) |
|
|
Considering that α is the attenuation coefficient of the loop, for zero loss mode, we should consider it equal to 1 (α = 1). The position angle θ is defined according to the relation (θ=ωL/c), in this relation L is the circumference of the ring and r is the radius of the ring. So L = 2πr. c is the phase speed that is related to the speed of light in vacuum and the effective refractive index according to the state (c=c0/"neff"). Also, ω is the angular frequency that is related to the speed of light in vacuum c0 and the wave number k according to ω = kc0. The vacuum wave number k depends on the wavelength λ, k = 2π/λ. Therefore, we can write the relations as follows:
(4)
|
|
Considering that β is the propagation constant, we have:
|
|
From (1) and (3) we get:
|
|
|
|
|
|
As a result, we can obtain the output power according to the following equation:
|
|
The coupling loss can be obtained from the relation t = |t| exp (jϕt) obtained, as previously stated |t| Coupling loss and 
is the coupling phase. Therefore, we get the power 
in the loop as follows:
In the intensified state, we have the relation , (θ+)=2πm. Note that m is an integer, so the relations are simplified as follows:
In a special case where the internal loss of the resonator ring is equal to the coupling loss, i.e.,
α = |t|, the transmission power becomes zero. This is the critical coupling state. The equations mentioned for a ring and a waveguide are a good model for other resonator ring configurations. And it can be used to analyze the complex structures of the resonator ring
The Sensitivity (S) is defined as:
(13)
FoM is expressed as:
(14)
Integrated resonators with high Q-factors are highly desirable because plasmonic biosensor with high Q, suggest narrower FWHM, high FoM, low resonator losses and large sensitivity. The Q-factor is defined as [61]:
(15)
Where λres is the wavelength in which the spectral slope reaches its maximum.
3. Results and Discussions
In this section, the Fano resonance is observed through modulation of geometric parameters and variation of refractive indices.
3.1 Numerical Results
Here, the resonances are defined as FR1 and FR2. For FR1, Tmax occurs at λpeak = 630nm and Tmax occurs at λdip = 780nm. Therefore, the FWHM for FR1 can be calculated as 150 nm. Similarly, for FR2, Tmax and and Tmin occur at λpeak = 640nm and λdip = 740nm, respectively. As a result, the FWHM for FR2 is 100 nm. Additionally, it can be seen that in the range of 650 - 850 nm, there are two symmetric Lorentzian like valleys which represent the first and the second eigen mode of the ring cavity (see Fig.3).
Fig. 3 The transmission of two Fano resonance
Physical analysis of the structure of the resonator ring is very important in order to achieve how the resonator ring works and requires complex mathematical operations. One of the methods of numerical analysis of instruments is Finite Difference Time Domain (FDTD) and it can perform analysis in the time domain as well. Therefore, it is perfect for the resonator loop and provides a very good view. We have presented a biosensor with a hybrid structure of plasmonic resonator ring along with modeling and numerical analysis. This hybrid structure based on highly doped n-graphene silicon waveguide is very suitable for biosensor application. We have proposed this new structure based on the research and investigation of different structures and different plasmonic devices according to the following findings to improve and improve the functional parameters of the biosensor.
A- The use of the ring structure of integrated resonators because they do not need a periodic surface under the wave or a mirror and a prism surface or a net for optical feedback. As a result, their structure is small and they can be made as a complex with other components.
B- We have used the hybrid structure of two lines of resonator ring. The use of degenerate semiconductor due to high doping, which reduces losses compared to noble conductors such as gold and silver, and because it is more compatible with CMOS integration technology.
C- Adding a layer of graphene to the structure, in fact, graphene is used to detect various types of organic and inorganic substances in biological and environmental applications, including glucose, cysteine, proteins, biological markers, DNA, heavy metals, etc. Also, biosensors in which graphene is used have been used for early detection of various diseases and cancers.
In order to achieve better parameters of the biosensor and improve the performance, we have taken the help of the gray wolf algorithm, and we have done the modeling using the FDTD method.
Optimization problems are ubiquitous across various domains, spanning single or multiple objectives and often characterized by intricate landscapes of high dimensionality. Traditional optimization methodologies frequently encounter limitations when confronted with such complexities. In response, metaheuristic algorithms have emerged as promising alternatives, drawing inspiration from natural or social systems to navigate complex problem spaces effectively. The field profile display in Fig.4.
Fig. 4 Demonstration of Fano resonance, FR1 and FR2, using magnetic field distributions (|Hz|) at (630 nm (a), 780 nm (c)) and (640 nm (b), 740 nm (d))
The effects of different noble metals display in Fig.5.
Fig. 5 The transmission of different noble metals.
As injected light comes from two through and drop ports. Inverse behavior of these ports calculated in Fig.6.
Fig. 6 The transmission in through and drop ports
when the thickness of the metal waveguide increases (see Fig. 7 (b)), the continua state is almost disappeared, and the transmission spectrum takes on a symmetric Lorentzian linestyle. The above characteristics indicate that we can tune the Fano resonance by changing the thickness of the metal waveguide.
3.2 Refractive index sensing
Refractive index sensing is a technique used to measure the refractive index of a substance, which is a dimensionless value that describes how light propagates through that substance. It is commonly used in various fields including chemistry, biology, and physics for applications such as detecting biomolecules, monitoring chemical reactions, and studying materials properties. The principle behind refractive index sensing is based on the fact that the speed of light changes as it passes through different mediums with varying refractive index. The effect of various L plots in Fig.7.
Fig. 7 The effect of L1.
Comparison Table is provided (see Table 1). In this realm some valuable works are presented [68-70].
Table 2 benchmark of the work.
Refrence | Frequency range | Sensitivity | Structure | Footprint (nm×nm×nm) |
Zhang [65] | Near infrared | 1060 | MIM Waveguide | 800 × 800 × 1000 |
Zafar [66] | Near infrared | 1100 | MIM Waveguide | >400 × >1000 × >1000 |
Zafar [67] | Near infrared | – | Split-Ring Metasurface | 700 × 700 × 110 |
This Work | Visible | 1160 | Split-ring resonator | 700 × 1000 × 100 |
4. Conclusion
Here, Fano resonance in plasmonic planar split-ring resonators, a tunable refractive index biosensor is proposed. It was shown variation of refractive indices leads to various exited modes. Such sharpness is an indication of narrow FWHM with the value of 50 nm, which in turn translates into high sensitivity as high as 1160 nm/RIU with large FoM of 33. Furthermore, thanks to the introduction of hexagonal resonators coupled with the Fano effects, the biosensor demonstrated extremely high Q-factor as large as 31 at the resonant wavelength of 740 nm. This, apparently, leads to small resonant losses and high integration which can be undoubtedly beneficial for a biosensor. Fano resonance sensing is an important application in the field of photonics and plasmonics. It involves detecting tiny changes in the environment or material properties by studying the asymmetric lineshape of Fano resonances. This technique is often used in sensor technology for detecting small variations in refractive index, temperature, pressure, or molecular interactions
Acknowledgment
This work was supported by Lorestan University.
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