Introduction

On-chip optical interconnect is a promising technique to satisfy the exponentially increasing demand of bandwidth for future massively-parallel chip multiprocessors1. 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 fibers2,3. 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-junctions4,5,6,7, multimode interferometer8,9 and adiabatic couplers10 mainly (de)multiplex two channels. In the recent years, schemes using asymmetrical directional couplers (ADC) have been proposed11,12 and 8-channel hybrid (de)multiplexing combing MDM and polarization-division multiplexing (PDM) has been demonstrated12. 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 ADC13.

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 networks14. 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 domain15,16,17,18,19,20, 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 exchange21.

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.

Results

Structure of the tapered directional coupler

Figure 1 illustrates the structure of the tapered directional coupler, which couples light from a narrow silicon access waveguide (waveguide width w1) to a tapered wide multimode bus waveguide (waveguide width from wa to wb with center width of w2).

Figure 1
figure 1

Schematic structure of a mode (de)multiplexer based on a tapered directional coupler.

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The fundamental mode TE0 in the access waveguide is coupled into the multimode bus waveguide through the tapered coupling region and converted to higher order mode TEm (m = 1, 2, 3…). The coupling length is L and the gap between the two waveguide is g. When wa = wb = w2, the structure is a conventional directional coupler and high efficiency TE0-TEm coupling occurs when a phase matching condition (neff0 = neffm, where neff0 is the effective index of the fundamental mode in the access waveguide and neffm is the mth 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.

Characterization of mode properties

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 TE0 mode versus waveguide width is larger than other modes, so the fabrication error induced effective refractive index deviation of TE0 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 w2a (w3a) and w2b (w3b) of the wide tapered waveguide, the corresponding widths of the narrow waveguide which satisfy the phase matching condition (neff0 (w1) = neffm (wm)) are w1a (w1a′) and w1b (w1b′), respectively, as indicated in Fig. 2. Consequently, tapering the wide waveguide from w2a (w3a) to w2b (w3b) will result in a deviation tolerance between w1a (w1a′) and w1b (w1b′) for the narrow waveguide, within which a phase matching position can always be found along the taper. One thing should be noted is that w1a (w1a′) should not be too close to the width where the TE1 (TE2) and TM0 modes are hybridized (~660 nm for TE1 and ~1040 nm for TE2 in Fig. 2).

Figure 2
figure 2

Effective indices of the TE0, TE1, TE2 and TM0 modes of an air-cladded SOI waveguide as a function of the waveguide width w for a waveguide height h = 220 nm.

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The mode distribution and effective refractive index of the TE0, TE1 and TE2 modes in the silicon nanowire are displayed in Fig. 3(a–g). As shown in Fig. 3(c,f), the effective refractive index of TE1 mode with the waveguide width of 800 nm and the effective refractive index of TE2 mode with the waveguide width of 1200 nm are nearly equal to the effective refractive index of TE0 mode with the waveguide width of 400 nm, which means the phase matching condition can be satisfied.

Figure 3
figure 3

Mode distribution and effective refractive index of (a) TE0 mode, (b–d) TE1 mode and (e–g) TE2 mode.

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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 TE0 mode launched in the input port 1 (I1) propagates directly in the wide multimode bus waveguide without any change. The TE0 modes launched in the input port 2 (I2) and input port 3 (I3) are coupled into the multimode bus waveguide and converted into the high-order TE1 mode and TE2 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, TE2 mode is coupled into the lower narrow access waveguide as TE0 mode and then coupled back into the multimode bus waveguide as TE1 mode, i.e. mode conversion from TE2 to TE1 in the multimode bus waveguide. On the other hand, TE1 mode is coupled into the upper narrow access waveguide as TE0 mode and then coupled back into the multimode bus waveguide as TE2 mode, i.e. mode conversion from TE1 to TE2 in the multimode bus waveguide. In this way, mode exchange function between the TE1 mode and TE2 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 4
figure 4

Schematic configuration of optical mode exchange.

