Design of All-Optical Directional Coupler Using Plasmonic MIM Waveguide for Switching Applications

In this paper, we have proposed, analyzed, and verified the performance of an optimized plasmonic 10-dB directional coupler and a 3-dB directional coupler in 2-D plasmonic waveguides using the finite-difference-time-domain (FDTD) method. A plasmonic 10-dB directional coupler and a 3-dB directional coupler are based on the metal–insulator-metal (MIM) slab waveguide and analyzed at the telecommunication wavelength (λ) of 1550 nm. Here, coupling and transmission characteristics are analyzed with the optimized separation distance between the two parallel waveguides. The developed approach ensures the minimization of the crosstalk and overall directional coupler length via simultaneous adjustment of the separation distance between the parallel waveguide and the length of the linear waveguide. Then, an optimized structure is acquired by trading off between coupling length and separation distance. The proposed 10-dB directional coupler and 3-dB directional coupler feature good energy confinement, ultra-compact, and low propagation loss, which has potential applications in photonic integrated devices, optical signal processors, and other all-optical switching devices.

In this paper, the structure of the optimized 10-dB and 3-dB directional couplers is proposed. The compact design of the directional coupler is proposed in the footprint of 8μm × 4μm . The proposed design is verified using the FDTD [1,6,7,15,19,27,29,30,32,41,43] method. There is much professional software to carry out the FDTD method. The software used to carry out the FDTD method is opti-FDTD. In this paper, the optimized design of 10-dB and 3-dB directional couplers is discussed in the "Design of Optimized Directional Coupler" section and the functionality of both the couplers is presented in the "Simulation Results and Discussions" section. Finally, the conclusion of the paper has been deliberated.

Design of Optimized Directional Coupler
The theoretical modeling of a directional coupler is represented that agrees with the simulation value, which is simulated and optimized with the professional software opti-FDTD. The properties of a directional coupler are bandwidth, directivity, and impedance matching. The coupling length for the upper input port can be defined as C(dB) = 10 log dB. An isolation of a directional coupler is defined as I(dB) = 10 log P TP P IP dB . The directivity of a directional coupler is directivity (dB) = isolation (dB) − coupling (dB). In this paper, the optimized 10-dB and 3-dB directional couplers are designed using a plasmonicbased MIM waveguide within the footprint of 8μm × 4μm . The structure of an optimized directional coupler is designed using plasmonic MIM configuration. For the desired operation of the directional coupler, the structure is constructed using two S-Bend and one linear waveguide. The width of the directional coupler and refractive index used in the channel is 0.5 µm and 2.01, respectively. The continuous wavelength of 1.55 µm exceeds the transverse magnetic (TM) mode with the input power of 0.0317 W/m (high intensity) and 0.017 W/m (low intensity). The design of an optimized directional coupler is represented in the XZ plane as shown in Fig. 1.
In the proposed design, the vertical input plane is used for the input port (upper input). This input port is used to send the input signal. The signal applied at the input port through the reference input port is very essential to get at the output port. The output power is detected by using the observation point at the coupled port (output 1) and through port (output 2).

Design of 10-dB Directional Coupler
In a 10-dB directional coupler, the input is given at the input port (upper input), and the output is detected at the through port (output 2). Hence, the lower input port is treated as an isolated port, and no power is at the coupled port (output 1). When the input is given at the lower input port, the output is detected at the coupled port (output 1). Hence, the upper input port is treated as an isolated port, and no power is at the through port (output 2) shown in Fig. 1. The separation distance between the two linear waveguides is less The high-intensity level input is applied at the input port (upper input) in a perfectly matched layer (PML) boundary condition where the air has been taken as a cladding material.

Design of 3-dB Directional Coupler
A 3-dB directional coupler is used to split an input signal into two signals of equal amplitude and a constant 90 • or 180 • phase difference. For designing a 3-dB directional coupler, the separation distance between two linear waveguides is more than 4 µm but less than or equal to 6 µm. An input signal is applied in the input port (upper input), and the output power is measured at the coupled port (output 1) and through port (output 2), where the lower input port is treated as an isolated port and vice versa. In the proposed design, the separation distance between two linear waveguides is taken as a constant where the coupling length varies from 3.2 to 2 µm to get a good result. The high-intensity level (logic "1") is applied at the upper input, i.e., 0.0317 W/m.

