1. Introduction

Silicon photonics is a promising technology for ultra-high bandwidth optical interconnects due to high index contrast and compatibility with commercial Complementary Metal Oxide Semiconductor (CMOS) processes [1]. Nowadays, modulation speed of the silicon Mach-Zehnder interferometer (MZI) and microring modulators has been approaching to a limit of 50~70 Gbit/s [2–5]. With the requirement of higher capacity, many kinds of multiplexing methods have been investigated, such as the wavelength-division multiplexing (WDM) [6], the polarization-division multiplexing (PDM) [7], and the mode-division multiplexing (MDM) [8–12]. Recently, MDM catches more and more attentions, because it can use the orthogonality of the different eigenmodes to increase the bandwidth density and spectral efficiency within a single waveguide channel. The mode converters used to convert one eigenmode to other eigenmodes play a very important role in MDM. Three methods for mode conversion have been reported, phase matching [8–19], coherent scattering [20–23], and beam shaping [24–29]. Many reported devices have achieved good performance in mode conversion, however, there are still challenges. For example, the sizes of devices based on the taper directional couplers [10], the asymmetric Y-junctions [12,14,15], and the multichannel branching waveguides [27,28] are usually large, while the asymmetric directional couplers [8,9] are sensitive to fabrication tolerance. Other devices based on grating couplers [16–19], photonic crystals [21,22,29] usually need high fabrication resolution because there are some subwavelength or ultra-fine features in the devices. Thus, realizing mode conversion is still a challenge in compromising conversion efficiency, device size, fabrication resolution and tolerance.

MZI based structure is a promising method for mode conversion. The traditional structure of MZI is based on multimode interferometer or Y junction [24,25], which suffers from above mentioned disadvantages. Recently using single waveguide such as S-bend waveguide [26] to realize the function of MZI is reported. The device can be designed compact and fabrication tolerant, but it only realizes the conversion between fundamental even and the first order odd modes so far. In principle, realizing higher order mode conversion is possible. The principle can be stated as (here we use TE polarization as the example): The Nth (N> = 1) order TE modes can be effectively regarded as a combination of N + 1 antiphase adjacent ‘TE0 modes’ (They are not the actual waveguides fundamental modes). If the designed structure allows the N + 1 antiphase components of the Nth-order mode to travel with different effective lengths thus achieving the same phase, the conversion between Nth-order TE and TE0 modes can be realized.

In this work, novel compact tapers based single waveguide designs are proposed for the mode-order conversion. By optimizing the shape of the tapers, conversions between TE1, TE2, TE3 and TE0 mode are achieved. Combining these converts, arbitrary conversion among TE3, TE2 and TE1 modes can be also achieved. The proposed converters show efficient conversion. Furthermore, the performance degradation caused by fabrication error is analyzed, showing that those devices have large fabrication tolerances.

2. Devices design

The proposed structure for TE1-to-TE0 mode converter is schematically shown in Fig. 1, which is based on a Silicon On Insulator (SOI) channel waveguide with 220 nm height covered by a SiO₂ upper-cladding (n_Si = 3.47, and n_SiO2 = 1.44). Because of the asymmetric tapered structure in y direction, when the TE1 mode is launched into the device, the antiphase components of the TE1 mode propagate with different effective lengths, thus induce different phase changes. The combination of the waveguide parameters is optimized to satisfy the phase matching condition, Δφ = 2π*ΔL_eff/λ = π (Δφ is the phase change differences of the two antiphase components, and ΔL_eff is the effective path difference of the two components), that both the components of TE1 mode become inphase. At last, TE0 mode is generated and tapered to port 2. The design principle is similar for higher order modes conversion, but the symmetries of the devices for even and odd modes may be different due to the mode parity, this will be discussed in the converters designs for higher order modes.

 

Fig. 1 Schematics of the proposed TE1-to-TE0 mode converter, (a) the initial design, and (b) the optimized design. It consists of six asymmetric tapers, and the total length of the device is L1 + L2 + L3. The blue dash dot line is the midline of the input waveguide.

