1. Introduction

In the past decades, silicon photonics has seen tremendous advancement in terms of active and passive component performance, and integration method and density. It has eventually reached its maturity and fruited in communications applications in the near-infrared (near-IR), as manifested by wafer-scale complementary metal-oxide-semiconductor (CMOS) compatible implementation of devices and interconnects. Given its success in shorter wavelengths, silicon-based (or group IV) photonics is believed to also hold great promise in mid-infrared (mid-IR) applications [1–3]. In the mid-IR range, the two-photon absorption vanishes, and silicon (λ > 2.2 µm) and germanium (λ > 3 µm) exhibit strong nonlinearity [1]. These features make silicon-based photonics an ideal platform for studying nonlinear phenomena (e.g. Kerr nonlinearity) in a compact on-chip setting [4,5].

Compared to the UV-visible region mid-IR (2-20 µm) is a less explored but technically and scientifically important portion of the electromagnetic spectrum. It covers two atmospheric windows (3-5 µm and 8-14 µm) that are important for environmental sciences [6], agricultural remote sensing [7], and defense applications [8]. It also embraces the so-called fingerprint region (7-20 µm) which is used to identify chemical and biological molecules by their fundamental vibrational absorptions [9]. Recently, many efforts have been directed to extending the operation wavelength of silicon-based photonics to the mid-infrared region. While much success has been achieved in passive components such as waveguides [5,10–12], grating couplers [13–15], splitters [16–18], resonators [19,20], and in active components such as modulators [21,22] and switches [23,24], the direct integration of efficient mid-IR light sources on the silicon-based photonics platform remains a formidable challenge [3,25]. In view of this difficulty, many schemes resort alternatively to steering the external mid-IR lights to the silicon chip plane by using grating couplers [26–28].

Grating couplers usually consist of one- or two-dimensional gratings that are connected to waveguides. These gratings are used to disperse the out-of-plane lights through diffraction and steer the proper orders to the in-plane waveguides. The performance of a grating coupler is commonly characterized by parameters including coupling efficiency (CE), polarization sensitivity, and wavelength bandwidth. In the near-IR region, previous efforts have led to considerable success in improving the performance parameters of grating couplers on the silicon-based platforms [29–32]. In contrast, only a handful of works have been done in the mid-IR range. In 2011, Cheng et al. examined the properties of mid-IR grating couplers constructed on the silicon-on-sapphire platform. At a wavelength of 2.75 µm, they obtained theoretically and experimentally transverse-magnetic (TM) mode coupling efficiencies of 39.6% and 11.6%, respectively [27]. A year later, the same group reported a simulated transverse-electric (TE) mode CE of 44.2% and a corresponding experimental efficiency of 24.7% at 2.75 µm by using a focusing subwavelength grating and a suspended membrane waveguide [13]. In 2016, Alonso-Ramos et al. proposed and fabricated mid-IR grating couplers for 3.8 µm wavelength on the Ge-on-Si platform. Their effort resulted in simulated and measured chip-to-fiber coupling efficiencies of 15% and 7.9%, respectively [28]. In the same year, Favreau et al. designed a suspended mid-IR grating coupler for TM polarized light on the SiGe/Si platform with a simulated fiber-to-chip CE of 64% at a wavelength of 4.5 µm [33]. A year later, Radosavljevic et al. theoretically and experimentally investigated the CE of 5.2 µm wavelength fiber-to-chip grating couplers on both Ge-on-Si and Ge-on-SOI platforms [14]. Their optimized grating couplers showed stimulated (measured) coupling efficiencies of 40% (32%) and 70% (40%) on Ge-on-Si and Ge-on-SOI platforms, respectively. Besides the higher efficiency, it was suggested that the Ge-on-SOI platform could provide more robustness to larger suspended devices than the Ge-on-Si platform could do. Sánchez-Postigo et al. proposed to use a high-index prism together with a subwavelength grating to achieve high-efficiency zeroth-order mid-IR fiber-to-chip coupling with a large bandwidth [34]. At an operating wavelength of 3.8 µm, the best simulation results showed coupling efficiencies of 92% and 90% on the SOI and Ge-on-silicon nitride (GON) platforms, respectively. While the simulated results are impressive, the implementation of their scheme entails complicated fabrications and substantial efforts for alignment. Recently, Chen et al. simulated and fabricated mid-IR two-dimensional subwavelength grating couplers on the SOI platform with a targeted wavelength of 3.7 µm. Their coupler achieved simulated and measured coupling efficiencies of 41% and 22.5% per facet, respectively [35]. It should be noted that all previous efforts have been centered around improving the performance parameters of mid-IR grating couplers working with one wavelength.

