Fiber Optics: Research and Development

Abstract

With twisted stacks of N polarizers P or retarders R, the polarization of a light beam can be cycled around the Poincaré sphere on N similar arcs of great P or small R circles. We calculate the phase changes around these cycles (geometric for P; geometric + dynamical for R). In the continuum limit N → ∞ of a smoothly twisting medium, a P stack forces the light to follow its changing polarization, and the phase is the solid angle of the associated loop on the sphere; for an R stack, on the other hand, it is only in the adiabatic limit of slow twist (where the dynamical phase is large) that the geometric phase corresponds to that of the loop specified by the changing eigenpolarization of the medium. The predicted phase shifts are observed as fringe shifts in an interferometer for N=2, 3 and 4.     

A Müller-Stokes Study of Polarization-mode Transformation in Randomly Perturbed Optical Fibres

Abstract

On the basis of Müller-Stokes marices for a uniformly perturbed fibre and the mode-coupling centre model polarization-mode transformation along randomly perturbed optical fibres has been studied. The process of spectral averaging in the quasimonochromatic case has been theoretically modelled and a computer simulation has been performed. The equivalent mode-coupling centre model has been applied to study the z-dependence of the polarization dispersion and the relationship between the degree of polarization, the polarization holding parameter and the coherence length in a single-mode fibre.     

Conchoidal transform of two plane curves

The conchoid of a plane curve C is constructed using a fixed circle B in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves B and C in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in P ² × P ². We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve C we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.     

Orientation of biological cells using plane-polarized gaussian beam optical tweezers

Abstract

Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of the trapped cells. We show that it is possible to controllably align or rotate disc-shaped cells—chloroplasts of Spinacia oleracea—in a plane-polarized Gaussian beam trap, using optical torques resulting predominantly from circular polarization induced in the transmitted beam by the non-spherical shape of the cells.     

Solitary Waves of Maxwell's Equations in Nonlinear Anisotropic Media

Abstract

The (1 + 1)-D solitary wave solutions of Maxwell's equations in nonlinearity induced anisotropic media (in liquids such as carbon disulphide, and in crystals, etc.) are investigated. We find that there is no arbitrarily linearly polarized (in the x-y plane perpendicular to the propagation direction z) soliton solution from Maxwell's equations except that with linear polarization either in alignment with or orthogonal to the geometric axis of the light induced refractive index change. This contradicts the prediction of the vector nonlinear Schroedinger equation (an approximation of Maxwell's equations) which yields soliton solutions with an arbitrary linear polarization. However, Maxwell's equations are found to admit stable elliptically polarized solitary wave solutions which reduce to the stable circularly polarized solitary wave solutions of the vector nonlinear Schroedinger equation when the induced refractive index change approaches zero.     

The Geometric Phase

Abstract

The change in the phase of a beam of light produced by a cyclic change in its state of polarization is an example of the geometric phase that can be verified by interferometric measurements. This paper presents a quantum-field theoretical analysis of the geometric phase interferometer in the limit of a small photon number, as well as some experimental results that confirm that the optical effects due to the geometric phase persist down to the single-photon level.     

Propagating and evanescent waves associated with inhibited reflection in uniaxial crystals: Extraordinary incidence

Abstract

When an extraordinary wave under inhibited reflection conditions is incident on an interface between a uniaxial crystal and an isotropic medium, the reflected extraordinary wave is evanescent and the polarization of the refracted wave changes from linear to elliptical. In the present paper it is shown that the refracted ray undergoes a shift which is not only longitudinal (as the Goos—Hänchen effect in total reflection in isotropic interfaces) but also transversal. The structure of the evanescent reflected wave is studied and the polarization of the transmitted wave is analysed.     

Multimode polarization degree of mixture optical states in integrated directional couplers

Mixture multimode optical field classical states propagating in N?×?N integrated directional couplers are analyzed by using the density matrix formalism in a N-dimensional optical space. These mutimode optical fields present a kind of generalized polarization and accordingly a definition of a multimode polarization degree is proposed. It is based on the distance measure between a mixture state and an unpolarized state in a N-dimensional optical space so that in the case N=2 the standard polarization degree is recovered. It is shown that directional couplers can reduce or increase remarkably the multimode polarization degree of a mixture state. Likewise a simple measurement technique, based on Y junctions, of this multimode polarization degree is proposed. Finally all the results can be formally extended to the special case of multimode single photon quantum states.     

The Geometric Phase in Optical Rotation

Abstract

The geometric phase arising from rotation of the plane of polarization of an electromagnetic wave is similar to that acquired by a spin-1/2 particle in a magnetic field. We describe an interferometric arrangement using an optically active medium that can be used to observe this change.     

Pancharatnam's Phase for Polarized Light

Abstract

This paper presents a classical theoretical analysis of the geometric phase arising in a cyclic change of the polarization state of light beams. We compare the results obtained this way with the quantum mechanical analysis.     

