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Jones, RC (1941a) A new calculus for the treatment of optical systems I Description and discussion of the calculus J Opt Soc Am, 31, 488 493 [49] Jones, RC (1941b) A new calculus for the treatment of optical systems III The Sohncke theory of optical activity J Opt Soc Am, 31, 500 503 [49] Jones, RC (1942) A new calculus for the treatment of optical systems IV J Opt Soc Am, 32, 486 493 [49] Jones, RC (1947a) A new calculus for the treatment of optical systems V A more general formulation, and description of another calculus J Opt Soc Am, 37, 107 110 [49] Jones, RC (1947b) A new calculus for the treatment of optical systems VI Experimental determination of the matrix J Opt Soc Am, 37, 110 112 [49] Jones, RC (1948) A new calculus for the treatment of optical systems VII Properties of the N-matrices J Opt Soc Am, 38, 671 685 [49] Jones, RC (1956) A new calculus for the treatment of optical systems VIII Electromagnetic theory J Opt Soc Am, 46, 126 131 [49] Jones, RC, Hurwitz, H Jr (1941) A new calculus for the treatment of optical systems II Proof of three general equivalence theorems J Opt Soc Am, 31, 493 499 [49] Mie, G (1908) Beitr ge zur Optik tr ber Medien, speziell kolloidaler Metall sungen Ann Phys, 330, 377 445 [55] Pancharatnam, S (1955a) Achromatic combinations of birefringent plates Part I An achromatic circular polarizer Proc Indian Acad Sci A, 41, 130 136 [56] Pancharatnam, S (1955b) Achromatic combinations of birefringent plates Part II An achromatic quarter-wave plate Proc Indian Acad Sci A, 41, 137 144 [56] Van de Hulst, HC (1957) Light Scattering by Small Particles John Wiley & Sons, Inc, New York [54]
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The form of the Jones vector, with its description of orthogonal classical waves maintaining a constant phase difference, obviously refers to beams of radiation which are perfectly coherent Such coherence automatically means that the radiation is perfectly polarized, displaying a unique and long-term polarization form and gure In nature, such radiation is rarely met Using a simplistic picture, it will be appreciated that within a beam of electromagnetic radiation, many waves and vibrations are simultaneously present, with their electric eld disturbances providing a distribution of orientations and phases As time progresses, some of the component vibrations die away to be replaced by others, without any phase coherence being maintained This kind of radiation is sometimes referred to as natural light, but the more precise terminology of unpolarized radiation is to be preferred If snapshot pictures could be made of the resultant electric disturbance in the orthogonal plane through which the radiation passes, with exposures of the order of a few times the reciprocal of the frequency of the radiation, a series of ellipses would be recorded (see Figure 41) Successive frames would show gures that progressively change ellipticity and orientation of the major axis Over longer experimental times, the ellipse patterns would appear to be more and more scrambled, and no preferred gure would emerge According to a simple model for the behaviour, Hurwitz (1945) has shown that fairly thin ellipses dominate For more than half the time, the ellipse being traced out has a major axis which is three and a half times larger than the minor axis; all orientations of the major axis are equally probable, as is the alternative choice of the handedness 2 2 2 2 Suppose that the quantities which de ne the ellipse, (E x0 C E y 0 ), (E x0 E y 0 ), 2E x0 E y 0 cos( y x ) and 2E x0 E y 0 sin( y x ), as given by (234), (235), (236) and (237), are determined in a normal experimental situation The measurements correspond to expectation values of these quantities over the observational time Thus, the recorded values correspond to time averages of the behaviour of the ellipses during the measurement integration time; the average also involves all the ellipses associated with the different wavelengths within the operating bandwidth
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Stellar Polarimetry David Clarke Copyright 2010 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40895-5
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