Lorentz group underpinnings for the Jones and Mueller calculi

F.U. Muhammad; Charles S. Brown

doi:10.1117/12.186683

14 September 1994 Lorentz group underpinnings for the Jones and Mueller calculi

F.U. Muhammad, Charles S. Brown

Proceedings Volume 2265, Polarization Analysis and Measurement II; (1994) https://doi.org/10.1117/12.186683
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

When preparing or examining a complicated optical system involving polarized light, one usually relies on one of a number of bookkeeping matrix formalisms that keep track of the various polarization components. The best-known are the 2 X 2 complex matrix calculus developed by Jones and the 4 X 4 real matrix calculus developed by Mueller. In this paper we show that both the Jones and Mueller calculi have their mathematical foundation in the Lorentz group. In the Jones approach one is working with one of the spinor representations of the Lorentz group. The Mueller approach involves the use of the vector representation of the Lorentz group. From the deterministic point of view the Jones and Mueller calculi are equivalent when considering completely-polarized monochromatic light. However, stochastically speaking, the two approaches do not yield the same physical predictions.

Citation Download Citation

F.U. Muhammad and Charles S. Brown "Lorentz group underpinnings for the Jones and Mueller calculi", Proc. SPIE 2265, Polarization Analysis and Measurement II, (14 September 1994); https://doi.org/10.1117/12.186683

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