Distributed MEMS Sensors Using Plasmonic Antenna Array Embedded Sagnac Interferometer

A micro Sagnac interferometer is proposed for electron cloud distributed sensors formed by an integrated (micro-electro-mechanical systems) MEMS resonator structure. The Sagnac interferometer consists of four microring probes integrated into a Sagnac loop. Each of the microring probes is embedded with the silver bars to form the plasmonic wave oscillation. The polarized light of 1.50 µm wavelength is input into the interferometer, which is polarized randomly into upstream and downstream directions. The polarization outputs can be controlled by the space–time input at the Sagnac port. Electrons are trapped and oscillated by the whispering gallery modes (WGMs), where the plasmonic antennas are established and applied for wireless fidelity (WiFi) and light fidelity (LiFi) sensing probes, respectively. Four antenna gains are 2.59 dB, 0.93 dB, 1.75 dB, and 1.16 dB, respectively. In manipulation, the sensing probe electron densities are changed by input source power variation. When the electron cloud is excited by the microscopic medium, the change in electron density is obtained and reflected to the required parameters. Such a system is a novel device that can be applied for brain-device interfering with the dual-mode sensing probes. The obtained WGM sensors are 1.35 µm−2, 0.90 µm−2, 0.97 µm−2, and 0.81 µm−2, respectively. The WGMs behave as a four-point probe for the electron cloud distributed sensors, where the electron cloud sensitivities of 2.31 prads−1mm3 (electrons)−1, 2.27 prads−1mm3 (electrons)−1, 2.22 prads−1mm3(electrons)−1, and 2.38 prads−1mm3(electrons)−1 are obtained, respectively.


Introduction
Sagnac provided the earliest demonstration of the viability of an optical experiment capable of demonstrating the state of rotation of a frame of reference, by making measurements within that frame. The fringe pattern recorded at the output of this interferometer is sensitive to any phase difference between the two opposing propagation beams. Sagnac interferometer is one of the interferometer types, which can be applied in many applications [1][2][3].
The principle is that the Sagnac interferometer setup usually involves a ring configuration where the light beam splits into two beams. The two beams travel around the ring path but in opposite directions, and the two beams undergo interference on returning to the entry point of the Sagnac interferometer. There are different types of Sagnac interferometers that have been designed, developed, and employed for sensing applications [4][5][6][7][8]. The microscale system known as micro-electro-mechanical system (MEMS) technology is used to develop resonators for various applications [9][10][11][12], where the resonators such as panda ring, micro ring, and MZI have been applied. Recently, microring resonators have been widely used in both theoretical and experimental works [13][14][15][16], where the realistic applications have been confirmed. Various works of MEMS using microring resonators have also been found [17][18][19][20]. The review of the micromachined resonator is presented by Abdolvand et al. [17], where the basic model with the electric circuit, resonant modes, and fabrication process are explained. Another MEMS application is the accelerometer-based optical modulator using MZI was presented [9], which was fabricated on silicon-on-insulator, where one branch of MZI is fixed, and another branch uses a floating waveguide. The waveguide-based MZI and gyroscope were already designed and presented [21,22]. Other forms of MEMS and interferometers have been proposed, where Arumona et al. [23] have proposed the use of microring resonator embedded Farby-Perot interferometer, which can be useful for sensing applications, especially for nano/microscale measurement regimes. The Fabry-Perot structure is different from the Sagnac one. Both are designed and used for microring structure and space-time control, where Fabry-Perot one has applications in quantum spectroscopy, quantum sensor, and microscopy regime. More details of interferometers and microring resonators can be found in the given references [24][25][26][27]. A microring embedded Sagnac interferometer is proposed for an integrated MEMS resonator structure, which can be applied for nano/microscale sensors, especially for micromachine applications. The integrated MEMS resonator provides compact, lightweight, and low-cost devices. The use of the integrated MEMS resonator structure has been proposed in various applications [28][29][30][31]. The integrated photonic circuits have also been applied in quantum communication and molecular sensing [32].
In this work, the proposed planar waveguide Sagnac interferometer dimensions are in the form of the integrated MEMS resonators. The main emphasis of the current work is to design an integrated Sagnac interferometer for electron cloud sensors. Four microrings are embedded with the silver bars at the center of the microrings, from which the electrooptic sensing probes can be formed. An isolator is used at the input to control the reflected signal. Four whispering gallery modes (WGMs) are formed by the nonlinear effect coupled by the two side rings, from which the electron cloud is trapped and oscillated by the plasmonic waves. These WGMs act as four-probe sensors.
The polarized laser is fed into the Sagnac interferometer, from which the output is split by a beamsplitter. The OptiFDTD software is employed for the design and simulation, while the Matlab program employs the extracted parameters from the simulation results to plot the graphs and obtain other results. In this current work, the Sagnac interferometer structure waveguide for brain interfacing device sensors is proposed. The polarized laser is applied to form the quantum distributed sensors. The quantum sensors and human quantum consciousness investigation can be applied using the electron cloud distribution within the brain-device interfacing system.

