Broadband and Lossless 50:50 Directional Coupler Using Silicon Bent Waveguides

Introduction

Directional couplers (DCs) play a crucial role in silicon photonics, enabling versatile applications such as power splitting, modulation, and wavelength division multiplexing. However, the inherent wavelength dependency due to dispersion poses a significant bandwidth limitation for traditional DCs. Ideally, a 50:50 DC should achieve this splitting ratio across a broad wavelength range, but in practice, it only achieves this ratio at a single wavelength. This unintended coupling variation severely degrades the performance of many silicon photonics applications.

To address this challenge, researchers have explored diverse schemes to achieve a broadband 50:50 DC. One approach involves adiabatic DCs based on mode evolution, where the light in the input waveguide adiabatically evolves to an even or odd mode in the DC, resulting in 50:50 splitting. However, adiabatic DCs are inherently long devices, often exceeding 300 μm, and exhibit high excess loss.

Another design strategy employs asymmetric DCs, utilizing waveguides of different widths to reduce wavelength dependency. Despite their potential, these designs are highly sensitive to linewidth variations and suffer from fabrication intolerance. Achieving broadband functionality and fabrication tolerance remains a significant challenge in silicon photonics due to the nanoscale dimensions and high index contrast.

Proposed Directional Coupler

Recently, bent DCs have emerged as a viable solution, offering broadband coupling, a relatively compact footprint, and high fabrication tolerance. By introducing asymmetry through bent waveguides, the need for different waveguide widths is eliminated, addressing the fabrication sensitivity observed in DCs with asymmetric waveguide widths.

Figure 1: (a) Schematic of the traditional straight DC with L as the coupling length. (b) Schematic and (c) microscope image of the proposed bent DC with R as the coupling radius and θ as the coupling angle. All curves are designed with low-loss bends.

In this work, a broadband 50:50 DC based on bent waveguides is presented, utilizing low-loss bends demonstrated in an earlier study to eliminate any excess loss caused by the bends [5]. The proposed lossless 50:50 DC is experimentally demonstrated with a mere 0.076 coupling variation over an 80 nm wavelength range, compared to a 0.369 variation for the traditional DC design.

According to coupled mode theory, the cross-coupling ratio (κ^2) and the thru-coupling ratio (r^2) in a lossless coupler can be expressed as:

κ^2 = A sin^2 (kx + φ)

r^2 = 1 - κ^2

Where x = L is the coupling length in a straight DC (Fig. 1a), and x = θ is the coupling angle in a bent DC (Fig. 1b). k denotes the coupling strength per unit length or angle, and A represents the maximum coupling ratio.

Figure 2: The measured coupling ratio of (a) the traditional straight DC and (b) the proposed bent DC. The colorful lines represent the measured data, while the black curves are the fitted curves.

To minimize the DC wavelength dependency, both |dA/dλ| and |dk/dλ| should be minimized. Notably, dk/dλ can reach 0 by properly designing the parameters in a bent DC. Therefore, the wavelength-insensitive DC design can be derived as an optimization problem:

min{g, R, θ} |∂nₑ𝒻𝒻₁/∂λ - ∂nₑ𝒻𝒻₂/∂λ|

s.t. n𝓰,ₑᵥₑₙ - n𝓰,ₒ𝒹𝒹 = 0

Where g is the coupling gap, R is the coupling radius, and θ is the coupling angle.

Guided by this optimization model, a wavelength-insensitive bent DC is achieved with g = 0.1 μm, R = 25 μm, and θ = 8.5°. The fabricated device is illustrated in Fig. 1c, with all bends designed as low-loss bends.

As shown in Fig. 2a, the coupling ratio of the traditional straight DC exhibits a linear dependency with wavelength, dκ^2/dλ = 4.59 μm^-1. In contrast, the coupling ratio of the proposed bent DC (Fig. 2b) follows a second-order polynomial relationship with wavelength, plateauing at κ^2 ≈ 0.5, where dκ^2/dλ is substantially reduced to zero around λ = 1.3 μm, enabling broadband behavior.

Within the measured 80 nm wavelength range, the coupling variation of κ^2 is merely 0.076, which is 4.85 times lower than the straight DC. Compared to existing literature, the proposed splitter has the least coupling variation within this measured wavelength range, and no significant excess loss was observed.

Conclusion

An optimization model for wavelength-insensitive DC design with bent waveguides has been derived. Based on this model, a broadband 50:50 splitter has been experimentally demonstrated with a drastic reduction in wavelength dependency, where the coupling variation is merely 0.076 within an 80 nm wavelength range, outperforming all existing broadband DC designs. Moreover, all bends in the proposed design are implemented with low-loss bends, enabling lossless coupling.

Reference

[2] H. El-Saeed et al., "Wavelength-insensitive and Lossless 50:50 Directional Coupler Based on Silicon Bent Waveguides," imec, Kapeldreef 75, 3001 Leuven, Belgium; Photonics Research Group, Department of Information Technology, Ghent University-imec, Ghent, Belgium, 2024, pp. 1-6, doi: 979-8-3503-9404-7/24/$31.00 ©2024 IEEE.