# An \(N\)-Port Universal Multimode Optical Router Supporting Mode-Division Multiplexing
## 2 Materials and Methods  
An optical router unit has the function of transmitting and steering the optical signals; therefore, it is very important to design the universal optical router to realize MDM. In the design of a traditional single-mode router, the optical router consists of single-mode optical waveguides and basic optical switching devices. Similarly, MDM-OR, which allows multimode transmission, is composed of multimode waveguides and basic optical switching devices. These devices include multimode bendings and multimode switching elements. Figure 1 is the general design scheme of component devices of optical transmission unit supporting mode multiplexing. We use multimode waveguide to replace the traditional single-mode waveguide, multimode bending to replace the single-mode bending, and multimode switching element to replace the \(1\times 2\) crossing switching element (CSE). These basic optical switching devices based on multiple modes are analyzed in detail below. Figure 1: Replacement scheme of component devices of optical transmission unit supporting mode multiplexing. Figure 2 shows the multimode bending. The insertion loss is generated when the input signal of multimode bending is TE\({}_{0}\), TE\({}_{1}\),..., TE\({}_{x}\) mode. Unlike the single-mode bending, the multimode bending can transmit TE\({}_{0}\), TE\({}_{1}\) and other modes simultaneously. When different modes pass through multimode bending, the corresponding loss is also different, which can be calculated by Equation (1). The \(P_{int}\) is the input power, the \(P_{intx}\) is the multimode bending output power of the TE\({}_{x}\) (\(x\) is the mode order of the signal) mode, and the \(L_{mbx}\) represents the bending loss coefficient of the TE\({}_{x}\) mode via the multimode bending. In addition, inter-mode crosstalk noise occurs when TE\({}_{0}\), TE\({}_{1}\),..., and TE\({}_{x}\) modes pass through a multimode bending. When the input is TE\({}_{m}\) mode, the output is TE\({}_{m}\) mode and a small amount of TE\({}_{n}\) mode. Equation (2) describes corresponding inter-mode crosstalk noise, where \(Cmb_{mm}\) represents the inter-mode crosstalk noise coefficient of TE\({}_{m}\) mode converted to TE\({}_{n}\) mode. \[P_{mbx} = P_{in}\cdot L_{mbx} \tag{1}\] \[P_{mb,mn} = P_{in}\cdot Cmb_{mn} \tag{2}\]  
In the traditional single-mode optical router, the microring resonator acts as a crucial optical element for transmitting optical signals, which can change or maintain the transmission direction of optical signals. At present, most of the microring resonators are composed of single-mode waveguides. In order to achieve multimode transmission, it is necessary to design an optical device that can maintain or change the transmission direction of multiple modes. The symmetrical switching element proposed in this paper can realize this function, and its schematic diagram is shown in Figure 3.  
Figure 3: Multimode switching element. The red and blue arrows represent the trajectories of TE\({}_{x}\) mode transmission in different states of MR.  
Figure 2: Multimode bending. It can be seen from Figure 3 that the multimode switching element includes mode (de)mu-ltiplexers, single-mode waveguides, microring resonators, single-mode bendings, and single-mode waveguide crossings. When the signals carry multiple modes are input from Port I, they are first directly demultiplexed to the fundamental modes through the mode demultiplexer. Immediately after, their transmission directions are changed by the microring resonators, which determine whether the fundamental modes are transferred to Port III or Port IV. Micoring resonators have ON state and OFF state. When the microring resonator is in the ON state, it means that the wavelength of the input optical signal is equal to the resonant wavelength of the microring resonator, and then the optical signal is coupled into the microring and transmitted to Port IV.