1. Introduction

Coupling losses pose a significant challenge in the push to develop low-loss active plasmonic components. Hybrid-plasmonic structures in a metal-insulator-semiconductor (MIS) configuration that combine the field enhancement of plasmonics and the small propagation loss of silicon photonics [1–3] are appealing for such components, but efficient coupling to the structures remains difficult. The mismatch between modes of silicon photonic access waveguides (where modes are mainly confined to the silicon core) and hybrid-plasmonic structures (where modes are mainly confined in the insulating layer between silicon and metal) precludes efficient conversion between the two.

Prior works suggested both butt-coupling [4–10] and evanescent coupling [11–15] to tackle this issue; however, most designs are typically infeasible to fabricate. The hybrid-plasmonic modulator presented in [6], uses butt-coupling for photonic-to-plasmonic conversion with only 0.25 dB of loss, but the 800 nm-wide hybrid-plasmonic section supports multiple modes that are launched. This effectively halves the efficiency of coupling to a single mode and leads to mode beating between the silicon and insulator layers. Although this is of little consequence to a modulator using electro-absorption, the efficiency of a modulator relying on phase shifts caused by a nonlinear material in the insulating layer would suffer from the electric field periodically beating out of the active region. Another demonstration shows butt-coupling to a 200 nm-wide hybrid-plasmonic waveguide, but the best measured efficiency (−1dB) falls short of the numerically calculated optimum (−0.55 dB) and launching multiple modes still remains an issue [16].

In this paper, we present fabrication-tolerant directional coupling between a silicon photonic waveguide to a hybrid-plasmonic waveguide with an efficiency of 94% (−0.27 dB). A schematic of the structure is presented in Fig. 1(a). The ideal structure is built on a silicon-on-insulator (SOI) wafer with a 340 nm top silicon thickness and has a photonic waveguide width of w_pho = 275 nm, a hybrid-plasmonic waveguide width of w_hyb = 240 nm, a waveguide separation of w_gap = 145 nm, and an insulator layer thickness of h_spacer = 85 nm that separates the metal and silicon layers.

 

Fig. 1 (a) Cross-sectional schematic of the coupler showing the layer stacks of the photonic waveguide (left) and hybrid waveguide (right). (b) Symmetric supermode and (c) anti-symmetric supermode $E_{\text{y}}$ field profiles of the coupler. (d) Top-view intensity profile of the coupler showing mode beating between the two waveguides along the propagation. The profile is a composite of two y cross-sections: the midpoint of the silicon for the left half (photonic) and the midpoint of the spacer layer for the right half (hybrid-plasmonic). In each of (b), (c), and (d), the fields are normalized to the maximum electric field intensity (i.e. |E|² = 1).

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We avoid the issue of launching multiple modes because only the fundamental transverse magnetic (TM) mode in the hybrid waveguide fulfills the phase-matching condition. The MIS hybrid waveguide is easily adaptable for use in CMOS processes by replacing the gold layer with copper, which performs similarly to gold for applications involving surface plasmon polaritons [17]. Active plasmonic devices can be realized by doping the silicon and using the Pockels effect with organic [9] or inorganic [18] electro-optic materials in the insulating layer, or by using electro-absorption with graphene-based structures [10,19]. The MIS structure is desirable for such applications; approximately 30% of the electric field is confined in the 85 nm insulator. The confinement factor can even approach 50% for a 30 nm insulator thickness at the expense of higher propagation loss. The design offers at least 50 nm of overlay misalignment tolerance between the metal and silicon layers, yielding a fabrication tolerance within the limits of modern lithography techniques.

2. Concept

Here, we discuss the operating principle and design considerations of the coupler. Figure 1(a) depicts a cross-sectional schematic. The photonic waveguide (left) and hybrid waveguide (right) are characterized by their respective widths, w_pho and w_hyb, as well as the distance that separates them, w_gap. The hybrid waveguide is further characterized by the height of the insulating spacer layer, h_spacer. We use a thin layer of titanium to improve the adhesion between gold and silicon dioxide. The field intensity profile of Fig. 1(b) shows the electric field enhancement in the hybrid waveguide’s spacer layer between the gold and silicon layers. We calculated an electric field confinement factor of 30.8% in the spacer layer between the silicon and metal for a standalone hybrid waveguide, compared to just 9.4% in the same region for a photonic waveguide with the same dimensions but without the metals. This would allow for shorter active devices such as electro-absorption modulators or phase shifters relying on the Pockels effect.