A simple demonstration of the Pancharatnam phase as a geometric phase

Abstract

To demonstrate the Pancharatnam phase as a geometric (Berry's) phase, each polarization state must be obtained by projecting the previous state on it. We describe a simple interferometric arrangement for such a demonstration which only uses a single rotation linear analyser to introduce a continuously variable phase difference between the two beams.     

Coherent quantum measurement for the direct determination of the degree of polarization and polarization mode dispersion compensation

Abstract

An example of a coherent measurement for the direct evaluation of the degree of polarization of a single-mode optical beam is presented. It is applied to the case of great practical importance where depolarization is caused by polarization mode dispersion. It is demonstrated that coherent measurement has the potential of significantly increasing the information gain, compared to standard incoherent measurements.     

Local polarization reversal of LiNbO3 by scanning the surface perpendicular to the axis of spontaneous polarization with a needle-shaped electrode

The principle of local polarization reversal of ferroelectrics using a moving needle-shaped electrode¹ was used to make a comparative study of the characteristics of polarization reversal of LiNbO₃ from the Z(001) and Y(010) surfaces. In addition to chemical etching, an optical polarization method was used to visualize the domain structure. It was noted that the different dependences of the domain length on the polarizing voltage observed for the different crystal surfaces may be caused by the conducting and polarization properties of the regions in which the domain growth occurs. It is shown that the depth of penetration of the created domains in the sample may be set. Pis’ma Zh. Tekh. Fiz. 24, 52–57 (March 26, 1998)     

Optical field-strength generalized polarization of multimode single photon states in integrated directional couplers

A quantum analysis of the generalized polarization properties of multimode single photon states is presented. It is based on the optical field-strength probability distributions in such a way that generalized polarization is understood as a significant confinement of the probability distribution along certain regions of the multidimensional optical field-strength space. The analysis is addressed to multimode integrated waveguiding devices, such as N?×?N integrated directional couplers, whose modes fulfil a spatial modal orthogonality relationship. For that purpose a definition of the quantum generalized polarization degree in a N-dimensional space, based on the concept of distance to an unpolarized N-dimensional Gaussian distribution, is proposed. The generalized polarization degree of pure and mixture multimode single photon states and also of some multi-photon states such as coherent and chaotic ones, is evaluated and analyzed.     

Isotropy and polarization in a statistically stationary electromagnetic field in three-dimensions

A parameter, called the degree of isotropy, used in conjunction with the degree of polarization defined by Ellis, Dogariu, Ponomarenko and Wolf (Opt. Commun. 248 333 (2005)) in a recent paper, is shown to more completely characterize the state of a statistically stationary electromagnetic field in three dimensions. A simple expression is presented that relates the maximum degree of polarization to a given degree of isotropy, and a simple graphical representation of a state is given that clearly shows where the state stands among all possible states.     

Polarization recording of holograms in partially polarized recording light

A theoretical approach is considered for media whose scalar and anisotropic responses are of opposite sign. The nondiffracted beam, and the imaginary and real images formed by a polarization hologram are analyzed under these conditions. It is shown that the imaginary image has its polarization transformed compared with the object field while a pseudoscopic object field reconstructed in terms of polarization state and degree is formed in the real image. Pis’ma Zh. Tekh. Fiz. 23, 38–42 (February 12, 1997)     

Phase properties of coherent phase and generalized geometric states

Abstract

We examine some properties of a class of partial phase states of a single field mode. The quasiprobability distribution function and the phase properties of both the generalized geometric and even geometric states are investigated. The relation between the coherent phase states and the SU(1, 1) coherent states is sought.     

Quantum Fluctuations in the Stokes Parameters of Light Propagating in a Kerr Medium

Abstract

The quantum theory of light propagation in a nonlinear Kerr medium is applied to calculate the Stokes parameters and their variances in the process of light propagation. Exact quantum formulae are derived for the expectation values of the Stokes operators and thus for the azimuth θ and ellipticity η of the beam. The role of quantum fluctuations in light polarization characteristics is discussed. The periodic behaviour of quantum evolution of the light polarization is revealed explicitly. It is shown that the degree of polarization is diminished at early stages of each period of the evolution but then reverts to its initial state of complete polarization at the end of the period. The variances of the Stokes parameters are also periodic and intensity-dependent; however, they never fall below their coherent state values.     

n-Fold Polarization Measures and Associated Thermodynamic Entropy of N Partially Coherent Pencils of Radiation

An n-fold (n=2,…,N) measure of the degree of polarization associated with an N×N coherency matrix characterizing N pencils of radiation is discussed. The measure is cast in terms of the N possible scalar invariants of the coherency matrix and automatically takes into account possible rank deficiency. When N = 2, the single polarization measure reduces to the usual expression for polarization as the fraction of the intensity contained in the polarized component. The N = 3 case is discussed as an illustrative example, with special reference to the rank deficiency of a plane wave arbitrarily oriented with respect to the given coordinate system. Finally, these results are used to redevelop von Laue's theory of the thermodynamic entropy of partially coherent pencils of radiation.