Download Full Size | PDF

The initial device design, shown in Fig. 1(a), consists of three parts: an asymmetric taper connecting to the input waveguide, an asymmetric taper connecting to the output waveguide, and a straight waveguide connecting the two asymmetric tapers. The input waveguide width is fixed at 1200 nm. The width of the narrow end of the asymmetric taper connecting to the input waveguide, labeled as W1, equals to the input waveguide width. The widths of the broader ends of the two asymmetric tapers are equal to the width of the straight waveguide, which are labeled as W2. The output waveguide width is fixed at 500 nm, and the width of the narrow end of the asymmetric taper connecting to the output waveguide, which is labeled as W3, equals to the output waveguide width. The lengths of the taper connecting to the input waveguide, the straight waveguide, and the taper connecting to the output waveguide are labeled as L1, L2, and L3, respectively. We use 2 dimension finite-difference time-domain (2D FDTD) method to simulate the device (the spatial resolution of the simulation in this work is 20 nm), and optimize W2, L1, L2, and L3 using particle swarm algorithm [30]. After optimizations, average conversion efficiency (over 1520nm to 1580nm) about 91.5% (−0.386 dB) is achieved, with the corresponding values of W2, L1, L2, and L3 are 2653 nm, 7051 nm, 5413 nm, and 6152 nm, respectively. The conversion efficiency T_m (or log10(T_m) in dB) is the power calculated by overlapping the fundamental mode of the output waveguide and the output optical field, normalized by the launch power. Then, we insert more asymmetric tapers into the device for higher efficiency. The lengths of inserted tapers are labeled as L12, L22, and L23, respectively. And the corresponding widths are labeled as W12, W22, and W23, respectively. All the parameters are marked in Fig. 1(b). After several loops of optimizations, we get an average mode conversion efficiency above 99% (−0.044 dB), with the corresponding values of L12, L22, L23, W12, W22, and W23 are 735 nm, 2617 nm, 3054 nm, 1550 nm, 2828 nm, and 1500 nm, respectively. At last, a 3D FDTD simulation is implemented to verify the optimization results, which are showed in Fig. 2. In Fig. 2(a)-2(c), we can see that the antiphase components of TE1 mode finally become inphase through the asymmetric tapered waveguide. In Fig. 2(d), it can be seen that the conversion efficiency over 1520 nm to 1580 nm is very flat and the conversion loss is quite low. The average TE1-to-TE0 conversion efficiency over 1520 nm to 1580 nm is 98.6% (−0.061 dB).

 

Fig. 2 Simulation results of the proposed TE1-to-TE0 mode converter: (a)-(c) simulated the Ey field propagation in the device at 1520 nm, 1550 nm, and 1580 nm, (d) simulated conversion efficiency over wavelength.

Download Full Size | PDF

Figure 3 shows schematics structures for the TE2-to-TE0 and the TE3-to-TE0 mode converter. Essentially, the design principles are the same as that used in the TE1-to-TE0 converter. However, odd modes and even modes have different parities, device designs for converting modes between the same parity and different parities need to be considered respectively. When converting odd modes to TE0 mode, because the parities of the modes before and after conversion are opposite, the parity of the initial mode must be broken for the conversion. In TE1-to-TE0 converter, using an asymmetric structure in the y direction of the waveguide which can break the parity has proved it. When converting even modes to TE0 mode, such as TE2-to-TE0 conversion, because the parities of the mode before and after conversion are the same, there is no need to break the parity. In order to achieve the phase matching condition for TE2-to-TE0 conversion, a symmetric structure shown in Fig. 3(a) is used, in which two inphase components at sides travel through the same lengths, which are different with that the middle component travels. Of course, the asymmetric structure similar to that shown in Fig. 1 can also be used for TE2-to-TE0 conversion, when all components travel through different lengths have integer 2*π phase difference. In TE3-to-TE0 converter design, we use coordinate to define the structure, as shown in Fig. 3(b). All of the final optimized parameters of the three devices are shown in Table 1. The simulation results obtained by 3D FDTD for the TE2-to-TE0 converter and TE3-to-TE0 converter are shown in Fig. 4. The average conversion efficiency of TE2-to-TE0 is 98.8% (−0.052 dB), and the average conversion efficiency of TE3-to-TE0 is 97.5% (−0.11 dB).