In this work, we theoretically examine, for the first time, high-efficiency simultaneous coupling of two mid-IR bands to a silicon chip using grating couplers constructed on a Ge-on-SOI platform. Without loss of generality, we select two representative wavelength bands (centered at 8.5 µm and 4.95 µm) in the atmospheric windows to showcase the operation principle of this grating coupler. The proposed coupler structure comprises a central one-dimensional (1D) grating connected at its opposite ends to two Ge waveguides. Each waveguide features an embedded Bragg grating for wavelength crosstalk suppression and CE improvement. The central grating fulfills the phase-matching conditions for both wavelength bands. The geometric parameters (i.e., period, duty cycle, and etch depth) and the period number of the central and Bragg gratings, the Ge layer thickness, and the mid-IR light incident angle have been systematically optimized to achieve fiber-to-chip coupling efficiencies of 46.38% and 59.93% for the 8.5 µm and 4.95 µm bands, respectively. Such mid-IR dual-band grating couplers may be useful for systems such as third generation infrared imagers which simultaneously detect two wavelengths to improve their capability of object identification, and may also assist in studies of on-chip nonlinear phenomena. For the latter, the grating coupling scheme is of paramount importance, since on-chip mid-IR light sources are still very far from mature.

2. Design and simulation of the mid-IR dual-band grating coupler

The grating coupler proposed here is used to simultaneously couple two mid-IR bands from the free space into the in-plane waveguides. After impinging on a properly designed grating, lights with two different wavelengths can, in principle, be separated in space. They can even travel in opposite directions when observing certain diffraction orders. The main effort of this work is thus directed to identifying the proper diffraction orders for the two mid-IR wavelengths traveling in opposite directions and maximizing the CEs of these orders through parameter optimization. To achieve high CEs for both wavelengths, the grating coupler needs to fulfill the phase-matching condition (Eq. (1)). This condition seeks to compensate the propagation constant mismatch between the air and the grating by introducing a grating vector.

Figure 1(a) is a three-dimensional (3D) schematic of the proposed mid-IR dual-band grating coupler constructed on a Ge-on-SOI platform. The top Ge layer thickness ${h_{Ge}}$ was 1.74 µm, the upper silicon layer thickness ${h_{si}}$ was 0.6 µm, and the buried oxide thickness ${h_{Box}}$ was 1 µm. The geometric parameters of the central and Bragg gratings are defined in Fig. 1(b). The central grating (CG) period ($\varLambda $) is optimized to simultaneously fulfill the phase-matching conditions for the +2 and −1 diffraction orders of the 4.95 µm and 8.5 µm bands, respectively. When a broadband mid-IR (2-14 µm) light shines on the coupler through an optical fiber (positioned a few microns above the CG), the above two bands are singled out by the CG and coupled into waveguides in opposite directions. The two Bragg gratings (BGs) embedded in the waveguides serve as band-stop filters to reflect wavelengths outside the pass band (centered at 4.95 µm or 8.5 µm) and thus suppress the crosstalk. 2D finite-difference time-domain (FDTD) simulations are used to find the optimal geometric parameters of CG and BGs that can achieve high coupling efficiencies for both 4.95 µm and 8.5 µm bands. Since this is a dual-objective optimization problem, tradeoffs are often required. In this work, the grating coupler is optimized for mid-IR lights with transverse-magnetic (TM) polarization. In the simulations, the minimum mesh size was set to 15 nm, and perfectly matched layer boundary condition (PML) was used.

 

Fig. 1. (a) 3D schematic of the dual-band grating coupler. $\theta $ is the fiber tilt angle with respect to the grating surface normal. (b) Cross-sectional views showing the definition of geometric parameters of the gratings. The detailed description of these parameters is in the main text.

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The detailed information of the CG and BGs is described below (Fig. 1(b)).

These design parameters are also summarized in Table 1.

