Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Polarization statistics of thermal microwave radiation

Daniel Kestner and Alex Kostinski*

  • *Contact author: kostinsk@mtu.edu

Phys. Rev. E 111, 044125 – Published 16 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044125

Abstract

Time series of thermal emissions from water vapor and air molecules at 2.8GHz, collected by the National Center for Atmospheric Research's (NCAR) S-band polarimetric radar S-Pol are examined for polarization probability distributions. A nearly uniform distribution of states on the Poincaré sphere surface is found. This uniformity is consistent with the four-dimensional circular Gaussian distribution of electric fields (pairs of in-phase and quadrature components for two orthogonal directions) for unpolarized radiation. Analysis of experimental data and the derived sampling distribution of the degree of polarization of the finite time series both yield a mean of about 0.02, within bounds of sampling variability of unpolarized Gaussian-distributed radiation. Weak inhomogeneity of polarization states on the Poincaré sphere detected in the experimental data is within the error bounds of the radar receiver.

Physics Subject Headings (PhySH)

Article Text

References (43)

  1. J. W. Goodman, Statistical Optics (John Wiley and Sons, New York, 1985).
  2. M. Rosskopf, T. Mohr, and W. Elsäßer, Ghost polarization communication, Phys. Rev. Appl. 13, 034062 (2020).
  3. K. H. Kim, B. H. Park, Y. Tu, T. Hasan, B. Lee, J. Li, and J. F. de Boer, Polarization-sensitive optical frequency domain imaging based on unpolarized light, Opt. Express 19, 552 (2011).
  4. C. Samlan and N. K. Viswanathan, Generation of vector beams using a double-wedge depolarizer: Non-quantum entanglement, Opt. Lasers Eng. 82, 135 (2016).
  5. F. Kroh, M. Rosskopf, and W. Elsäßer, Tailoring spatially unpolarized light on the poincaré sphere: From equator states via meridian states to generalized great-circle states, Phys. Rev. Res. 3, 043131 (2021).
  6. S. Restuccia, G. M. Gibson, L. Cronin, and M. J. Padgett, Measuring optical activity with unpolarized light: Ghost polarimetry, Phys. Rev. A 106, 062601 (2022).
  7. V. L. Quito and R. Flint, Floquet engineering correlated materials with unpolarized light, Phys. Rev. Lett. 126, 177201 (2021).
  8. A. Kostinski, D. Kestner, and J. Vivekanandan, Estimating polarization purity with noise, IEEE Trans. Geosci. Remote Sens. 62, 1 (2024).
  9. M. Charnotskii, Improper statistics of the radiation from a randomly rotating source, J. Opt. Soc. Am. A 41, 1098 (2024).
  10. M. Charnotskii, Statistics of narrow-band partially polarized light, J. Opt. 19, 095603 (2017).
  11. P. J. Schreier and L. L. Scharf, Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals (Cambridge University Press, Cambridge, 2010).
  12. A. J. Park, L. R. B. Picard, G. E. Patenotte, J. T. Zhang, T. Rosenband, and K.-K. Ni, Extended rotational coherence of polar molecules in an elliptically polarized trap, Phys. Rev. Lett. 131, 183401 (2023).
  13. A. B. Kostinski, B. D. James, and W.-M. Boerner, Optimal reception of partially polarized waves, J. Opt. Soc. Am. A 5, 58 (1988).
  14. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, 2007).
  15. J. Lehner, U. Leonhardt, and H. Paul, Unpolarized light: Classical and quantum states, Phys. Rev. A 53, 2727 (1996).
  16. G. G. Kozlov, I. I. Ryzhov, A. Tzimis, Z. Hatzopoulos, P. G. Savvidis, A. V. Kavokin, M. Bayer, and V. S. Zapasskii, Hidden polarization of unpolarized light, Phys. Rev. A 98, 043810 (2018).
  17. J. Ellis and A. Dogariu, Differentiation of globally unpolarized complex random fields, J. Opt. Soc. Am. A 21, 988 (2004).