 

Fig. 3 Schematics of the proposed mode converter, (a) TE2-to-TE0, (b) TE3-to-TE0. Blue dash dot line is the midline of the input waveguide.

Download Full Size | PDF

Table 1. Final optimized parameters of the three converters

View Table

 

Fig. 4 (a) Simulated the Ey field propagation in the device at 1550 nm of TE2-to-TE0 mode converter, and (b) conversion efficiency over wavelength range from 1520 nm to 1580 nm. (c) Simulated the Ey field propagation in the device at 1550 nm wavelength of TE3-to-TE0 mode converter, and (d) conversion efficiency over wavelength range from 1520 nm to 1580 nm.

Download Full Size | PDF

Combining those devices, we can realize the mode conversion among TE3, TE2, and TE1. The 3D FDTD simulation results of the combined devices are shown in Fig. 5. From Fig. 5(d), we can see that the combined devices have good performance of the original two devices, the conversion efficiency over 1520 nm to 1580 nm is flat and the conversion loss is low. The average conversion efficiencies of the TE2-to-TE1, TE3-to-TE1, and TE3-to-TE2 mode convertors are 97.3% (−0.119 dB), 96.2% (−0.168 dB) and 96.5% (−0.154 dB).

 

Fig. 5 (a)-(c) Simulated field intensity distributions at 1550 nm wavelength of TE2-to-TE1, TE3-to-TE1, and TE3-to-TE2 mode converter, and (d) corresponding conversion efficiency over wavelength range from 1520 nm to 1580 nm, TE2-to-TE1 is in olive, TE3-to-TE1 is in orange, TE3-to-TE2 is in blue.

Download Full Size | PDF

3. Fabrication tolerance analysis

To investigate the fabrication tolerance of the mode converters, we simulate the average conversion efficiency (wavelength range from 1520 nm to 1580 nm) versus the width and the height deviation of the waveguide. In consideration of the process precisions, we set the width deviation within ± 50 nm. According to the actual condition, the top-Si thickness deviation of the SOI wafer is set to be ± 20 nm. As shown in Fig. 6, the average conversion efficiencies of TE1-to-TE0 and TE2-to-TE0 mode converter experience negligible degradations with the waveguide dimension variations. When the waveguide width deviates far from the design value, the degradation of the average conversion efficiency of TE3-to-TE0 mode converter is larger but not significant. If the width deviation is controlled within ± 50 nm which can be guaranteed in most foundry, the average conversion efficiency is above −0.5 dB. In general, all of the three devices have high fabrication tolerance. Moreover, the combined devices for TE2-to-TE1, TE3-to-TE1, and TE3-to-TE2 can also benefit from the large tolerance. The results indicate that all devices converting modes among TE0, TE1, TE2 and TE3 can be readily fabricated using the standard 180 nm CMOS process.

 

Fig. 6 (a) Simulated average conversion efficiency varied with the waveguide width deviation, (b) simulated average conversion efficiency varied with the waveguide thickness deviation. TE1-to-TE0 is in magenta, TE2-to-TE0 is in olive, TE3-to-TE0 is in blue.

Download Full Size | PDF

4. Conclusions

In conclusion, the broadband and low loss mode-order converters based on novel compact taper structures are proposed. Different designs with and without breaking parities of odd and even modes are illustrated. The proposed devices show high conversion efficiency over a broad wavelength range from 1520 nm to 1580 nm. The average conversion losses of the devices converting TE1, TE2, and TE3 modes to TE0 are 0.061 dB, 0.052 dB, and 0.11 dB, respectively. To the best of our knowledge, the designed devices show the highest conversion efficiency between the high order mode and fundamental mode over a broad wavelength range. Combining these devices, arbitrary conversion among TE3, TE2 and TE1 modes can be achieved with high efficiencies. Those mode converters can be readily fabricated by commercial 180 nm CMOS processing and have high fabrication tolerance.