Table 1. Optimized geometric parameters of the gratings

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3. Results and discussion

3.1 Central grating for mid-IR band separation and coupling

As a key component of the proposed coupler, the CG serves to screen out the 4.95 µm and 8.5 µm bands from the incident light and couple them into the opposite waveguides. To this end, the phase-matching condition (Eq. (1)) needs to be fulfilled simultaneously for the two wavelengths. Since the grating period appears explicitly in Eq. (1), it can be used as a knob to tune the CG toward phase-matching and thus achieving better coupling efficiency (CE0). In addition, duty cycle, which is implicitly included in ${n_{eff}}$ in Eq. (1), can also be varied to optimize CE0. Here, by using 2D FDTD simulations, we found the optimal values of grating period and duty cycle for achieving high CE0s. Figure 2(a) and Fig. 2(b) show the color-coded mappings of CE0 as a function of grating period and duty cycle for the 4.95 µm and 8.5 µm bands, respectively. The CE0 was evaluated by calculating the ratio of the light power measured near the CG-waveguide interfaces and the corresponding incident powers from the fiber. With the colorbars set to the same scale, the CE0 mapping in Fig. 2(b) appears more extended and slow-varying than the mapping in Fig. 2(a), implying a potentially larger tolerance of the 8.5 µm band to geometric parameter variation. The CE0 achieved maximum values of 50.7% and 40.77% for the 4.95 µm and 8.5 µm bands, respectively, when setting the grating period and duty cycle to 2.71 µm and 0.51 in Fig. 2(a) and 2.75 µm and 0.48 in Fig. 2(b). The grating period values for achieving maximum CE0 were close for both wavelengths. Therefore, we used a period of $\varLambda = 2.71{\ \mathrm{\mu} \mathrm{m}}$ for the rest of the optimization. On the other hand, as the duty cycle increased to 0.51 from 0.48 in Fig. 2(b), the CE0 only dropped by 0.48% to 40.29%. Hence, a CG duty cycle of 0.51 was set for further optimization unless otherwise noted. Figure 2(c) and Fig. 2(d) show the change of CE0 with grating period (with $DC = 0.51$) and duty cycle (with $\varLambda = 2.71{\ \mathrm{\mu} \mathrm{m}}$) along the cuts indicated by the dashed lines in Fig. 2(a) and Fig. 2(b).

 

Fig. 2. CE0 of central grating as a function of geometric parameters. The dependence of coupling efficiencies of 4.95 µm and 8.5 µm bands on grating period and duty cycle are displayed in (a) and (b), respectively. The colorbars are made identical in these panels for the ease of comparison. (c) and (d) show respectively the data along the vertical and horizontal cuts indicated by dashed lines in (a) and (b). (e) and (f) displays respectively the change of CE0 with Ge layer thickness and etch depth.

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Apart from the grating period and the duty cycle, other parameters may also have an effect on the dual-wavelength CE0 of the CG. Since the difference between the refractive indices of Ge and Si is relatively small ($\varDelta {n_1} = 0.593$ at 4.95 µm and $\varDelta {n_2} = 0.5838$ at 8.5 µm) [36,37], the fraction of the modes confined in the Ge layer is largely dependent on its thickness. On the one hand, if the Ge layer is too thin, considerable portion of the modes will leak into the underlying Si layer, resulting in a power loss. On the other hand, if the Ge layer is too thick, the fundamental mode coupling efficiency will be compromised. Hence, the Ge layer thickness needs to be optimized to achieve high CE0. In addition, the grating etch depth also deserves an optimization as it directly affects the mode-matching between the CG and the fiber [38]. Figure 2(e) and Fig. 2(f) present the variation of CE0 as a function of the Ge layer thickness and the grating etch depth, respectively. We swept the Ge layer thickness ${h_{Ge}}$ from 1.4 µm to 2 µm and the etch depth ${d_E}$ from 0.7 µm to 1.74 µm. Based on these results, we opted for using ${h_{Ge}} = \textrm{1}\mathrm{.74\ \mu m}$ and ${d_E} = \textrm{1}\mathrm{.2\ \mu m}$ for the dual-wavelength operation of the CG.

Given the wavelength and the finite size of the incident light beam, the number of grating periods ($N$) can also affect the CE0. We investigated the change of CE0 while setting the point of incidence as origin and increasing the number of periods (${N_\textrm{L}}$ for left and ${N_\textrm{R}}$ for right direction) along both transmission directions. The total number of grating periods N is a sum of ${N_\textrm{L}}$ and N_R. The color-coded CE0 of the 8.5 µm and 4.95 µm bands corresponding to different combinations of ${N_\textrm{L}}$ and ${N_\textrm{R}}$ are shown in Fig. 3(a) and Fig. 3(b), respectively. The CE0 show maximum values of 44.02% and 53.55% for the 8.5 µm and 4.95 µm bands with (${N_\textrm{L}}$, ${N_\textrm{R}}$) of (4, 9) and (9, 4), respectively. While high CE0 values in Fig. 3(a) are mainly distributed near the upper left corner of the mapping, those in Fig. 3(b) are crowded around the lower right corner. Apparently, trade-offs are required in order to have favorable CE0 for both bands. In this respect, we chose (${N_\textrm{L}}$, ${N_\textrm{R}}$) of (5, 4) as a good set of numbers of periods.

 

Fig. 3. The CE0 of left port (8.5 µm) (a) and right port (4.95 µm) (b) as a function of number of periods (${N_\textrm{L}}$ and ${N_\textrm{R}}$) optimized simultaneously on both transmission directions.

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The tilt angle of the optical fiber is another important parameter that needs to be evaluated for the CE0 optimization. The fiber tilt or incidence angle θ is defined as the angle between the direction of the incident light relative to the CG surface normal, with a convention of this angle being positive when rotating counterclockwise. Figure 4 shows the impact of the incidence angle $\theta $ on the CE0 of the CG. By varying $\theta $ from −11° to 0°, both CE0 first increased to maximum values and then fell off. At $\theta ={-} 5^\circ $, the CE0 of the 4.95 µm band topped at 51.4%, while the CE0 of the 8.5 µm band was 38.1%, only 4% lower than its peak value. Therefore, we selected a $\theta $ of −5° as the incidence angle of the light beams.

 

Fig. 4. Variation of CE0 of two bands with incidence (fiber tilt) angle $\theta $.

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3.2 Wavelength crosstalk suppression by Bragg gratings

In previous discussions, we have focused our attention on the right-traveling +2 diffraction order of the 4.95 µm band and the left-traveling −1 order of the 8.5 µm band. However, it should be noted that other diffraction orders (or bands) with wavelengths close to 4.95 µm or 8.5 µm could also travel toward the opposite direction. These bands may interfere with the use of the 4.95 µm or the 8.5 µm signal band and thus act as wavelength crosstalks, as illustrated in Fig. 1(a). The wavelength crosstalk is defined as the ratio of the power coupled into the opposite port and the total incident power. It can have a detrimental effect on the use of dual-band grating couplers for future applications. To suppress the crosstalks, we introduced two Bragg gratings (BGs) that functioned as band-stop filters in the Ge waveguides (Fig. (1)). BGs are valuable optical structures that can be used to construct microcavities for various applications including on-chip biosensing [39,40]. Prior to the introduction of BGs, we found that a slight increase in coupling efficiency (3.23% and 0.66% for the 4.95 µm and 8.5 µm bands, respectively) could be achieved by reducing the right-hand waveguide thickness from 1.74 µm to 1.2 µm (Fig. 1(b)). This improvement can be ascribed to the better mode confinement of the 4.95 µm band offered by the thinner waveguide. The BG periods, $DCs$, and the numbers of periods were varied to adjust the stop-band width and location, while the change of coupling efficiency (CE1) and crosstalk were evaluated. The etch depths of BGs were fixed to the respective waveguide thickness.

Figure 5 shows the effect of BGs on the CE1 and crosstalk. Note that the CE1was hereafter determined after the lights passed the BGs. The strategy here was to suppress crosstalk to a low level (<15%) without compromising too much CE1. As will be seen later, the CE1 actually increased by a few percentage points due to the recollection of the reflected powers. In Fig. 5(a) and Fig. 5(b), near the minima of the crosstalk curves the grating coupler exhibited acceptable CE1. Therefore, for the left-port crosstalk (4.75 µm), the grating period $\varLambda { _1}$ was chosen to be 0.73 µm, and the duty cycle $D{C_1}$ to be 0.71. The $D{C_1}$ was defined as $D{C_\textrm{1}} = {d_1}/\varLambda { _\textrm{1}}$ (see Fig. 1(b)). Following a similar line of argument, the right BG period $\varLambda { _\textrm{2}}$ (Fig. 5(d)) and duty cycle $D{C_2}$ (Fig. 5(e)) were determined to be 1.28 µm and 0.78, respectively. Figure 5(c) shows the effect of the left BG period number on the left-port crosstalk and CE1. With the number of periods ${N_1}$ increased from 0 to 10, the crosstalk creeped down as expected from 47.61% to 4.55%. On the other hand, the CE1 first fluctuated slightly with period below 8 and then decreased due to the increase of loss. The inset in Fig. 5(c) shows the gradual suppression of the crosstalk band with increasing period number. Based on the crosstalk and CE1 trends shown in Fig. 5(c), we set the left BG period number to 8. As expected, the 8.95 µm crosstalk band also decreased with increasing right BG period number (Fig. 5(f)). An ${N_2}$ of 5 that corresponded to a local maximum of the CE1 was selected as the optimal right BG period number.

 

Fig. 5. Wavelength crosstalk suppression by Bragg gratings. The effect of left BG’s grating period (a), duty cycle (b), and the number of periods (c) on the coupling efficiency and crosstalk. (d)-(e) are the corresponding data for the right BG. Insets in (c) and (f) are the wavelength dependence of the crosstalks with the period number varying from 0 to 10.

