Waveplates

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Optical waveplates (also called wave plates or retarder plates) are transparent plates with a carefully chosen amount of birefringence. They are mostly used for manipulating the polarization state of light beams. A waveplate has a slow axis and a fast axis, both being perpendicular to the beam direction, and also to each other. The phase velocity of light is slightly higher for polarization along the fast axis. The designed value of optical retardance (difference in phase delay for the two polarization directions) is achieved only in a limited wavelength range (see below) and in a limited range of incidence angles.

Common Types and Applications

The most common types of waveplates are quarter-wave plates (λ/4 plates) and half-wave plates (λ/2 plates), where the difference of phase delays between the two linear polarization directions is <$\pi /2$> or <$\pi$>, respectively, corresponding to propagation phase shifts over a distance of <$\lambda / 4$> or <$\lambda / 2$>, respectively.

Some important cases are:

• When a light beam is linearly polarized, and the polarization direction is along one of the axes of the waveplate, the polarization remains unchanged.
• When the incident polarization does not coincide with one of the axes, and the plate is a half-wave plate, then the polarization stays linear, but the polarization direction is rotated. For example, for an angle of 45° to the axes, the polarization direction is rotated by 90°.
• When the incident polarization is at an angle of 45° to the axes, a quarter-wave plate generates a state of circular polarization. (Other input polarizations lead to elliptical polarization states.) Conversely, circularly polarized light is converted into linearly polarized light.

Within a laser resonator, two quarter-wave plates around the gain medium are sometimes used for obtaining single-frequency operation (→ twisted-mode technique). Inserting a half-wave plate between a laser crystal and a resonator end mirror can help to reduce depolarization loss. The combination of a half-wave plate and a polarizer allows one to realize an output coupler with adjustable transmission.

Many waveplates are made of quartz (crystalline SiO₂), as this optical material exhibits a wide wavelength range with very high transparency, and can be prepared with high optical quality. Other possible materials (to be used e.g. in other wavelength regions) are calcite (CaCO₃), magnesium fluoride (MgF₂), sapphire (Al₂O₃), mica (a silicate material), and some birefringent polymers. The choice of material can depend on many requirements, e.g. concerning wavelength range, open aperture, absorption losses and high-power capability.

Zero-order and Multiple-order Plates

There are different kinds of waveplates:

• True zero-order waveplates are so thin that the relative optical phase delay between the two polarization directions is just <$\pi$>, for example, for a half-wave plate. The key advantage of true zero-order waveplates is that they can be used in a substantial wavelength range and range of incidence angles. In addition, their temperature sensitivity is weak.
• While zero-order waveplates offer best performance, the device thickness can be inconveniently small, particularly for strongly birefringent materials such as calcite, so that the optical fabrication becomes difficult and the handling delicate. The latter problem can be eliminated by cementing (or bonding) a zero-order plate to a thicker glass plate, which is not birefringent but provides mechanical stabilization. The resulting interface, however, leads to a lower damage threshold such as 10 MW/cm².
• Multiple-order waveplates (= multi-order plates) are made so that the relative phase change is larger than the required value by an integer multiple of 2<$\pi$>. Although the performance at the design wavelength can be essentially the same, the optical bandwidth in which the plate has roughly the correct relative phase change is quite limited, e.g. to a few nanometers. Similarly, the allowed range of incidence angles can be quite small. Also, the retardance has a higher temperature sensitivity.
• Low-order waveplates are multiple-order plates with a relatively small order, keeping the mentioned detrimental effects low.
• Effective zero-order waveplates (or net zero-order waveplates) can be made from two multiple-order plates with slightly different thicknesses, which are cemented or optically contacted, or air-spaced for application with higher optical power levels. The slow axis of one plate is aligned with the fast axis of the other plate, so that the birefringence of the two plates is nearly canceled. The difference in thickness must be adjusted to obtain the required net phase change. Such devices can work in a broad wavelength range, since wavelength-induced changes in retardance in one plate are compensated by the other plate. However, the problem of a small usable angular range and temperature range remains.

It is also possible to make achromatic waveplates, combining materials with different chromatic dispersion (e.g. quartz and MgF₂), which can have a nearly constant retardance over a very wide spectral range (hundreds of nanometers). Also, there are dual-wavelength waveplates, which have well-defined retardance values at some discrete very different wavelengths. Such features are sometimes required in the context of nonlinear frequency conversion, such as frequency tripling.

