Degree of polarization for optical near fields
Open accessAbstract
We investigate an extension to the concept of degree of polarization that applies to arbitrary electromagnetic fields, i.e., fields whose wave fronts are not necessarily planar. The approach makes use of generalized spectral Stokes parameters that appear as coefficients, when the full 3 x 3 spectral coherence matrix is expanded in terms of the Gell-Mann matrices. By defining the degree of polarization in terms of these parameters in a manner analogous to the conventional planar-field case, we are led to a formula that consists of scalar invariants of the spectral coherence matrix only. We show that attractive physical insight is gained by expressing the three-dimensional degree of polarization explicitly with the help of the correlations between the three orthogonal spectral components of the electric field. Furthermore, we discuss the fundamental differences in characterizing the polarization state of a field by employing either the two- or the three-dimensional coherence-matrix formalism. The extension of the concept of the degree of polarization to include electromagnetic fields having structures of arbitrary form is expected to be particularly useful, for example, in near-field optics.
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Between the extremes of fully random and pure states, P3D characterizes the strength of correlations among orthogonal field components.
“Between the two extremes P 3D characterizes, in analogy to the 2D degree of polarization [3], the strength of correlations among orthogonal field components [8].”
From Polarimetric purity and the concept of degree of polarization (2018) · cites this paper as [8]
The inequality P3D ≥ 1/2 holds for 2D states, as a natural consequence of the fact that they are characterized by Pd=1.
“The fact that the inequality P 3D ⩾ 1 / 2 holds for 2D states [2,8,32] is nothing else than a natural consequence of the fact that they are characterized by Pd = 1.”
From Polarimetric purity and the concept of degree of polarization (2018) · cites this paper as [8]
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Some comments on the descriptions of the polarization states of waves
Samson, J. C., & Olson, J. V. (1980) · Geophysical Journal International · doi:10.1111/j.1365-246x.1980.tb04308.x · Cited by 239 · see citing works
Descriptions of the Polarization States of Vector Processes: Applications to ULF Magnetic Fields
Samson, J. C. (1973) · Geophysical Journal International · doi:10.1111/j.1365-246x.1973.tb02404.x · Cited by 150 · see citing works
Degree of Polarization in Near Fields of Thermal Sources: Effects of Surface Waves
Setälä, T., Kaivola, M., & Friberg, A. T. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.123902 · Cited by 135 · see citing works
Self-citationParameters characterizing electromagnetic wave polarization
Carozzi, T. D., Karlsson, R., & Bergman, J. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.61.2024 · Cited by 130 · see citing works
Degree of polarization and the principal idempotents of the coherency matrix
Barakat, R. (1977) · Optics Communications · doi:10.1016/0030-4018(77)90292-9 · Cited by 109 · see citing works
Generalized stokes parameters for waves with arbitrary form
Román, P. (1959) · Il Nuovo Cimento · doi:10.1007/bf02724825 · Cited by 58 · see citing works
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Research works printed but not linked: 3
- ͓1͔ C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach ͑Wiley, New York, 1998͒.
- ͓2͔ L. Mandel and E. Wolf, Optical Coherence and Quantum Op- tics ͑Cambridge University Press, Cambridge, England, 1995͒.
- ͓3͔ M. Born and E. Wolf, Principles of Optics, 7th ed. ͑Cambridge University Press, Cambridge, England, 1999͒.
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Gil, J. J. (2007) · The European Physical Journal Applied Physics · doi:10.1051/epjap:2007153 · Cited by 272 · see citing works
Invariant indices of polarimetric purity
San José, I., & Gil, J. J. (2011) · Optics Communications · doi:10.1016/j.optcom.2010.08.077 · Cited by 110 · see citing works
Degree of polarization for three-dimensional fields as a distance between correlation matrices
Luis, A. (2005) · Optics Communications · doi:10.1016/j.optcom.2005.04.046 · Cited by 71 · see citing works
Interpretation of the coherency matrix for three-dimensional polarization states
Gil, J. J. (2014) · Physical Review A · doi:10.1103/physreva.90.043858 · Cited by 59 · see citing works
Structure of polarimetric purity of three-dimensional polarization states
Gil, J. J., Friberg, A. T., Setälä, T., & San José, I. (2017) · Physical Review A · doi:10.1103/physreva.95.053856 · Cited by 47 · see citing works
Self-citationGil, J. J., & San José, I. (2010) · Optics Communications · doi:10.1016/j.optcom.2010.04.090 · Cited by 46 · see citing works
Manifestations of geometric phase and enhanced spin Hall shifts in an optical trap
Roy, B., Ghosh, N., Banerjee, A., Gupta, S. D., & Roy, S. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/8/083037 · Cited by 43 · see citing works
Polarimetric purity and the concept of degree of polarization
Gil, J. J., Norrman, A., Friberg, A. T., & Setälä, T. (2018) · Physical Review A · doi:10.1103/physreva.97.023838 · Cited by 36 · see citing works
Self-citationComponents of purity of a three-dimensional polarization state
Gil, J. J. (2016) · Journal of the Optical Society of America A · doi:10.1364/josaa.33.000040 · Cited by 35 · see citing works
Partial polarization of optical beams and near fields probed with a nanoscatterer
Leppänen, L.-P., Friberg, A. T., & Setälä, T. (2014) · Journal of the Optical Society of America A · doi:10.1364/josaa.31.001627 · Cited by 21 · see citing works
Self-citation
- Authors
- Setälä, T., Shevchenko, A., Kaivola, M., & Friberg, A. T.
- Affiliations
- KTH Royal Institute of Technology (SE)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2002-07-30
- Volume
- 66
- Issue
- 1
- Pages
- 016615-016615
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W2047300681
- Cited by
- 287
- References
- 6
- Citations by year
- 2026: 9 · 2025: 10 · 2024: 6 · 2023: 14 · 2022: 13 · 2021: 15 · 2020: 9 · 2019: 19 · 2018: 13 · 2017: 9 · 2016: 18 · 2015: 20 · 2014: 21 · 2013: 11 · 2012: 16
- FWCI
- 7.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (publishedVersion)
- PubMed (publishedVersion)
- Aaltodoc (Aalto University) (submittedVersion, other-oa)
- Aaltodoc (Aalto University) (submittedVersion)
- Funders
- Academy of Finland
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Keywords
- degree of polarization, optical near-field, Gell-Mann matrices, three-dimensional polarization, polarization state, near-field optics, scalar invariants
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