  18. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, Englewood Colorado, 2007).
  19. E. T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, Cambridge, 2003).
  20. J. Tinbergen, Astronomical Polarimetry (Cambridge University Press, Cambridge, 1996).
  21. S. Wang, S. Wen, Z.-L. Deng, X. Li, and Y. Yang, Metasurface-based solid poincaré sphere polarizer, Phys. Rev. Lett. 130, 123801 (2023).
  22. J. Ritter, N. Ma, W. Osten, M. Takeda, and W. Wang, Depolarizing surface scattering by a birefringent material with rough surface, Opt. Commun. 430, 456 (2019).
  23. N. Ma, S. G. Hanson, M. Takeda, and W. Wang, Coherence and polarization of polarization speckle generated by a rough-surfaced retardation plate depolarizer, J. Opt. Soc. Am. A 32, 2346 (2015).
  24. D. Kestner and A. Kostinski, Simple formula for the jones product and the pancharatnam connection in optics, Phys. Rev. A 109, 023517 (2024).
  25. J. Yu, S. Häfner, T. Legero, S. Herbers, D. Nicolodi, C. Y. Ma, F. Riehle, U. Sterr, D. Kedar, J. M. Robinson et al., Excess noise and photoinduced effects in highly reflective crystalline mirror coatings, Phys. Rev. X 13, 041002 (2023).
  26. M. Born and E. Wolf, Principles of Optics Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon Press, Oxford, 1983).
  27. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley-Interscience, New York, 1998).
  28. G. Horváth and D. Varjú, Circulary polarized light in nature, in Polarized Light in Animal Vision: Polarization Patterns in Nature (Springer, Berlin, Heidelberg, 2004), pp. 100–103.
  29. Y. Ding and S. Pau, Circularly and elliptically polarized light under water and the umov effect, Light Sci. Appl. 8, 32 (2019).
  30. H. Hurwitz, The statistical properties of unpolarized light, J. Opt. Soc. Am. 35, 525 (1945).
  31. R. Barakat, The statistical properties of partially polarized light, Opt. Acta: Int. J. Opt. 32, 295 (1985).
  32. J. Hubbert, S. Ellis, M. Dixon, and G. Meymaris, Modeling, error analysis, and evaluation of dual-polarization variables obtained from simultaneous horizontal and vertical polarization transmit radar. Part I: Modeling and antenna errors, J. Atmos. Ocean. Technol. 27, 1583 (2010).
  33. Z. Zhu and F. Weng, A mystery of the inconsistency between microwave polarimetric observations and radiative transfer simulations, Geophys. Res. Lett. 51, e2024GL111553 (2024).
  34. Earth observing laboratory: Spol specifications https://www.eol.ucar.edu/observing_facilities/s-pol (2024).
  35. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Polarization time and length for random optical beams, Phys. Rev. A 78, 033817 (2008).
  36. A. Shevchenko, M. Roussey, A. T. Friberg, and T. Setälä, Polarization time of unpolarized light, Optica 4, 64 (2017).
  37. F. J. Massey, The Kolmogorov-Smirnov test for goodness of fit, J. Am. Stat. Assoc. 46, 68 (1951).
  38. S. M. Cohen, D. Eliyahu, I. Freund, and M. Kaveh, Vector statistics of multiply scattered waves in random systems, Phys. Rev. A 43, 5748 (1991).
  39. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Government Printing Office, Washington, DC, 1972).
  40. N. Johnson, S. Kotz, and B. N., Continuous Univariate Distributions (John Wiley and Sons, New York, 1994).
  41. A. Kostinski and W. Boerner, On foundations of radar polarimetry, IEEE Trans. Antennas Propag. 34, 1395 (1986).
  42. J. P. Y. Lee, I/Q demodulation of radar signals with calibration and filtering, Defence Research Establishment Ottawa, Tech. Rep. 1119 (1991).
  43. M. Kulkarni and A. Kostinski, A simple formula for monitoring quadrature phase error with arbitrary signals, IEEE Trans. Geosci. Remote Sensing 33, 799 (1995).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation