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The aim of the present work is the description of a novel interferometric approach to the commonly known Malus law. In this approach we have described an analyzer as an element realizing the interference of two waves being the components of the linearly polarized wave emerging from the polarizer. We have proposed a decomposition of the polarization state of the light incident on the analyzer into two different bases. The choice of a first base – linearly polarized – allows interpreting Malus law as an interference of two linearly polarized waves with the same polarization state, different amplitudes and the same phases. The second decomposition, based on circularly polarized vectors, leads to the description in which Malus law can be interpreted as an interference of two waves with the same amplitudes but different phases. This allows the introduction of the concept of the geometric phase into Malus law as well as the visualization of this phase on the Poincaré sphere.
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s. 237--246
Opis fizyczny
Bibliogr. 23 poz., rys.
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- Institute of Physics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
- wladyslaw.wozniak@pwr.wroc.pl
autor
autor
Bibliografia
- [1] HARIHARAN P., The geometric phase, [In] Progress in Optics, [Ed.] E. Wolf, Vol. 48, Elsevier, Amsterdam, 2005, pp. 149–201.
- [2] PANCHARATNAM S., Collected Works, Oxford University Press, Oxford, 1975.
- [3] BERRY M.V., Anticipation of the geometric phase, Physics Today 43(12), 1990, pp. 34–40.
- [4] LOVE G.D., The unbounded nature of geometrical and dynamical phases in polarization optics, Optics Communications 131(4–6), 1996, pp. 236–240.
- [5] CHYBA T.H., WANG L.J., MANDEL L., SIMON R., Measurement of the Pancharatnam phase for a light beam, Optics Letters 13(7), 1988, pp. 562–564.
- [6] BERRY M.V., KLEIN S., Geometric phases from stacks of crystal plates, Journal of Modern Optics 43(1), 1996, pp. 165–180.
- [7] HARIHARAN P., MUJUMDAR S., RAMACHANDRAN H., A simple demonstration of Pancharatnam phase as a geometric phase, Journal of Modern Optics 46(9), 1999, pp. 1443–1446.
- [8] VON BERGMANN J., VON BERGMANN H., Foucault pendulum through basic geometry, American Journal of Physics 75(10), 2007, pp. 888–892.
- [9] GIL S., A mechanical device to study geometric phases and curvatures, American Journal of Physics 78(4), 2010, pp. 384–390.
- [10] BHANDARI R., SU(2) phase jumps and geometrical phases, Physics Letters A 157(4–5), 1991, pp. 221–225.
- [11] WAGH A.G., RAKHECHA V.C., SUMMHAMMER J., BADUREK G., WEINFURTER H., ALLMAN B.E., KAISER H., HAMACHER K., JACOBSON D.L., WERNER S.A., Experimental separation of geometric and dynamical phases using neutron interferometry, Physical Review Letters 78(5), 1997, pp. 755–759.
- [12] GALVEZ E.J., CRAWFORD P.R., SZTUL H.I., PYSHER M.J., HAGLIN P.J., WILLIAMS R.E., Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum, Physical Review Letters 90(20), 2003, article 203901.
- [13] BEN-ARYEH Y., Berry and Pancharatnam topological phases of atomic and optical systems, Journal of Optics B: Quantum and Semiclassical Optics 6(4), 2004, pp. R1–R18.246 W.A. WOŹNIAK et al.
- [14] BLIOKH K.Y., Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient--index medium, Journal of Optics A: Pure and Applied Optics 11(9), 2009, article 094009.
- [15] VISSER T.D., VAN DIJK T., SCHOUTEN H.F., UBACHS W., The Pancharatnam–Berry phase for non-cyclic polarization changes, Optics Express 18(10), 2010, pp. 10796–10804.
- [16] COURTIAL J., Wave plates and the Pancharatnam phase, Optics Communications 171(4–6), 1999, pp. 179–183.
- [17] KURZYNOWSKI P., WOŹNIAK W.A., SZARYCZ M., Geometric phase: two triangles on the Poincaré sphere, Journal of the Optical Society of America A 28(3), 2011, pp. 475–482.
- [18] KURZYNOWSKI P., WOŹNIAK W.A., Geometric phase for dichroic media, Journal of the Optical Society of America A 28(9), 2011, pp. 1949–1953.
- [19] GLADDEN S.C., An experiment on Malus’ law for the elementary laboratory, American Journal of Physics 18(6), 1950, pp. 395–395.
- [20] TEWARSON S.P., Law of Malus from phenomenological matrix calculus, American Journal of Physics 36(9), 1968, 841–842.
- [21] BORN M., WOLF E., Principles of Optics, Cambridge University Press, Cambridge, 1999, pp. 25–38.
- [22] WOŹNIAK W.A., KURZYNOWSKI P., Compact spatial polariscope for light polarization state analysis, Optics Express 16(14), 2008, pp. 10471–10479.
- [23] KURZYNOWSKI P., WOŹNIAK W.A., Phase difference superposition rule for dichroic media, Optik 103(2), 1996, pp. 66–68.
Typ dokumentu
Bibliografia
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