Total internal reflection

Total internal reflection (TIR) is the complete reflection of light at the boundary between two transparent media, which happens when light travelling in the medium with the higher refractive index strikes the boundary at an angle of incidence larger than the critical angle. Below that angle part of the light is refracted out and part is reflected; above it, all of the optical power is reflected back into the denser medium. Light guidance in typical optical fibers can be understood on the same basis.

In augmented reality hardware, TIR is the mechanism behind the waveguide combiner, the thin see-through plate used in headsets and smart glasses such as the Microsoft HoloLens 2 and the Meta Ray-Ban Display. Light from a display engine is injected into the plate at angles of incidence large enough to be trapped, travels across the lens by repeated internal reflections, and is released toward the eye in front of the pupil. Because the range of angles that can be trapped depends on the refractive index of the plate, TIR also sets the upper limit on the field of view such a combiner can carry, and AR optics developers have pursued higher-index glass and crystalline materials such as silicon carbide for that reason. TIR is also used in folded prism eyepieces, including freeform prisms and the flat-prism optics of some birdbath-type AR glasses.

Reviewed 15 October 2026. Physics, Colladon history, waveguide and TIR-prism claims checked against RP Photonics, HyperPhysics, the EPFL abstract, PubMed abstracts and Crossref records of the cited papers, the Xiong 2021 and Rolland 2024 full texts, the Lumus patent and pages, Coherent, Meta, Microsoft, OPN, Laser Focus World and Guttag sources. About review dates.

Physics

Critical angle

When light passes from a medium of refractive index n₁ into a medium of lower index n₂, it bends away from the normal, so the refracted ray leaves at a larger angle than the incident ray. As the angle of incidence grows, the refracted angle approaches 90 degrees; the angle of incidence at which it reaches 90 degrees is the critical angle. Setting the refraction angle to 90 degrees in Snell's law gives the critical angle as the inverse sine of n₂/n₁. TIR can only occur for light arriving from the higher-index side of the boundary; light entering glass from air never undergoes it.

The critical angle depends only on the two indices. HyperPhysics gives 48.6 degrees for light going from water into air. RP Photonics gives 43.6 degrees for light leaving a medium of index 1.45 (silica at 1064 nm) into air, and notes that above that angle the reflectivity reaches 100 percent for both s and p polarization, assuming a perfect surface. A higher-index medium has a smaller critical angle, so it reflects totally over a wider range of incidence angles. For angles below the critical angle, part of the light is transmitted and part reflected, in proportions given by the Fresnel equations.

Evanescent wave and frustrated TIR

Although no power is transmitted during TIR, the optical field penetrates a short distance into the lower-index medium. This evanescent wave decays exponentially away from the interface, usually over a very short length, and carries no energy across the boundary. The reflected beam is also displaced slightly along the interface, an effect known as the Goos-Hänchen shift.

If a second high-index medium is brought close enough to the boundary to reach the evanescent field, some light tunnels across the gap and the reflection is no longer total. This is called frustrated total internal reflection (FTIR). The coupling is very sensitive to the gap width, which is why prisms placed near a reflecting surface can be used to couple light in or out of an optical resonator.

History

According to a 2011 EPFL symposium abstract, guiding light by total internal reflection was first demonstrated in 1841 by the Geneva physicist Jean-Daniel Colladon (1802-1890), who guided light in a jet of water at the Academy of Science in Geneva (now the University of Geneva) and described the experiment in the French Academy of Sciences' journal Comptes rendus in 1842. The experiment was later reproduced many times and applied to the illumination of water fountains, including at the 1889 Paris World Exposition. John Tyndall performed similar experiments at the Royal Institution in London in 1854; the same abstract says he is still often, mistakenly, considered the inventor of light guiding in the English-speaking world. The same principle underlies the guidance of light in optical fibers.

Planar substrates that guide light by TIR were later applied to see-through displays. In 1995 Y. Amitai, S. Reinhorn and A. A. Friesem published a visor display based on planar holographic optics in Applied Optics: one holographic element on a flat substrate collimated light from each display point into a plane wave trapped in the substrate by TIR, and a second element on the same substrate diffracted that light into the observer's eye. A later patent by Yaakov Amitai, "Substrate-guided optical beam expander" (priority date June 2000, granted as US 6,829,095 in December 2004, original assignee Lumus), described a light-transmitting substrate, optics that couple light into it by total internal reflection, and a series of parallel partially reflecting surfaces inside it. Lumus's current geometric waveguides likewise use arrays of mirrors to expand the guided light and couple it out.

TIR in AR waveguide combiners

How light is trapped and released

A waveguide combiner has three stages. An in-coupler (for example a prism or a diffraction grating) sends light from the display engine into the plate at an angle greater than the critical angle, so it cannot escape through the surfaces. The light then zigzags along the plate by TIR until it reaches an out-coupler, which redirects it toward the viewer's eye. Xiong, Hsiang, He, Zhan and Wu, in their 2021 review of AR and VR displays, define the term this way: "The term 'waveguide' indicates the light is trapped in a substrate by the TIR process."

Waveguides do not release the light in one place. In the exit pupil expansion (EPE) process, "a portion of the trapped light is repeatedly coupled out of the waveguide in each TIR", which replicates the small projector pupil across a larger area and enlarges the effective eye box. Rolland and Goodsell describe how each ray is replicated in an expander region through interactions with mirrors (in geometric waveguides) or gratings (in diffractive waveguides), then expanded again in the orthogonal direction at the out-coupler; this enlarges the eye box without reducing the field of view, at the expense of displayed brightness.

