Editor-in-Chief : V.K. Rastogi
Asian Journal of Physics | Vol. 30 Nos 8 & 9 (2021) 1213-1224 |
Propagation of optical coherence and polarization through linear optical systems
A Yelashetty1, N Gupta1, D Dhirhe1 and G Unnikrishnan2
Abstract
Coherence Stokes parameters, also known as generalized or two-point Stokes parameters, are being widely studied in partial coherence theory. These coherence Stokes parameters can define the degree and state of polarization and degree of scalar and electromagnetic coherence. Linear Canonical Transforms (LCT) form an elegant mathematical tool to study the coherence and polarization properties by using matrix elements of linear optical systems. In this article, we review the propagation of coherence and polarization in linear optical systems such as free space and simple lens system developed in terms of LCT of underlying the electric field components. Simulation results are presented to compare the Gaussian and multi-Gaussian Schell model beams propagating through such systems. © Anita Publications. All rights reserved.
Keywords: Partial coherence, Linear Canonical Transforms, Generalized Stokes parameters, Multi-Gaussian Schell model beams.
Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserved
References
-
- Mandel L, Wolf E, Coherence properties of optical fields, Rev Mod Phys,37(1965)231; org/10.1103/RevModPhys.37.231.
- Born M, Wolf E, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, (Elsevier), 2013.
- Gbur G J, In memory of Emil Wolf, 1922-2018, http://www.cambridgeblog.org/2018/09/in-memory-of-emil-wolf-1922-2018/.
- Wolf E, Optics in terms of observable quantities, Nuovo Cim, 12(1954)884–888.
- Korotkova O, Wolf E, Generalized Stokes parameters of random electromagnetic beams, Opt Lett, 30(2005)198–200.
- Partanen H, Hoenders B J, Friberg A T, Setälä T, Young’s interference experiment with electromagnetic narrowband light, J Opt Soc Am A, 35(2018)1379–1384.
- Tervo J, Setälä T, Roueff A, Réfrégier P, Friberg A T, Two-point Stokes parameters: interpretation and properties, Opt Lett, 34(2009)3074–3076.
- Kanseri B, Sethuraj K R, Experimental observation of the polarization coherence theorem, Opt Lett, 44(2019)159-162.
- Wolf E, Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation, Opt Lett, 28(2003)1078–1080.
- Salem M, Wolf E, Coherence-induced polarization changes in light beams, Opt Lett, 33(2008)1180–1182.
- Korotkova O, Shchepakina E, Rectangular multi-Gaussian Schell-model beams in atmospheric turbulence, J Opt, 16(2014)45704; doi.org/10.1088/2040-8978/16/4/045704.
- Yelashetty A, Gupta N, Dhirhe D, Unnikrishnan G, Propagation of Stokes parameters in oceanic turbulence, Proc SPIE, 11205(2019)112050H; doi.org/10.1117/12.2542150.
- Zhao X, Visser T D, Agrawal G P, Degree of polarization in the focal region of a lens, J Opt Soc Am A, 35(2018)1518–1522.
- Yelashetty A, Gupta N, Dhirhe D, Unnikrishnan G, Evolution of Stokes parameters in quasi- homogeneous electromagnetic sources in the far field, Optik, 207(2020)163811; doi.org/10.1016/j.ijleo.2019.163811.
- Zhu Y, Zhao D, Generalized Stokes parameters of a stochastic electromagnetic beam propagating through a paraxial ABCD optical system, J Opt Soc Am A, 25(2008)1944–1948.
- Visser T D, Agrawal G P, Milonni P W, Fourier processing with partially coherent fields, Opt Lett, 42(2017)4600–4602.
- Unnikrishnan G, Joseph J, Singh K, Optical encryption by double-random phase encoding in the fractional Fourier domain, Opt Lett, 25(2000)887–889.
- Healy J J, Kutay M A, Ozaktas M H, Sheridan J T, (Eds), Linear canonical transforms: Theory and applications, (Springer-verlag), 2015.
- Yelashetty A, Gupta N, Dhirhe D, Unnikrishnan G, Linear canonical transform as a tool to analyze coherence properties of electromagnetic beams propagating in a quadratic phase system, J Opt Soc Am A, 37(2020)1350-1360.
- Al-Qasimi A, James D F V, Maximal coherence and degree of polarization in linear optical systems, J Mod Opt, 66(2019)2037–2042.
- Gase R, Time-dependent spectrum of linear optical systems, J Opt Soc Am A, 8(1991)850–859.
- Ozaktas H M, Oktem F S, Phase-space window and degrees of freedom of optical systems with multiple apertures, J Opt Soc Am A, 30(2013)682–690.
- Namias V, The fractional order Fourier transform and its application to quantum mechanics, IMA J App Math, 25(1980)241–265.
