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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 9 — Sep. 1, 2001
  • pp: 2138–2145

3 × 3 Matrix for unitary optical systems

S. T. Tang and H. S. Kwok  »View Author Affiliations

JOSA A, Vol. 18, Issue 9, pp. 2138-2145 (2001)

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We introduce a 3×3 matrix for the study of unitary optical systems. This 3×3 matrix is a submatrix of the 4×4 Mueller matrix. The elements of this 3×3 matrix are real, and thus complex-number calculations can be avoided. The 3×3 matrix is useful for illustrating the polarization state of an optical system. One can also use it to derive the conditions for linear and circular polarization output for a general optical system. New characterization methods for unitary optical systems are introduced. It is shown that the trajectory of the Stokes vector on a Poincaré sphere is either a circle or an ellipse as the optical system or input polarizer is rotated. One can use this characteristic circle or ellipse to measure the equivalent optical retardation and rotation of any lossless optical system.

© 2001 Optical Society of America

OCIS Codes
(080.2730) Geometric optics : Matrix methods in paraxial optics
(230.3720) Optical devices : Liquid-crystal devices

Original Manuscript: November 10, 2000
Revised Manuscript: February 27, 2001
Manuscript Accepted: February 27, 2001
Published: September 1, 2001

S. T. Tang and H. S. Kwok, "3 × 3 Matrix for unitary optical systems," J. Opt. Soc. Am. A 18, 2138-2145 (2001)

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