User:TMM53/Lyot filter-2024-02-21

A Lyot filter (polarization-interference monochromator, birefringent filter), named for its inventor and French astronomer Bernard Lyot, is a type of optical filter that uses birefringence to produce a narrow passband of transmitted wavelengths. Lyot filters are used in astronomy, particularly for solar astronomy, lasers, biomedical photonics and Raman chemical imaging.

Single plate optical filter
For a typical single plate Lyot filter, light travels through a horizontal polarizer, then through a uniaxial anisotropic waveplate (retarder), then through a second horizontal polarizer. The waveplate's face and optic axis are perpendicular to the light's path, and its optic axis is oriented 45 degrees relative to the direction of horizontal polarization. The waveplate may transform the light's polarization from full horizontal polarization to a polarization that may be attenuated by the second horizontal polarizer. This single plate optical filter transmits light intensity $$I_{T}$$ from an input of horizontally polarized light intensity $$I_{X}$$ with wavelength $$\lambda$$, waveplate thickness $$d$$, waveplate ordinary refractive index $$n_{o}$$ and waveplate extraordinary refractive index $$n_{e}$$:
 * $$ I_{T}=I_{X} \cdot \operatorname{cos}^{2} \left( \frac{\pi (n_{o}-n_{e}) d}{\lambda} \right) $$

Multiplate optical filter
Multiplate filters are series of single plate filters with each waveplate half the thickness of the preceding plate. The addition of thicker waveplates reduces the width of the transmission curve, and the narrowest plate determines the free spectral range which is the wavelength interval between adjacent major peaks of transmitted light. Extending the prior equation to $n$ plates, this multiplate optical filter transmits light intensity $$I_{T}$$ from an input of horizontally polarized light intensity $I_{X}$ :
 * $$ I_{T}=I_{X} \cdot \operatorname{cos}^{2} \left( \frac{2 \pi (n_{o}-n_{e}) d}{2 \lambda} \right) \cdot \operatorname{cos}^{2} \left( \frac{2 \pi (n_{o}-n_{e}) d}{2^{2} \lambda} \right) \cdot \ldots \cdot \operatorname{cos}^{2} \left( \frac{2 \pi (n_{o}-n_{e}) d}{2^{n} \lambda} \right) $$

Design features
The waveplates are commonly quartz or calcite. Rotating the waveplate may shift the wavelength of the transmission peaks. Splitting the crystals in half and adding a 1/2 waveplates in the middle increases the filter's field of view. The separation and narrowness of the transmission peaks depends on the number, thicknesses, and orientation of the plates. Due to the temperature dependent birefringent properties of quartz and calcite, the Lyot filter requires a thermostat to minimize temperature fluctuations.

Tunable filters
A electrically tunable Lyot filter contains tuneable electro-optic or liquid crystal birefringent elements. The tunable electro-optic Lyot filter uses lead magnesium niobate-lead titanate (PMN-PT) opto-ceramic to tune the filter. Liquid crystal tunable filters allow analog tuning of the transmitted wavelength by carefully adjusting the voltage over the liquid crystal cells. Liquid crystal Lyot filter spectral bandpass may range from 30 nm to 0.05 nm. The two categories of Lyot liquid crystal filters are polarizing interference retardance filters and electro-optical photonic crystals. Often these filters are based on the original Lyot design, but many other designs exist in order to achieve other properties such as narrow or broad band transmission, or polarization selectivity.

Comparative performance
The Lyot filter and Fabry-Perót filter are the most common tunable electro-optic filters. In comparison to the Fabry-Perót filter, the tunable Lyot filter has broader and more stable adjustable range, but the Lyot filter transmits less light. Poor transmittance occurs due to the large number of highly absorbing polarizers and imperfect waveplate action. Lyot filters may contain up to 12 individual filters, making the Lyot filter expensive, limiting its use in compact instruments. In contrast to Lyot filters, the Solc filter relies on only 2 polarizers leading to less light reduction.

Applications
In solar astronomy, viewing the sun's chromosphere, the sun's second atmospheric layer, requires narrow band optical filters (spectroheliograph),such as a Lyot filter, using wavelengths for viewing solar flares, prominences, filaments, and plages arising from calcium and hydrogen.

Single and multi-plate Lyot filters are often used inside the optical cavity of lasers to allow tuning of the laser. In this case, Brewster losses from the plate and other intracavity elements are usually sufficient to produce the polarizing effect and no additional polarizers are required. Lyot filters are used also in broadband Ti—sapphire lasers, and dye laser oscillators for wavelength selection.

Although their mechanisms are different, modelocking lasers and Lyot-filter lasers both produce a comb of multiple wavelengths which can be placed on the ITU channel grid for dense wave division multiplexing (DWDM) or used to give each suburban home its own return-signal laser wavelength in a passive optical network (PON) used to provide FTTH (Fiber To The Home).

Another application has been use of Lyot filters is for Raman chemical imaging. Other applications have been in microspectrometer and hyperspectral imaging devices and biomedical photonics.