- Mustard D A, ‘The fractional Fourier transform and a new uncertainty principle’, School of Mathematics Preprint AM87/14, The University of New South Wales, Kensington, Australia, 1987.
- James D F V, Agarwal G S, The generalized Fresnel transform and its application to optics, Opt Commun, 126(1996)207–212.
- Wolf K B, Development of linear canonical transforms: a historical sketch in Linear Canonical Transforms, (Springer), 2016, pp 3–28.
- Zhao L, Sheridan J T, Healy J J, Unitary algorithm for nonseparable linear canonical transforms applied to iterative phase retrieval, IEEE Signal Process Lett, 24(2017)814–817.
- Zhao L, Sheridan J T, Healy J J,Constraints on additivity of the 1D discrete linear canonical transform, Appl Opt, 54(2015)9960–9965.
- Healy J J, Sheridan J T, Fast linear canonical transforms, J Opt Soc Am A, 27(2010)21–30.
- Healy J J, Sheridan J T, Sampling and discretization of the linear canonical transform, Signal Process, 89(2009),641–648.
- Sun Y N, Li B Z,Segmented fast linear canonical transform, J Opt Soc Am A, 35(2018)1346–1355.
- Koç A, Bartan B,Ozaktas H M, Discrete linear canonical transform based on hyperdifferential operators, IEEE Trans Signal Process, 67(2019)2237–2248.
- Korotkova O, Hoover B G, Gamiz V L, Wolf E, Coherence and polarization properties of far fields generated by quasi-homogeneous planar electromagnetic sources, J Opt Soc Am A, 22(2005)2547–2556.
- Wolf E, Unified theory of coherence and polarization of random electromagnetic beams, Phys Lett A, 312(2003)263–267.
- Wolf E, Introduction to the Theory of Coherence and Polarization of Light, (Cambridge University Press), 2007.
- Friberg A T, Setälä T, Electromagnetic theory of optical coherence, J Opt Soc Am A, 33(2016)2431–2442.
- Setälä T, Tervo J, Friberg A T, Stokes parameters and polarization contrasts in Young’s interference experiment, Opt Lett, 31(2006)2208–2210.
- Ping C, Liang C, Wang F, Cai Y, Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties, Opt Express, 25(2017)32475–32490.
- Korotkova O, Salem M, Wolf E, Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source, Opt Lett, 29(2004)1173–1175.
- Korotkova O, Sufficient condition for polarization invariance of beams generated by quasi-homogeneous sources, Opt Lett, 36(2011)3768–3770.
- Mei Z, Korotkova O, Shchepakina E, Electromagnetic multi-Gaussian Schell-model beams, J Opt (UK), 15(2013)2; doi.org/10.1088/2040-8978/15/2/025705.
- Seshadri S R, Polarization properties of partially coherent Gaussian Schell-model electromagnetic beams, J Appl Phys, 87(2000)4084–4093.
- Korotkova O, Changes in statistics of the instantaneous Stokes parameters of a quasi-monochromatic electromagnetic beam on propagation, Opt Commun, 261(2006)218–224.
- Korotkova O, Wolf E, Changes in the state of polarization of a random electromagnetic beam on propagation, Opt Commun, 246(2005)35–43.
- Korotkova O, Visser T D, Wolf E, Polarization properties of stochastic electromagnetic beams, Opt Commun, 281(2008)515–520.
- Pu J, Korotkova O, Wolf E, Polarization-induced spectral changes on propagation of stochastic electromagnetic beams, Phys Rev E, 75(2007)56610; doi.org/10.1103/PhysRevE.75.056610.
- Zhao L, Healy J J, Sheridan J T, Unitary discrete linear canonical transform: analysis and application, Appl Opt, 52(2013)C30–C36.
- Bastiaans M J, Wigner distribution function and its application to first order optics, J Opt Soc Am A, 69(1979)1710–1716.
- Sahin S, Generalized Stokes parameters in phase space, Opt Lett, 35(2010)1704–1706.
- Xu X Y, Basic Concepts of Linear Optical System, In: Applied Research of Quantum Information Based on Linear Optics, Springer, (2016), pp 1–50.
- Kanseri B, Rath S, Kandpal H C, Direct determination of the generalized Stokes parameters from the usual Stokes parameters, Opt Lett, 34(2009)719–721.
- Sethuraj K R, Kanseri B, Characterization of the electromagnetic Gaussian Schell-model beam using first-order interference, J Opt Soc Am A, 37(2020)458–465.
- Lahiri M, Wolf E, Theory of refraction and reflection with partially coherent electromagnetic beams, Phys Rev A, 86(2012)43815; doi.org/10.1103/PhysRevA.86.043815.