Radial polarization

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A beam of light has radial polarization if at every position in the beam the polarization (electric field) vector points towards the center of the beam. In practice, an array of waveplates may be used to provide an approximation to a radially polarized beam. In this case the beam is divided into segments (eight, for example), and the average polarization vector of each segment is directed towards the beam centre.{{cite journal |title=z-Polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light |first=Y. |display-authors=4 |last=Saito |author2=Kobayashi, M. |author3=Hiraga, D. |author4=Fujita, K. |author5=Kawano, S. |author6=Smith, N. I. |author7=Inouye, Y. |author8= Kawata, S. |journal=Journal of Raman Spectroscopy |date=March 2008 |doi=10.1002/jrs.1953 |volume=39 |issue=11 |pages=1643–1648|bibcode = 2008JRSp...39.1643S}}

File:Radial and Azimuthal Polarisation.svg

Radial polarization can be produced in a variety of ways. It is possible to use so-called q-devices{{Cite journal|title = Design of broadband terahertz vector and vortex beams: I. Review of materials and components|journal = Light: Advanced Manufacturing|date = 2022-08-02|pages = 43|volume = 3|doi = 10.37188/lam.2022.043|first1 = N. V.|last1 = Petrov|first2 = B.|last2 = Sokolenko|first3 = M. S.|last3 = Kulya|first4 = A.|last4 = Gorodetsky|first5 = A. V.|last5 = Chernykh| issue=4 |doi-access = free}} to convert the polarization of a beam to a radial state. The simplest example of such devices is inhomogeneous anisotropic birefringent waveplate that performs transversally inhomogeneous polarization transformations of a wave with a uniform initial state of polarization. The other examples are liquid crystal,{{cite web|publisher=ARCoptix|url= http://www.arcoptix.com/radial_polarization_converter.htm|title=Radial-Azimuthal Polarization Converter|access-date=2008-09-30}} and metasurface q-plates. In addition, a radially polarized beam can be produced by a laser, or any collimated light source, in which the Brewster window is replaced by a cone at Brewster's angle. Called a "Rotated Brewster Angle Polarizer," the latter was first proposed and put into practice (1986) to produce a radially-polarized annular pupil by Guerra {{cite journal |title=Photon Tunneling Microscopy|first=John |last=Guerra |journal=Applied Optics |volume=29 |issue=26 |pages=3741–3752 |date=1990|bibcode=1990ApOpt..29.3741G |doi=10.1364/AO.29.003741 |pmid=20567479 |s2cid=23505916 }} at Polaroid Corporation (Polaroid Optical Engineering Dept., Cambridge, Massachusetts) to achieve super-resolution in their Photon Tunneling Microscope. A metal bi-cone, formed by diamond-turning, was mounted inside a glass cylinder. Collimated light entering this device underwent two air-metal reflections at the bi-cone and one air-glass reflection at the Brewster angle inside the glass cylinder, so as to exit as radially-polarized light. A similar device was later proposed again by Kozawa.{{cite journal |title=Generation of a radially polarized laser beam by use of a conical Brewster prism |first=Yuichi |last=Kozawa |author2=Sato, Shunichi |journal=Optics Letters |volume=30 |issue=22 |pages=3063–3065 |doi=10.1364/OL.30.003063 |pmid=16315722 |date=2005|bibcode = 2005OptL...30.3063K}}

A related concept is azimuthal polarization, in which the polarization vector is tangential to the beam. If a laser is focused along the optic axis of a birefringent material, the radial and azimuthal polarizations focus at different planes. A spatial filter can be used to select the polarization of interest.{{cite journal|title=Radial and azimuthal polarizer by means of a birefringent plate|first=Miklós|last=Erdélyi|author2=Gajdátsy, Gábor|journal=Journal of Optics A: Pure and Applied Optics|volume=10|issue=5|pages=055007|doi=10.1088/1464-4258/10/5/055007|date=2008|bibcode = 2008JOptA..10e5007E}} Beams with radial and azimuthal polarization are included in the class of cylindrical vector beams.{{cite journal|title=Cylindrical vector beams: from mathematical concepts to applications|first=Qiwen|last=Zhan|journal=Advances in Optics and Photonics|volume=1|issue=1|pages=1|doi=10.1364/AOP.1.000001|date=2009|bibcode=2009AdOP....1....1Z }}

