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A compact 1 × 3 two-mode selective silicon photonic router/switch using two tunable phase shifters

In this work, we propose a design in the proof-of-concept of a 1×3 two-mode selective silicon-photonics router/switch. The proposed device composes of a Y-junction coupler, two multimode interference (MMI) couplers, and two phase-shifters on the silicon-on-insulator (SOI) rib waveguides. The input modes of TE0 and TE1 can be arbitrarily and simultaneously routed to the yearning output ports by setting appropriate values (ON/OFF) for two tunable phase shifters (PSs). The structural optimization and efficient characterization processes are carried out by numerical simulation via three-dimensional beam propagation method. The proposed device exhibits the operation ability over the C-band with good optical performances in terms of insertion loss smaller than 1 dB, crosstalk under -19 dB, and relatively large geometry tolerances. Moreover, the proposed device can integrate into a footprint as compact as 5 μm × 475 μm. Such significant advantages are beneficial and promising potentials for very large-scale photonic integrated circuits, high-speed optical interconnects, and short-haul few-mode fiber communication systems. Received on 30 July 2021; accepted on 13 September 2021; published on 17 September 2021


Introduction
Recently, multimode division multiplexing (MDM) has received remarkable consideration due to its superior capacity for short-reach optical fiber communication systems, photonics on-chip interconnects, and photonic computing systems [1][2][3]. By combination between the MDM technique and the wavelength division multiplexing (WDM) technique on a merged platform, we can attain a multifold increase of the aggregated channel capacity, because various orthogonal mode division signals from the MDM channels can share a specific wavelength without the impacts of inter-frequency crosstalk and nonlinearity. Typically, multimode fibers using in MDM communication systems only support a relatively small number of guided modes which are thus called few-mode fibers because a large number networks (DCNs) [17] due to utilizing significant highlights of silicon photonics, such as high compactness, low loss, broad-spectrum response, reasonable manufacturing cost. Silicon photonics-based MDM devices also play the important roles to construct chip-scale systems through many photonic mode division signal processing functionalities, such as mode (de)multiplexing [18][19][20][21], mode add/drop multiplexing [22,23], mode conversion [24,25], mode routing [26,27], and mode switching [28][29][30][31]. It is seen that since the thermooptic (TO) effect has been widely applied to control the phase angle of light when traveling through the silicon waveguides [31,32], the MDM devices based on the SOI platform could operate much more flexibly via the phase-driven process by manipulating metallic microheaters. Researchers on MDM devices meet a good chance to invent as a farmer found a fertile field for sowing. For instance, a lot of reconfigurable MDM devices based on silicon photonic which are demonstrated in fact [32][33][34][35][36][37][38] or numercially simulated [39,40] can be configured quickly by using the thermo-optic conductive microheaters.
Among various functional MDM devices, currently, the conventional mode (de)multiplexers are being renovated to become the simultaneous mode-selective routers by introducing the switchable functionality which is implemented via controllable phase shifters based on thermal-optically conductive microheater [32,33,39,40]. That means, we can integrate the switchable functionality into the mode (de)multiplexers in order to realize the mode exchanging and routing functions. Such investigations are paying attention to the silicon photonics community because they can give an enhancement for the feasible and flexible allphotonic complexity signal processing functionalities. However, some recent innovative investigations on twomode selective routers are existing some drawbacks due to needing many cascaded and tailed sections or many tunable phase shifters thus leading to a relatively large size or a highly electrical power consumption.
