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ls1_unit_6 - ON CLASSICAL ELECTROMAGNETIC FIELDS VI PAGE 50...

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O N C LASSICAL E LECTROMAGNETIC F IELDS P AGE 50 R. Victor Jones, February 17, 2000 VI. D ESCRIPTIONS OF P OLARIZED L IGHT 22 Consider a totally coherent wave propagating in the positive direction E x = E x 0 cos ω t + δ x ( ) = E x 0 exp i ω t + δ x ( ) [ ] + c . c . [ ] [ VI-1a ] E y = E y 0 cos ω t + δ y ( ) = E y 0 exp i ω t + δ y ( ) [ ] + c . c . [ ] [ VI-1b ] For later reference, we note that the full (non-normalized) Jones vector represe ntation 23 of this field is given by r J = E x 0 exp i δ x E y 0 exp i δ y Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ [ VI-2 ] We can be easily shown that cos ω t = sin δ y −δ x ( ) [ ] 1 E x E x 0 sin δ y E y E y 0 sin δ x Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ [ VI-3a ] sin ω t = sin δ y −δ x ( ) [ ] 1 E x E x 0 cos δ y E y E y 0 cos δ x Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ [ VI-3b ] 22 The best references on this subject are the following: 1.) William A. Shurcliff, Polarized Light: Production and Use , Harvard University Press (1962); 2.) D. Clarke and J.F. Grainger, Polarized Light and Optical Measurement , Pergamon Press (1971); 3.) Max Born and Emil Wolf, Principles of Optics , Pergamon Press (Particularly Section 1.4). 23 R. Clarke Jones, "New calculus for the treatment of optical systems. I. Description and discussion of calculus," J. Opt. Soc. Amer. 31 , 488 (1941). To quote Shurcliff, “The Jones vector, … describes a polarized beam with the maximum algebraic brevity, and is
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