Grating coupler

A grating coupler is a periodic set of grooves etched into a waveguide on a photonic integrated circuit that diffracts the guided light out of the chip surface, into a fiber held above it, or couples light from the fiber into the waveguide. Each groove scatters a little of the guided wave, and at one angle the scattered wavelets add in phase. For light leaving a grating of period $\mathrm{\Lambda }$ into air, first-order phase matching gives the angle $\theta$ from the vertical,

$$\sin \theta =n_{\text{eff}}-\frac{{\lambda }_0}{\mathrm{\Lambda }},$$

where $n_{\text{eff}}$ is the effective index of the guided mode in the grating region and ${\lambda }_0$ the vacuum wavelength; layers of cladding above the grating do not change the angle in air, by Snell's law. A positive angle means the beam leans forward, along the direction of propagation. Unlike an edge coupler, a grating needs no polished facet and can sit anywhere on the chip, so chips can be tested on the wafer before dicing (wafer-level test); in exchange it is selective in wavelength and polarization.

Choosing the period

Exactly vertical emission, $\theta =0$, needs $\mathrm{\Lambda }={\lambda }_0\mathrm{/}{n}_{\text{eff}}$, which is also the condition for the second diffraction order to reflect the guided wave straight back into the waveguide (Bragg condition). Gratings are therefore usually designed for a fiber tilted by several degrees, which removes the reflection and makes light from the fiber couple into one direction of the waveguide rather than both.

A first estimate of $n_{\text{eff}}$ in a shallow-etched grating is the average of the effective indices of its etched and unetched sections, weighted by the filling factor. Computed for the TE slab modes at 1550 nm under an oxide cladding, a 220 nm silicon layer has an effective index of 2.85 and the 150 nm left by a 70 nm etch 2.54, an average of 2.69 for a grating etched over half its period. With a 630 nm period that gives an angle of about 13.5° in air, and a fiber at 10° would call for a period of about 615 nm. The estimate ignores the scattering of the grooves themselves, and real designs are refined by simulation. The TM slab modes have effective indices of 2.05 and 1.61, so the same grating sends TM light out at about −39°, far from the fiber; the coupler works in one polarization only.

Efficiency

The fraction of the guided power that reaches the fiber is the product of three factors.

• Directionality, the share of the diffracted power that goes up rather than down into the substrate. In a standard silicon grating a substantial part goes down, and how much depends on the thickness of the buried oxide, which fixes the phase of the light reflected back up from the substrate.
• Overlap of the radiated beam with the fiber mode. A uniform grating radiates a field that decays exponentially along its length, and the overlap of an exponential with a Gaussian mode cannot exceed 80% (computed, one dimension), reached when the power decays over 3.8 µm for a 10.4 µm fiber mode. Apodizing the grating, weak at the start and stronger further on, shapes the beam closer to a Gaussian.
• Back-reflection into the waveguide, from the grooves and from the grating's ends.

Uniform gratings in 220 nm silicon typically lose 3 to 6 dB per coupler. Overlays that thicken the grating, and reflectors beneath it, such as a distributed Bragg reflector or a metal mirror, raise the directionality, and an apodized, fully etched grating over a metal mirror has reached a loss of 0.58 dB, 87% (Ding and colleagues). The reviews by Marchetti and colleagues and by Cheng and colleagues compare the designs.

How grating couplers are simulated, and how that differs from other devices, is covered in Choosing a Photonics Simulation Method.

Bandwidth

The angle of the beam changes with wavelength, at a rate that follows from the phase-matching condition,

$$\mid \frac{d\theta }{d\lambda }\mid =\frac{n_g-\sin \theta }{\lambda \cos \theta },$$

where $n_g$ is the group index of the grating region. A fiber held at a fixed angle loses coupling as the beam turns away from it: for a beam matched to a 10.4 µm fiber mode, 1 dB is lost at an angular mismatch of 2.6° (mode mismatch loss). With the silicon estimate above, $n_g$ = 3.6, the beam turns by 0.13° per nanometer, which gives a 1 dB bandwidth of about 40 nm, in line with the 30 to 40 nm typically measured on silicon gratings. The same estimate, $2\times 2.6\mathrm{°}$ divided by $\mathrm{\mid }d\theta \mathrm{/}d\lambda \mathrm{\mid }$, shows why silicon nitride gratings are broader: a nitride film 200 to 400 nm thick has a group index near 1.8 to 2.0, which gives 75 to 85 nm. Tilting the fiber moves the peak wavelength by the inverse of the same rate, about 8 nm per degree for the silicon grating.

Polarization and two-dimensional gratings

Because TE and TM light have different effective indices, a one-dimensional grating couples one polarization and sends the other off at a different angle, as in the example above. Since the polarization arriving through a standard fiber is not controlled, circuits that must accept any polarization, such as receivers, can use a two-dimensional grating, a square lattice of holes that couples the two orthogonal polarizations of the fiber into two separate waveguides, each then carrying TE light (Taillaert and colleagues). The two paths pass through identical circuits whose outputs are then combined, a scheme called polarization diversity.

Alignment and testing

The fiber, or a fiber array for several couplers, is held above the grating at the design angle, usually in air or in index-matching fluid, which changes the angle. For a grating whose beam matches a 10.4 µm fiber mode, the computed 1 dB tolerances are ±2.5 µm of lateral offset and ±2.6° of tilt. Active fiber alignment to surface grating couplers describes the procedure, Edge couplers vs grating couplers sets out the trade against edge coupling, and the de-embedding procedure removes the coupler loss from measurements of the devices between two gratings. Fiber-to-Chip Coupling for Silicon Photonics compares all the methods.

Common questions

What is a grating coupler?

A periodic structure etched into a waveguide on a chip that diffracts the guided light up out of the chip into a fiber held above it, or the reverse. It is the usual way to couple light to silicon photonic chips during wafer testing.

Why is the fiber tilted on a grating coupler?

Because a grating designed for vertical emission also reflects the guided light back into the waveguide by second-order diffraction. Tilting the fiber by several degrees moves the design away from that condition.

What is the coupling efficiency of a grating coupler?

Typically 25 to 50% (3 to 6 dB of loss) for a uniform grating in 220 nm silicon. Apodized gratings with a reflector beneath them have reached 87% (0.58 dB).

What limits the bandwidth of a grating coupler?

The diffraction angle changes with wavelength while the fiber stays at a fixed angle, so the coupling falls as the beam turns away from the fiber. For silicon gratings the 1 dB bandwidth is typically 30 to 40 nm; gratings in lower-index materials such as silicon nitride are broader.

References: D. Taillaert et al., "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Japanese Journal of Applied Physics 45, 6071 (2006). D. Taillaert et al., "A compact two-dimensional grating coupler used as a polarization splitter," IEEE Photonics Technology Letters 15, 1249 (2003). Y. Ding et al., "Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency," Optics Letters 39, 5348 (2014). R. Marchetti et al., "Coupling strategies for silicon photonics integrated chips," Photonics Research 7, 201 (2019). L. Cheng et al., "Grating couplers on silicon photonics: design principles, emerging trends and practical issues," Micromachines 11, 666 (2020). L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University Press, 2015).