Theoretical Background
The Sagnac interferometer circuit is shown in Fig. 1. The input signal is the polarized laser [23,33], which is given by an Eq. (1): where k z = 2 is the wave numberof the wave vector in the z-axis, is the wavelength, E 0 is the initial amplitude of the field, and z is the propagation distance in the z-axis.
The propagation of light pulse within the nonlinear material and in refractive index ( n ) is given as [23,33] where n 0 , n 2 , I and P , and A eff are the linear and nonlinear refractive indices, optical intensity and optical power, and effective core area, respectively. The light pulse follows the two paths for propagation which are clockwise and anticlockwise. After traveling through two paths, a phase shift is introduced in the output pulse.
The electron behavior of the silver bars at the four center microrings is described by the Drude model [21], which is given as where n e is the electron density, m is the mass, is the angular frequency, 0 is the relative permittivity, and e is the electron charge. The plasma frequency ( p ) at the resonance is obtained from the angular frequency, which is given by Eq. (4) [21]: where A, ω, and t are amplitude, angular frequency, and time. A space-time modulation signal is applied to achieve polarized output. The ± shows both axes of time.
The excited electrons are trapped inside the four microring resonators, where the four of WGMs' formations are taken place. The output at throughput ( E th ) and drop ports ( E dr ) are given by [21,34] where m 2, m 3, m 5, and m 6 are constants. The system outputs are normalized intensities, which are given as Fig. 1 The device fabricated/simulated structure of proposed work, where a micro-electron cloud sensors network system E in , E th , E dr , and E add are electric fields at input, throughput, drop and add ports, respectively. κ is coupling constants. PBS polarizing beamsplitter, PD photodetector. The polarized electron cloud components can be obtained, b an equivalent sensing probe circuit. The micro rings are embedded with silver (Ag) nano-bars. The optical isolator is applied to project the feedback to the laser source where I th , I in , and I dr are the throughput, input, and drop port intensities, respectively. The phase shift is given in Eq. (10) [35]: where 2 , 4 are coupling coefficients, is insertion loss, α is attenuation coefficient, β is propagation constant, and L = 2 r , where r is the radius of the center microring.
The integrated system for the microring distributed electron cloud sensor network is designed and simulated in OptiFDTD. The four microring circuits inside the Sagnac form the WGM. The designed system is explained using Eqs. (1), (2), (3), (4), (5), (6), (7), (8), (9) and (10). Figure 1 shows the designed structure of the microring distributed electron cloud sensors system. The input signal is applied at the input port. The input light is a polarized laser. The materials of Sagnac and microring are silica and Si, respectively. The light travels in the upper and lower branches of the Sagnac loop. The Sagnac loop is embedded with four microring resonator circuits. The radius of center microring (R D ) is bigger than the side ring radius (R L , R R ). The design parameters of the proposed system are shown in Table 1. The applied microring circuit ports depend on the light flow direction in the Sagnac loop, which is the two-way propagation, where the Sagnac closed loop is the required result.