In this paper, we introduce a proof-of-concept design of a compact 1 × 3 mode selective switch/router for two modes TE 0 and TE 1 based on the SOI material platform which utilizes a Y-junction coupler, and two multimode interference couplers, and two tunable phase shifters (PSs) controlled by two states (ON and OFF). We choose the design for two lowest order modes of transverse electric (TE) modes because they are two modes guided in silicon waveguides possessing lowest cutoff frequencies and so-called the dominant modes. In general, only the dominant mode has a sinusoidal dependence upon distance and thus possesses fields that are periodic in the wave propagating space. This structure is simpler or supports more output ports than that of the previous publications [31,32,36]. By using the numerical simulation methods, including beam propagation method (BPM) and effective index method (EIM), from Rsoft's commercial simulation tools with the sufficient enough grid sizes of ∆x= ∆y= ∆z= 1 nm for the whole device, we show that the proposed switch/router can be an arbitrary mode exchange and arbitrary mode selective router from two input modes of TE 0 and TE 1 to optional three output ports by setting suitable phase difference values for two tunable phase shifters. Furthermore, the device also verifies low insertion loss levels (> -1 dB), relatively small crosstalk (< -19 dB) levels, and relatively low fabrication tolerances over the C band.

Structure design and optimization
2.1. General description Fig. 1 illustrates a schematic diagram in the proofof-concept of 1 × 3 two-mode selective switch/router. It comprises a symmetrical Y-junction coupler, a 2 × 3 multimode interference (MMI) coupler, and a 3 × 3 MMI coupler. This designed structure is equipped with two tunable phase shifters (PSs). The function of the Y-junction coupler is to equally split the input signals to branched waveguides and convert the optical modes to fundamental mode (TE 0 ). The first MMI coupler is to straightforwardly guide two optical fields, which are transmitted from two arms of the Y-junction coupler or combine into a unique field at the central line of the first MMI coupler following the suitable phase difference from the first tunable phase shifter. Whereas, the second MMI coupler plays the role of a mode combiner to desired outputs through interference 2 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 06 2021 -09 2021 | Volume 8 | Issue 28 | e4 mechanisms according to the suitable phase difference of the second tunable phase shifters. To improve the coupling efficiency, tapered waveguides are inserted into output ports of MMI couplers before connecting to access waveguides. Design and optimization processes of the whole device are carried out via the 3D-BPM simulation method incorporated into the effective index method.
The proposed device is embedded into the rib/ridge waveguides from a standard SOI wafer. As shown in Fig.  1(b), the heights of the silicon layer and the slab layer are initially chosen corresponding to 220 nm and 120 nm, respectively. In this paper, the refractive index of Si is as equal as 3.46 and the refractive index of SiO 2 is equal as 1.444 at the wavelength of 1550 nm which are determined from the reference [41,42]. To optimize the device, we utilize the beam propagation method (BPM) and the effective index method (EIM) together [43]. The device is also designed to support the operation of only two lowest-order TE modes.

Y-junction coupler
The 1 × 2 Y-junction coupler operates as an ideal optical power splitter, and transform guided modes to TE 0 modes at the outputs. The input lights are divided equally at two output waveguides with the same phase for TE 0 input light and out of phase for TE 1 one [44]. The structure of the Y-junction coupler begins with a stem waveguide having a width W IN . This width is large enough to support the propagation for both modes of TE 0 and TE 1 . To find out the beneficial width of the stem waveguide, we use numerical simulations to investigate the refractive indices of TE modes [45]. By employing the mode solver tool, we obtain the refractive index of guided modes as a function of the stem waveguide W IN , as exhibited in Fig. 2. From the calculated diagram of effective indices of TE modes following the variation of the input stem width of the Y-junction, we select W IN = 1.2 µm at the cutoff point where the device can support only two guided modes TE 0 and TE 1 .
