1.

Introduction

With continuously increasing demand for broadband services, such as big data, cloud computing, and large-capacity communications, wavelength division multiplexing (WDM) technology has been widely used thanks to its ability to increase the number of channels and the transmission bandwidth.¹ Significant attention is paid to wavelength demultiplexers with features of compact size, low insertion loss (IL), high extinction ratio (ER) and broad bandwidth.² What’s more, silicon on-insulator (SOI) is an attractive platform for wavelength multiplexers due to its high integration density and fabrication compatibility with the complementary metal-oxide-semiconductor technology.

Several solutions to demultiplex two wavelengths in O-band and C-band have been demonstrated such as diffraction grating couplers,^3,4 micro-ring resonators,⁵ directional couplers,^6–9 and multimode interference (MMI) couplers.^2,10–12 Diffraction grating couplers can demultiplex multiple wavelengths by diffracting them into different spatial directions, which is not suitable for on-chip interconnects. Wavelength demultiplexers using cascaded silicon micro-ring resonators are compact and scalable, but they are limited by the small bandwidth and the high temperature sensitivity. Directional couplers also suffer from the limited bandwidth and fabrication tolerance due to their precise phase matching condition. MMI-based demultiplexers that provide a relatively broad optical bandwidth, relax fabrication tolerance, and low IL have drawn much attention as the most potential candidates. However, the length of the MMI section must be odd times or even times of the beat lengths for both wavelengths, which leads to a long device length of larger than $100\mu \mathrm{m}$. To reduce the device length, slotted MMI devices have been proposed. It has been verified that introducing $N$ slots reduces the self-imaging length by a factor of $N+1$.¹³ However, effective indices of slots need to be carefully adjusted by varying etching depths, which makes the fabrication process complicated.

On the other hand, subwavelength grating (SWG) has been widely investigated for designing new photonic components because the SWG provides a new degree of freedom to manipulate the refractive index by regulating structural parameters.^14–16 It is worth noting that the SWG’s period is smaller than its operating wavelength, consequently, the reflection and diffraction effects of the grating are suppressed.^17,18 As a result, the SWG behaves as a homogeneous medium with an equivalent refractive index ($n_e$), and $n_e$ can be adjusted by changing the period and the duty circle. SWG exhibits the capability of reducing the device length or broadening the bandwidth. The SWG has been inserted into the middle of the MMI section to reduce the beat length for 3-dB coupler¹⁹ and wavelength demultiplexer,²⁰ and the devices’ lengths are reduced. Also, the broadband wavelength demultiplexer assisted by SWG-based directional coupler is proposed and simulated.²¹

In this paper, we propose an ultra-compact $1310/1550\mathrm{nm}$ wavelength demultiplexer based on MMI coupler with two parallel SWG-based slots. Instead of varying the slot index using a shallow etch depth, two longitudinal SWG structures with the same etch depth are inserted into the MMI section, and equivalent refractive indices of slots are judiciously engineered to shrink the device length. The designed device is only $34.48\text{-}\mu \mathrm{m}$-length long. The IL, 1-dB bandwidth, ER, and fabrication tolerances of the proposed wavelength demultiplexer are evaluated subsequently. In addition, the performance for the wavelength multiplexer is also demonstrated.

2.

Design and Analysis

Schematics of the proposed MMI wavelength demultiplexer are shown in Fig. 1. This device is designed based on the SOI wafer with top Si thickness of 220 nm and the ${\mathrm{SiO}}_2$ is employed as the upper cladding material. The wavelength demultiplexer is composed by two S-bent input channels, the MMI section, and two S-bent output channels. To reduce the IL and the number of stimulated high-order modes, linear tapered waveguides are used to connect the input and output waveguides with the multimode waveguide. Two parallel SWG-based slots are located symmetrically in the MMI section with lateral offsets of approximately $\pm w_{\mathrm{MMI}}/6$. The period is denoted as $\mathrm{\Lambda }$ and segment length of the high-index medium (Si) along the propagation direction is denoted as $a$, namely, the segment length of low-index medium (${\mathrm{SiO}}_2$) is $\mathrm{\Lambda }-a$. According to the effective medium theory,²² the SWG-based slot can be considered as homogenous medium with an equivalent refractive index of $n_e$, which is shown in Fig. 1(c).

Fig. 1

Schematics of the SWG-based MMI wavelength demultiplexer. (a) Three-dimensional view, (b) top view and (c) the SWG-based slot can be represented as homogeneous medium with an equivalent refractive index $n_e$.

To keep the SWG operating at the subwavelength region, the grating period must be smaller than the Bragg period (${\mathrm{\Lambda }}_{\text{Bragg}}$). For the wavelength with ${\lambda }_{\min }$ of 1200 nm, the equation of $\mathrm{\Lambda }<{\mathrm{\Lambda }}_{\text{Bragg}}=\lambda /(2n_{\mathrm{eff}})\approx 220\mathrm{nm}$ must be fulfilled. In addition, taking the practical fabrication ability into account, we choose the period $\mathrm{\Lambda }$ of 180 nm, and the dimension of Si or ${\mathrm{SiO}}_2$ segment should be within a range of 40 to 140 nm.