Methods
The system is designed and simulated in OptiFDTD for 20,000 time-steps. The data is extracted from OptiFDTD, and graphs are plotted using MATLAB software, where Figs. 2, 3, 4, 5, 6 and 7 show the results of the designed system. The working of the designed system is as follows. First, the input signal of wavelength 1.50 µm is applied at the input port, which is a polarized laser as shown in Eq. (1). Half-light energy propagates into the upper branch (upstream) and the other half into the lower branch (downstream) directions, respectively. The signal flow of the upper branch is in the clockwise direction. The lower branch is the anticlockwise direction, which is shown in Fig. 1 where four microrings are integrated with the Sagnac loop. The two rings are with the upper branch and the other two with the lower branch. The micro rings are embedded with silver nano-bars. Light propagates into the input port of microring-1(antenna-1) and then from the throughput port of antenna-1 enters into the input port Similarly, from the throughput signals of antenna 4, enter the input port of antenna 3 and from the throughput of antenna 2 to antenna 1. Both paths of propagated lights return at the 3 dB coupler. The optical isolator is applied at the input port to prevent the reflection of the backlight. The light goes into outer microring at the output port. The propagation of the light pulse in the nonlinear material is given by Eq. (2). The real-time experiment of the Sagnac interferometer consists of a beamsplitter. Here, the proposed system is manipulated using space-time modulation at the add port of the microrings. The Sagnac output enters into the microring, which is polarized light. The light propagates inside the microring circuits, from which the phase shift between the polarization components is obtained by the space-time projection control. The Kerr effect is a nonlinear effect induced by the system, and with suitable parameters, as shown in Table 1, where the WGMs are formed. The WGM is the trapping of light at the center microring. These WGMs form the antennas inside the Sagnac which consist of the trapped electrons resulting from the illumination of the silver nano-bars by light at the center microring. Figure 2 shows the graphical results of the simulated structure.  Figure 2a shows the formation of the four WGMs at the center microrings. Figure 2b shows the plasmons that propagate through the system with intense electromagnetic field. Figure 3a shows the frequency and input intensity plot of the four WGMs.  Figure 4 shows the antenna gain plot. Antenna gain is plotted by varying the input power from 10 to 15 mW. A linear trend of gain is achieved with input power. The gain of antennas 1 to 4 are 2.59 dB, 0.93 dB, 1.75 dB, and 1.16 dB, respectively. Figure 5 shows the  Table 1, where z is the propagation axis antennas' directivities. Equation (5) gives the space time applied at the add port, and Eqs. (6) and (7) give the microring output at throughput and drop ports. The output at the throughput and drop ports are normalized using Eqs. (8) and (9). Figure 6a-b are the plot of the normalized electron density of antennas 1 to 4 in the frequency domain and wavelength domain. The frequency domain is employed for the WiFi (wireless fidelity) band, while the wavelength domain is employed for LiFi (light fidelity) band. Antennas 1 to 4 are recognized for both WiFi and LiFi transmission. Gain and directivity are calculated using the standard formula [21,37]. Figure 7 shows the output intensity plot of the four WGMs. The input power is varied from 10 to 15 mW. A linear trend of the output intensity of the four WGMs is achieved with input power. The sensitivities of 1.35 µm −2 , 0.90 µm −2 , 0.97 µm −2 and, 0.81 µm −2 are obtained, respectively. The plasma frequency and electron density are related as given in Eq. (4). In the silver nano-bars, the electron density oscillations depend on the plasma frequency. Figure 8  The motivation is to design and model the quantum distributed sensors using large area MEMs sensors. The trapped electron clouds are plotted in terms of electron components (spins) density and used for distributed sensors. The new findings are the MEMs sensors and four-point probe technique, which can apply to largearea sensors using the distributed sensing probes. It has the potential of a brain-interfacing device, where selfcalibration among the four-point sensing probes can be applied. From Fig. 1, the trapped electron clouds are distributed within the circuit. The polarized control is applied to the sensing probe add port. The total electron cloud phase shift of each sensing probe within the system is given by Eq. (10), which is obtained by the polarized electron cloud phase shift of Eq. (5). The result of each probe can be identified by the different traveling times. A polarizing beamsplitter is arranged before the detector at the Sagnac interferometer output, from which the electron cloud spin-up or spin-down components can be obtained by polarization orientation arrangement. In manipulation, when the input light power varied, the sensor sensitivity relates to electron cloud density can be obtained.

Conclusion
A Sagnac interferometer and microring integrated circuit for electron cloud sensors is proposed. When light propagates inside the Sagnac loop, it goes in both clockwise and anticlockwise directions. The microrings are embedded with silver nano-bars. The electron cloud is trapped and oscillated inside the microrings, where the WGM formation takes place and the plasmonic wave generates. Four plasmonic antennas formed at the center microrings, where the frequency wavelength spectra are employed for WiFi and LiFi sensing probes, respectively. The proposed MEMs sensors can be applied to sense the physical parameters related to the electron excitation, where the changes can be detected and measured. The new findings are the MEMs sensors and four-point probe technique, which can apply to large-area sensors using the distributed sensing probes. It has the potential of a brain-interfacing device, where self-calibration among the four-point sensing probes can be applied. In application, the deep-brain signal detection related to quantum consciousness for human deeplearning investigation can be realized.