The Y-junction waveguide divides the optical guided modes into two ideal fields at two symmetrically branched waveguides, possessing the vertical length L S and horizontal width G S . The width of each branched waveguide is W S , which is dedicated to guiding only the fundamental modes. Two branched waveguides of Yjunction are the sinusoidal waveguides so-called S-bent waveguides because they are beneficial for reducing the power loss at a large enough radius [46,47]. In this design, we optimized the geometric structure of the symmetric Y-junction to reach an acceptable transmission efficiency when it acts in the role of an ideally optical splitter. It is well-known that when a field Ψ (x, z) is introduced in the Y-junction length of L IN and width of W IN , the output field can be estimated as [44]: where m is the order number of the coupler branches, ν is the mode-grade index of each eigenmode, and ε mν is called the power-excited-coefficient of each mode per each branch. In our design, two branches of the Y-junction has the same width W S = W IN /2 ( Fig. 1). We need to find an optimal value of the length L S of the Y-junction coupler. This process can be done via numerical simulations. To this end, we set C mν = |ε mν | 2 and investigate L S with respect to each mode TE 0 /TE 1 . Fig. 3 shows that the behavior of TE 0 power excitation is significantly different from that of TE 1 mode. Particularly, the power excitation coefficient of TE 0 fluctuates strongly from an approximate portion from 44.46 % to 44.62 %, while the similar coefficient of TE 1 mode varies slightly around 44.58 %. To achieve a balanced power between the two modes, we selected L S = 187 µm as the optimal length of the Y-junction coupler.
As can be seen in Fig. 1, two output waveguides of the Y-junction coupler are connected to a 2 × 3 MMI coupler (MMI 1 ), which is characterized by a width W MMI 1 and a vertical length L MMI 1 . The two input waveguides of MMI 1 coupler are placed at the positions of ±W MMI 1 /4, while the middle output waveguide is located right at the center of MMI 1 . To obtain the desired switching functionality, MMI 1 is designed to exhibit symmetric interference mechanisms [48]. It means that if the two input lights are in phase, the lights will be combined and directed to the center output port of MMI 1 . Meanwhile, if the two input lights are out of phase, the lights will be straightforward to outer arms of MMI 1 , respectively. These mechanisms will well operate in principle if the length of MMI 1 satisfies the following condition: where m and n are integers with m is the number of interference periods, n is the number of single images and L π is half-beat length of the MMI 1 coupler, given by where λ is the operating wavelength, n e is the effective refractive index of the core. Here W eff is the effective width of W MMI 1 , defined by [48] where n c is the refractive index of cladding layer.
In the case of TE 0 mode led, to make the device length minimum, we apply eq. (2) with m = 1 and n = 2. Through numerical simulations around L MMI 1 = 3L π /8, the optimal values for W MMI 1 and L MMI 1 are found at 6.8 µm and 43 µm respectively to obtain the smallest insertion loss at the outputs of MMI 1 .

3 × 3 MMI coupler (MMI 2 )
Three input ports of the MMI 2 coupler are then connected directly to the output ports of MMI 1 as shown in Fig. 1. To attain desirable functions, MMI 2 is designed to operate the general interference mechanism of 2 × 2 MMI [48]. It means that MMI 2 will work as a 3-dB coupler when the lights are injected to two outer input ports with a phase difference of ± π/2. Meanwhile, the light injected through the center input port will be reproduced to the central output port of MMI 2 since it has also performed the symmetric interference mechanism of 1 × 1 MMI with m = 2 and n = 1 [48]. Therefore, the length of MMI 2 is determined to be L MMI 2 = 3L π /2. Through the optimization process by the numerical simulation BPM, the optimal values of L MMI 2 and W MMI 2 are respectively found at 98 µm and 5 µm in order to obtain the highest transmission efficiency for MMI 2 .