Various Issues

In addition to the fundamental optical performance, various other issues can be relevant:

• The materials should have a high transparency in the wavelength region of interest.
• The sensitivity of the phase retardance to temperature and angle depends on the design.
• High-quality waveplates exhibit a uniform retardance over the full open aperture, or a large portion of it. Where that is not the case, depolarization (more precisely, spatially dependent polarization states) can result.
• Surface reflections can be disturbing, and may be reduced with anti-reflection coatings.
• The optical damage threshold can be important for applications in pulsed laser systems.
• Some waveplates are provided with a housing which makes it easy to rotate the plate by a well-defined angle, and/or to see the orientation of the fast and slow axis.

For some applications, it can be difficult to obtain a waveplate fulfilling all the requirements. Therefore, one sometimes has to use alternative methods, for example for turning the polarization direction of a laser beam. For example, a 90° rotation of polarization (and also the beam profile) can be obtained with a combination of three 45° mirrors, subsequently deflecting the beam to the right, then upwards and finally into the original direction.

Depolarization Compensators

There are waveplates with spatially varying polarization properties, which are used within a laser resonator to reduce depolarization loss [9].

Diffractive Waveplates

Waveplates can also be realized based on an entirely different principle of operation: with photonic metasurfaces containing sub-wavelength gratings. These devices are also called diffractive waveplates [6]. They can have remarkable properties, e.g. very wideband operation.

Related Devices

There are optical devices which are somewhat related to waveplates:

• Fresnel rhomb retarders and other types of prism retarders have the same basic function as waveplates, but exploit polarization-dependent phase changes during total internal reflection. This principle allows broadband (achromatic) operation.
• A Babinet–Soleil compensator, containing a pair of birefringent wedges, can be used as a waveplate with a variable degree of retardation. Other versions of tunable waveplates such as the Berek compensator are based on variable tilting of birefringent plates.
• There are various types of fiber polarization controllers with similar functions.
• Electro-optic crystals and liquid crystal devices can be used to make electrically controllable waveplates, also called active retarders.

More to Learn

Bibliography

(Suggest additional literature!)

Suppliers

The RP Photonics Buyer's Guide contains 94 suppliers for waveplates. Among them:

Workshop of Photonics

WOP offers polarization converters which are exceptional for their ultra-high damage threshold, suitable even for high-power lasers.

S-Waveplate converts linear polarization to radial or azimuthal polarization and circular polarization to an optical vortex.

Main features:

• converts linear polarization to radial or azimuthal polarization
• converts circular polarization to an optical vortex
• high 94% transmission at 1030 nm (no AR coating)
• stand-alone – no additional optical elements needed
• high damage threshold: 63,4 J/cm² at 1064 nm, 10 ns and 2,2 J/cm² at 1030 nm, 212 fs
• suitable for high LIDT applications and high-power lasers
• reliable and resistant surface – the structure is inside the bulk

Additional waveplate assortment:

• higher order S-Waveplate: converts linear polarization to higher-order polarization patterns
• custom waveplate: enable patterned polarization control at the specific point of the laser beam

Shalom EO

Hangzhou shalom EO offers an extensive range of off-the-shelf and custom waveplates and retarders including zero-order waveplates, true zero-order waveplates, achromatic waveplates, super achromatic waveplates, dual wavelength zero-order waveplates, low-order waveplates. These waveplates composed of quartz or MgF₂ crystal plates enable unrestrained control of polarization states with the additional advantage of high damage threshold. While we also provide polymer true zero order waveplates that are less sensitive to the angles of incidence. The structures of the waveplates can be varied for different requirements, such air spaced, cemented, or optically contacted designs. Retardation values like quarter waveplates, half waveplates, λ/8, or other custom retardance are accessible. Different coatings, standard diameter 1/2”, 1” and 2” mounts, including manual rotation mounts are available.

Fresnel rhombs that create uniform λ/4 or λ/2 retardance over a wider range of wavelengths than possible with birefringent waveplates are also procurable.

Edmund Optics

Edmund Optics offers a variety of waveplates with crystalline or polymer materials, including multiple order, zero order, or achromatic waveplates. Polymer waveplates offer superior performance over a wider range of incidence angles. Multiple order waveplates are ideal for use with monochromatic light that deviates less than 1% of the waveplate’s design wavelength. Zero order retarders offer high performance over wider wavelength or temperature ranges. Achromatic waveplates offer the most constant performance over the widest wavelength or temperature ranges.

