Lyot filter

Astronomical spectral light processor

A Lyot filter (polarization-interference monochromator, birefringent filter),^[1]^: 106 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.^[2]^[3]^: 177 Lyot filters are used in astronomy, particularly for solar astronomy, lasers, biomedical photonics and Raman chemical imaging.^[4]^: 2.5.2^[5]^: 163^[6]^: 5.8.3^[7]^: 202^[8]^: 327^[9]^: 14

Basic principles

The light's path (red dashed line) through a single plate Lyot filter. The 1st polarizer transmits horizontally polarized light to the waveplate. The waveplate's fast (F) and slow (S) transmission directions make a 45 degree angle to the horizontal. For the wavelength in this example, the waveplate transforms the light's horizontal polarization to a circular polarization. The 2nd polarizer transmits only part of the light, the horizontal component of the circularly polarized light, leading to a wavelength dependent amount of light transmission.

This section describes how the Lyot filter's wavelength dependent transmission of light arises from birefrigence.

Single plate optical filter

The Lyot filter relies on light's polarization property, a vector (Jones vector) perpendicular to light's path that has a fixed direction (linear polarization) or a time-varying rotating direction (circular or elliptical polarization). For a typical single-plate Lyot filter, light passes through 3 consecutive optical elements that modify the light's polarization: the first horizontal polarizer, a waveplate (retarder) and a second horizontal polarizer.^[10]^[11]^: 95–96 Lineaerly polarized light travels fastest when aligned with the waveplate's fast F direction, and slowest when aligned with the waveplate's orthogonal slow S direction.^[12]^: 125^: 127 The speed difference depends on the difference between the waveplate's ordinary refractive index and extraordinary refractive index.^[11]^: 95–96 This example assumes that the horizontal makes a 45 degree angle with the waveplate's F and S directions.^[11]^: 95–96

The first horizontal polarizer transforms the incoming light's polarization to horizontally polarized light by passing only the incoming light's horizontal polarization component. The waveplate may modify the incoming horizontally polarized light to a different polarization based on the light's wavelength. The second horizontal polarizer passes only the horizontal polarization component of the light exiting the waveplate. For example, at one wavelength, if the light exiting the waveplate is horizontally polarized, then the light passes through the second horizontal polarizer fully, exiting the optical filter with no attenuation. At a different wavelength, if the light exiting the waveplate is vertically polarized, then no light passes through the second horizontal polarizer, and no light exits the optical filter. At most wavelengths, some wavelength-dependent attenuation will occur.

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 $n_{e}$ :^[11]^: 95–96^[10]

I_{T}=I_{X}\cdot \operatorname {cos} ^{2}\left({\frac {\pi (n_{o}-n_{e})d}{\lambda }}\right)

Multiplate optical filter

Multiplate filters are a series of consecutive single plate filters with each waveplate half the thickness of the preceding plate.^[10] Using this design, a graph describing the transmitted light intensity at each wavelength will show sharper major peaks (narrower bandwidth) of transmitted light and a greater wavelength interval between the major peaks of transmitted light (free spectral range).^[11]^: 95–96^[1]^: 108 As an example, extending the single plate equation to a 3-plate optical filter with maximum waveplate thickness $d$ , this multiplate optical filter transmits light intensity $I_{T}$ from an input of horizontally polarized light intensity ${\textstyle I_{X}}$ :^[10]

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 \operatorname {cos} ^{2}\left({\frac {2\pi (n_{o}-n_{e})d}{2^{3}\lambda }}\right)

Design features

The waveplates are commonly quartz or calcite.^[1]^: 109 Rotating the waveplate may shift the wavelength of the transmission peaks.^[4]^: 2.5.2 Splitting the crystals in half and adding a 1/2 waveplate in the middle increases the filter's field of view.^[10] The separation and narrowness of the transmission peaks depends on the number, thicknesses, and orientation of the plates.^[12]^: 125 Due to the temperature dependent birefringent properties of quartz and calcite, the Lyot filter requires a thermostat to minimize temperature fluctuations.^[1]^: 109

Tunable filters

An electrically tunable Lyot filter contains tuneable electro-optic or liquid crystal birefringent elements. ^[13]^: 30 The tunable electro-optic Lyot filter uses lead magnesium niobate-lead titanate (PMN-PT) opto-ceramic to tune the filter.^[6]^: 5.8.3 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.^[3]^: 177 The two categories of Lyot liquid crystal filters are polarizing interference retardance filters and electro-optical photonic crystals.^[5]^: 167 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.^[14]