Phase shifters (PS)
As we all know that the shifted phase of a mode field when passing through an optical waveguide does not only depend on the width of the waveguide but also depends on its effective refractive index N eff [25] as expressed in (5) by L. Soldano [40,48]. In order to demonstrate the proof-of-concept of the proposed device, we consider the dependence of such the phase angle on the variation of PS's effective index under the impact of temperature [41]. This effect is called the thermo-optic effect. For instance, heaters adjusted by external voltages may cause the refractive index change N eff of the core silicon layer [49]. The evolution phase angle change propagating through a silicon waveguide with the variable width can be calculated by the following relation [25]: where L PS and W PS are the central length and the central width of PS (as seen in Fig. 1), β 0 and β v are propagation constants of the mode fields with v being the order index of a guided mode. Based on the working principle of the symmetric Yjunction coupler, we classify the PS 1 states into two control states: ON and OFF. We set the ON-state to make the injected mode of TE 1 traveling through the Y-junction and MMI 1 to the central output of MMI 1 , whereas OFF-state is when the TE 0 mode is diverted to this output of MMI 1 . To find out the necessary phase shift for switching, we look into the N eff of PS 1 relating to two the control states [49]. First, we experientially choose the dimension values of the PS 1 . Then, we excite the mode TE 0 at the input of the Y-junction and investigate the phase difference between the outputs of two branches as a function of N eff within the range of [2.77, 2.78]. From the investigation plotted in Fig. 4a, we obtain N eff 1 = 2.747 and N eff 2 = 2.775 corresponding to OFF and ON control states of PS 1 , respectively. In our design, the phase difference caused by the variation in the width of PS 1 , and investigated as a function of W PS 1 in Fig. 4b    Otherwise, the PS 2 only works well when it is designed to make a phase deviation of ± π/2 [6]. In order to use such conditions of control states ON and OFF of PS 1 for PS 2 , the phase difference of guided mode before working through PS 2 has to be shifted a angle of ± π/2. To do this work, we investigated the width of the W S 2 which close to PS 2 (instead of W S = 0.6 µm chosen above). The investigated result in Fig. 5 shows that, the light will be shifted a phase angle of − π/2 at W S 2 = 0.657µm before entering into PS 2 . Therefore, when the PS 2 in OFF state (zero radians), the guided mode needs to be shifted a quantity of − π/2 before propagating the MMI 2 . Alternatively, when PS 2 in ON state (π radian), this phase angle is equal to π/2. Consequently, two guided modes in two cases are led to two individual outer arms of the MMI 2 . Otherwise, in the rest cases for both TE 0 and TE 1 , guided modes are traveled to the central output port of this MMI after passing through a center output port of the MMI 1 in principle with the symmetric interference mechanism [6]. As a result, all required working states of the proposed device can list in Table 1. One can see that TE 0 and TE 1 modes are always selectively routed to three different outputs of the designated device when simultaneously injecting into the input.

Performance Evaluation and Discussions
To realize and indicate feasible functions of the proposed structure, numerical simulation of BPM has been manipulated to demonstrate the operation ability in the proof-of-concept. First, we are interested in the visual electric-field pattern observation of the optical guided modes from the input port to output ports. Fig. 6 (g)-(h) shows the electric-field patterns of TE 0 and TE 1 modes at the 1550 nm wavelength. Their revolutions for all happenable cases of guided modes in Fig. 6 (a)-(f) can be briefly summarized in Table 1 that are true with the theoretically analyzed results. The upper and lower rows of Fig. 6 (a)-(f) successively show the exciting fields at the input port corresponding to TE 0 and TE 1 modes, respectively. The color bar on the right side of Fig. 6 indicates the normalized field intensity. Such six states fulfill enough cases for operation states of the proposed device, as listed in Tab. 1. One can see that distributed optical fields in all cases are clear and acceptable in our design and optimization. As shown in Fig. 6 (a)-(f), one may observe that a small number of optical power fractions of the guided modes have radiated to the outside or leaked to the cladding layers when propagating from the input port to the output ports. and inavoidable crosstalk in the multimode regions. 5 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 06 2021 -09 2021 | Volume 8 | Issue 28 | e4 To further characterize the optical performances of the suggested device, we introduce two indispensable specific parameters composing of insertion loss (I.L) and crosstalk (Cr.T), which are defined by the following expressions: Cr.T = −10 log 10 where P in is the injected power at the device input, P out is the optical power at a yearned output, P disregarded is the disregarded power propagating to a yearned output port. I.L has a relation to the total lossy power portions out of the device, Cr.T is the total crosstalked power fractions from disregarded output ports associating with a yearned output port.
