Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes through complex ABCD optical systems

The change of coherence and polarization of an electromagnetic beam modulated by a random anisotropic phase screen passing through any optical system is found within the framework of complex ABCD-matrix theory This means that the formalism can treat imaging and Fourier transform and free-space optical systems, as well as fractional Fourier transform systems, with finite-size limiting apertures of Gaussian transmission shape. Thus, the current paper shall be considered as a continuation, extension, and generalization of a previous work by Shirai and Wolf [J. Opt. Soc. Am. A21, 1907 (2004)]. It will be shown that the inclusion of apertures in the optical system strongly influences not only the propagation of spatial coherence but also the degree of polarization of a propagating field. Analytical expressions of coherence and polarization propagation will be given in terms of the matrix elements for any complex optical system.     

Generation of nondiffracting quasi-circular polarization beams using an amplitude modulated phase hologram

We propose an approach to the generation of nondiffracting quasi-circularly polarized beams by a highly focusing azimuthally polarized beam using an amplitude modulated spiral phase hologram. Numerical verifications are implemented in the calculation of the electromagnetic fields and Poynting vector field near the focus based on the vector diffraction theory, and the polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the electric field, magnetic field, and Poynting vector field can simultaneously be uniform and nondiverging over a relatively long axial range of ~7.23λ. In the transverse plane, the ellipticity and azimuthal angle of the local polarization ellipse varies from point to point. No polarization singularity and phase singularity are found at the beam center, which makes the bright spot possible.     

Coherence of two interfering beams modulated by a uniformly moving diffuser

Abstract

Coherence properties are discussed of light which emerges from two pinholes after it has passed through a moving diffuser. The results are used to show how the correlation function of the heights of the diffuser surface and the speed with which the diffuser is moving may be determined from simple interference experiments.     

On experimental characterization of polarization fluctuation dynamics in random optical beams

Polarization correlation functions that characterize the rate of change of the instantaneous polarization state of an arbitrary fluctuating electromagnetic beam were recently introduced. In this work, we describe techniques that enable the measurement of these functions leading to the determination of the so-called polarization time of a random field.     

Rotation of multimode Gauss-Laguerre light beams in free space

An iterative algorithm is presented for calculating diffractive phase optical elements that form light beams which are an effective superposition of a small number of nonradially symmetric Gauss-Laguerre modes with a prescribed energy contribution from each mode. Pis’ma Zh. Tekh. Fiz. 23, 1–6 (September 12, 1997)     

Arbitrary three-dimensional polarization control based on cylindrical vector beams and binary phase coding

To obtain an arbitrary polarization in three dimensions is of significant interest for many applications. Here, we demonstrate a configuration to achieve it. After phase coding by binary phase plates, two cylindrical polarized beams are superposed and focused by a high-numerical aperture lens to obtain transversally and radially polarized components in the focus vicinity. By adjusting their intensity and phase difference, the desired three-dimensional polarization can be achieved. The proportion of the desired polarization is extremely high and the focus spot is smaller than the diffraction-limited spot size.     

Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere

We study the changes in the degree of polarization of an electromagnetic Gaussian Schell-model beam, as the beam propagates through the turbulent atmosphere. We demonstrate that, within the framework of the Tatarskii model of the turbulent atmosphere, the degree of polarization of the beam changes appreciably at relatively short propagation distances in the atmosphere. In the long-propagation distance limit, however, we find that the degree of polarization of the beam tends to the value that it has in the source plane.     

Generation of electromagnetic waves by electrons rotating in a radial electrostatic field in free space

A theoretical analysis is made of mechanisms for the generation of electromagnetic waves by electrons rotating in a radial electrostatic field formed by a positively charged filament in free space. A dispersion equation is obtained to describe the interaction between the waves and nonrelativistic electrons. It is shown that electromagnetic fields can be generated by means of Čerenkov resonance. The frequencies and growth rates of the emitted waves are determined and their dependence on the parameters of the problem is investigated. Pis’ma Zh. Tekh. Fiz. 25, 1–4 (November 12, 1999)     

Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers: errata

We correct a mistake in the expression of the coupled power into an optical fiber that led to some erroneous conclusions in Opt. Lett. 34, 2829 (2009) and J. Opt. Soc. Am. A 26, 2452 (2009).     

Scattering-induced changes in the degree of polarization of a stochastic electromagnetic plane-wave pulse

The scattering of a stochastic electromagnetic plane-wave pulse on a deterministic spherical medium is investigated. An analytical formula for the degree of polarization (DOP) of the scattered field in the far zone is derived. Letting pulse duration T(0) → ∞, our formula can be applied to study the scattering of a stationary stochastic electromagnetic light wave. Numerical results show that the DOP of the far zone field is closely determined by the size of the spherical medium when the incident field is a stochastic electromagnetic plane-wave pulse. This is much different from the case when the incident field is a stationary stochastic electromagnetic light wave, where the DOP of the far zone field is independent of the size of the medium. One may obtain the information of the spherical medium by measuring the scattering-induced changes in the DOP of a stochastic electromagnetic plane-wave pulse.     

