Waveplate

A waveplate (also written wave plate, and also called a retarder plate or retarder) is a transparent optical element with a chosen amount of birefringence that changes the polarization state of light passing through it. It has two perpendicular axes, a fast axis and a slow axis, and delays light polarized along the slow axis relative to light polarized along the fast axis. The difference in phase delay between the two polarization directions is the plate's retardance. The two most common types are the quarter-wave plate, which converts linear polarization to circular polarization and back, and the half-wave plate, which rotates the direction of linear polarization.

In virtual reality (VR) and augmented reality (AR) hardware, waveplates are part of the polarization optics that fold the light path in pancake lenses, whose typical components include a half mirror, a quarter-wave plate and a reflective polarizer. Liquid crystal waveplates, both fixed polymer films and electrically switchable cells, are also used in research and prototype near-eye displays to switch focal planes and steer beams, and the flat liquid crystal lenses and gratings known as Pancharatnam-Berry phase optical elements are patterned half-wave plates.

Reviewed 19 October 2026. Checked every claim against RP Photonics, Jones 1941, Crossref metadata for Pancharatnam 1955, the Mukhopadhyay 2020, Lavrentovich 2004, Komanduri 2013 and Luo 2024 abstracts, the Yin 2022 and Zhan 2019 full texts, the 3M SPIE paper, three patents and Meta's Half Dome blog post. About review dates.

How it works

Axes and retardance

A waveplate is made from a birefringent material, so its refractive index depends on the polarization direction of the light. Its fast and slow axes are both perpendicular to the direction of the beam and to each other, and the phase velocity of light is slightly higher for polarization along the fast axis. The plate reaches its design retardance only within a limited range of wavelengths and a limited range of incidence angles, although slightly non-perpendicular incidence is usually acceptable. The retardance of a uniform layer is set by its birefringence (Δn) and thickness (d) relative to the wavelength (λ); Zhan and colleagues, for example, give the half-wave condition for a liquid crystal cell as Δnd = λ/2.

R. Clark Jones introduced a matrix method for such elements in a 1941 paper in the Journal of the Optical Society of America. He noted that the effect of a retardation plate on a collimated beam of polarized light is a linear transformation of the two transverse components of the electric field, so it can be written as a two-by-two matrix with complex elements. Zhan and colleagues use the Jones calculus to explain the liquid crystal elements described below.

Quarter-wave and half-wave plates

In a quarter-wave (λ/4) plate the difference in phase delay between the two linear polarization directions is π/2, which corresponds to a propagation distance of λ/4. In a half-wave (λ/2) plate it is π, corresponding to λ/2. The phase delay may also be larger by a whole multiple of 2π without changing the basic function.

Effect of a waveplate on polarized light

Incident light	Plate	Output
Linearly polarized along the fast or slow axis	Any	Unchanged
Linearly polarized at another angle to the axes	Half-wave	Still linear, with its direction rotated (by 90 degrees for light at 45 degrees to the axes)
Linearly polarized at 45 degrees to the axes	Quarter-wave	Circularly polarized
Linearly polarized at other angles	Quarter-wave	Elliptically polarized
Circularly polarized	Quarter-wave	Linearly polarized

A circular polarizer combines a linear polarizer with a quarter-wave retarder. A RealD patent on eyewear for circularly polarized 3D projection by Lenny Lipton and Rod Archer, granted on 14 April 2009, states that "a circular polarizer comprises a linear polarizer and a quarter-wave retarder" and that "the axis of a quarter-wave retarder is at 45 degrees to the linear polarizer axis"; orienting the retarder at +45 or -45 degrees gives filters of opposite handedness, so that each eye passes circularly polarized light of one handedness and blocks the other. In that eyewear the retarder faces the screen and the polarizer faces the eye.

Zero-order, multiple-order and achromatic plates

Because retardance depends on wavelength, temperature and angle, waveplates are made in several designs.