A radially polarized beam can be used to produce a smaller focused spot than a more conventional linearly or circularly polarized beam,{{Cite book |title=Radial polarization minimizes focal spot size |display-authors=4 |last=Quabis |first=S. |author2=Dorn, R. |author3=Muller, J. |author4=Rurimo, G.K. |author5= Leuchs, G. |journal=Quantum Electronics Conference 2004 (IQEC) |doi=10.1364/IQEC.2004.IWG3 |isbn=978-1-55752-778-3 |date=2004 |publisher=Optical Society of America |location=Washington, OSA, Optical Society of America}} and has uses in optical trapping.{{cite journal |title=Trapping metallic Rayleigh particles with radial polarization |author=Qiwen Zhan |journal=Optics Express |volume=12 |issue=15 |pages=3377–3382 |doi=10.1364/OPEX.12.003377 |pmid=19483862 |date=2004 |bibcode=2004OExpr..12.3377Z|doi-access=free }}

It has been shown that a radially polarized beam can be used to increase the information capacity of free space optical communication via mode division multiplexing,{{cite journal |title=4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer |author=Giovanni Milione|journal=Optics Letters |volume=40 |issue=9 |pages=1980–1983 |doi=10.1364/OL.40.001980 |pmid=25927763|date=2015|display-authors=etal|arxiv = 1412.2717 |bibcode = 2015OptL...40.1980M |s2cid=31723951}} and radial polarization can "self-heal" when obstructed.{{cite journal |title=Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams |author=Giovanni Milione|journal=Journal of Optics |volume=17 |issue=3 |pages=035617 |doi=10.1088/2040-8978/17/3/035617 |date=2015|bibcode = 2015JOpt...17c5617M |s2cid=53445904|display-authors=etal}}

At extreme intensities, radially-polarized laser pulses with relativistic intensities and few-cycle pulse durations have been demonstrated via spectral broadening, polarization mode conversion and appropriate dispersion compensation.{{cite journal |last1=Carbajo |first1=Sergio |last2=Granados |first2=Eduardo |last3=Schimpf |first3=Damian |last4=Sell |first4=Alexander |last5=Hong |first5=Kyung-Han |last6=Moses |first6=Jeff |last7=Kärtner |first7=Franz |title=Efficient generation of ultra-intense few-cycle radially polarized laser pulses |journal=Optics Letters |date=2014-04-15 |volume=39 |issue=8 |pages=2487–2490 |doi=10.1364/OL.39.002487|pmid=24979025 |bibcode=2014OptL...39.2487C |url=http://bib-pubdb1.desy.de/record/168726 }} The relativistic longitudinal electric field component has been proposed as a driver for particle acceleration in free space{{cite journal |last1=Salamin |first1=Yousef |last2=Hu |first2=S.X. |last3=Hatsagortsyan |first3=Karen Z. |last4=Keitel |first4=Christoph H. |title=Relativistic high-power laser–matter interactions |journal=Physics Reports |date=April 2006 |volume=427 |issue=2–3 |pages=41–155 |doi=10.1016/j.physrep.2006.01.002|bibcode=2006PhR...427...41S }}{{cite journal |last1=Wong |first1=Liang Jie |last2=Hong |first2=Kyung-Han |last3=Carbajo |first3=Sergio |author-link3=Sergio Carbajo |last4=Fallahi |first4=Arya |last5=Piot |first5=Phillippe |last6=Soljačić |first6=Marin |last7=Joannopoulos |first7=John |last8=Kärtner |first8=Franz |last9=Kaminer |first9=Ido |title=Laser-Induced Linear-Field Particle Acceleration in Free Space |journal=Scientific Reports |date=2017-09-11 |volume=7 |issue=1 |pages=11159 |doi=10.1038/s41598-017-11547-9 |pmid=28894271 |pmc=5593863 |bibcode=2017NatSR...711159W |doi-access=free}} and demonstrated in proof-of-concept experiments.{{cite journal |last1=Carbajo |first1=Sergio |last2=Nanni |first2=Emilio |last3=Wong |first3=Liang Jie |last4=Moriena |first4=Gustavo |last5=Keathlye |first5=Phillip |last6=Laurent |first6=Guillaume |last7=Miller |first7=R. J. Dwayne |last8=Kärtner |first8=Franz |title=Direct longitudinal laser acceleration of electrons in free space |journal=Physical Review Accelerators and Beams |date=24 February 2016 |volume=19 |issue=2 |at=021303 |doi=10.1103/PhysRevAccelBeams.19.021303|arxiv=1501.05101 |bibcode=2016PhRvS..19b1303C |doi-access=free }}