In this research, we design a plasmonic refractive index sensor based on metal insulated metal waveguide (MIM) and examine it numerically.

 To design the structure of this sensor, we use five cavities with different dimensions and coordinates and two plasmonic waveguides. The resonant wavelengths and refractive index of the resonators are investigated and simulated by the finite difference time domain (FDTD) method. Due to the fact that the sensors and conduction characteristics of plasmonic waves are affected by the structure parameters, by changing the refractive index and changing the dimensions of the cavities, we can weak nor strengthen the passage coefficient in the resonant modes. As a result, we obtain the sensitivity coefficient, the competency digit (FOM) and the sensor quality coefficient.  These plasmonic sensors with a simple frame and high optical resolution can be used to measure the refractive index in the medical, chemical and food industries, and due to the special correct distribution of resonances, they are highly sensitive to changes in the refractive index of the environment.

Optical integrated circuits are one of the most important and practical tools in technology. To further exploit them and reduce barriers, compression of plasmonic structures began. These structures are made of metal and dielectric with dimensions below the excitation wavelength. Plasmonic science expresses the interaction of radiant electromagnetic waves on the surface of metals and their conducting electrons and has the ability to enclose electromagnetic waves at dimensions much smaller than the radiant wavelength in plasmonic structures. The term plasmon polariton is used to describe the cause of this married condition. Plasmonics are divided into two parts: [1] localized surface plasmons and [2] surface polariton plasmons, each of which is an application of metals and electromagnetic waves (in nanometer dimensions) in two-dimensional and one-dimensional structures. In localized surface plasmons [1], the oscillations of metal electrons and the intensification of plasmons are stimulated by the radiation beam, and the condition of the oscillation is that the frequency of the surface electrons is equal to the frequency of the radiation beam. 

The interaction of electromagnetic waves with excitation wavelength λ with a particle of size d can be studied in various numerical, analytical and semi-analytical methods.

 In this Nano volume, the electromagnetic fieldis compressed and modified.  Also, small changes in the dielectric of this nanoparticle change the surface plasmoninten sification, wavelength, absorbed and scattered beam, and the amount of these changes can be obtained by using optical characteristics. Plasmon Surface polaritons are electromagnetic waves that are coupled to surface free electrons in metals so that they can propagate longitudinally across the dielectric metal surface and have longitudinal polarization (P-polarized). One of the important applications of surface plasmon plasmon is to reduce the scattering of the electromagnetic field in optical waves and to confine the emission modes of the transverse electric field or the transverse magnetic field in the planes perpendicular to the direction of propagation. Surface plasmon amplification is an electromagnetic mode in which an electric field with TM polarization at the boundary between a metal surface and a dielectric material oscillates with paired electrons and two waves intensively occur, which increases the field strength. Electrical and sensor performance correction. Plasmonic structures are divided into metal-dielectric-metal and dielectric-metal-dielectric structures to study the propagation of waves. The most important plasmonic components are based on the structure of passive devices (such as waveguides, couplers, filters, etc.) and active devices (such as amplifiers, amplifiers, switches, modulators, etc.) and will be simulated numerically. Inactive environments are isotropic and have only one refractive index. As a result, they are unsuitable for switches and sensors, but active environments are anisotropic, and we can change the refractive index and length by applying an external factor. Plasmonic nano sensor systems are key components of optical integrated circuits that need to be developed. Parameters such as high transmission efficiency, high resolution, high quality factor, optical stability, sensitivity enhancement and adjustability in a range of wavelengths should be considered in the structure of plasmon sensors. Obtaining and improving these parameters increases the speed of information processing in optically integrated circuits. In this research, arrays of metal-dielectric waveguides and plasmonic resonators (MIM) are simulated and analyzed to design and fabricate plasmonic sensors. The aim of this work is to achieve the desired parameters in plasmonic sensors and to improve and develop it. Is. Therefore, we change the geometry of the waveguides and resonators, the refractive index of the dielectric region, and the direction of coupling to achieve our goal. Plasmonic sensors are divided into three categories based on their geometric shape: [1] plasmonic converters in which flat nanofilm is used, [2] nano sensors with periodic nanowires, and [3] nano sensors containing single nanoparticles. In this research, changing the refractive index of the rims and changing the distance of the rims is used to improve the performance and adjust the plasmonic sensor systems.

Each waveguide with any geometricshape has the ability to transmit waves and can limit their energy in one and two dimensions. This transition is interpreted by the wave equation. The geometry of a waveguide indicates its function, and the frequency of the transmitted wave determines the size of a waveguide. Maxwell's equations describe the shape of electromagnetic cross waves and the linear electricity equation describes the shape of sound waves. At longer wavelengths, wider wavelengths are guided, and at higher frequencies, narrower wavelengths are guided. Above a frequency range, the optical properties of metals are explained by the plasma model, which is the resultof Maxwell's equations, and the electrons will be dampedby collisions with the frequency υ = 1 / τ. For visible frequencies (microwave and far infrared), the spectrum of metals is very reflective and does not allow electromagnetic waves to propagatethrough them. At higher frequencies (near-infrared and visible from the spectrum) the field penetration and dissipation increase.

