1. Introduction

On-chip optical interconnect is a promising communication technology for future massively-paralleled chip multiprocessors, it offers broader bandwidth performance compared to its electrical counterpart. To keep up with the increasing demand of high bandwidth, the interconnect transmission capacity has to be increased further. Traditionally, wavelength division multiplexing (WDM) technology is employed which relies on multiple laser light source to carry information across channels. Mode division multiplexing (MDM), however, offers a new dimension for increasing the capacity of an optical interconnect without the need to have multiple laser sources [1–3]. A single core multimode waveguide is more appealing compared to a multicore technology. It can be fabricated on a chip with high precision and offers more compactness to the photonic integrated circuit (PIC) as only a single multimode waveguide is needed to carry different data channels.

Mode (de)multiplexer is a key component to realize on-chip MDM technology. Recently, several structures were proposed based on multimode interference [1], adiabatic coupler [2], asymmetric directional coupler [3], and tapered directional coupler [4,8]. Among them, the tapered directional coupler provides a superior fabrication tolerance, low crosstalk, and minimum insertion loss. Nevertheless, factors such as: insertion loss and mode cross talk limit the number of modes that can be accommodated on a single photonic link. Thus, it is essential to consider the wavelength dimension in conjunction with the mode multiplexing to enhance the capacity further without having to incur noticeable crosstalk and loss. Such a hybrid approach needs a simultaneous mode and wavelength (de) multiplexing components. In this paper, we propose a novel two-mode, two wavelength 1310/1550nm hybrid (de)multiplexer structure employing a tapered directional coupler and multimode interference (MMI) waveguides.

2. Operation principle

In order to realize a dual wavelength and a dual mode multiplexer, we propose two architectures shown in Figs. 1(a) and 1(b). Both architectures support a total of four data channels (D1...D4). In the first architecture (design A) shown in Fig. 1(a), one mode multiplexer is used to combine data channel pairs belonging to wavelength λ₁: D1, D2, and a second one is used to combine channel pairs D3, D4 belonging to λ₂. After the mode multiplexer, D1 will be on TE₀ mode while D2 will be on TE₁ mode, similarly, D3 will be on TE0 mode and D4 will be on TE1 mode. The two mode multiplexers are then followed by an MMI based wavelength multiplexer. This MMI merges the two data channel pairs into one multimode output waveguide independent of the input eigenmode order. The challenge here is designing a wavelength multiplexer that have equal performance for both the TE₀ and TE₁ modes.

 

Fig. 1 Schematic configurations of the mode and wavelength multiplexer (MWDM) (a) two mode multiplexer followed by one MMI wavelength multiplexer; (b) two MMI wavelength multiplexer followed by one mode multiplexer.

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An alternative configuration (design B) is shown in Fig. 1(b). In this architecture, the wavelength multiplexer comes before the mode multiplexer. This wavelength multiplexer is an MMI based which operates in single mode input/output condition. One MMI is used to combine data channels D1 of λ₁ and D3 of λ₂, while the other one combines data channels D2, and D4 of λ₁ and λ₂, respectively. This design is simpler and it allows to make the structure more compact and to have a low crosstalk. Following the MMI multiplexers, a single stage mode multiplexer is then used to combine both wavelengths such that, D1 and D3 are in TE₀ eigenmode while D2, and D4 are in TE₁ eigenmode. The advantage of this approach is that the mode multiplexer can have a uniform response over a broad wavelength range. In addition, such a configuration is scalable; it allows to add more than two modes (channels) in a single wavelength.

2.1 Mode multiplexer

Figure 2(a) shows the schematic of a two optical mode multiplexer design using asymmetric directional coupler. This component is composed of a single mode access waveguide and a multimode bus waveguide. The coupling region is formed by evanescently coupling the access waveguide with the bus one, in which the bus waveguide is adiabatically tapered in the coupling region. In the tapered coupler section, the TE₀ mode of the access waveguide is coupled to TE₁ of the bus waveguide. In a conventional directional coupler, for the TE₀ and TE₁ mode multiplexing to happen, the effective index of the TE₀ mode in the access waveguide should be equal to that of the TE₁ mode of the wider waveguide. Figure 2(b) shows the calculated effective indices as a function of waveguide width for first two waveguide eigenmodes calculated for the wavelengths 1310nm and 1550nm, λ₁ and λ₂ respectively. As indicated in this figure, the effective indices of the fundamental mode (TE₀) in the access waveguide of width W_a, should equal to the effective index of the first higher order mode (TE₁) in the wider bus waveguide of width W_c. This phase matching condition is shown in the same figure (Fig. 2(b)) for both 1310nm and 1550nm wavelengths. To make the directional coupler insensitive to both wavelength and process variations, the bus waveguide is tapered from W_c1 to W_c2. This tapering process will result in a more robust design as it increases the tolerance in width variation of the access waveguide to ΔW = W_a2-W_a1.