Comparative performance

The Lyot filter and Fabry-Perót filter are the most common tunable electro-optic filters.^[6]^: 5.8.3 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.^[6]^: 5.8.3 Poor transmittance occurs due to the large number of highly absorbing polarizers and imperfect waveplate action. ^[3]^: 177 Lyot filters may contain up to 12 individual filters, making the Lyot filter expensive, limiting its use in compact instruments.^[5]^: 166 In contrast to Lyot filters, the Solc filter relies on only 2 polarizers leading to less light reduction.^[10]

Applications

In solar astronomy, viewing the sun's chromosphere, the sun's second atmospheric layer, requires narrowband optical filters (spectroheliograph),such as a Lyot filter, using wavelengths for viewing solar flares, prominences, filaments, and plages arising from calcium and hydrogen.^[8]^: 327^[9]^: 14

Single and multi-plate Lyot filters are often used inside the optical cavity of lasers to allow tuning of the laser.^[7]^: 202 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.^[11]^: 96

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).^[6]^: 5.8.3

Another application has been use of Lyot filters is for Raman chemical imaging.^[15]^: 205 Other applications have been in microspectrometer and hyperspectral imaging devices and biomedical photonics.^[5]^: 163

Citations

^ ^a ^b ^c ^d Stix 2012.
^ Lyot 1933.
^ ^a ^b ^c Li-Chan, Chalmers & Griffiths 2010.
^ ^a ^b Ambastha 2020.
^ ^a ^b ^c ^d Crawford 2007.
^ ^a ^b ^c ^d ^e Bain & Chand 2017.
^ ^a ^b Binh & Ngo 2018.
^ ^a ^b Bhatnagar & Livingston 2005.
^ ^a ^b Harrison 2016.
^ ^a ^b ^c ^d ^e ^f Lizana et al. 2019.
^ ^a ^b ^c ^d ^e ^f Meschede 2004.
^ ^a ^b Ammann 1971.
^ Bhargava & Levin 2008.
^ Beeckman et al. 2009.
^ Lewis & Edwards 2001.

References

Ambastha, Ashok (2020). Physics of the Invisible Sun: Instrumentation, Observations, and Inferences. CRC Press. pp. 2.5.2. ISBN 978-1-000-76087-3.
Ammann, E.O. (1971). "Synthesis of optical birefringent networks". In Wolf, E. (ed.). Progress in Optics Volume IX. Elsevier. pp. 125–180. ISBN 978-0-08-087973-4.
Bain, Ashim Kumar; Chand, Prem (2017). Ferroelectrics: Principles and Applications. John Wiley & Sons. ISBN 978-3-527-80533-4.
Beeckman, Jeroen; Hui, Tian; Vanbrabant, Pieter J. M.; Zmijan, Robert; Neyts, Kristiaan (2009). "Polarization Selective Wavelength Tunable Filter". Molecular Crystals and Liquid Crystals. 502 (1): 19–28. Bibcode:2009MCLC..502...19B. CiteSeerX 10.1.1.159.2814. doi:10.1080/15421400902813626. S2CID 9235494.
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Bhatnagar, A.; Livingston, William Charles (2005). Fundamentals of Solar Astronomy. World Scientific. ISBN 978-981-256-787-1.
Binh, Le Nguyen; Ngo, Nam Quoc (2018). Ultra-Fast Fiber Lasers: Principles and Applications with MATLAB® Models. CRC Press. ISBN 978-1-4398-1130-6.
Crawford, Gregory Philip (2007). Liquid Crystals: Frontiers in Biomedical Applications. World Scientific. ISBN 978-981-277-887-1.
Lewis, Ian R.; Edwards, Howell (2001). Handbook of Raman Spectroscopy: From the Research Laboratory to the Process Line. CRC Press. ISBN 978-1-4200-2925-3.
Harrison, Ken M. (2016). Imaging Sunlight Using a Digital Spectroheliograph. Springer. ISBN 978-3-319-24874-5.
Li-Chan, Eunice; Chalmers, John M.; Griffiths, Peter R. (2010). Applications of Vibrational Spectroscopy in Food Science, 2 Volume Set. John Wiley & Sons. ISBN 978-0-470-74299-0.
Lizana, Angel; Yzuel, María Josefa; Escalera, Juan Carlos; Campos, Juan (2019). Poulin-Girard, Anne-Sophie; Shaw, Joseph A. (eds.). "Training in polarization through a virtual learning environment". Proceedings of SPIE. 11143: 87. doi:10.1117/12.2523772. ISBN 978-1-5106-2979-0.
Lyot, B. (1933). "Optical apparatus with wide field using interference of polarized light". Acad. Sci. 197.
Meschede, Dieter (2004). Optics, Light and Lasers. Wiley. ISBN 978-3-527-40364-6.
Stix, Michael (2012). The Sun: An Introduction. Springer Science & Business Media. ISBN 978-3-642-56042-2.