3D Fringe Pattern Coding and Recognition Using Plasmonic Sensing Circuit

3D interference fringe pattern recognition using a plasmonic sensing circuit is proposed. The plasmonic sensing in the form of a panda ring comprises an embedded gold grating at the microring center. WGM (whispering gallery mode) is observed at the microring center with suitable parameters. The dark soliton of 1.50 µm wavelength excites the gold grating which leads to electron cloud oscillation and forms the electron densities where the trapped electrons inside the silicon microring are transported via wireless connection using WGM and cable connection. The spin down ↓1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| \downarrow \right\rangle\left( {\left| 1 \right\rangle } \right)$$\end{document} and spin up ↑0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| \uparrow \right\rangle\left( {\left| 0 \right\rangle } \right)$$\end{document} result from the electron cloud oscillation. By using the changes in gold lengths, the excited electron pattern recognition can be manipulated, where the values “0” and “1” are useful for pattern recognition. The fringe patterns of the plasmonic interferometric sensor are recorded, which means that the novel 3D pattern recognition can be possibly implemented and used in many applications. Therefore, the plasmonic sensing circuit can be used to form the quantum code, quantum encryption, quantum sensor, and pattern recognition.


Introduction
Pattern recognition involves the observation and recognition of regularities in a data set, which is generally classified according to the procedure or method used in generating the patterns. In other words, it involves recognizing patterns in data automatically by using pattern recognition systems. Pattern recognition systems use different mathematical models and algorithms in recognizing patterns in data sets. Several researchers have developed different pattern recognition systems that have been applied in recognizing patterns in different data sets [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Motivated by the abovementioned works, this present work has proposed a pattern recognition system. The principle behind the operation of the pattern recognition system is the space-time function. The pattern recognition system consists of a plasmonic sensing circuit. The plasmonic sensing circuit which is in the form of a panda ring comprises gold gratings embedded at the microring center and is useful for wide applications due to the nonlinear effect it exhibits. The plasmonic sensing circuit is employed for the construction and recognition of 3D fringe patterns that result from the interference of the input light of the circuit. Interference fringe patterns involve the merging of two or more sources of light and these patterns have valuable information for various applications. The interference fringe can also be formed when two light waves of the same phase, frequency, and amplitude respectively meet at a point and are superimposed. To produce interference fringe patterns, different instruments are used for this purpose. One such instrument is the interferometer, which comes in different shapes and sizes, but the main working principle is the interference of light from different sources to produce the interference fringe patterns [20]. There are two main kinds of interferometer, namely classical and quantum interferometer. Classical interferometer makes use of classical resources to produce classical interference fringe while quantum interferometer makes use of quantum resources to produce quantum interference fringe. The plasmonic sensing circuit in this present work has been employed for 3D quantum interferometer [21]. In a simulation, two programs are employed. Firstly, for simulating the plasmonic sensing circuit and the observation of the whispering gallery mode (WGM), the OptiFDTD software is used. Secondly, extracted parameters from the OptiFDTD results are used by the MATLAB program to simulate 3D interference fringe and the results have been interpreted for 3D interference fringe pattern recognition.

Background
The 3D pattern recognition system is given in Fig. 1, where the plasmonic sensor is formed by a gold grating driven by a space function. The input source is a soliton pulse, from which the electron cloud is generated by the whispering gallery mode (WGM), which transport in the circuit. The transport electrons can be controlled by the space-time input function. The change in electron cloud densities can transfer to plasmonic sensors and transported electron clouds, which can be applied for pattern recognition using the interference fringes related to the electron transport projections.
The input source is the space function called a dark soliton pulse, given by Eq. (1) [22].
The dark soliton pulse forms the input light of the circuit where in Eq. (1), B , z , T 0 , L D , and T are the amplitude of the input light, propagation distance, initial time of the soliton pulse, length dispersion, and final time of the soliton pulse respectively.
At the add port ( E add ) of the pattern recognition, the input light multiplex with the time function is multiplexed by the space-time function signal, which is employed to form the spin projection given by Eq. (2).
where in Eq. (2), the e ±i t is the control time and ± signs indicate full-time slot axis. The pattern recognition system generates fringe patterns by means of interference of the input light as described by Eq. (4) [23], and the fringe contrast (V(ΔI)) is given in Eq. (4). (3) The 3D pattern recognition system, where (a) fabrication system, where nonlinear phase modulator is labelled NLM. The microring center has embedded gold gratings. The reference and sensing arm tips have gold layer, (b) sensor circuit, where E in (input port), E add (add port), E d (drop port), and E th (throughput port), microring center radius is labelled Rd, small ring radii are labelled RL, and RR are the side ring radii, while coupling constants K 1 − K 4 . The other parameters are given in Table 1. The feedback is protected by applying the isolator where I, I 0 , p e , N, λ 0 ,r A , r B , D, V(ΔI), and k ij are the output irradiance, input source irradiance, waveguide elastic coefficient, waveguide effective refractive index, wavelength of light source, waveguide end reflection coefficients, arm length difference, fringe contrast, and amplitude coefficients, ΔI 1 − p e , Δλ 1 , H q, , and Δλ are the mode spacing, mode amplitude, and spectral width respectively. The Drude model [24] describes the behavior of the electrons in the gold grating as given in Eqs. (5) and (6) as: where 0 , n, m, e , and are relative permittivity, electron density, electron mass, electron charge, and angular frequency. At resonance, angular frequency becomes plasma frequency given as: From Eq. (6), the electron density n = 2 p e 2 0 m , the output fields of the pattern recognition system are described as (Prateep et al. 2016) where the terms m 2 -m 6 are constants in Eqs. (7) and (8)  From the system's output in Fig. 1, the normalized intensities are written as [25] The nonlinearity also known as Kerr effect exists throughout the system and is included in the n=n 0 + n 2 I = n 0 +n 2 P∕A eff equation, where n, n 0 , n 2 , I, P, and A eff are refractive index, linear refractive index, nonlinear refractive index, optical intensity, and effective core area, respectively. The Bragg wavelength = B 2n e Λ , where Λ and n e are grating period and gold grating's effective refractive index.