UltraFast Innovations

AURORA, by UltraFast Innovations (UFI®), is a phase retarder (quarter waveplate) with a four-mirror grazing incidence reflection geometry for the extreme ultraviolet (XUV). It covers the range from 10 to 35 eV or 40 to 85 eV photon energy and reaches >25% transmittivity around 66 eV. A clear aperture of 3 mm allows the low divergent XUV from a high-harmonic-generation HHG cell to pass through without clipping.

Knight Optical

Knight Optical offers a range of stock and custom waveplates. Our stock catalogue consists of zero and low order quartz waveplates, achromatic waveplates, mica retarders, and plastic retarders. With our custom capabilities we are able to offer a wider variety including multiple order waveplates.

OPTOMAN

OPTOMAN offers high quality zero-order air-spaced waveplates, that ensure precise and reliable polarization control across several wavelengths. These waveplates are engineered with an air-spaced design, which significantly enhances their performance by minimizing the impact of thermal effects, ensuring consistent operation even in demanding environments.

The precision engineering of these waveplates allows for stable and reliable performance, making them perfect for a wide range of laser applications, including scientific research.

In-stock waveplates can be found on OPTOSHOP.

Optogama

Optogama provides crystalline quartz waveplates, achromatic (broadband) waveplates, and mid-infrared waveplates:

• Mounted crystalline quartz zero-order compensated, air-spaced half-wave and quarter-wave retardance waveplates are designed for a particular wavelength in the range of 257 – 1550 nm. Zero-order design features lower temperature and wavelength dependence compared to low and multiple order waveplates.
• Mounted achromatic (broadband) half-wave and quarter-wave retardance waveplates are intended for several bands in the wavelength range of 460 nm – 1700 nm.
• Unique zero-order, monolithic design mid-infrared (MWIR and LWIR) waveplates for the spectral range of 2800 nm – 10600 nm are available with quarter-wave, half-wave or any other custom retardance.

Artifex Engineering

Artifex Engineering offers a wide range of custom waveplates for many applications. Waveplates, also known as retardation plates, are birefringent optical elements. Our portfolio covers achromatic, low order, zero and true zero order and MID-IR waveplates. Mounts are available for our waveplates on request. For example, we can provide true zero order plates mounted on an annular glass frame. In this manner, a robust optic is available with the full optical properties of a true zero order waveplate. In addition to single components, we will gladly provide functional subunits according to your needs. For example, we can supply isolators comprising a quarter-waveplate and polarizing beamsplitter cube mounted together in a single drop-in unit. Visit our product page for more information on each waveplate. We look forward to your inquiry.

EKSMA OPTICS

We offer a wide choice of zero-order, multiple-order and low-order waveplates made from crystalline quartz. Also, we have dual-wavelength waveplates for Ti:sapphire, Yb:KGW/KYW and Nd:YAG lasers, and achromatic waveplates for tunable lasers.

Sinoptix

We offer flat windows waveplates. λ/2 and λ/4 waveplates, custom wavelengths and cuts.

ALPHALAS

ALPHALAS offers unique tunable and standard phase retardation plates (waveplates). A single UVIR type quarter-wave or half-wave plate can be adjusted to the desired phase retardation for an arbitrary wavelength from 150 nm (vacuum-UV) to 6500 nm (far infrared) and the FIR type waveplate from 1 μm to 21 μm. The bandwidth is up-to 200 nm. They replace hundreds of ordinary phase retardation plates required to cover these ultrawide spectral ranges. The tunable waveplates are by design zero-order and can be used for polarization control of broad-spectrum laser sources like femtosecond lasers and OPOs.

Conventional zero-order, low-order and high-order waveplates for all standard wavelengths as well as customized designs and Fresnel rhombs are also available.

Applications span from polarization measurement and control, polarimetry, laser research, spectroscopy up to nonlinear optics.

Avantier

Avantier produces microwaveplates with extremely small dimensions, as small as 0.35 mm × 0.35 mm, with a tolerance of ±0.05 mm and a thickness of about 0.19 mm. For more information on our manufacturing limits or to request custom specifications, please contact us.

Shanghai Optics

Shanghai Optics manufacturers micro-waveplates as small as 0.35 mm × 0.35 mm with tolerance of ±0.05 mm and thickness about 0.19 mm. Please contact us for manufacturing limit or custom specifications.

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