arXiv subjects

Rajendra Bhandari

Publications and source records attributed to Rajendra Bhandari.

14 recordsLinked to original sources

arXiv2011

The nonmodular topological phase and phase singularities

Generalizing an earlier definition of the noncyclic geometric phase (R.Bhandari, Phys.Lett.A, 157, 221 (1991)), a nonmodular topological phase is defined with reference to a generic time-dependent two-slit interference experiment involving particles with N internal states in which the internal state of both the beams undergoes unitary evolution. A simple proof of the shorter geodesic rule for closure of the open path is presented and several useful new insights into the behaviour of the dynamical and geometrical components of the phase shift presented. An effective hamiltonian interpretation of the observable phase shifts is also presented.

physics.optics↗

arXiv2010

Comment on " Topological phase in two flavor neutrino oscillations"

We critically analyze the claims with regard to the relevance of topological phases in the physics of neutrino oscillation made in a recent paper [Phys. Rev. D 79, 096013 (2009)] and point out some inappropriate exaggerations and misleading statements. We find that the $π$ phase described in this paper, while interesting, is an artefact of two major approximations made in the paper. We point out a more robust and more familiar $π$ phase in the neutrino oscillation formulae which can be interpreted as a pure Pancharatnam phase. We also make some relevant remarks on the distinction between the geometric and the topological phase made in the commented paper.

hep-ph↗

arXiv2010

A simple inverter for polarization transformations

It is shown that a transparent birefringent element whose eigenstates are a pair of elliptical polarizations with principalaxes along the x and y axes, sandwiched between a pair of orthogonal halfwave plates with principal axes along directions at 45 deg to the x and y axes, is equivalent to an element with the same eigenstates and eigenvalues but with the fast and the slow eigenstates interchanged. The device thus produces the inverse of the original unitary transformation. A similar result holds for a puredichroic element. With electrically switchable halfwave plates such a device can be used to switch the sign of optical activity or to rotate through 90 deg, without any moving parts, a linear retarder or a linear polarizer.

physics.optics↗

arXiv2009

Reciprocity constraints on the matrix of reflection from optically anisotropic surfaces

We derive certain constraints on the reflection matrix for reflection from a plane, nonmagnetic, optically anisotropic surface using a reciprocity theorem stated long ago by van de Hulst in the context of scattering of polarized light. The constraints are valid for absorbing and chiral media and can be used as tools to check the consistency of derived expressions for such matrices in terms of the intrinsic parameters of the reflecting medium as illustrated by several examples.

physics.optics↗

arXiv2008

Cancellation of simple optical anisotropies without use of a Faraday mirror

We first derive the round-trip Jones matrix for double passage through a reciprocal optical medium by means of reflection off a plane mirror that could be optically anisotropic. We then show that if a medium with only linear birefringence and linear dichroism is placed between a pair of orthogonal quarterwave plates with principal axes at 45 deg to that of the medium and the sandwich is placed in front of an isotropic mirror it behaves, under double passage, like an isotropic medium. We describe a simple liquid crystal device that behaves, in reflection, as an isotropic medium whose refractive index can be varied by application of an electric field, thus acting as a phase only modulator for light in any polarization state.

physics.optics↗

arXiv2008

Transpose symmetry of the Jones Matrix and topological phases

The transmission Jones matrix of an arbitrary stack of reciprocal plane parallel plates which has been turned through 180 degrees about an axis in the plane of the stack is, in an appropriate basis, the transpose of the transmission matrix of the unturned slab with a change in the sign of the off-diagonal elements. We prove this convention-free result for the case where reflection at the interfaces can be ignored and use it to devise an experimental scheme to separate isotropic and topological phase changes in a reciprocal optical medium.

physics.optics↗

arXiv2007

Light propagation through a coiled optical fiber and Pancharatnam phase

The nature of changes in the interference pattern caused by the presence of polarization-changing elements in one or both beams of an interferometer, in particular those caused by an effective optical activity due to passage of a polarized beam through a coiled optical fiber are clarified. It is pointed out that for an incident state that is not circularly polarized so that the two interfering beams go to different polarization states, there is an observable nonzero Pancharatnam phase shift between them which depends on the incident polarization state and on the solid angle subtended by the track of the $\vec{k}$-vector at the centre of the sphere of k-vectors. The behaviour of this phase shift is singular when the two interfering states are nearly orthogonal. It is shown that for zero path difference between the two beams, the amplitude of intensity modulation as a function of optical activity is independent of the incident polarization state.