Common waveplate designs

Design	Construction	Properties
True zero-order	A plate thin enough that the phase delay is exactly the required value (for example π for a half-wave plate)	Usable over a substantial range of wavelengths and incidence angles, with weak temperature sensitivity; very thin plates are hard to make and handle, so they may be bonded to a thicker non-birefringent glass plate, which lowers the damage threshold
Multiple-order	A thicker plate whose phase delay exceeds the required value by a whole multiple of 2π	Easier to make and mechanically more stable, but the usable bandwidth can be limited to a few nanometers, the angular range is small and the temperature sensitivity is higher; low-order plates keep these effects smaller
Effective (net) zero-order	Two multiple-order plates of slightly different thickness, with the slow axis of one aligned with the fast axis of the other	Works over a broad wavelength range because the two plates compensate each other, but the angular and temperature ranges stay small
Achromatic	Materials with different chromatic dispersion combined, for example quartz and magnesium fluoride	Nearly constant retardance over hundreds of nanometers
Dual-wavelength	Designed for defined retardance at several widely separated wavelengths	Used, for example, in nonlinear frequency conversion such as frequency tripling

Achromatic retarders can also be built from combinations of several birefringent plates. S. Pancharatnam published "Achromatic combinations of birefringent plates" in two parts in the Proceedings of the Indian Academy of Sciences in April 1955. A 2020 paper by N. Mukhopadhyay, A. Saha and K. Bhattacharya summarizes his approach as a combination of three wave plates in which the fast axes of the first and last plates are parallel, and in which achromatic quarter-wave or half-wave retarders are obtained by orienting the central plate appropriately. Their own three-plate quarter-wave design, studied over 500 to 700 nm, had a reported retardation variation as low as plus or minus 0.13 degrees.

Liquid crystals allow other broadband designs. In 2004 M. D. Lavrentovich, T. A. Sergan and J. R. Kelly described a switchable achromatic half-wave retarder made of one uniformly aligned nematic liquid crystal cell between two twisted nematic layers with identical 135 degree twist angles; with no field applied it rotated linear polarization by 90 degrees, and with a high enough voltage it left the polarization nearly unchanged, with an achromatic response from 400 to 700 nm in both states. In 2013 Ravi K. Komanduri, Kristopher F. Lawler and Michael J. Escuti reported multi-twist retarders: two or more twisted liquid crystal layers on a single substrate and a single alignment layer, each layer aligned by the one below it. Quarter-wave retarders they made from a commercial polymerizable liquid crystal showed achromatic behavior over 450 to 650 nm and 400 to 800 nm.

Materials and related devices

Many waveplates are made of crystalline quartz, which is highly transparent over a wide wavelength range and can be made with high optical quality. Calcite, magnesium fluoride, sapphire, mica and some birefringent polymers are also used, depending on wavelength, aperture, absorption and power requirements. High-quality plates have uniform retardance over the open aperture, and anti-reflection coatings can reduce surface reflections. A Meta patent on pancake lenses lists quartz, stretched organic sheets and liquid crystal as possible quarter-wave plate materials.

Liquid crystal waveplates come in two forms. Passive waveplates are liquid crystal polymer films that have been stabilized with ultraviolet light, which makes them thin and light; active waveplates are liquid crystal cells that switch between states when a voltage is applied. Electro-optic crystals can also act as electrically controlled waveplates, called active retarders.

Several related devices perform the same function in other ways. A Babinet-Soleil compensator uses a pair of birefringent wedges to give a variable retardance, and a Berek compensator varies the tilt of a birefringent plate. Fresnel rhomb retarders and other reflective retarders use the polarization-dependent phase change on total internal reflection or oblique reflection, which allows very broadband operation. Waveplates can also be made as diffractive devices from photonic metasurfaces containing sub-wavelength gratings.

Applications in VR and AR

Pancake lenses

Pancake optics fold the optical path with polarization-selective elements so that a VR headset can be thinner and lighter. In their 2022 review in Light: Science & Applications, Kun Yin, Shin-Tson Wu and colleagues list the typical components of a pancake VR system as a display panel, a circular polarizer, a half mirror, a magnifying lens, a quarter-wave plate and a reflective polarizer. Because of the losses from multiple partial reflections, the optical efficiency of such a system is reduced about four times, so the display must be about four times brighter to give the same image brightness.

A patent granted to Facebook Technologies in January 2022, with Gary Dean Sharp as inventor, describes the folded light path. Linearly polarized light from the display passes a first quarter-wave retarder (in the patent's examples an achromatic compound of three quarter-wave plates), oriented at about 45 degrees to the incoming polarization, and becomes circularly polarized. About half of it is transmitted by a partially reflecting mirror, and a second quarter-wave plate turns it back to linear polarization so that the reflective polarizer reflects it. On the way back the second quarter-wave plate makes the light circular again, the mirror reflects it with the opposite handedness, and after passing the second quarter-wave plate once more its linear polarization is perpendicular to its first pass, so the reflective polarizer transmits it toward the eye.