 

Fig. 2 (a) A schematic configuration of tapered directional coupler. (b) The calculated effective indices as a function of the waveguide width for the 1st two optical eigenmodes for wavelengths of 1310nm and 1550nm. (Thickness of the Si core layer is 220 nm. Blue curve stands for 1310 nm and red for 1550 nm.).

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2.2. Wavelength multiplexer

The MMI structure uses the self – imaging principle to produce multiple images of the input optical field at the output. For optimized imaging to occur, the input waveguide normally operates in a single mode condition. The MMI is normally suitable for a broadband wavelength operation. However, recently published papers showed that a slotted waveguide MMI structure or a multi-section MMI can be used for wavelength (de)multiplexing as reported in [6] and [7], respectively. Nevertheless, those devices only operate in a single mode input/output operation. So far, there has been no attempt to design a wavelength multiplexer which simultaneously supports multimode operation. In this paper we propose a MMI based wavelength multiplexer for 1310 nm and 1550 nm (de)multiplexing operation where its input and output waveguides support 2 waveguide eigenmodes. Therefore, it concurrently operates as the MDM multiplexer used for the layout shown in Fig. 1(a).

As indicated in [5], for an MxN self-imaging of MMI, the imaging distance is an integer multiple of 3 times L_π, where L_π is the beat length between the fundamental mode and the first higher order mode. The length L_π is directly proportional to the square of the MMI width and inversely proportional to wavelength. For example, in order to split two 1310 nm and 1550 nm wavelengths, the MMI should be designed such that the length of the MMI matches several odd or even multiple of the beat length for both wavelengths. However, as it will be shown in the next section, starting with a wavelength multiplexer followed by a mode multiplexer (the layout shown in Fig. 1b) provides a much more compact design.

3. Results

Mode multiplexer: The proposed structures have been simulated using the Eigen Mode Expansion (EME) method. Figures 3(b)-3(e) show simulated results for directional coupler based mode multiplexer operating at wavelengths of 1310 nm and 1550nm. In this simulation, we assume integration in a silicon photonics platform. The waveguide thickness is 220 nm, and the SiO2 box thickness is 2 μm on top and bottom of the waveguide. For the single mode access waveguide, width Wa = 500 nm was chosen as a starting point. From the phase matching curve, shown in Fig. 2(b), the corresponding width of the bus waveguide is therefore, Wc = 1025nm. This waveguide is tapered from Wc1 = 950 nm to Wc2 = 1100 nm with centered around Wc. The $\pm 75$ width variation around Wc is chosen such that the directional coupler is process insensitive and yet compact. Note that, the larger the taper final width, the better the tolerance, but it requires a much longer device length.

 

Fig. 3 (a) The schematic configuration of two mode multiplexer. The simulated light propagation, (b) & (c) when 1550nm light launched at access and bus waveguide respectively, (d) & (e) when 1310 nm light launched at access and bus waveguide respectively.

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The coupling gap g is 200 nm, and the coupling length Lc is 45 μm.This figure confirms that the fundamental optical mode (TE0) propagating in the narrow access waveguide couples to the tapered bus waveguide as a first higher order mode, whereas the fundamental mode of the bus waveguide keeps propagating in the same mode order. This is due to the fact that the effective index of the fundamental mode (TE0) is substantially different from the first higher order mode (TE1); therefore the crosstalk between those two modes is very low. In the full circuit, we start with a single mode waveguide that supports only the fundamental mode, and then the width of this waveguide is adiabatically tapped to the final width Wc. By doing that, only the fundamental mode is injected to Wc and no higher order modes are excited.

Due to fabrication errors, a waveguide width deviation of Δw will result in a larger effective index deviation in the access waveguide than the bus waveguide. As shown in Fig. 2(b), this is evident; where the change in the TE0 effective index around Wa is larger than the TE1 one. Figure 4 demonstrates the impact of film thickness variation of +/− 5nm (nominal thickness is 220nm) on the directional coupler insertion loss (upper axis). As shown in this figure, a waveguide thickness error of ΔH yields no significant penalty in the excess loss. Furthermore, a typical a waveguide width variation of +/− 10 nm results in a maximum of 0.7dB increases in the total excess loss.

 

Fig. 4 Insertion loss for the coupler, with the access waveguide variation (blue) and waveguide thickness variation (red).