physics.optics↗

arXiv2003

Nonachromaticity and reversals of topological phase as a function of wavelength

In an earlier work (R. Bhandari, Phys. Lett. A 204 (1995) 188), it was shown that, contrary to the property of achromaticity (independence of wavelength) usually associated with topological phases, topological phases encountered in polarization optics can, under certain conditions, show sharp changes and reversals as a function of wavelength, a phenomenon originating in the occurrence of phase singularities, earlier observed in interference experiments. It was shown that a proposed flat lens capable of focussing light with pure geometric phase shifts can switch from being convex to a concave lens or vice versa under these conditions. In this paper conditions under which such reversals can take place for small changes in wavelength are described. Some general implications of phase singularities in the physics of interference are pointed out.

physics.optics↗

arXiv2001

Observable Dirac-type singularities in Berry's phase and the monopole

The physical reality and observability of 2nπBerry phases, as opposed to the usually considered modulo 2πtopological phases is demonstrated with the help of computer simulation of a model adiabatic evolution whose parameters are varied along a closed loop in the parameter space. Using the analogy of Berry's phase with the Dirac monopole, it is concluded that an interferometer loop taken around a magnetic monopole of strength n/2 yields an observable 2nπphase shift, where n is an integer. An experiment to observe the effect is proposed.

quant-ph↗

arXiv2001

On singularities of the mixed state phase

A recent proposal of Sjoqvist et.al. to extend Pancharatnam's criterion for phase difference between two different pure states to the case of mixed states in quantum mechanics is analyzed and the existence of phase singularities in the parameter space of an interference experiment with particles in mixed states pointed out. In the vicinity of such singular points the phase changes sharply and precisely at these points it becomes undefined. A closed circuit in the parameter space around such points results in a measurable phase shift equal to 2nπ, where n is an integer. Such effects have earlier been observed in interference experiments with pure polarization states of light, a system isomorphic to the spin-1/2 system in quantum mechanics. Implications of phase singularities for the interpretation of experiments with partially polarized and unpolarized neutrons are discussed. New kinds of topological phases involving variables representing decoherence (depolarization) of pure states are predicted and experiments to verify them suggested.

quant-ph↗

arXiv2001

Comment on ``Experimental Separation of Geometric and Dynamical Phases Using Neutron Interferometry"

We analyse a recently reported neutron interference experiment to measure a geometric phase and attempt to bring out the inadequacy of the ``phase modulo 2π" approach to the geometric phase. A modified neutron interferometer experiment to observe 2nπphase changes of topological origin resulting from closed circuits around singularities in the parameter space of the experiment is proposed.

quant-ph↗

arXiv2000

Geometric phase in phasing of antenna arrays

The response of a pair of differently polarized antennas is determined by their polarization states AND a phase between them which has a geometric part which becomes discontinuous at singular points in the parameter space. Such phase singularities have been observed in optical polarization experiments [R.Bhandari, Physics Reports 281 (1997) 1]. It is pointed out that such a phase is implicit in an equation for the response derived in the sixties [Morris et al Ap.J. 139 (1964) 551]. When a source emitting partially polarized radiation is observed with a correlation interferometer consisting of two antennas with different polarizations, curiously, fringes can be made to vanish for an appropriate choice of the polarization states, in general non orthogonal [V Radhakrishnan, Current Science 67 (1994) 257]. The result follows by considering the interference as a superposition of two patterns due to the two orthogonal polarization components of the radiation, which have a phase difference of magnitude π, a geometric phase.

astro-ph↗

arXiv1998

On Geometric Phase from Pure Projections

The geometric phase is usually treated as a quantity modulo 2π, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present author (reviewed in R.Bhandari, Phys. Rep. 281 (1997) p.1) question the usefulness of such a definition of the geometric phase in that it throws away useful and measurable information about the system, for example strengths of singularities giving rise to the geometric phase. Such singularities have been directly demonstrated by phase-shift measurement in interference experiments. In this paper, two recent polarization experiments (Hariharan et.al., J.Mod.Opt. 44 (1997)p.707 and Berry and Klein, J.Mod.Opt. 43 (1996)p.165) are analysed and compared with previous experiments and potentially detectible singularities in these experiments pointed out.

physics.optics↗

arXiv1998

Comment on "Neutron Interferometric Observation of Noncyclic Phase"

A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].

quant-ph↗