1. Introduction

Photonic integration is considered to be a key technology for future advancements in optical communication technologies. Scaling down the optical building blocks enables complex and ultra-compact photonic circuits at a fraction of the cost of conventional systems consisting out of discrete components. Choosing an appropriate platform for developing this miniaturization technology is guided by functionality, compatibility, performance, yield and cost. Regarding the last two issues, Silicon-on-Insulator (SOI) is by far the leading technology for low-cost and high-volume photonic integration since it can benefit from the processes developed in the mature electronics industry. Although the high refractive index contrast of SOI reduces the footprint of the integrated photonic devices considerably, it becomes more difficult to achieve a high-performance mode-size convertor between a single-mode optical fiber (100μm²) and an integrated optical waveguide (0.1μm²). A possible solution is a grating coupler which is a periodic structure that couples light out of the chip to free space or to an optical fiber [1]. Fiber-to-chip grating couplers with very high efficiency have been demonstrated [2]. However, as most papers focus on coupling efficiency, polarization dependency, ease of fabrication and bandwidth, a solution for the back reflection of these grating couplers is only recently being investigated. A typical reflection back in the silicon waveguide circuit for a high-efficiency grating coupler is around −17dB [3]. Other reported high back reflections are −10dB [4], [5] and −8dB [6]. These levels of back reflections are unacceptable for integrated circuits which contain integrated lasers and amplifiers. Furthermore, back reflections are highly unwanted in interferometer based designs. Most approaches to reduce the reflection of the grating focus on optimizing the dimensions of the grating profile itself, thereby achieving back reflections of −22dB [7], −28dB [8] and −27dB [9]. In this paper we will introduce a solution for curved grating couplers which decouples the reflection at the grating from the reflection back into the waveguide, by refocusing the reflected light away from the entrance waveguide.

2. Theoretical outline

There are two main sources which contribute to the reflection from a grating coupler back into the entrance waveguide. The most important source is the second order reflection of the grating, which can be relatively broadband for high-index contrast gratings. Typically one eliminates this second order reflection by tilting the optical fiber under a small angle of around 10° with respect to the surface normal [10]. The second source of back reflection is due to the Fresnel reflection at the waveguide/grating coupler interface. This reflection is highly dependent on the grating structure itself and is very difficult to eliminate. In the proposed grating coupler design, we will refocus both sources of reflection away from the entrance waveguide thereby extinguishing the reflection almost completely.

In [11] a compact focusing grating coupler is presented which uses a curved grating to focus the coupled light into a single-mode waveguide, achieving an eight-fold length reduction as compared to a standard linear grating and adiabatic taper, without performance penalty. For the reflectionless grating coupler we follow the same design rules. The grating is curved such that a plane wavefront originating from the tilted optical fiber is diffracted to the TE-polarized mode of a broad SOI waveguide, so that the wavefront is curved cylindrically and focusing occurs in the center of curvature of the wavefront. The easiest way to describe this system is to use a polar coordinate system (r, δ) with the origin placed at the exit point of the entrance waveguide, as shown in Fig. 1. The beam will expand in the slab region with an effective refractive index n_s and after a certain length r₀ it will encounter the grating, thereby experiencing a different effective refractive index n_g. As a first approximation we assume that these effective refractive indices n_s and n_g are equal and thus α = 180° (no refraction between slab and grating region).

 

Fig. 1 Focusing grating coupler geometry parameters. The light (yellow arrows) is refracted and reflected at the first grating ellipse E_q0. τ and η are the tangent and normal line respectively of ellipse E_q0 at point (r₀, δ₀).

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The phase matching condition is now [11]:

 

Fig. 2 Reflection from curved grating couplers for different waveguide angles σ. The k-diagram is drawn for σ = 0° (a), σ = 45° (b) and $\sigma ={\text{cos}}^{-1}\left(\frac{n_c\text{sin}\varphi }{n_s}\right)$ (c) which corresponds to both the optimal reflection waveguide angle and second order reflection angle. (K⃗ = reciprocal lattice vector) The entrance waveguide is optimized for low reflection (d).

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To obtain the appropriate first grating line number q₀, we calculate the in plane aperture opening angle ε of the entrance waveguide using a 3D mode propagation tool. This angle will determine the focusing length of the slab r₀ and thus q₀ such that the width of the diffracted beam matches the width of the Gaussian fiber mode. In [11] it was shown that this focusing length has no influence on the grating coupler performance and can be chosen freely. However, in the reflectionless grating coupler design, the larger the focusing length, the larger is the distance from entrance waveguide to the the closest focal point f_2,q0 whereto the reflected light is refocused, thereby minimizing the reflection coupled back into the entrance waveguide. On the other hand, a larger focusing length is accompanied by a broader waveguide aperture and thus a larger chance to recapture reflected light back into the entrance waveguide. Depending on the exact entrance waveguide geometry, a proper waveguide width should be chosen.