In this section, we will characterize the optical performances including I.L and Cr.T for the proposed switch, corresponding to configurations of TE 0 and TE 1  This reason can be addressed by MMI 2 operating in the symmetric interference mechanism better than operating general interference mechanism in this wavelength range.
On the other hand, Cr.T has the best values within the wavelength range from 1545 nm to 1555 nm, from -25 dB to -32.5 dB, as seen in Fig. 7b. It also exhibits that Cr.T of the TE 1 mode to O 3 is the lowest in the wavelength range of 1550 nm to 1570 nm, expanding from -23 dB to -32.5 dB. On the contrary, the remaining cases fluctuate similarly with a small gap 6 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 06 2021 -09 2021 | Volume 8 | Issue 28 | e4 from 3 dB to 4 dB and reach the highest value of -19 dB. Such a good performance covering the whole Cband is a significant result for applications in shorthaul optical communication systems and photonic integrated circuits [50,51]. In order to characterize the functioning of the silicon device, evaluating the fabrication tolerances of the photonic devices is indispensable, especially, for a photonic design based on numerical simulations. Because, fabrication tolerances can come from computing algorithms of the simulation program, the resolution quality of the photolithography or electron beam lithography technologies using in the experimental manufacturing process, imperfect quality of the supplied SOI wafer, imperfect etching process, etc. Noted that, the larger fabrication tolerances are, the higher producibility can reach. In particular, it is well-known that MMI couplers typically have relatively large geometry tolerances because their widths are very large compared to typical single-mode access waveguides. Hence, in this paper, we only consider the fabrication tolerances of the device under the influence of geometrical parameters including the width of input-waveguide (W IN ), the length of MMI 1 (L MMI 1 ), the length of MMI 2 (L MMI 2 ), and the slab height layer (H S ) in the rib/ridge waveguide structure. The results investigated at the wavelength of 1550 nm are plotted correspondingly in Figs. 8 -11. The first one we can observe from Figs. 8b -11b is that Cr.T of all cases is less than -19 dB to reach the acceptable values of device fabrication tolerances. In addition, it is interesting to see that the length tolerance of two MMI couplers is very close in the gap of [-1.5, 1.5]µm, as illustrated in Figs. (9,10).
For the insertion loss cases, we inquire the similar impact of the length tolerances of L MMI on I.L (Figs. 9a and 10a) like in the cases of wavelength behavior (Fig.7a) whereas the I.Ls of ∆W IN (Fig. 8a) and of ∆H S (Fig. 11a) are behaved differently. Particularly, I.L of the three paths of TE 1 mode in Fig. 8a   of both TE 0 and TE 1 modes at Output 2 of MMI 2 . Finally, althought I.L and Cr.T are available in the ranges from -0.88 dB to -0.45 dB and -37 dB to -20 dB respectively, the tolerance of H S in Fig. 11 is the smallest, about ± 2 nm. However, such a high requirement for height tolerances is completely able to attain by using current advanced fabrication techniques for very large scale integrated circuits (VLSI), such as 193-nm lithography [52].

Conclusion
This paper presented the design of a compact 1 × 3 two-mode selective router/switch constructed from a symmetrical Y-junction coupler and two MMI couplers based on the SOI platform through numerical simulations. The proposed device could well operate in the broad wavelength range from 1530 nm to 1570 nm with absolute values of insertion loss always smaller than 1 dB and crosstalk smaller than -19 dB. Moreover, the estimated circuit footprint of the device was very compact, as small as 5 µm × 475 µm, and geometry tolerances were relatively large. Therefore, such an excellent property makes the proposed device strongly promising potential for applications in photonic integrated circuits as well as MDM-WDM systems.