The waveplates' imperfections affect image quality. The same patent notes that a single quarter-wave plate gives an exact quarter-wave of retardance only at its design wavelength and angle: in a color display blue light may be over-retarded and red light under-retarded, which can "lead to artifacts called see-through ghosts". As an example it gives a 15 degree retardance error causing light leakage of about 6.7%. It describes compound retarders made of three quarter-wave plates, in which the first two together act as a half-wave plate for the third, to convert broadband linearly polarized light. In a 2024 Optics Express paper, Zhenyi Luo, Yuqiang Ding, Qian Yang and Shin-Tson Wu attributed ghost images in pancake systems to stray light from multiple surface reflections and to imperfect polarization control inside the optics, and noted that the half mirror lowers the optical efficiency to 25%. See Ghost image for the wider problem.

Waveplates also have to fit curved lens assemblies. In a 2017 SPIE paper on folded optics with birefringent reflective polarizers, 3M engineers Timothy L. Wong, Zhisheng Yun, Gregg Ambur and Jo Etter described a cemented doublet design in which the beamsplitter lens and the reflective polarizer lens are made separately and a quarter-wave retarder can be built into the bond line when the two are joined. A Meta patent granted in August 2022 (inventors Jacques Gollier, Fenglin Peng, Junren Wang and Lu Lu) states that a conventional achromatic quarter-wave plate typically includes a half-wave plate and a quarter-wave plate, that its fabrication is complex and costly, and that attaching it to a highly curved optical element is difficult. It describes broadband devices built from liquid crystal polymer coatings that can be formed on a curved substrate, as an added degree of freedom in pancake lens design. Yin and colleagues also note that a cholesteric liquid crystal reflector can replace the quarter-wave plate and reflective polarizer in a pancake design, giving a simpler structure.

Switchable waveplates for focus control and beam steering

Active liquid crystal waveplates are used with polarization-dependent lenses and gratings. Yin and colleagues describe a multiplane near-eye display proposed by Lu and co-workers in which an active liquid crystal half-wave plate works with a passive liquid crystal lens: switching the waveplate rotates the polarization, which changes the lens's optical power. If the lens is replaced by a polarization-selective grating, the same switching steers the output beam, which has potential for pupil steering and foveated imaging in AR and VR. The review notes that a broadband active waveplate can be made from a twisted nematic cell or from negative-dispersion liquid crystal, but that steering and multiplexing need response times of about 1 ms and that no fast-response negative-dispersion liquid crystal had been reported at the time.

Facebook Reality Labs used this approach in the Half Dome 3 varifocal prototype it described in September 2019. Half Dome 3 replaced the moving mechanical parts of the original Half Dome with a stack of polarization-dependent lenses and switchable half-wave plates; changing the voltage on the switchable plates toggles each lens between two focal lengths, and in Meta's example six liquid crystal lenses sweep through 64 focal planes, with each additional pair doubling the number of focal planes. Creating multiple focal planes in this way is one approach to the vergence-accommodation conflict.

Geometric-phase optics

Liquid crystal Pancharatnam-Berry phase optical elements, also called diffractive wave plates, geometric phase optics or geometric phase holograms, are planar films in which the orientation of the liquid crystal varies across the surface. Zhan and colleagues describe their working principle with the Jones calculus as a half-wave plate whose local orientation angle sets the phase given to circularly polarized light, while the handedness of the light is reversed. Their cell gap is chosen to match the half-wave retardation at the intended wavelength. Lenses made this way have positive optical power for one circular polarization and negative power for the other, and they can be switched passively, with an electrically switchable polarization rotator such as a 90 degree twisted nematic cell with a λ/4 plate in front of them, or actively by applying a voltage to the element itself. Yin and colleagues describe how a liquid crystal grating is obtained by introducing a linearly varying phase profile into a liquid crystal waveplate, and a liquid crystal lens by introducing a parabolically varying phase.

See also

• Birefringence
• Polarizer
• Pancake lenses
• Catadioptric system
• Pancharatnam-Berry phase
• Liquid crystal lens
• Polarized 3D system
• Varifocal display
• Ghost image