Prism coupler

A prism coupler couples free-space light into a thin-film waveguide through its top surface. A high-index prism is pressed against the film so that a gap of roughly 0.1 µm or less remains, and a laser beam entering through the prism strikes its base beyond the critical angle. The beam is totally reflected, but its evanescent field reaches across the gap into the film, and at a discrete set of angles, one for each guided mode, power tunnels into the film and propagates along it. The arrangement is an application of frustrated total internal reflection. Analyzed by Tien and Ulrich in 1970, it is mainly used today for the measurement of the index and thickness of dielectric films: an accuracy in index of about 10⁻⁴ is typical for films that support two or more modes.

Phase matching

Light couples into mode $m$ when the component of its wavevector along the base equals the mode's propagation constant:

$$n_p \sin\theta_m = n_{\text{eff},m}$$

where $n_p$ is the prism index, $\theta_m$ the angle of incidence on the base inside the prism, and $n_{\text{eff},m}$ the effective index of the mode. For $n_p$ = 2.2 and $n_\text{eff}$ = 1.9 the coupling angle is 59.7°. The condition can be met only when $n_p > n_\text{eff}$, so films of high index need prisms of higher index still. Instruments convert this internal angle to the external angle at the entrance face with Snell's law.

The air gap sets the coupling strength. The evanescent field in the gap decays over a length

$$d = \frac{\lambda}{2\pi\sqrt{n_\text{eff}^2 - 1}}$$

which is 62 nm at 633 nm for $n_\text{eff}$ = 1.9, so the gap must be comparable, and it is adjusted by the clamping pressure. Because the same gap also lets guided light leak back out into the prism, the best input efficiency is obtained with the beam centered near the prism's edge, so that the light leaves the coupling region once it is in the film; for a Gaussian beam and a uniform gap the theoretical limit is about 80 %.

Measuring films: the mode spectrum

In a measurement the prism and film rotate together while a detector records the light reflected from the base. At each mode angle part of the beam enters the film and the reflected signal dips; light scattered within the film into other modes couples back out through the prism and shows on a screen as bright lines, the m-lines that give the method its common name. Each dip gives one $n_{\text{eff},m}$. Since every effective index of a slab waveguide depends on the film index $n_f$ and thickness $t$ through the mode equation, two modes of the same polarization fix both unknowns, and further modes test whether the film is uniform.

As an example, a film of index 2.0 and thickness 1.0 µm on fused silica (1.457) in air guides five TE modes at 633 nm:

The angular sensitivity is high: near 59.7°, a change of 10⁻⁴ in $n_\text{eff}$ moves the coupling angle by 90 µrad, about 19 arcseconds. TE and TM modes are measured separately with the corresponding polarization, which gives the film's birefringence directly. The same film supports two TE modes only above a thickness of 279 nm; thinner films give a single mode, and then either the index or the thickness must be known in advance. The procedure is compared with ellipsometry and bulk methods in How to Measure Refractive Index.

Comparison with other couplers

A grating coupler performs the same phase matching with a diffraction grating etched into the waveguide and must be fabricated for a design angle and wavelength. An edge coupler launches light into a polished or cleaved end facet. The prism coupler needs no fabrication on the sample, which suits it to unpatterned layers, but it is too bulky for packaged devices.

Pitfalls

The prism's refractive index and its dispersion must be known accurately, since every result scales from $n_p$. Pressing a hard prism onto a soft polymer or sol-gel film can deform or scratch it. A film on a substrate of higher index, such as silicon, does not guide and shows broad, shallow dips instead of sharp ones, so such films are measured on a lower-index buffer layer.

Common questions

Why must the prism index exceed the film's?

It must exceed the effective index of each mode to be excited. The tangential wavevector available in the prism is at most $n_p k_0$, reached at grazing incidence, and a mode with a larger propagation constant cannot be matched.

Can a prism coupler measure a single-mode film?

Yes, with a known thickness or index. One mode angle gives one equation, so only one of the two film parameters can be found from it.

References: P. K. Tien and R. Ulrich, "Theory of prism-film coupler and thin-film light guides," J. Opt. Soc. Am. 60, 1325 (1970); R. Ulrich and R. Torge, "Measurement of thin film parameters with a prism coupler," Appl. Opt. 12, 2901 (1973); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).