Other parameters used for designing the device are as follows: widths of the input and output channels are $0.45\mu \mathrm{m}$ to keep a single-mode operation. Bends with the radius of $15\mu \mathrm{m}$ are used to decouple the input and output waveguides. For adiabatic conditions, the taper width $w_{\text{taper}}$ and length $L_{\text{taper}}$ are set to 0.9 and $5\mu \mathrm{m}$, respectively. The MMI width $w_{\mathrm{MMI}}$ is set to $2\mu \mathrm{m}$, which is a tradeoff between a shorter beat length and an easier beam splitting.

The fundamental principle of MMI demultiplexer is the self-imaging effect.²³ Single image or multiple images of the input field can be periodically reproduced after propagating in the multimode waveguide region. When the input field is launched off-center into the MMI device, a direct image (bar state) will be formed at the length of $L=p(3L_{\pi })$ with $p$ of an even integer and a mirrored image (cross state) will be formed with $p$ of an odd integer. Here, $L_{\pi }$ is the beat length of the two lowest-order modes. The expected beat length of a standard off-center-stimulated MMI device is given roughly as

In order to demultiplex the two wavelengths of 1310 and 1550 nm, the length $L_{\mathrm{MMI}}$ should satisfy the following equation,

With the purpose of shrinking the MMI length, we need to decrease self-imaging length on the one hand and make $p$ smaller on the other hand. Introducing two parallel SWG-based slots to the MMI region can dramatically alter the self-imaging properties.¹³ As a result, by properly designing the SWG-slots’ parameters, the self-imaging length is reduced by a factor of 3. Therefore, Eq. (2) can be written as

The SWG is considered as homogenous medium, and the equivalent index $n_e$ and the SWG width $w_{\mathrm{SWG}}$ play a key role in manipulating the beat length as well as the value of $p$. 2D mode analysis is used to calculate the effective index of the two lowest modes and beat lengths at 1310 and 1550 nm are obtained based on Eq. (1), respectively. The ratio between $L_{\pi }$ (1310) and $L_{\pi }$ (1550) as functions of $w_{\mathrm{SWG}}$ and $n_e$ is shown in Fig. 2(a). We can see that limited by the practical fabrication ability, the ideal condition with ratio of 2, namely, $p$ value of 1, can hardly be achieved. But the ratio of 1.5, can be obtained by judiciously designing $w_{\mathrm{SWG}}$ and $n_e$ of the two SWG-based slots. In a word, the ratio of 1.5 that resulting in $p=2$ in Eq. (3) are selected and the contour line is highlighted. Dependence of $L_{\pi }$ (1310) and $L_{\pi }(1550)$ on $w_{\mathrm{SWG}}$ and $n_e$ are shown in Fig. 2(b) and 2(c), respectively. Considering that a narrower slot has a larger absolute tolerance for $n_e$,¹³ $w_{\mathrm{SWG}}$ is chosen to be 60 nm, therefore, $n_e$ is set to 2.44, which is illustrated as a star marker in Fig. 2(a). In that case, $L_{\pi }$ (1310) is $17.82\mu \mathrm{m}$ and $L_{\pi }(1550)$ is $11.89\mu \mathrm{m}$. The total MMI length that satisfies the following equation is achieved: $L_{\mathrm{MMI}}=2L_{\pi }(1310)=3L_{\pi }(1550)\approx 35.65\mu \mathrm{m}$.

Fig. 2

(a) The ratio between $L_{\pi }(1310)$ and $L_{\pi }(1550)$ as functions of SWG width $w_{\mathrm{SWG}}$ and equivalent index $n_e$. Dependence of $L_{\pi }(1310)$ and $L_{\pi }(1550)$ on (b) SWG width $w_{\mathrm{SWG}}$ and (c) equivalent index $n_e$.

3.

Results and Discussion

The relationship between the equivalent refractive index $n_e$ and the grating parameters can be estimated by Rytov’s formulas roughly.¹⁴ However, it is not accurate enough especially when the SWG do not operate at the deep subwavelength region. To improve the performance of the wavelength demultiplexer, the actual length and duty circle (or the Si segment length $a$) need to be optimized by the 3D finite-difference time-domain (FDTD) method.

Taking the wavelength demultiplexer for instance, the 3D FDTD simulation is applied. The optimal silicon segment length $a$ is 80 nm, namely, the duty circle is about 0.44. Field distribution of the optimized demultiplexer at 1310 and 1550 nm are shown in Figs. 3(a) and 3(b), respectively. It shows that light of 1310 nm transmits from Port 1 to Port 3 (bar-state) and that of 1550 nm transmits from Port 1 to Port 4 (cross-state), which is consistent with the aforementioned theoretical analysis. In that case, the actual MMI length $L_{\mathrm{MMI}}$ is only $34.48\mu \mathrm{m}$.

