Rapid adiabatic couplers with arbitrary split ratios for broadband DWDM interleaver application

2.1 Device design

The RACs are implemented on a silicon photonic platform with a 220-nm-thick device layer. The corresponding layout is shown in Figure 1(a), where the coupler is divided into three sections. In Section I, the structure begins at the initial gap (g _s), where the coupling between two waveguides is negligible. This gap is gradually narrowed to g for Section II, while the waveguide widths (w _s,1 and w _s,2) remain unchanged. Section II is where mode evolution takes place, with waveguide widths tapering from w _s,1 and w _s,2 to w _e,1 and w _e,2, respectively, while the gap (g) is maintained. By the end of Section II, we obtain the desired power split ratio. Finally, in Section III, the gap is again increased to a value (g _e) while the power split ratio of the two waveguides is maintained.

Figure 1:

Design procedure for the rapid adiabatic coupler. (a) Schematic of RAC structure. (b) Power coupling (|κ|²) between the first two TE modes versus translational offset in Sections I and II; black dashed line shows the selected optimal offset for each segment. All offsets represent the incremental shift. (c) Simulated TE₀ even-to-odd crosstalk in Section II as a function of length. The red line represents a conventional adiabatic coupler with linear tapers, while the blue line represents the proposed RAC. (d) Output transmission as a function of width difference w _e,1 − w _e,2; markers indicate target split ratios. (e) Simulated spectra of 71:29 output bends designed using translational offset optimization (solid) and conventional Bezier S-bends (dashed).

The initial waveguide widths, w _s,1 and w _s,2, were defined relative to a 500 nm bus waveguide (w _bus), with Δw _s denoting their difference: w _s,1 = w _bus + Δw _s/2 and w _s,2 = w _bus − Δw _s/2. If Δw _s is too large, the narrower waveguide suffers from excessive optical loss. If it is too small, the unwanted coupling at the end of Section I increases, requiring a longer adiabatic transition. After several iterations, we chose to use Δw _s = 160 nm, which is nearly optimal.

To determine the appropriate value for g _s, we used a finite difference eigenmode (FDE) solver to analyze the coupling between two waveguides. With waveguide widths of 580 and 420 nm, we found that g _s = 700 nm results in negligible coupling. In contrast, the gap g used in Section II should be small enough to support effective power transition and allow for shorter device length. Although smaller gaps enhance coupling, they introduce fabrication challenges, especially cladding voids that can degrade device performance [8], [9]. Considering both optical performance and fabrication reliability, we chose g = 100 nm.

Following the approach in [4], [5], we added a geometric degree of freedom to control mode evolution along the coupler by applying curvature through translational offsets perpendicular to the propagation direction in Sections I and II. This approach effectively suppresses coupling between the first and second TE eigenmodes, which are even-like and odd-like supermodes, enabling shorter coupler designs. For the 50:50 baseline design, we set equal output widths at w _e,1 = w _e,2 = 500 nm. Sections I and II were each discretized into 100 segments, and the optimal offset for every segment was calculated with the FDE solver. Section I segments differ in gap, whereas Section II segments differ in core width; the optimum translational offset must, therefore, be determined for each segment individually, and we optimize sequentially from start to end. Figure 1(b) shows the relationship between translational offset and coupling between the first and second TE modes. Afterward, the final coupler geometry was obtained by smoothly interpolating these discrete offsets. For further optimization, the segment lengths were adaptively stretched in regions with stronger coupling and compressed in weaker regions. As shown in Figure 1(c), this design achieves significantly shorter coupler lengths compared to a conventional linear taper-based approach while maintaining low intermodal crosstalk.

Although the baseline design achieves a 50:50 power split, arbitrary split ratios require introducing asymmetry along the transition from Section II to Section III. Following the method in [6], we varied the widths of the output waveguides to induce an effective index difference, which shifts the relative fraction of modal power in each waveguide: the even-like fundamental mode becomes more confined in the wider waveguide, while the odd-like second mode becomes more confined in the narrower one. Section III must then widen the gap while maintaining this power distribution and avoiding crosstalk.

To determine the widths of two waveguides at the end of Section II to achieve target split ratios, we performed a parameter sweep around the 500 nm bus width – setting w _e,1 = 500 nm + Δw _e/2 and w _e,2 = 500 nm − Δw _e/2 – and obtained optimal Δw _e. We swept Δw _e on the optimized Section I baseline structure to identify the width difference required for the desired power split. The optimized Δw _e values for each target split ratio are summarized in Supplementary Tab. S.1. Figure 1(d) shows the corresponding power-split curves as a function of Δw _e, with the target ratios indicated by markers.

After obtaining two waveguide widths, w _e,1 and w _e,2, we design Section III to only perform the fan-out function without disturbing the established power distribution of the two waveguides at the end of Section II. In the case of a 50:50 coupler, Section III typically consists of two symmetric Bezier S-bends that preserve mirror symmetry between the waveguides. As a result, the even and odd modes remain eigenmodes throughout Section III, and there is no coupling between them.

However, when asymmetric waveguide widths are introduced to achieve imbalanced power splitting, the same Bezier S-bends with different waveguide widths break mirror symmetry and increase modal overlap between the two supermodes. This overlap induces residual coupling in Section III that alters the split ratio given at the end of Section II. To mitigate this issue, we applied the same translational offset technique used in Sections I and II to Section III. In this way, Section III can only spatially separate two waveguides while keeping the power split ratios achieved at the end of Section II. Figure 1(e) compares the spectral characteristics of 71:29 output bends for the two cases: Section III waveguides were implemented with conventional Bezier S-bends versus those designed using offset optimization. The result shows that the latter provides wider bandwidth performance by better suppressing residual coupling.