Xiong et al. divide waveguide combiners by the kind of coupler they use; both kinds guide the light by TIR:

Type	In-coupler	Out-coupler	Notes
Diffractive waveguide	Usually a diffraction grating	A grating, usually with the same period as the in-coupler	The grating shifts the light's in-plane wave vector into the range that is trapped by TIR; unwanted diffraction can leak light outward or produce rainbow artifacts from ambient light
Geometric (reflective) waveguide	Usually a prism, to avoid the color dispersion of a diffractive element	An array of partial mirrors that couple out TIR light one after another	Usually better MTF and color uniformity than diffractive designs, but the discontinuous mirrors can leave gaps in the eye box

Lumus describes its current 2D-expansion geometric waveguides this way: light enters through a coupling prism, expands along a first array of mirrors that also diverts it toward a second array, and is coupled out to the eye by the second array. Lumus states that its waveguide is the one used in the Meta Ray-Ban Display glasses. Microsoft lists the display optics of the HoloLens 2 as "See-through holographic lenses (waveguides)".

Refractive index and field of view

Every field angle the display shows must travel inside the plate at an angle that satisfies the TIR condition, so the substrate index bounds the field of view. Xiong et al. show this with wave-vector (k-space) diagrams: trapped light lies in a ring between radius k₀ and n times k₀, where n is the substrate index, and the usable field of view is "mostly limited by the width of TIR band". To fit a larger field of view, "the outer boundary of TIR band needs to be expanded, which amounts to increasing waveguide refractive index"; the theoretical upper limit is set by that index. Rolland and Goodsell likewise list "the maximum FOV constrained by the waveguide refractive index and the critical angle of TIR" among the fundamental constraints on waveguide combiners, noting that light shifted inside the ring's inner limit fails the TIR condition and leaks out.

The practical range is smaller than the theoretical one. Near the outer edge of the band, light travels through the plate at close to 90 degrees from the normal, so the distance between consecutive TIR bounces becomes so large that the out-coupled beams separate and the image loses uniformity.

Material makers have used this relationship to argue for higher-index substrates. Quoted in a 2018 Optics & Photonics News article, Rüdiger Sprengard, head of AR operations at Schott, said that a high refractive index "basically translates directly into a wide field of view" and that the roughly 1.5 index of standard display glass was "not good enough". The article explained that a high index contrast with air gives a larger acceptance angle for TIR, and reported that Schott's RealView glass raised the index to about 1.6 to 2.0. Coherent, which makes crystalline substrates, wrote in 2024 that the highest index then achievable with glass was about 2.0, compared with 2.3 for lithium niobate and 2.7 for silicon carbide, and that silicon carbide could allow red, green and blue to share a single waveguide instead of two or three plates.

Meta described the same relationship in a 2025 post about the silicon carbide waveguides developed for its Meta Orion AR glasses: the larger a material's refractive index, the larger the field of view the display can support. According to Meta, when Giuseppe Calafiore joined Oculus Research in 2016 the highest-index glass available to the team was 1.8, which required stacking multiple plates to reach the desired field of view; silicon carbide has an index of 2.7. Meta gives Orion's field of view as approximately 70 degrees and says Orion proved that silicon carbide is a viable option for AR glasses.

Image artifacts

Several artifacts of diffractive waveguides come from the gratings that move light into and out of the TIR path. Xiong et al. describe light leakage (out-coupled light escaping outward, which lowers efficiency, produces a "bright-eye" appearance and raises privacy concerns), see-through ghost images formed by consecutive in-coupling and out-coupling of real-world light at the out-coupler grating, and rainbow effects from ambient light diffracted into the eye.

TIR prisms and free-space combiners

Optical designers also use one or two TIR reflections inside a solid prism to fold the light path of an eyepiece, without the many bounces of a waveguide. Xiong et al. list the TIR prism alongside birdbath optics as a way of folding the optical path in free-space AR combiners.

One example is the wedge-shaped freeform prism. In a 2009 Applied Optics paper, Dewen Cheng, Yongtian Wang, Hong Hua and M. M. Talha described an optical see-through head-mounted display built from a plastic prism with three freeform surfaces, cemented to a freeform lens that keeps the real-world view undistorted. With a 0.61 in microdisplay it gave a 53.5 degree diagonal field of view at f/1.875, with an 8 mm exit pupil, 18.25 mm eye relief, and an optical system per eye no larger than 25 by 22 by 12 mm and weighing 8 g. Xiong et al. cite this design as a freeform TIR-prism combiner. Writing in Laser Focus World in 2012, Cheng, Wang, Hua and José Sasián explained that designing such prisms needs "total internal reflection (TIR) constraints and anti-TIR constraints" to form a correct ray path, and described tiling freeform prism eyepieces to widen the field of view, with a design example of 56 by 45 degrees and a six-prism example of up to 119 by 56 degrees.

TIR also appears in newer birdbath variants. In his 2025 analysis of the "flat prism" optics of the Xreal One Pro, Karl Guttag explained the design with Ant-Reality concept diagrams that he found identical to Xreal's. Ant-Reality's Crossfire design sends the display light by a TIR bounce into a polarizing beam splitter at a shallower angle than the roughly 45 degree splitter of a common birdbath, and Guttag wrote that the same concept can be applied to a single display and prism. In the flat-prism layout the splitter no longer has to sit at 45 degrees because of the angle at which light reaches it after the TIR reflection, so the eye can get closer to the curved mirror; an air gap between the beam-splitter prisms and the curved mirror enables the TIR. Guttag noted that TIR requires solid optics, whereas a birdbath can be in air, so such designs tend to be heavier even when they are smaller. He also noted that LetinAR used a single TIR reflection with a spherical collimating mirror in its PinTilt design.

See also

• Waveguide display
• Optical combiner
• Freeform optics
• Birdbath optics
• Exit pupil
• Eye box
• Near-eye display
• Holographic optical element
• Diffraction grating