AR waveguide display

An AR waveguide display is a combiner that superimposes a virtual image on the real world in augmented-reality glasses. A projector with a microdisplay (LCoS, a micro-LED array, or a scanned laser diode) produces a collimated image, one plane wave per pixel. An in-coupler injects these waves into a glass plate typically 0.5–1.5 mm thick, where they travel by total internal reflection toward the eye region. The beam is split repeatedly so the small projector pupil is copied over a larger area (exit-pupil expansion), and an out-coupler releases part of the light at each bounce.

Couplers

Three coupler families are in use:

• Surface relief gratings: etched or imprinted diffraction gratings with periods of a few hundred nanometers, often slanted to favor one order.
• Volume holograms: refractive-index gratings recorded in a photopolymer by holography. They diffract only near the Bragg condition, so each one is selective in angle and wavelength.
• Reflective arrays: a row of embedded partially reflecting mirrors at an angle to the plate. Reflection makes them nearly dispersion-free.

For a reflective array to send equal power out at each of $N$ mirrors, the $k$-th mirror must reflect a fraction $1/(N-k+1)$ of the light reaching it; for five mirrors the reflectances are 20%, 25%, 33%, 50% and 100%. Metasurfaces are also studied as couplers.

Field of view and refractive index

The field of view is limited by the range of angles the plate can guide. A ray inside glass of index $n$ at angle $\theta$ from the normal is trapped only above the critical angle, $\sin\theta > 1/n$. Near grazing incidence the bounces become so sparse that replicated pupils separate, so designs keep $\theta$ below a practical maximum, assumed here to be 75°.

Writing the in-plane wavevector in units of $k_0 = 2\pi/\lambda$, a guided ray occupies the band

$$1 < n\sin\theta < n\sin 75^\circ$$

A grating of period $\Lambda$ shifts an incoming field angle $\theta_a$ (in air) along one direction by $\lambda/\Lambda$:

$$n\sin\theta = \sin\theta_a + \frac{\lambda}{\Lambda}$$

The width of the guided band, $n\sin 75^\circ - 1$, is the total span of $\sin\theta_a$ that fits. Centering the field on the display axis gives a horizontal field of view

$$\text{FOV} = 2\arcsin\!\left(\frac{n\sin 75^\circ - 1}{2}\right)$$

with the grating period chosen so that $\lambda/\Lambda$ sits at the center of the band. For a single grating at 530 nm, considering one in-plane direction only:

Hence the demand for high-index glass. Two-dimensional designs with a turning grating have a more complicated k-space geometry, but the guided band still sets the limit.

Color and rainbow artifacts

The shift $\lambda/\Lambda$ depends on wavelength, so a grating designed for green moves red and blue fields to different parts of the guided band. With $n = 1.5$ and the 433 nm period above, the guided range runs from about −3.6° to 22.7° for 460 nm and from about −27.1° to −0.4° for 630 nm; the field common to 460, 530 and 630 nm is only about 3° wide. Full-color displays therefore often stack two or three plates. Gratings also diffract ambient light from bright off-axis sources such as ceiling lamps into the eye, producing colored streaks called rainbow artifacts.

Eye box and efficiency

The eye box is the region in which the eye can move and still see the whole image, typically on the order of 10 mm across. Exit-pupil expansion fills this region by spreading the projector's light over its whole area, while the eye pupil, a few millimeters wide, collects only part of it. A 4 mm pupil in a 10 mm × 10 mm eye box intercepts about 13% of the area; together with coupler losses this is why overall efficiency from display to eye is low, commonly reported at a few percent or less. This follows from conservation of étendue: a larger eye box at fixed field of view needs more étendue, which replication supplies at the cost of brightness. Pupil replication also depends on plate thickness: in a 1 mm plate at a 50° guided angle, successive bounces on the same surface are 2.4 mm apart, and this replica spacing must stay below the eye pupil diameter to avoid dark bands.

Pitfalls

Coupler efficiency varies with angle and wavelength, so brightness and color are often non-uniform. A small wedge or warp in the plate sends each replica in a slightly different direction and blurs the image. Ghosts from unwanted diffraction orders and bright surroundings limit contrast.

Common questions

Why do AR glasses use waveguides instead of conventional optics?

The projector can sit at the temple while the image appears in front of the eye, through a plate as thin as a spectacle lens.

What limits the field of view of AR glasses?

For diffractive waveguides, the range of angles that stay guided between the critical angle and a grazing limit, which depends on the refractive index of the plate. Higher index allows a wider field, as the table shows.

Why do some waveguide displays show rainbows?

Gratings are dispersive: they send different wavelengths in different directions. Diffracted ambient light and imperfect color matching between plates appear as colored fringes.

References: B. C. Kress, Optical Architectures for Augmented-, Virtual-, and Mixed-Reality Headsets (SPIE Press, 2020); Saleh & Teich, Fundamentals of Photonics 3rd ed. (2019); Goodman, Introduction to Fourier Optics 4th ed. (2017).