Then, at ultraviolet frequencies, the metals acquire dielectric properties and allow the propagation of electromagnetic waves with differentdegrees of attenuation. In the free electron model at high frequencies, the dielectric functiontends to zero, and for noble metals,generalizing this model to a frequency range greater than the plasma frequency creates a polar environment. As a result, real metals are expressed by the greeting model:

ω is the angular frequency, 

Fracture coefficient simulation and measurement methods

The proposed plasmonic resonance behavior is investigated numerically and theoretically. In the numerical approach to simulate the reflection spectrum and distribution of the optical field in the sensor structure, we use the time domain finite difference simulation (FDTD) method with perfectly matched layer boundary conditions (PML) because this method effectively reduces the numerical reflection. Gives. The uniform mesh sizes for the x and y directions are 8 and 8 nm, respectively, and the transmission line model is used to analyze the theory of structure. Two-dimensional simulation is performed, which is infinite in one dimension. The reason for this is to reduce the simulation time and achieve the desired result. The effective refractive index of a four-cavity sensor with a step of 0.01 from 1 to 1.2 in the wavelength range of 400 to 1500 nm has been calculated, which leads to a change in spectra and resonance wavelength. Figure 3 shows.

The first characteristic to be measuredfor a sensor is the S sensitivity, which is used to quantify the sensitivity of refractive index sensors:

S= Δ λ/ Δn (nm/RIU)    [2]

In this equation, Δλ is the change in resonance wavelength and Δn is the change in refractive index. In this simulation, we only change the refractive index of the middle cavity, and the refractive index of the other cavities is constant, which will make the sensor design more accurate and practical. According to Figure 3, the sensor transmission spectra have two peaks, which according to Figure 4, have the highest sensitivity for the refractive index n = 1.19 (in mode2), which is equal to 1647 nm / RIU and the lowest value for the refractive index n = 1.18 (In mode1) is equal to 0.

Using Figure 4, we analyze the refractive index and the amount of change in each wavelength to design our desired sensor. According to this diagram, there is a relatively linearrelation ship between the two parameters of resonance wavelength andrefractive index, and the TM resonancegradually shifts. Therefore, using Equation 2, the sensitivity of different wavelengths is obtained. Let (Figure 5).

According to the figure, mode 2, which corresponds to the right peak of Figure 3, is more sensitive, and mode1, which corresponds to the left peak of Figure 3, has less sensitivity. Sincesensitivity aloneis not a measure of good performance for comparing different types of sensors,and light resolution is also very important for sensors, we need two more to measure the capabilities of a plasmonic sensor: Q quality factor and FOM suitability. Higher sensitivity reduces the FOM at the desired point. Obviously, increasing the length of the cavities can improve the sensitivity performance of the sensor with a smaller FOM size, which may result in a longer light path and more energy loss, respectively. The FOM merit is obtained from Equation (3):

FOM= S / FWHM 3)

Using Equation 3, we plot the FOM competency chart

The quality coefficient is also obtainedfrom Equation 4:

Q =  λres / FWHM (4)

We see the qualitycoefficient diagram in Figure 7.

Using Equation 4 and dividing the wavelength by FWHM, the quality coefficient Q is obtainedand its value in the refractive index n = 1.19, which has the highest sensitivity coefficient, reaches 11.7935. Equations 2, 3 and 4 are the capabilities of measuring plasmon sensors obtained by changing the refractive indexin the structure. Using these three equations, we draw the graphs of sensitivity coefficient, quality coefficient and competence. The remarkable thingabout the proposed method is that its sensitivity coefficient is higher compared to previous sensors. As shown in Table 1, the proposed method offers better results compared to some similar articles. According to this table, the maximum sensitivity coefficient S among these papers belongs to the structure studied in this paper, which is equal to 1647 nm.

Plasmonic refractive index sensor is a widespread issue and has become very popular in chemicaland biological measurements because of a small changein the cavity refractive indexthat causes a large change in wave propagation properties. In this research,the latest developments in refractive index sensors basedon two plasmonic waveguides and four cavitieswith different dimensions are highlighted. This sensor is considered because with a small change in the refractive index of the middle cavity causes a significant change in the propagation characteristics of the wave. Also, as a sensor, it requires both high sensitivity (S) and high competence number (FOM) to provide excellent performance with high optical resolution. For clarityof results and for bettercomparison, the refractive index of the structure is changed from 1 to 1.2 and the resonant wavelength is calculated at each stage. Due to its high resolution resolution, this sensor can easily detect changes in the refractive index of 0.01 for materialswith a refractive index between1 and 1.2. These resultsand physical analysisdue to the small configuration size, high FOM value and high sensitivity, can lead to further development of plasmonic waveguides in the field of loss reduction and excellent light control in plasmonic structures.