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Multiplexer design A: Fig. 5 shows the layout and simulation results of the field distribution in the proposed MMI multimode wavelength (de)multiplexer. For a MMI width of 7.55μm, the first imaging distance for the 1550nm and 1310nm wavelengths is located at around 316μm and 390μm, respectively. In this case, the exact greatest common factor of the two numbers will be very large in excess of millimeters. Therefore, it is inconvenient for compact integration. However, a less optimal imaging length can be obtained, for example, at the average of 4 times the imaging distance of 1310 nm wavelength and five times the imaging distance of 1550 nm wavelength. This distance is located at 1560 μm and 1580 μm, respectively. In this case, the optimal MMI length is 1570μm. Simulations results shown in Figs. 5(b)-5(e) confirm this finding. If the fundamental or the first higher order modes of both wavelengths are injected into the bar port of the MMI, most of the 1310nm light power propagates to the bar output port, whereas the 1550 nm light propagates to the cross output port. This is true for both the fundamental and the first order mode excitation. However, designing a MMI based multimode wavelength multiplexer is a challenging task as it is difficult to get an optimum MMI length while maintaining acceptable insertion loss and crosstalk across all the channels. This is visible particularly in Fig. 4(e), the fourth channel (first higher order mode of the 1310 nm wavelength) has a noticeable insertion loss of 2.2 dB and crosstalk level of −10.9 dB with respect to the other channels.

 

Fig. 5 a) A schematic of design A: full layout. The light propagation in the proposed multimode wavelength (de)multiplexer with W_mmi = 7.55μm and L_mmi = 1570μm when the input field is: (b) fundamental mode of the 1550 nm wavelength (c) first higher order mode of the 1550 nm wavelength(d) fundamental mode of the 1310 nm wavelength (e) first higher order mode of 1310nm.

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Multiplexer design B: For a single mode input/output operation, the proposed MMI is shown in Fig. 6(a). It has a width of 2.4μm which results in a first imaging formation at a distance of 41 μm and 51 μm for the 1550 nm and1310 nm wavelengths, respectively. Looking at the odd/even multiple of the two lengths, ideally, we can successfully de-multiplex/multiplex 1550/1310nm light in to the cross and the bar output ports at around 205μm (which is five times 41 μm or four times 51 μm). Figures 6(b) and 6(c) show the simulation results for this case, we find that an optimal cross-talk performance is obtained for a length of 198 μm. The insertion loss is less than 1.2 dB and the crosstalk is better than −15.5 dB.

 

Fig. 6 a) A schematic configuration of the proposed wavelength (de)multiplexer. (b)-(c) Simulated light propagation when 1550 nm and 1310 nm wavelengths are launched, respectively. (Lmmi = 198 µm). (d)- (e) Simulated light propagation when 1550 nm and 1310 nm wavelengths are launched, respectively. (Lmmi = 41.2 µm).

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We can still obtain a more compact design if we place the MMI output at the 1st imaging distance of the 1550nm wavelength (i.e. 41 μm). However, this will result in a noticeable cross-talk at the cross port. Taking a closer look at the simulated field distribution shown in Figs. 6(d) and 6(e), as expected, the 1550 nm wavelength is perfectly guided to the cross port, whereas most of the 1310 nm wavelength power is focused at the bar output port. The insertion loss of the 1550 nm and 1310 nm is 0.25 and 1.2 dB, respectively, while the cross-talk of cross-to-bar state is below −30 dB and −14 dB for the bar-to-cross state. Though the bar-to-cross port crosstalk is high, we can still improve it by reducing the width of the waveguide at the cross port at the expense of adding a little more insertion loss. For example, by reducing the waveguide width of the cross port from 950 nm to 800 nm we can improve the cross-talk level to −18 dB but increase the insertion loss of the cross port to 0.5 dB.

Figure 7 demonstrates the impact of film thickness variation of +/− 5nm on the MMI insertion loss. As shown in this figure, a waveguide thickness error of ΔH yields no significant penalty in the excess loss. Additionally, a typical waveguide width variation of +/− 10 nm can result in an additional excess loss of 0.9dB. Figure 8 shows simulation results of the entire device (MMI (de)multiplexer and directional coupler: Design B) taken by injecting channels D1-D4 (Fig. 8(b)-8(e) into the corresponding device ports depicted Fig. 8(a). The results verify the working principle of the device.

 

Fig. 7 MMI insertion loss change for waveguide width and thickness variations (blue and red, respectively).

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Fig. 8 a) A schematic of design B full layout. 8(b) - 8(e) Simulated light propagation for channels D1, D2, D3 and D4, respectively.

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4. Conclusions

In this paper, we propose two types of structures for mode and wavelength (de)multiplexing. We found out that by first combining the wavelength and then perform mode multiplexing results in a much better performance in terms of device size, insertion loss, and cross-talk. We refer to this structure as design B. The total design can be integrated in an area of 500μm x 127μm including the fiber input/output couplers. The dimension of the device B itself is less than 100μm x 6μm. Furthermore, simulation results show that the overall insertion loss, including the wavelength and mode multiplexer sections, is 1.2 dB, 1.4dB, 1.9dB and 2.1 dB for D1, D2, D3, and D4 channels, respectively. A cross-talk of less than −18 dB is also observed across all the channels. Although this structure has a higher insertion loss, it is extremely appealing for its ultra-compactness, acceptable crosstalk and mode scalability.