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To see more clearly the crosstalk suppression effect of the BGs, the spatial distribution of the optical power of crosstalk bands (4.75 µm and 8.95 µm) in the absence and presence of BGs are visualized in Fig. 6(a) and Fig. 6(b), respectively. The power values have been normalized in all color-coded mappings for the ease of comparison. In the absence of BGs (Fig. 6(a)), there was significant amount of power of the 4.75 µm (8.95 µm) crosstalk band traveling in the left (right) direction. On the contrary, the powers of the crosstalk bands were effectively suppressed with the addition of BGs, as shown in Fig. 6(b). In fact, these crosstalk bands were reflected by the BGs and reinforced the CE1 of the reverse direction, as evidenced by comparing the signal color mappings at the bottom of Fig. 6(a) and Fig. 6(b). Figure 6(c) and Fig. 6(d) show the suppression of the crosstalk bands in the wavelength domain. The crosstalk at 4.75 µm was drastically reduced from 47.61% to 5.4% (Fig. 6(c)), while the crosstalk at 8.95 µm was reduced from 19.22% to 11.14% (Fig. 6(d)). The dips on the curves in Fig. 6(c) were due to the reflection of the incident beam at ∼4.6 µm by the grating coupler surface.

 

Fig. 6. Comparison of the crosstalks and signals with and without BGs. (a) and (b) display the spatial distribution of the powers of crosstalk wavelengths (4.75 µm and 8.95 µm) and signal wavelengths (4.75 µm and 8.95 µm). Top: profile of the structure used; middle: crosstalk mappings; bottom: signal mappings. (c) and (d) show the crosstalk suppression in the wavelength domain. For the blue curves, the left and right BG period numbers were set to ${N_1} = 8$ and ${N_2} = 5$, respectively.

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Figure 7(a) and Fig. 7(b) reveal more clearly the reinforcement effect of BGs on the CE1s. For the left port (8.5 µm), the CE1 increased by 7.57% to 46.38%, while it increased by 5.29% to 59.93% for the right port (4.95 µm). In Table 2, we compare our results with previous studies conducted in the 3-8 µm range. It can be concluded that the proposed coupler showed reasonably high simulated coupling efficiencies for both bands, and thus hold great potential for future mid-IR on-chip applications. Finally, we analyzed the modification to the coupler’s bandwidth caused by the BGs. Following the convention, we expressed CE1 (coupling losses) in dBs. For both coupling wavelengths, we evaluated the 3 dB bandwidth of the grating couplers with and without BGs. In the absence of BGs (structure shown in Fig. 6(a)), the 8.5 µm band featured a 3 dB bandwidth of 580 nm, while that for the 4.95 µm band was 186 nm. The 3 dB bandwidth of 4.95 µm band was comparable to that reported in the literature in the same wavelength range [14]. The 3 dB bandwidth of the 8.5 µm band was smaller than the value reported in a recent work [41], where a bandwidth of ∼730 nm was achieved at an operating wavelength of 7.67 µm. This discrepancy might be attributed to the introduction of a micro-antenna structure which promoted light coupling efficiency between the optical fiber and the grating coupler in Ref. [41]. After the inclusion of BGs (structure shown in Fig. 6(b)), the bandwidths shrank by 16.4% for the 8.5 µm band, and 12.9% for the 4.95 µm band. The reduction in the bandwidth could be attributed to the band-stop filtering nature of the BGs.

 

Fig. 7. Change of the left (a) and right (b) port CE1 with wavelength, in the absence and presence of BGs. The insets are the enlarged views of the peak areas, showing the CE1 differences. (c) and (d) show the impact of BGs on the bandwidth (BW) of the grating coupler.

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Table 2. Comparison of the performance and parameters of mid-IR grating couplers

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4. Conclusion

In summary, a dual-band mid-IR grating coupler with Bragg gratings for wavelength crosstalk suppression has been proposed and simulated by FDTD methods on a Ge-on-SOI platform. The parameters of the central and Bragg gratings, and the fiber tilt angle were optimized to yield high theoretical CEs of 46.38% and 59.93% for the 8.5 µm and 4.95 µm bands, respectively. The introduction of the Bragg grating in the waveguides helped suppress the 4.75 µm crosstalk to 5.4% and the 8.95 µm crosstalk to 11.14%. The grating coupler proposed here may be useful for future system-on-a-chip applications that require high-efficiency mid-IR dual-band coupling capabilities.