Inverse taper

An inverse taper is a waveguide that narrows toward the edge of a chip so that its guided mode grows to match the mode of an optical fiber. In a high-index-contrast waveguide such as a silicon strip, narrowing the core pushes the mode out of it: the effective index falls toward the cladding index, the evanescent field in the cladding decays more slowly, and the mode spreads over an area many times that of the core. A standard silicon edge coupler narrows a 500 × 220 nm strip over a few hundred micrometers to a tip of about 180 nm, where the TE mode is about 2.6 µm across, and couples it to a lensed fiber or high-NA fiber with a spot of similar size. The name distinguishes it from a conventional taper, which widens a low-contrast waveguide to enlarge its mode.

Tip width and mode size

Computed at 1550 nm for a silicon tip 220 nm thick with oxide cladding on all sides, the fundamental TE-like mode:

The mode diameter is that of the Gaussian beam that best matches the mode, and the losses are the overlap with a perfectly aligned Gaussian fiber mode 2.5 µm across (a lensed fiber) or 10.4 µm across (standard single-mode fiber at 1550 nm), before Fresnel reflection, fabrication errors and substrate leakage. Between 200 and 150 nm the mode grows more than threefold while its effective index moves by only 0.03, because the decay length of the field in the cladding, $1\mathrm{/}(k_0\sqrt{n_{\text{eff}}^2-n_{\text{clad}}^2})$, grows without limit as $n_{\text{eff}}$ approaches the cladding's 1.444: it is 0.78 µm at a 200 nm tip and 2.9 µm at 150 nm. Even the best tip loses about 0.4 dB to a lensed fiber, since the mode of a small core in a uniform cladding is more sharply peaked than a Gaussian and overlaps one by only about 91% (mode mismatch loss). Its slowly decaying tails work the other way for a larger fiber mode: the 180 nm tip loses 5.0 dB to standard fiber, where a Gaussian of the same 2.56 µm diameter would lose 6.7 dB.

The TM-like mode, with its electric field along the 220 nm thickness, stays smaller at the same width: 1.7 µm across at a 180 nm tip, against 2.6 µm for TE. The two polarizations couple equally well to a 2.5 µm spot, within 0.1 dB, near a tip width of 170 nm, so a tip close to that width keeps the polarization-dependent loss low. Near 180 nm the coupling to a lensed fiber also tolerates the variation of fabrication: a tip 10 nm wider or narrower loses 0.50 or 0.58 dB instead of 0.43 dB.

Taper length

The mode follows the changing width without scattering power into radiation modes only if the width changes little over one beat length between the guided mode and the cladding, $z_b={\lambda }_0\mathrm{/}(n_{\text{eff}}-n_{\text{clad}})$, the adiabaticity criterion for tapers set out by Love and colleagues. The beat length is 1.5 µm in the 500 nm strip but 106 µm at a 180 nm tip and 600 µm at 150 nm, so a taper can narrow quickly at first and has to slow down as it approaches the tip. Tapers are typically 100 to 300 µm long; one made in two sections, or with a profile that slows toward the tip, meets the criterion in less length than a linear taper. The narrower tips that would suit standard fiber need tapers of the order of a millimeter.

Substrate leakage

In silicon on insulator the expanded mode approaches the silicon substrate beneath the buried oxide, and the part of its field that reaches the substrate leaks into it. Computed for the TE-like mode with the substrate included:

On a standard 2 µm buried oxide, every 10 µm of waveguide at a 180 nm width loses 0.18 dB to the substrate, so the section where the mode is large is kept short, the oxide is made thicker, or the substrate is etched away beneath the tip, as in suspended and cantilever couplers. The smaller TM mode leaks far less, 1.6 dB/mm at a 180 nm tip on a 2 µm oxide.

Facet and measured loss

The tip ends at a facet made by dicing and polishing, by cleaving or by a deep etch. With most of the mode in the oxide, an uncoated facet reflects about 3.5% of the power, 0.15 dB, which is still enough to form a weak Fabry-Perot cavity with the facet at the other end of a waveguide and put fringes on its transmission spectrum; an anti-reflection coating, index-matching fluid or an angled facet suppresses them. Measured losses for a lensed fiber on a standard inverse taper are typically 1 to 2 dB per facet (Edge coupler alignment). The difference from the 0.4 dB of an ideal overlap comes from variation of the tip width, facet quality, substrate leakage, loss in the taper and residual misalignment.

Coupling to standard fiber

Cleaved standard single-mode fiber, with its 10.4 µm mode, needs a larger mode than a practical silicon tip provides. The 150 nm tip comes closest, 1.2 dB in the ideal case, but with a 600 µm beat length and strong leakage into the substrate. Couplers for standard fiber therefore add a second, larger waveguide or remove what limits the mode: a silicon nitride, polymer or oxynitride overlay several micrometers across that takes the light from the silicon tip, as in the design of Shoji and colleagues; a suspended tip with the substrate removed below it; stacked or trident tapers that expand the mode in both directions; and subwavelength-grating tapers that lower the average index of the core. These structures are collectively spot-size converters, and Marchetti and colleagues review them.

Compared with a grating coupler

An inverse taper couples over more than 100 nm of bandwidth and in both polarizations, where a grating coupler has a 1 dB bandwidth of 30 to 40 nm and works in one polarization. For the 180 nm tip and a 2.5 µm spot, the computed overlap loss is 0.51 dB at 1500 nm, 0.43 dB at 1550 nm and 0.56 dB at 1600 nm. In exchange it needs a prepared facet, which in most processes exists only after dicing, so it is not normally tested on the wafer. The trade is set out in Edge couplers vs grating couplers, and the methods are compared in Fiber-to-chip coupling for silicon photonics.

Common questions

What is an inverse taper?

A waveguide that narrows toward the chip facet so that its mode expands for coupling to a fiber. It is the usual form of the edge coupler in silicon photonics.

Why does a narrower waveguide give a larger mode?

Because in a high-contrast waveguide a narrower core confines less of the field. The effective index approaches the cladding index, the evanescent field in the cladding decays more slowly, and the mode spreads out. In a 220 nm silicon layer the TE mode is about 1.0 µm across at a width of 250 nm, 1.75 µm at 200 nm and 2.6 µm at 180 nm.

What tip width does an inverse taper use?

Usually 150 to 200 nm in 220 nm silicon, set by the mode size wanted and by the smallest feature the process prints reliably. A 180 nm tip gives a TE mode about 2.6 µm across, suited to a lensed fiber with a 2.5 to 3 µm spot.

How long is an inverse taper?

Typically 100 to 300 µm. It has to be long compared with the beat length between the guided mode and the cladding near the tip, 106 µm at a 180 nm tip, so the final part of the taper changes most slowly.

References: V. R. Almeida, R. R. Panepucci, and M. Lipson, "Nanotaper for compact mode conversion," Optics Letters 28, 1302 (2003). T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, "Low loss mode size converter from 0.3 µm square Si wire waveguides to singlemode fibres," Electronics Letters 38, 1669 (2002). J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria," IEE Proceedings J 138, 343 (1991). R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, "Coupling strategies for silicon photonics integrated chips," Photonics Research 7, 201 (2019). Z. Zhu and T. G. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Optics Express 10, 853 (2002), for the mode solver.