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Mode exchange results

Figure 5 depicts the light propagation simulation results. Shown in Fig. 5(a) is the overall view of the light propagation with mode exchange. TE0 mode is launched into both I2 and I3, leading to the simultaneous excitation of both TE1 and TE2 modes in the multimode bus waveguide. Shown in Fig. 5(b,c) are the zoomed in views of TE1 mode excitation and TE2 mode excitation by the launched TE0 mode. In this way, both TE1 mode and TE2 mode exist and propagate in the multimode bus waveguide and mode multiplexing is achieved. The TE1 (TE2) mode is then coupled into an access waveguide (TE0 mode) which is further coupled back into the multimode bus waveguide as the TE2 (TE1) mode. Shown in Fig. 5(d) is the zoomed in view of TE2-TE0-TE1 mode conversion process. Shown in Fig. 5(e) is the zoomed in view of TE1-TE0-TE2 mode conversion process. As a consequence, mode exchange between TE1 and TE2 modes (TE1 ↔ TE2) is implemented.

Figure 5
figure 5

3D FDTD simulation results of light propagation for optical mode multiplexing and mode exchange.

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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 TE0 mode. Figure 6(a) shows the case when only I1 port is launched by TE0 mode. It can be seen that the TE0 mode propagates directly in the multimode bus waveguide. Figure 6(b–h) show the case when only I2 port is launched by TE0 mode. The whole mode evolution process from TE0-TE1-TE0-TE2 is depicted in Fig. 6(h), implying the mode conversion from TE1 to TE2 in the multimode bus waveguide. Shown in Fig. 6(f) is the zoomed in view of the TE1 mode excitation by the input TE0 mode. Figure 6(b,c) are the corresponding field profiles of TE0 mode and TE1 mode monitored in the waveguide cross section. Shown in Fig. 6(g) is the zoomed in view of back conversion from TE1 mode to TE0 mode and its further conversion to TE2 mode. Figure 6(d,e) are the corresponding field profiles of TE0 mode and TE2 mode monitored in the waveguide cross section. Figure 6(i–o) show the case when only I3 port is launched by TE0 mode. The whole mode evolution process from TE0-TE2-TE0-TE1 is depicted in Fig. 6(i), implying the mode conversion from TE2 to TE1 in the multimode bus waveguide. Shown in Fig. 6(j) is the zoomed in view of the TE2 mode excitation by the input TE0 mode. Figure 6(l,m) are the corresponding field profiles of TE0 mode and TE2 mode monitored in the waveguide cross section. Shown in Fig. 6(k) is the zoomed in view of back conversion from TE2 mode to TE0 mode and its further conversion to TE1 mode. Figure 6(n,o) are the corresponding field profiles of TE0 mode and TE1 mode monitored in the waveguide cross section. According to the mode conversion from TE1 to TE2 in the multimode bus waveguide shown in Fig. 6(b,h) and the mode conversion from TE2 to TE1 in the multimode bus waveguide shown in Fig. 6(I–o), one can expect the mode exchange between the TE1 mode and TE2 mode in the multimode bus waveguide.

Figure 6
figure 6

3D FDTD simulation results of light propagation when only (a) I1 port, (b–h) I2 port, or (i–o) I3 port is launched by TE0 mode.

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Figure 7(a–c) show the normalized transmission responses at the three output ports O1, O2 and O3, in which the light is launched into the input ports I1, I2 and I3, respectively. Note that output ports O1, O2 and O3 correspond to the total three modes (TE0, TE1, TE2) after mode exchange between TE1 and TE2, the residual TE0 mode during the TE1-TE0-TE2 process (mode conversion from TE1 to TE2) and the residual TE0 mode during the TE2-TE0-TE1 process (mode conversion from TE2 to TE1), respectively. It can be seen that O1 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·log10(P1 /Pi) (P1 and Pi are normalized response at output port O1 and Oi, 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, 6, 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.

Figure 7
figure 7

Normalized responses at output ports (O1, O2 and O3) when light is launched into input port (a) I1, (b) I2 and (c) I3.

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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 TE1 and TE2 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 COMSOLTM. 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.

Additional Information

How to cite this article: Zhang, Z. et al. On-chip optical mode exchange using tapered directional coupler. Sci. Rep. 5, 16072; doi: 10.1038/srep16072 (2015).