Effects of linear non-image-forming devices on spectra and on coherence and polarization properties of stochastic electromagnetic beams: part II: examples

In this paper we derive the three-dimensional scalar theory of the overall imaging process in a high-aperture interference, holographic, and correlation (heterodyne) microscope. The influence of low spatial and temporal coherence of light is completely described by means of a coherent transfer function. The results are compared with those for an ideal confocal microscope.     

A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel-Arago interference laws

A new general interference law is derived for the superposition of two random electromagnetic beams of any state of coherence and of any state of polarization when the beams are transmitted through polarizers and rotators. It includes, as special cases, a variety of interference laws that apply to particular situations. Some of them have a close bearing on the classic interference experiments of Fresnel and Arago that have played a basic role in elucidating the concept of polarization of light.     

Probing of a random phase screen by a focused spatially modulated laser beam: Deflection of interference fringes

Deflection of interference fringes in a diffraction field was investigated under conditions in which a laser beam with a regular interference structure was finely focused onto a random phase screen. It was established that the contrast of the average-intensity fringes depends analytically on the statistical parameters of the screen. Pis’ma Zh. Tekh. Fiz. 25, 56–61 (January 12, 1999)     

Effects of linear non-image-forming devices on spectra and on coherence and polarization properties of stochastic electromagnetic beams: part I: general theory

The classic theoretical techniques of polarization optics are the Jones calculus and the Stokes-Mueller calculus. Both deal with transmission of certain ‘one-point’ quantities, which are associated with a light beam. Recently ‘two-point’ quantities were introduced, which are the elements of a 2?×?2 cross-spectral density matrix that characterizes the correlations at two points in a beam or which are expressible in terms of them. Unlike the quantities with which the Jones and the Stokes calculus deal, these generalized quantities contain information not only about the polarization properties of the beam but also about its coherence properties. In this paper we present a generalization of the Jones calculus and of the Stokes-Mueller calculus for transformations of the new two-point quantities by linear non-image-forming devices. They may act on the beam in a deterministic or in a random manner.     

Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media

The propagation of inhomogeneous and elliptically polarized plane waves in absorbing uniaxial anisotropic media is described using complex unitary vectors to represent the direction of propagation and the direction of polarization. Detailed expressions for electric displacement, electric field, and magnetic field vectors are obtained for the ordinary and extraordinary waves, and their geometry is discussed. According to the complex direction of propagation, three particular cases are studied: the real case (homogeneous wave), the case perpendicular to the optical axis, and the case coplanar with the optic axis. The case of isotropic media is also analyzed.     

Effects of phase changes on reflection and their wavelength dependence in optical profilometry

The method as well as an appropriate instrumentation for measuring phase changes of reflected light is described. The phase changes on samples of Au, Al, Ag, and Cr evaporated films are measured for five wavelengths (lambda) from 442 to 633 nm, with respect to the phase change at the glass-air interface, where it should be zero. The measured results for the Au film are in fairly good agreement with values calculated by use of optical constants from a handbook or the complex refractive index measured by an ellipsometer. The phase changes for Al and Ag films are different from calculated values by ~5 degrees or a shift length of 4.4 nm at lambda = 633 nm, while those of the Cr film show large shifts as high as 16 degrees or a shift length of 9.8 nm at lambda = 442 nm.     

The effect of degree of prestressing and age of concrete beams on frequency and damping of their free vibration

The programme of dynamic investigations, described partially in this paper, was originated in 1958 during work carried out by the author at the Federal Technical University in Zurich. These investigations are mainly aimed at the determination of the effect of the degree of prestressing on the frequency and logarithmic decrement of free vibration damping in concrete beams.

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Résumé Le programme d'études dynamiques, partiellement décrit dans cet article, a débuté en 1958 quand l'auteur faisait un stage à l'Ecole Polytechnique Fédérale de Zürich. Ces études avaient pour but de déterminer l'effet du degré de précontrainte sur la fréquence et la decrément logarithmique de l'amortissement de la vibration libre dans les poutres de béton.

     

Probing of a random phase screen by a focused spatially modulated laser beam. Diffraction at a large number of inhomogeneities

The contrast of the Young’s interference fringes formed in the diffraction field when a dynamic random phase screen is illuminated by a focused, spatially modulated laser beam is obtained analytically as a function of the statistical parameters of the screen. A threshold relative bleaching effect is established for a highly dispersive medium when a low-divergence illuminating beam is used. Pis’ma Zh. Tekh. Fiz. 23, 47–53 (October 12, 1997)