Simulation Results and Discussions
The continuous wave (CW) source is fed to the directional coupler to control the signal with the transverse magnetic polarization and the half-width of 0.5 µm with a wavelength of 1550 nm. The FDTD method is used here to analyze the directional coupler due to its simplicity in both concept and implementation. The PML is used as a boundary condition because of its ability to restrict almost all reflections during the propagation of the wave. The proposed design is analyzed with the mesh size of ∆x = 0.0738 µm and ∆y = 0.0738 µm, which is very small enough to capture the change in the magnetic field. According to the above parameters, the analysis has been done.

Simulation Results of 10-dB Directional Coupler
The design of a 10-dB directional coupler is verified by the FDTD method. In this case, the separation distance between two linear waveguides is kept constant, but the coupling length is varied from 2.6 to 0.9 µm to get the best result, which is shown in Table 1. The propagation of light through the 10-dB directional coupler is shown in Fig. 2. In Fig. 2a, the input is applied at the upper input port and the output at the through port; similarly, in Fig. 2b, the input is applied LC = 2k , where k = wavelength dependent constant at the lower input port and the output at the coupled port as per Fig. 1. From the above Table 1, the extinction ratio is shown with the variation of coupling length. The extinction ratio between the optical intensity at the on state and the off state is determined by Eq. (1): where P ON is the output power at the on state, and P OFF is the power at the off state. Based on the above equation, the ER is calculated as shown in Table 1. When the coupling length is 1.8 µm and 1.9 µm, the proposed design ER got more desired results.
In Fig. 3, the performance analysis between ER and coupling length is shown. The best ER found out at the coupling length of 1.9 µm is 9.99 dB.

Simulation Results of 3-dB Directional Coupler
For the designing of a 3-dB directional coupler, the coupling length is varied from 3.2 to 2 µm, and the normalized output power is calculated. In the case of a 3-dB directional coupler, the input power is equally split into two equal powers of amplitude at the coupled port (output 1) and through port (output 2). The normalized output power varies with the coupling length is shown in Table 2 where we got the maximum efficient value at the coupling length of 2.4 µm and the wavelength of 1.55 µm.
Propagation of light through a 3-dB directional coupler is split into two equal power amplitudes, which are shown in Fig. 4. In Fig. 4a, the input is given at the upper input (1) Extinction Ratio (ER) = 10 log 10 P ON P OFF of high intensity and the output power detected at both the output, i.e., coupled port (output 1) and through port (output 2); and in Fig. 4b, the input is given at the lower input of high intensity and in a similar fashion; the output is detected at the coupled port (output 1) and through port (output 2). In Fig. 5, the graph between output port power versus coupling length is shown wherein both the ports have been shown, i.e., through port power as well as the coupled port power. The best result is found at the coupling length of 2.4 µm where the through port power is 0.49 dB, and the coupled power is 0.48 dB.
The comparison table with respect to the previous and the proposed work is shown in Table 3. Fig. 2 Propagation of light through a 10-dB directional coupler. a Input is given at the upper input port; b input is given at the lower input port Fig. 3 Result analysis of a 10-dB directional coupler: coupling length versus extinction ratio  . 4 Propagation of light through a 3-dB directional coupler. a Input is given at the upper input port; b input is given at the lower input port  Insertion loss (dB) n.r. a n.r. a 0.756 n.r. a n.r. a

Conclusion
A novel and compact design of 10-dB and 3-dB directional couplers using a plasmonic waveguide has been proposed and successfully verified using FDTD. The design of both the directional couplers is constructed on the footprint of 8μm × 4μm and the continuous wavelength of 1.55 µm. In simulation results and discussion, some parameters like extinction ratio and normalized output power at the coupled port and through port obtained 9.99 dB,0.48 dB, and 0.49 dB, respectively. The directional coupler has numerous applications in signal routing and sample monitoring and can be useful for developing optical circuits in the future.