There exists a waveguide angle σ of the entrance waveguide wherefor the angle between the incident light and the reflected light is maximal. This optimal reflection waveguide angle $\sigma ={\text{cos}}^{-1}\left(\frac{n_c\text{sin}\varphi }{n_s}\right)$ is derived by maximizing the reflection angle θ₀(δ₀) given by

 

Fig. 3 The reflection angle θ₀ as a function of δ₀ for ϕ = 15° (a) and the optimal entrance waveguide angle σ and corresponding θ₀ as a function of ϕ (b) for λ₀ = 1.55μm. Simulated coupling efficiency (c) for different waveguide angles σ (etch of 70nm, ϕ = 15°).

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3. Design improvements

Achieving ultra-low reflections means reducing every possible reflection source. One important source of parasitic reflections is due to discontinuities such as at the exit of the entrance waveguide. These can be minimized by angling the trenches as is shown in Fig. 2(d). The grating reflected and refocused light can be reflected back onto the grating and thus back into the waveguide. Therefore we also need to make sure that the reflected light is not normally incident on any feature.

Another improvement is to differentiate between the effective refractive index of the grating n_g and the effective refractive index of the slab region n_s (see Fig. 1). The phase matching condition for the first grating line corresponding to q₀ will stay the same, i.e. Eq. (1). At this first grating line, the light will transition from a slab with refractive index n_s to a grating region with refractive index n_g and thus be refracted at this interface under an angle ${\theta }_1={\text{sin}}^{-1}\left(\frac{n_s\text{sin}{\theta }_0}{n_g}\right)$ according to Snell’s law. The angle between the incoming beam and refracted beam is thus α = π + θ₀ − θ₁. Solving the phase condition numerically

4. 3D FDTD simulations

The grating couplers, designed using Eq. (4), were simulated using full-vectorial 3D FDTD software such as [12]. To calculate the reflection spectra, a pulse with a Gaussian time profile was launched in the single-mode access waveguide and the reflected flux was measured in that same waveguide (see Fig. 4(a) ( Media 1)). The coupling efficiency was simulated by the normalized power in the single-mode waveguide after launching a Gaussian mode under the correct angles and polarization (see Fig. 4(b) ( Media 2)). We have found that the optimal reflection waveguide angle does indeed have the lowest back reflection, but at the price of a coupling efficiency penalty of around 2dB (see Fig. 3(c)). This is because this waveguide angle corresponds to the angle for second order Bragg reflection (case σ = cos⁻¹(n_c sinϕ/n_s)) when K⃗.k⃗_z = 0 (see Fig. 2(c)). Figure 5 shows the spectra of the reflection back in the entrance waveguide of the proposed grating coupler for different waveguide angles σ. For the shallow etched gratings (70nm etch in a 220nm Si core) and for fiber tilt angle ϕ = 10°, the second order back reflection present at the higher wavelengths decreases by 5dB to 10dB for waveguide angles up to 45° without coupling efficiency penalty (typical grating coupler efficiency is around 30%) achieving a back reflection of −40dB (Fig. 5(a)). We see that mainly the second order reflection (case σ = 0°) present at the higher wavelengths is reduced. This second order reflection can be easily reduced by increasing the fiber tilt angle to 15° and even more using the novel grating coupler design. The reflection reduction is the most pronounced in the case of fully etched grating couplers (220nm etch in a 220nm Si core) having a typical efficiency around 10%. The back reflection decreases from −7dB to −28dB for σ = 45° (Fig. 5(b)).

 

Fig. 4 3D FDTD simulations showing (a) the refocusing of the reflection using an over-saturated electrical field ( Media 1) and (b) waveguide coupling when excited from the fiber ( Media 2) (σ = 90°, ϕ = 15°)

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Fig. 5 Reflection spectra for shallow (a) and fully etched (b) grating couplers, each time for different values of the waveguide angle σ and fiber tilt angle ϕ.

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5. Conclusion

We have investigated a reflectionless grating coupler design by means of 3D FDTD simulations. The grating is curved and refocuses the reflection away from the entrance waveguide thereby realizing a 5dB to 10dB reflection reduction down to −40dB for shallow etched gratings, the same back reflection performance of a typical optical fiber connector, without introducing a coupling efficiency penalty. Furthermore, we showed that this method can be used to reduce the reflection of highly reflective (−7dB) deeply etched grating couplers to useful reflections of −28dB. These devices could become key components in interferometer based designs and circuits using integrated lasers and amplifiers.