On-chip optical mode exchange using tapered directional coupler

We present an on-chip optical mode exchange between two multiplexed modes by using tapered directional couplers on silicon-on-insulator platform. The device consisting of mode multiplexing and mode exchange is compact with relatively large fabrication error tolerance. The simulation results show efficient higher order mode excitation and mode exchange. A low excess loss less than 0.5 dB and high extinction ratio larger than 15 dB over 10 nm wavelength range from 1535 to 1545 nm are achieved.


On-chip optical mode exchange using tapered directional coupler Zhonglai Zhang * , Xiao Hu * & Jian Wang
We present an on-chip optical mode exchange between two multiplexed modes by using tapered directional couplers on silicon-on-insulator platform. The device consisting of mode multiplexing and mode exchange is compact with relatively large fabrication error tolerance. The simulation results show efficient higher order mode excitation and mode exchange. A low excess loss less than 0.5 dB and high extinction ratio larger than 15 dB over 10 nm wavelength range from 1535 to 1545 nm are achieved.
On-chip optical interconnect is a promising technique to satisfy the exponentially increasing demand of bandwidth for future massively-parallel chip multiprocessors 1 . Several techniques have been employed to extend the capacity of optical interconnections. Among them, wavelength-division multiplexing (WDM) is a straightforward way to expand the capacity with multiple wavelengths and has been widely used in long-haul optical communication systems. However, the requirement of multiple laser sources with different wavelengths could be expensive and complicated for on-chip optical interconnection applications. Space-division multiplexing (SDM), which only employs a single wavelength carrier, is another simple way and has been demonstrated by employing multi-core or few-mode fibers 2,3 . Mode-division multiplexing (MDM) is a kind of SDM technique which could provide an alternative approach to increasing the link capacity of optical interconnects. The key challenge of an on-chip MDM system is the efficient mode (de)multiplexer. Several kinds of (de)multiplexer have been proposed. The designs based on Y-junctions 4-7 , multimode interferometer 8,9 and adiabatic couplers 10 mainly (de)multiplex two channels. In the recent years, schemes using asymmetrical directional couplers (ADC) have been proposed 11,12 and 8-channel hybrid (de)multiplexing combing MDM and polarization-division multiplexing (PDM) has been demonstrated 12 . The ADC can be easily fabricated on silicon-on-insulator (SOI) platform. In order to improve the fabrication tolerance of the ADC, a tapered coupling region is introduced into the ADC 13 .
Very recently, on-chip MDM technology has attached increasing interest. Beyond basic functions such as (de)multiplexer, a laudable goal would be to develop data traffic grooming functions in on-chip MDM systems. Data traffic grooming is considered to be an attractive technique for enhancing the efficiency and flexibility of networks 14 . Lots of data traffic grooming functions have been well studied in WDM systems. Among these functions, data exchange, also known as wavelength exchange/interchange in the wavelength domain [15][16][17][18][19][20] , is an important technique which can efficiently utilize network resources and facilitate superior network performance. In this scenario, one might also expect to implement data exchange in the mode domain in an on-chip MDM system, i.e. on-chip optical mode exchange 21 .
In this paper, we present an optical exchange function in the mode domain based on tapered directional couplers on SOI platform. We calculate the mode properties of the SOI based nanowires and numerically study the light propagation for optical mode exchange by three dimensional finite difference time domain (3D FDTD) simulations.
Scientific RepoRts | 5:16072 | DOi: 10.1038/srep16072 The fundamental mode TE 0 in the access waveguide is coupled into the multimode bus waveguide through the tapered coupling region and converted to higher order mode TE m (m = 1, 2, 3…). The coupling length is L and the gap between the two waveguide is g. When w a = w b = w 2 , the structure is a conventional directional coupler, and high efficiency TE 0 -TE m coupling occurs when a phase matching condition (n eff0 = n effm , where n eff0 is the effective index of the fundamental mode in the access waveguide and n effm is the m th higher order mode in the multimode bus waveguide) is satisfied. However, a large fabrication error of the access waveguide can easily break the phase matching condition in the conventional directional coupler. Figure 2 shows the calculated effective refractive indices of the guided-modes in an SOI nanowire with different waveguide width. It can be seen that the slope of the effective refractive index of the TE 0 mode versus waveguide width is larger than other modes, so the fabrication error induced effective refractive index deviation of TE 0 mode is also larger than other modes, which means the phase matching condition is more easily to be broken. A tapered wide bus waveguide in the coupling region can relax the limitation. For the two widths w 2a (w 3a ) and w 2b (w 3b ) of the wide tapered waveguide, the corresponding widths of the narrow waveguide which satisfy the phase matching condition (n eff0 (w 1 ) = n effm (w m )) are w 1a (w 1a ′) and w 1b (w 1b ′), respectively, as indicated in Fig. 2. Consequently, tapering the wide waveguide from w 2a (w 3a ) to w 2b (w 3b ) will result in a deviation tolerance between w 1a (w 1a ′) and w 1b (w 1b ′) for the narrow waveguide, within which a phase matching position can always be found along the taper. One thing should be noted is that w 1a (w 1a ′) should not be too close to the width where the TE 1 (TE 2 ) and TM 0 modes are hybridized (~660 nm for TE 1 and ~1040 nm for TE 2 in Fig. 2).