The solid blue line and the dashed-dot red lines in Figure 2 show the simulated spectral response of the entire RAC structure for each target split ratio, which confirms the broadband behavior. The simulations were performed using the 3D finite-difference time-domain (FDTD) method. The corresponding total lengths of the RACs are summarized in Supplementary Table. S.2.

Figure 2:

Simulated and experimental results of each RAC.

2.2 Experimental result

To verify the power splitting ratios experimentally, asymmetric Mach–Zehnder interferometers (AMZI) were constructed using two couplers of the same type. The splitting ratio of each coupler was extracted from the extinction ratio of the AMZI, assuming that the two couplers are identical [10]. TE-pass filters were included at the input of each AMZI to only excite the fundamental TE mode, designed based on the method described in [11] to suppress higher-order and TM-like modes.

The scatter plot in Figure 2 presents the extracted power splitting ratios derived from the measured spectral responses of the AMZIs. At the center wavelength of 1,550 nm, all six designs exhibit split ratios within ±3 % of their respective targets, showing good agreement with the design values. Furthermore, four of the six designs, other than 50:50 and 92:8 couplers, maintain this ±3 % error throughout the entire 160 nm wavelength range tested (1,480–1,640 nm), which was only limited by the CW laser tuning range. The remaining two designs, 50:50 and 92:8, satisfy the ±3 % condition in narrower ranges: 1,512.8–1,588.6 nm and 1,480–1,599 nm, respectively. These results confirm the effectiveness of the proposed design method in realizing compact, broadband adiabatic couplers with accurate power splitting. With more advanced fabrication processes offering tighter control over waveguide width, even higher precision can be expected.

To our knowledge, our 80:20 RAC achieves a length comparable to or shorter than previously reported 78:22 adiabatic couplers [6], [12], while significantly improving spectral performance. For reference, Table 1 summarizes recent experimental results on unbalanced adiabatic couplers, comparing bandwidth and coupler length. To ensure a fair comparison among known results, we have used only the length of the mode evolution region, which corresponds to Section II of Figure 1(a). We limit the comparison to this region because g _s and g _e in Sections I and III can be chosen case by case – e.g., to match input bus waveguides or meet packaging clearances – so their lengths can vary widely across reports and are not directly comparable.

3.1 Device design

Based on well-known lattice filter theories [7], we designed third-, second-, and first-order AMZIs by connecting 50:50, 71:29, 80:20, 92:8, and 96:4 RACs previously described. Figure 3(a) shows the configuration of the DWDM interleaver used in our study. To achieve 100 GHz channel spacing, a cascading structure of AMZIs with 200 GHz, 400 GHz, and 800 GHz free spectral range (FSR) is employed. Phase delay arm lengths were adjusted to align the center wavelengths of each channel with the ITU grid. The optimized values for each AMZI stage are summarized in Section 3 of Supplementary information. Figure 3(b) shows the simulated spectral response of the designed DWDM interleaver.

Figure 3:

Schematic design and simulated transmission spectrum of the DWDM interleaver. (a) Schematic of DWDM interleaver and first-, second-, and third-order AMZIs. (b) Simulated spectrum of DWDM interleaver. Simulation was performed from 1,480 to 1,640 nm. The magnified figure for the range 1,520–1,580 nm was separately depicted for direct comparison with the experimental data.

3.2 Experimental result

Figure 4(a) shows a microscope image of the fabricated device. The devices were fabricated by Applied Nanotools Inc. using electron beam lithography. TiW heaters were included on each MZI arm to compensate for phase errors caused by fabrication. Similarly to the AMZI devices described in the previous section, a TE-pass filter was added to the input port of the interleaver.

Figure 4:

Microscope image of the fabricated DWDM interleaver and its measured transmission spectra. (a) Microscope image of DWDM interleaver. (b) Experimental spectra of the 8-channel DWDM interleaver with 100 GHz channel spacing (top) and a 4-channel interleaver with 200 GHz spacing (bottom) implemented using part of the same device. Each color represents a different output channel.

The top plot in Figure 4(b) presents the measured transmission spectra of the 8-channel DWDM interleaver. The measured crosstalk is less than −20 dB for more than eight channels around 1,550 nm, and the −0.5 dB flat-top bandwidth of each channel exceeds 30 GHz (0.24 nm). Due to the broadband nature of our coupler, the interleaver exhibits low crosstalk (< −10 dB) across more than 40 channels within the 1,530–1,570 nm wavelength range. Current performance is primarily limited by one block of the entire circuit, second-order AMZI A, where phase mismatch arises primarily from fabrication-induced width errors in the long differential arm. The accumulated phase error could not be fully corrected by the integrated heater, because the available phase tuning range did not reach the full 2π. This limitation, in principle, can be mitigated by adopting a dispersion-aware AMZI arm design, as demonstrated even under fabrication imperfections that caused group index variations [13].

To further evaluate the broadband potential of the architecture, a partial configuration that excludes AMZI A was experimentally tested. In the configuration shown in Figure 3(a), the unconnected input port of the second-order AMZI B is utilized, while the two connected first-order AMZIs remain unchanged. This partial structure, consisting of one second-order AMZI B and two first-order AMZI C and D, functions as a second-order lattice filter with 200 GHz channel spacing. In this configuration, crosstalk levels below −10 dB were observed around the 1,525–1,640 nm wavelength range, covering over 60 channels with 200 GHz spacing except for one channel that slightly exceeded −10 dB near 1,558 nm. These results highlight the broadband performance of the proposed RAC-based interleaver design and its scalability, demonstrating its suitability for compact and flexible PIC implementations.