When placed next to each other, the photonic and hybrid waveguides create a superstructure that supports symmetric and anti-symmetric supermodes. These supermodes are a result of coupling between the eigenmodes of the individual waveguides. The superposition of these two supermodes when in phase with each other results in constructive interference in one waveguide and destructive interference in the other waveguide. The two supermodes have different propagation constants and therefore accumulate a phase difference while propagating. When this phase difference reaches π the constructive interference will occur in the opposite waveguide, thus facilitating the power transfer from one waveguide to the next. The nature of this power exchange between waveguides is visualized in Fig. 1(c). It is a top-view cross-section of the simulated field intensity in the coupling structure. The power initially starts in the photonic waveguide at the bottom left and beats back and forth between the two waveguides along the direction of propagation. Once again, the advantage in confinement that the hybrid plasmonic waveguide provides over the photonic waveguide is apparent when comparing the intensity in each.

The power transfer between waveguides in a directional coupler, whether photonic or plasmonic, is well studied [12,20–22]. It depends on the effective indices of the supermodes of the structure and the length of the coupler according to Eq. (1).

3. Numerical design

In this section, we describe how we designed the hybrid coupler with numerical simulations. We used the finite difference eigenmode solver and eigenmode expansion solver in Lumerical’s MODE Solutions software for all numerical calculations in this work. Figure 2(a) shows numerically calculated effective indices of the hybrid (solid green) and photonic (dashed green) waveguides for various waveguide widths. If we want to achieve F close to unity, we must choose waveguide dimensions that give n_pho ≈ n_hyb, such that δ ≈ 0. We therefore chose w_pho = 275 nm and w_hyb = 240 nm.

 

Fig. 2 (a) Effective indices of the fundamental TM modes in the hybrid (solid green) and photonic (dashed green) waveguides as a function of the waveguide width. The grey dots mark the widths used for the measurements in Fig. 4. The propagation loss of the hybrid plasmonic mode is plotted in blue. (b) Dependence of the symmetric (solid green) and anti-symmetric (dashed green) supermode effective indices on the distance separating the two waveguides. The difference between the curves determines the coupling length (blue) as per Eq. (1). (c) Simulated spectral response of the coupler.

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The coupling length depends on the difference in effective index between the two supermodes, which in turn is strongly dependent on the width of the gap between the two waveguides, w_gap. This dependence is plotted in Fig. 2(b) along with the coupling length, L_coup, calculated from the supermode effective indices at a wavelength of 1550 nm. The index difference grows and the coupling length decreases with decreasing gap width because the mode coupling increases. We chose w_gap = 145 nm as the optimal tradeoff between a short coupling length and a dimension that can be fabricated reliably. As a final design consideration, we reduced the width of the metal by 100 nm compared to w_hyb. This allows for a misalignment of ± 50 nm between mask layers to make the device more fabrication tolerant. Our simulations showed that misalignments of this magnitude have minimal effect on the coupling efficiency because the effective index of the hybrid waveguide changes by less than 1% and we still have δ²≪ κ².

The ideal coupler has a theoretical 96% efficiency at the telecommunication wavelength of 1550 nm. Figure 2(c) shows the coupling efficiency as a function of the incident wavelength. The coupler maintains an efficiency above 90% (below 0.5 dB) across a 160 nm bandwidth and an efficiency above 80% (below 1 dB) across a 268 nm bandwidth.

4. Results

After determining the essential dimensions of the coupler, the focus shifts to the fabrication process and measurement procedure that led to the coupling efficiency results. Figure 3(a) shows a schematic of the devices used to measure the coupling efficiency. Light enters the device in the bottom silicon waveguide from the left. When the hybrid waveguide is introduced a fraction of the power – the coupling efficiency |κ|² – couples into the hybrid waveguide from the input waveguide. A small amount is lost to sidewall scattering and ohmic losses. The remaining fraction, |τ|², continues in the input waveguide to the through port. The light that couples into the hybrid waveguide propagates along a length, L, before reaching a second silicon waveguide. Here, the light couples from the hybrid to the photonic waveguide with the same efficiency, |κ|², and continues to the cross-port. For measurement purposes, the through port gives the quantity |τ|² whereas the cross-port gives |κ|² × |κ|² × (1 – γ_prop) where γ_prop = exp(-L/L_prop) is the fraction lost during propagation in the hybrid waveguide. This arrangement allows us to extract the coupling loss from the cutback method and then verify through propagation losses that we couple to a plasmonic mode in the hybrid waveguide instead of a photonic mode.

