## Paraxial Maxwell beams: transformation by general linear optical systems

JOSA A, Vol. 2, Issue 8, pp. 1291-1296 (1985)

http://dx.doi.org/10.1364/JOSAA.2.001291

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### Abstract

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

© 1985 Optical Society of America

**History**

Original Manuscript: November 20, 1984

Manuscript Accepted: March 25, 1985

Published: August 1, 1985

**Citation**

N. Mukunda, R. Simon, and E. C. G. Sudarshan, "Paraxial Maxwell beams: transformation by general linear optical systems," J. Opt. Soc. Am. A **2**, 1291-1296 (1985)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-8-1291

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### References

- R. C. Jones, “A new calculus for the treatment of optical systems I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941);H. Hurwitz, R. C. Jones, “A new calculus for the treatment of optical systems. II. Proof of three general equivalence theorems,” J. Opt. Soc. Am. 31, 493–499 (1941).All the papers of this series and several other important contributions to polarization optics have been reprinted in W. Swindell, ed., Polarized Light (Dowden, Hutchinson and Ross, Stroudsburg, Pa., 1975). [CrossRef]
- See, for example, S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Ind. Acad. Sci. A 44, 247–262, 398–417 (1956);Proc. Ind. Acad. Sci. A 45, 402–411 (1957);Proc. Ind. Acad. Sci. A 46, 1–18 (1957).
- E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959);G. B. Parrent, P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370–388 (1960);N. Wiener, “Generalized harmonic analysis,” Acta Math. 55, 182–195 (1930). [CrossRef]
- G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Phil. Soc. 9, 399–416 (1852);H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661 (1948);S. Chandrasekhar, Radiative Transfer (Dover, New York, 1950), Chap. 1.
- R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982);R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981). [CrossRef]
- E. C. G. Sudarshan, R. Simon, N. Mukunda, “Paraxial wave optics and relativistic front description I: the scalar theory,” Phys. Rev. A 28, 2921–2932 (1983). [CrossRef]
- N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial wave optics and relativistic front description II: the vector theory,” Phys. Rev. A28, 2933–2942 (1983).See also H. Bacry, “Group theory and paraxial optics,” invited talk at the XIIIth International Colloquium on Group Theoretical Methods in Physics, University of Maryland, College Park, Md., May 1984. [CrossRef]
- P. A. M. Dirac, “Forms of relativistic dynamics,” Rev. Mod. Phys. 21, 392–399 (1949). [CrossRef]
- N. Mukunda, R. Simon, E. C. G. Sudarshan, “Fourier optics for the Maxwell field: formalism and applications,” J. Opt. Soc. Am. A 2, 416–426 (1985). [CrossRef]
- See in this connection M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
- P. Roman, “Generalized Stokes parameters for waves of arbitrary form,” Nuovo Cimento 13, 974–982 (1959);G. Ramachandran, M. V. N. Murthy, K. S. Mallesh, “SU(3) representation of the polarization of light,” Pramāna 15, 357–369 (1980). [CrossRef]
- E. C. G. Sudarshan, “Quantum electrodynamics and light rays,” Physica 96A, 315–320 (1979);“Quantum theory of radiative transfer,” Phys. Rev. A 23, 2802–2809 (1981).

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