Characterization of mode properties.
The mode distribution and effective refractive index of the TE 0 , TE 1 and TE 2 modes in the silicon nanowire are displayed in Fig. 3(a-g). As shown in Fig. 3(c,f), the effective refractive index of TE 1 mode  with the waveguide width of 800 nm and the effective refractive index of TE 2 mode with the waveguide width of 1200 nm are nearly equal to the effective refractive index of TE 0 mode with the waveguide width of 400 nm, which means the phase matching condition can be satisfied.
Configuration of mode exchange. The proposed mode exchange configuration is depicted in Fig. 4.
The left part in the dashed rectangle is a mode multiplexer. The TE 0 mode launched in the input port 1 (I 1 ) propagates directly in the wide multimode bus waveguide without any change. The TE 0 modes launched in the input port 2 (I 2 ) and input port 3 (I 3 ) are coupled into the multimode bus waveguide and converted into the high-order TE 1 mode and TE 2 mode by tapered directional couplers, respectively. The three multiplexed modes carrying different data information propagate through the wide multimode bus waveguide simultaneously. The right part in the dashed rectangle accomplishes the mode exchange function. On one hand, TE 2 mode is coupled into the lower narrow access waveguide as TE 0 mode and then coupled back into the multimode bus waveguide as TE 1 mode, i.e. mode conversion from TE 2 to TE 1 in the multimode bus waveguide. On the other hand, TE 1 mode is coupled into the upper narrow access waveguide as TE 0 mode and then coupled back into the multimode bus waveguide as TE 2 mode, i.e. mode conversion from TE 1 to TE 2 in the multimode bus waveguide. In this way, mode exchange function between the TE 1 mode and TE 2 mode can be realized. Meanwhile, the data information carried by the two modes is also exchanged. Mode coupling in the mode exchange part is also achieved by tapered directional couplers. Figure 5 depicts the light propagation simulation results. Shown in Fig. 5(a) is the overall view of the light propagation with mode exchange. TE 0 mode is launched into both I 2 and I 3 , leading to the simultaneous excitation of both TE 1 and TE 2 modes in the multimode bus waveguide. Shown in Fig. 5(b,c) are the zoomed in views of TE 1 mode excitation and TE 2 mode excitation by the launched TE 0 mode. In this way, both TE 1 mode and TE 2 mode exist and propagate in the multimode bus waveguide and mode multiplexing is achieved. The TE 1 (TE 2 ) mode is then coupled into an access waveguide (TE 0 mode) which is further coupled back into the multimode bus waveguide as the TE 2 (TE 1 ) mode. Shown in Fig. 5(d) is the zoomed in view of TE 2 -TE 0 -TE 1 mode conversion process. Shown in Fig. 5(e) is the zoomed in view of TE 1 -TE 0 -TE 2 mode conversion process. As a consequence, mode exchange between TE 1 and TE 2 modes (TE 1 ↔ TE 2 ) is implemented.

Mode exchange results.
In order to clearly show the mode exchange process, we further simulate the light propagation with field monitors placed in the waveguide cross section when only one input port is launched by TE 0 mode. Figure 6(a) shows the case when only I 1 port is launched by TE 0 mode. It can be seen that the  TE 0 mode propagates directly in the multimode bus waveguide. Figure 6(b-h) show the case when only I 2 port is launched by TE 0 mode. The whole mode evolution process from TE 0 -TE 1 -TE 0 -TE 2 is depicted in Fig. 6(h), implying the mode conversion from TE 1 to TE 2 in the multimode bus waveguide. Shown in Fig. 6(f) is the zoomed in view of the TE 1 mode excitation by the input TE 0 mode. Figure 6(b,c) are the corresponding field profiles of TE 0 mode and TE 1 mode monitored in the waveguide cross section. Shown in Fig. 6(g) is the zoomed in view of back conversion from TE 1 mode to TE 0 mode and its further conversion to TE 2 mode. Figure 6(d,e) are the corresponding field profiles of TE 0 mode and TE 2 mode monitored in the waveguide cross section. Figure 6(i-o) show the case when only I 3 port is launched by TE 0 mode. The whole mode evolution process from TE 0 -TE 2 -TE 0 -TE 1 is depicted in Fig. 6(i), implying the mode conversion from TE 2 to TE 1 in the multimode bus waveguide. Shown in Fig. 6(j) is the zoomed in view of the TE 2 mode excitation by the input TE 0 mode. Figure 6(l,m) are the corresponding field profiles of TE 0 mode and TE 2 mode monitored in the waveguide cross section. Shown in Fig. 6(k) is the zoomed in view of back conversion from TE 2 mode to TE 0 mode and its further conversion to TE 1 mode. Figure 6(n,o) are the corresponding field profiles of TE 0 mode and TE 1 mode monitored in the waveguide cross section. According to the mode conversion from TE 1 to TE 2 in the multimode bus waveguide shown in Fig. 6(b,h) and the mode conversion from TE 2 to TE 1 in the multimode bus waveguide shown in Fig. 6(I-o), one can expect the mode exchange between the TE 1 mode and TE 2 mode in the multimode bus waveguide. Figure 7(a-c) show the normalized transmission responses at the three output ports O 1 , O 2 and O 3 , in which the light is launched into the input ports I 1 , I 2 and I 3 , respectively. Note that output ports O 1 , O 2 and O 3 correspond to the total three modes (TE 0 , TE 1 , TE 2 ) after mode exchange between TE 1 and TE 2 , the residual TE 0 mode during the TE 1 -TE 0 -TE 2 process (mode conversion from TE 1 to TE 2 ), and the residual TE 0 mode during the TE 2 -TE 0 -TE 1 process (mode conversion from TE 2 to TE 1 ), respectively. It can be seen that O 1 always has the maximum output response among the three output ports. The excess loss is less than 0.5 dB, showing efficient operation of mode exchange. Meanwhile, the extinction ratio defined by 10·log 10 (P 1 /P i ) (P 1 and P i are normalized response at output port O 1 and O i , i = 2, 3) is assessed to be larger than 15 dB within a 10 nm wavelength range from 1535 to 1545 nm. The obtained results shown in Figs 5-7 indicate favorable operation performance of efficient optical mode exchange, which might find interesting applications in robust on-chip network management by exploiting the spatial mode dimension.

Discussion
In summary, we have proposed on-chip optical mode exchange on SOI platform. The device is based on tapered directional couplers and has a relatively large fabrication error tolerance. The fabrication of the device could be easily realized by single step electron beam lithography followed by inductively coupled plasma etching. The obtained simulation results show effective mode excitation and efficient mode exchange between TE 1 and TE 2 modes. A low excess loss less than 0.5 dB and a high extinction ratio larger than 15 dB over a 10 nm wavelength range from 1535 to 1545 nm are achieved. With the obtained results, we believe that optical data exchange in the mode domain could be further realized when each mode carries different data information. The proposed optical mode exchange might facilitate flexible optical data processing functions in an on-chip mode multiplexing systems.

Method
The mode properties (mode distribution and effective refractive index) of the guided modes in the silicon nanowire are calculated by using finite-element method (FEM) with COMSOL TM . The scattering bound condition is considered and the simulation domain is surrounded by rectangular perfectly matched layer (PML). The light propagation is simulated by a three dimensional finite difference time domain (3D FDTD) method.