Polarization of light and topological phases

Abstract The phase shifts experienced by a polarized light wave when it propagates through media with arbitrary birefringence, dichroism and depolarizing properties, while on the one hand provide the basis for a variety of optical devices and experiments, on the other provide a powerful means of understanding unitary evolution, nonunitary evolution and decoherence of two-state quantum systems by virtue of a mathematical isomorphism of the two systems. These also help understand aspects of evolution of classical systems under the group of rotations in three-dimensional space, namely the SO(3) group, by virtue of its homomorphism with the group SU(2) governing unitary evolution of polarized light waves. In this review we present a survey and analysis of recent work on topological phases with polarization of light which has revealed several counterintuitive features of such phase shifts such as 2 nπ anholonomies, nonlinear and discontinuous behaviour originating hi singularities, peculiar spectral dependence, etc. We point out several areas where these results may find practical application, for example endless phase correction in interferometric sensors, fast switching spatial light modulators, phase shifters with unusual chromatic properties, phasing of antenna arrays, etc. Several useful theoretical insights relevant to polarization optics, quantum mechanics, classical mechanics and other areas of physics, obtained from the work on polarization states are described and some directions for future work are indicated.

[1]  P. Gennes,et al.  The physics of liquid crystals , 1974 .

[2]  Alexander B. Kostinski,et al.  A Simple Necessary and Sufficient Condition on Physically Realizable Mueller Matrices , 1993 .

[3]  M Martinelli,et al.  Polarization noise suppression in retracing optical fiber circuits. , 1991, Optics letters.

[4]  R. Clark Jones,et al.  A New Calculus for the Treatment of Optical Systems. VII. Properties of the N-Matrices , 1948 .

[5]  S. Tiwari,et al.  Geometric Phase in Optics: Quantal or Classical? , 1992 .

[6]  Weinfurter,et al.  Nondispersive phase of the Aharonov-Bohm effect. , 1993, Physical review letters.

[7]  M. Berry.  The Adiabatic Phase and Pancharatnam's Phase for Polarized Light , 1987 .

[8]  Observation of random π phase jumps in a ring laser with backscattering , 1988 .

[9]  Wu,et al.  Manifestations of Berry's topological phase for the photon. , 1986, Physical review letters.

[10]  A. Pines,et al.  Berry's Phase , 1990 .

[11]  L J Wang,et al.  Measurement of the Pancharatnam phase for a light beam. , 1988, Optics letters.

[12]  J. N. Ross.  The rotation of the polarization in low birefringence monomode optical fibres due to geometric effects , 1984 .

[13]  Martin H. Edwards,et al.  Zero angular momentum turns , 1986 .

[14]  R. Clark Jones,et al.  A New Calculus for the Treatment of Optical SystemsIII. The Sohncke Theory of Optical Activity , 1941 .

[15]  Decoherence due to the geometric phase in a "welcher-weg" experiment. , 1992, Physical review letters.

[16]  P. Milonni,et al.  Some Recent Development, In the Fundamental Theor of Light , 1990 .

[17]  A Novel Beamsplitter for Optical Polarization State Interferometry , 1993 .

[18]  A. Messiah.  Quantum Mechanics , 1961 .

[19]  M. Martinelli.  A universal compensator for polarization changes induced by birefringence on a retracing beam , 1989 .

[20]  Optical properties of magnetically doped cholesterics , 1993 .

[21]  Philip Birch,et al.  Binary adaptive optics: atmospheric wave-front correction with a half-wave phase shifter. , 1995, Applied optics.

[22]  D. Walba,et al.  Quantized complex ferroelectric liquid crystal spatial light modulators. , 1992, Applied optics.

[23]  G. Love,et al.  Intensity-only modulation for atmospheric scintillation correction by liquid-crystal spatial light modulators. , 1996, Optics letters.

[24]  Daan Lenstra,et al.  Analogies in Optics and Micro Electronics , 1990 .

[25]  Optical mode-coupling in a ring due to a back-scatterer , 1993 .

[26]  Richard Montgomery,et al.  How much does the rigid body rotate? A Berry’s phase from the 18th century , 1991 .

[27]  Aharonov,et al.  Phase change during a cyclic quantum evolution. , 1987, Physical review letters.

[28]  T. F. Jordan.  Berry phases and unitary transformations , 1988 .

[29]  Hübner,et al.  Homoclinic and heteroclinic chaos in a single-mode laser. , 1988, Physical review letters.

[30]  Wilkinson,et al.  Observation of a topological phase by means of a nonplanar Mach-Zehnder interferometer. , 1988, Physical review letters.

[31]  H. Bernstein.  SPIN PRECESSION DURING INTERFEROMETRY OF FERMIONS AND THE PHASE FACTOR ASSOCIATED WITH ROTATIONS THROUGH 2$pi$ RADIANS. , 1967 .

[32]  Dieter Suter,et al.  Berry's phase in magnetic resonance , 1987 .

[33]  F. Wilczek,et al.  Geometry of self-propulsion at low Reynolds number , 1989, Journal of Fluid Mechanics.

[34]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[35]  Sudarshan,et al.  Evolving geometric phase and its dynamical manifestation as a frequency shift: An optical experiment. , 1988, Physical review letters.

[36]  Richard Phillips Feynman,et al.  Geometrical Representation of the Schrödinger Equation for Solving Maser Problems , 1957 .

[37]  P. Hariharan,et al.  White-light Phase-stepping Interferometry for Surface Profiling , 1994 .

[38]  Samuel,et al.  Observation of topological phase by use of a laser interferometer. , 1988, Physical review letters.

[39]  R. Sridhar,et al.  Normal form for Mueller Matrices in Polarization Optics , 1994 .

[40]  R. Azzam.  Polarization-independent Beam Splitter Based on Light Reflection by a Uniaxial Crystal Surface, and an Immersion Method for Determining the Crystal's Principal Refractive Indices , 1994 .

[41]  E. Sudarshan,et al.  Hamilton’s theory of turns and a new geometrical representation for polarization optics , 1989 .

[42]  Mark A. A. Neil,et al.  Programmable binary phase-only optical device based on ferroelectric liquid crystal SLM , 1992 .

[43]  W. Weber,et al.  Evidence for broken time reversal symmetry in cuprate superconductors , 1990 .

[44]  G. Baym.  Lectures On Quantum Mechanics , 1969 .

[45]  J. Steeds,et al.  Sir Charles Frank OBE, FRS, An Eightieth Birthday Tribute , 1991 .

[46]  Klein,et al.  Nonlinearity of Pancharatnam's topological phase. , 1993, Physical Review Letters.

[47]  R. Leighton,et al.  Feynman Lectures on Physics , 1971 .

[48]  R. Tycko,et al.  Adiabatic rotational splittings and Berry's phase in nuclear quadrupole resonance. , 1987, Physical review letters.

[49]  Dean Lenstra,et al.  Optical bandstructure and polarization modes in the Sagnac ring resonator , 1990 .

[50]  A. VanderLugt,et al.  Optical Signal Processing , 1990 .

[51]  N. Abraham,et al.  Phase and frequency jumps in a bidirectional ring laser , 1988 .

[52]  Tomita,et al.  Observation of Berry's topological phase by use of an optical fiber. , 1986, Physical review letters.

[53]  C. Mead,et al.  On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei , 1979 .

[54]  Beijersbergen,et al.  Classical realization of a strongly driven two-level system. , 1990, Physical review letters.

[55]  H. C. Longuet-Higgins,et al.  Intersection of potential energy surfaces in polyatomic molecules , 1963 .

[56]  M. Berry.  Interpreting the anholonomy of coiled light , 1987, Nature.

[57]  F. Wilczek,et al.  Geometric Phases in Physics , 1989 .

[58]  J. Byrne.  Young's double beam interference experiment with spinor and vector waves , 1978, Nature.

[59]  Mario Martinelli,et al.  A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits , 1990 .

[60]  Spreeuw,et al.  Photon band structure in a Sagnac fiber-optic ring resonator. , 1988, Physical review letters.

[61]  H. Jehle,et al.  Albert Einstein: Philosopher-Scientist. , 1951 .

[62]  Grant,et al.  Fractional quantization of molecular pseudorotation in Na3. , 1986, Physical review letters.

[63]  C. Mead,et al.  The geometric phase in molecular systems , 1992 .

[64]  M. O. van Deventer.  Full duplex coherent optical communication with one in-line polarisation controller , 1990 .

[65]  R. Azzam,et al.  Ellipsometry and polarized light , 1977 .

[66]  M. O. van Deventer.  Preservation of polarisation orthogonality of counterpropagating waves through dichroic birefringent optical media: proof and application , 1991 .

[67]  Kwiat,et al.  Observation of a nonclassical Berry's phase for the photon. , 1991, Physical review letters.

[68]  R. Colella,et al.  Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field , 1975 .

[69]  Samuel,et al.  General setting for Berry's phase. , 1988, Physical review letters.

[70]  J. Huignard,et al.  Frequency shifters for photorefractive crystals. , 1985, Applied optics.

[71]  G. Love,et al.  Polarization eigenmodes of a QHQ retarder — some new features , 1994 .

[72]  Eom,et al.  Test for nonreciprocal circular birefringence in YBa2Cu3O7 thin films as evidence for broken time-reversal symmetry. , 1990, Physical review letters.

[73]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[74]  Maitreyee Roy,et al.  A geometric-phase interferometer , 1992 .

[75]  Pines,et al.  Study of the Aharonov-Anandan quantum phase by NMR interferometry. , 1988, Physical review letters.