 

Fig. 3 (a) Top-view schematic of the devices used to measure the efficiency of the hybrid couplers. (b) Colourized SEM image of the coupling region in a fabricated device showing the hybrid waveguide (left) and photonic waveguide (right).

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We fabricated the structures with a simple 3-step process involving only a single alignment layer. Starting with a 340 nm silicon-on-insulator chip, we first patterned the silicon using electron beam lithography (EBL) and dry etching. Next, we used PECVD to deposit the 85 nm silicon dioxide spacer layer. Finally, we evaporated the 2 nm titanium adhesion layer and 135 nm of gold using a liftoff process patterned by EBL. The colourized scanning electron micrograph in Fig. 3(b) shows the coupling region of a fabricated device.

We performed cutback measurements to characterize the efficiency of the hybrid plasmonic couplers as well as the propagation loss in the hybrid waveguides. A single-mode fiber brought 1 mW of power at a wavelength of 1550 nm from a continuous-wave laser source to the chip. A grating coupler provided fiber-to-chip coupling and then silicon access waveguides brought the light to the device of Fig. 3(a). At the two outputs of the device, silicon waveguides carried the transmitted light to two separate grating couplers for the through and cross ports in order to couple the light from chip-to-fiber. The total transmission was measured with a photodetector at the end of the output fiber.

Figure 4(a) shows the measured transmission of more than 60 devices with w_gap = 145 nm at their through (blue) and cross (green) ports for varying lengths L, of propagation in the hybrid waveguide. Each measured device is represented with a semi-transparent marker, many of which overlap for devices with the same dimensions due to the consistency of the simple fabrication process. The dashed lines represent linear fits for the through port and cross port measurement sets. The results have been normalized by subtracting from the raw measurement results the losses due to fiber-to-chip coupling, propagation in the silicon access waveguides and propagation in the bends of the hybrid-plasmonic waveguides. Fiber-to-chip coupling loss (6.5 dB per coupler) and silicon waveguide propagation loss (3.1 dB/cm) were determined using the cutback method with silicon waveguides, while hybrid-plasmonic waveguide loss was determined from the cutback measurements in Fig. 4(a). Both the reference photonic waveguides and the hybrid-plasmonic devices were fabricated on the same chip.

 

Fig. 4 (a) Hybrid plasmonic waveguide cutback measurements at the cross-port (green) and through port (blue) at a free-space wavelength λ = 1550 nm. The slope of the cross-port’s line of best fit gives the hybrid plasmonic propagation loss while the y-intercept gives the loss of two hybrid couplers. (b) Measured coupling efficiencies |κ|² (green) and uncoupled powers |τ|² (blue) for various designed gap widths. The solid lines are values calculated from simulations.

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The cross-port measurements show a steady dependence on the hybrid length, from which we extract a propagation loss of 0.16 dB/µm corresponding to a propagation length of 27 μm. This loss is larger than the 0.07 dB/µm from simulation in Fig. 2(a). We attribute this excess loss to scattering caused by surface roughness in the silicon and gold sidewalls, surface roughness in the 2 nm titanium adhesion layer, and grain boundaries in the gold layer. We calculate a coupling efficiency of 1.37 dB (73%) by halving the y-intercept of the cross-port’s trend line to account for coupling to and from the hybrid waveguide.

In contrast to the cross-port, the through port measurements expectedly show no dependence on the hybrid length. The residual power in the through port indicate that the fabricated dimensions varied from the design and that the coupling efficiency could still be improved. To account for these fabrication errors, we included devices with varying gap widths, w_gap, which effectively alters the coupling length. Those measurements are shown in Fig. 4(b) together with values calculated from simulations using the as-fabricated dimensions (solid lines). Each device measured in Fig. 4(b) has a hybrid length, L = 0 μm (i.e. only the bends in the hybrid-plasmonic waveguide remain). Here, we directly extract and plot the coupling efficiency |κ|² and the uncoupled fraction |τ|². Indeed, the gap width of 145 nm from the devices in Fig. 4(a) is roughly 20 nm larger than the ideal of 125 nm. In the best case, we measure a coupling efficiency of 94%, or 0.27 dB.

5. Conclusion

We presented efficient and fabrication-tolerant directional coupling between silicon photonic and MIS hybrid-plasmonic waveguides. The measured coupling efficiency of 94% is—to the best of our knowledge—the highest reported to date for coupling to hybrid-plasmonic waveguides. The fabrication process involves only one alignment step between mask layers and is easily adaptable to be CMOS compatible. We expect this hybrid-plasmonic coupler to be a critical component in low-loss passive and active plasmonic devices.