Fig. 3

Field distribution of the SWG-based MMI wavelength demultiplexer at the wavelength of (a) 1310 nm and (b) 1550 nm.

Then the transmission spectrum from 1200 to 1650 nm is obtained and shown in Fig. 4, and the IL, ER, and 1-dB bandwidth can be read from the spectrum. IL is 0.12 dB at 1310 nm and 0.24 dB at 1550 nm. ERs of 15.2 and 16.8 dB are achieved at these two wavelengths, respectively. The SWG-based slots introduce disturbance to the original waveguide modes, which leads to a relatively low ER. That’s why we bring two slots into the MMI section rather than three or more, regardless of the shorter beat length. As the blue stripes in Fig. 4 indicate, the designed demultiplexer shows a broad 1-dB bandwidth of larger than 90 nm at both wavelengths.

Fig. 4

Transmission spectrum of the wavelength demultiplexer.

Figure 5 shows the numerical results of fabrication tolerances at 1310 and 1550 nm. IL and ER dependence on the variation of the Si segment length ($\mathrm{\Delta }a$), SWG-based slot width ($\mathrm{\Delta }{w}_{\mathrm{SWG}}$), MMI width ($\mathrm{\Delta }{w}_{\mathrm{MMI}}$) and MMI length ($\mathrm{\Delta }{L}_{\mathrm{MMI}}$) are demonstrated in Figs. 5(a)–5(d), respectively. Here, the tolerances are characterized by the IL of lower than 1 dB and the ER of higher than 10 dB. Under these conditions, the tolerances on $\mathrm{\Delta }a$ and $\mathrm{\Delta }{w}_{\mathrm{SWG}}$ are $\pm 10\mathrm{nm}$ and $\pm 15\mathrm{nm}$, respectively. Furthermore, $\mathrm{\Delta }{w}_{\mathrm{MMI}}$ can varies from $-40$ to 70 nm and the tolerance on $\mathrm{\Delta }{L}_{\mathrm{MMI}}$ is much larger with the range from $-2.5$ to $2\mu \mathrm{m}$. Compared with the MMI parameters, the fabrication process is more sensitive to the variation on SWG parameters, and this happens because $a$ and $w_{\mathrm{SWG}}$ manipulate the equivalent index greatly.

Fig. 5

Fabrication tolerances on the variation of (a) Si segment length $\mathrm{\Delta }a$, (b) SWG-based slot width $\mathrm{\Delta }{w}_{\mathrm{SWG}}$, (c) MMI width $\mathrm{\Delta }{w}_{\mathrm{MMI}}$, and (d) MMI length $\mathrm{\Delta }{L}_{\mathrm{MMI}}$.

Besides, performance of the device when working as a wavelength multiplexer is numerically analyzed using the 3D-FDTD method. Figures 6(a) and 6(b) illustrate the field distributions at the two wavelengths. We can see that light of 1310-nm transmits from Port 1 to Port 3 and that of 1550-nm transmits from Port 2 to Port 3. As a result, wavelength multiplexing function is implemented. Also, the ILs are $<0.24\mathrm{dB}$ and the ERs are higher than 15.2 dB for both wavelengths.

Fig. 6

Field distribution of the SWG-based MMI wavelength multiplexer at the wavelength of (a) 1310 nm and (b) 1550 nm.

Table 1 summarizes the comparison for the representative MMI-based wavelength demultiplexer reported. It can be seen that the designed device is one of the best wavelength demultiplexers regarding the most compact footprint ($\sim 34.48\mu \mathrm{m}$) and low IL ($<0.3\mathrm{dB}$).

Table 1

Comparison of the wavelength demultiplexer reported.

4.

Conclusion

We demonstrated the design and performance evaluation of the $1310/1550\mathrm{nm}$ wavelength demultiplexer based on MMI coupler with two SWG slots. The most compact MMI wavelength demultiplexer with length of $34.48\mu \mathrm{m}$ is obtained. Compared with the shallow etched slots, the using of the SWG simplifies the fabrication process by only one-step lithography. Beat lengths for 1310 and 1550 nm and their ratio are effectively adjusted by engineering SWG structures including the period, duty circle and slot width. Finally, the ratio of 1.5 is selected, that is, the $p$ value is 2. According to the results, ILs are $<0.24\mathrm{dB}$ while ERs are higher than 15.2 dB for both wavelengths. 1-dB bandwidths of 90 nm have been obtained, which are broad enough to cover the entire O-band and C-band. From the fabrication tolerance analysis, the device performance is more sensitive to SWG parameters than MMI parameters, which is caused by the significant impact of the SWG structure on the equivalent refractive index. The proposed method of manipulating the beat length using two SWG-based slots offers excellent perspectives for the practical realization of MMI couplers with substantially reduced footprint. Once the fabrication accuracy is improved, $p$ value of 1 can be selected and the device footprint will be shrunk further.