Results and Discussion
The OptiFDTD and MATLAB programs were used for the simulation. The OptiFDTD of version 12.0 [26] is firstly used for simulating the fabricated system as shown in Fig. 1a. The input light (dark soliton) of 1.50 µm wavelength enters the system via the input port as given in Eq. (1) and the system outputs are described in Eqs. (7) and (8). The small side rings also known as the phase modulators induce the nonlinearity effect in the plasmonic sensing system and the WGM is observed at the microring center with optimized parameters in Table 1 as shown in Fig. 2. The nonlinearity effect enables the trapping of light at the microring center. The number of time steps employed in simulation is 20,000, which was applied for the resonant condition. The embedded gold gratings produce the Bragg wavelength when polaritons induced by the gratings lead to dipole oscillations. The MATLAB program uses the extracted parameters from the OptiFDTD results as a second step in simulating the 3D fringe pattern. The schematic diagram in Fig. 1b outlines the 2 p e 2 0 m ] is formed by the electron cloud oscillations. In manipulation, the change in the trapped electron density is formed by changing the gold sensing arm length.
The length of the gold layer at the tip of the reference arm is fixed, while for the tip of the sensing arm, it is varied. The space signal is multiplexed with time at the add port to produce the space-time function as written in Eq. (2), in which the electron spin projection can be applied. The interference fringe is formed by the reflected and sensing arms, which is described in Eq. (4). When the length of the gold layer is changed at the sensing arm, it changes the detector's output as written in Eqs. (9) and (10). The final output is detected at the drop port, where the spin down and spin up of the trapped electrons are the projections from the x-y, x-z, and y-z planes, respectively. The trapped electron is transported along the z-axis, which is lead to the construction of the 3D interference fringe pattern. By using the space-time control, the required spin projection can be obtained. Figure 3a-c is the 3D interference fringe pattern for three different gold lengths of 100 nm, 200 nm, and 300 nm where the obtained codes can form the pattern recognitions. The interaction  Table 2. The specific codes of the 3D electron spin projections can be formed. The spin up is 0 and spin down is 1. The transporting electrons can be configured as no code, which leads to having the triple codes as [0, -, 1]. The sign "-" represents the code of transmitted electrons without the projection.

Conclusion
A plasmonic sensing circuit for the construction of a 3D interference fringe pattern is proposed. WGM is generated and excited by the embedded gold gratings at the microring center. The trapped electrons are excited and interfered by the applied stimuli. The plasmonic sensing circuit produced the transport electron cloud that can be applied to form the quantum interference based on the Michelson interferometer. The interference fringes are formed by the reflected sensing and reference arms, from which the fringe patterns can be formed by the trapped electron interference and detected at the detector. The 3D interference fringes are constructed from the trapped electron spin down �↓⟩(�1⟩) in the x-axis and spin up �↑⟩(�0⟩) in the y-axis, respectively, while the trapped electrons propagate in the z-axis. In application, a proposed circuit can be applied to pattern any form of disturbances, which can be coded and used for pattern recognition and recovery. Moreover, the high-density quantum codes known as quantum cellular automata (QCA) can also be applied by the proposed circuit, where the changes in the electron cloud spins can be identified and specific codes obtained.