Parametric study of uniformly polarized stochastic electromagnetic beam and its imaging

A parametric study is performed in investigating the stochastic electromagnetic beam generated by a uniformly polarized electromagnetic Gaussian Schell-model source and passing through ABCD optical systems. Through theoretical analysis, the requirement is derived that the uniformly polarized electromagnetic field can be obtained at the output plane of the imaging optical system. Furthermore, the general imaging formula of the stochastic electromagnetic beam is derived. Numerical examples are also presented to illustrate the application.     

A Novel Method for Enhancing Goos-Hänchen Shift in Total Internal Reflection

Due to the tiny shift in order of optical wavelength for Goos-Hǎnchen （GH） shift, it is very difficult to directly measure and apply the GH shift. We develop a new method for enhancing GH shift of both TE and TM polarized waves. The method is based on a total reflection prism made of BK9 glass combined with a precise measurement of the resulting spatial displacement with a one-dimensional charge coupled device （CCD）. Measurements are performed to examine the validity of the method. Experimental and theoretical results indicate the feasibility of the method with an enhancement in optical wavelenghth shift at millimetre scale. The method is advantageous to application the GH shift in the optical domain, and is also meaningful for measuring even smaller changes in the refractive index of a liquid.     

Overall parameters for the characterization of non-uniformly totally polarized beams

Several overall parameters are introduced to characterize the linear or circular polarization content of a non-uniformly totally polarized beam over the region of its wavefront where the irradiance is significant. These figures of merit are determined from the values of the Stokes parameters. The physical meaning of the proposed parameters is tested by computing some numerical examples, and their measurability is checked by considering non-uniformly totally polarized fields generated after propagation through uniaxial anisotropic materials.     

Near-field effect in two-atom system

The self-consistent problem is solved for the interaction of two dipole atoms situated at arbitrary distance from one another with the field of quasiresonant light wave. Atoms are considered to be linear Lorenz oscillators. Polarizing fields inside the system include both Coulomb and retarding parts. The solutions obtained are investigated for the case when atoms have the same polarizabilities and interatomic distance is much less than external light wavelength. Formulas for electric fields inside and outside of small object are obtained. It is shown that longitudinal and transverse optical oscillations are possible to exist inside small two-atom object. Dispersion laws of these oscillations depend upon interatomic distance and upon angle between axis of the system and the direction of propagation of external wave. The field outside the small object in wave zone is linearly polarized with the choice of linear polarization of external field. However, the directions of polarization of these waves are different and depend essentially upon frequency. The amplitude of field outside small object in wave zone is shown to depend essentially on the frequency of external field and interatomic distance. The results obtained are treated as near-field effect in the optics of small objects making it possible to investigate the structure of small objects with optical radiation. Received 26 October 1998 and Received in final form 26 January 2000     

Spatial coherence properties of azimuthally polarized laser modes

Understanding of coherence properties of optical fields is of basic importance both in classical optics and in quantum physics. Coherence properties of electromagnetic laser modes are only now beginning to be explored and have not yet been tested experimentally, except in the simplest cases. In this paper, we first study theoretically the coherence properties of azimuthally polarized laser modes and we clarify the distinction between coherence and correlations in stochastic electromagnetic fields, a distinction which has up to now not been fully understood and has, in fact, been a subject of controversy. Our analysis clearly illustrates the distinction between these two concepts. After elucidating theoretically the coherence properties of radially polarized laser modes, we describe an experimental study of their properties, made by the use of a recently introduced reversed-wavefront Young’s interferometer. A good agreement between theory and experiment has been found.     

Beam moments and angular momentum in non-uniformly polarized beams

The angular momentum of non-uniformly totally polarized beams is investigated using methods from the beam characterization approach. The relationship between the elements of the beam matrix for the two components of the field and the angular momentum is given. The unconventional distribution of the polarization across the beam profile could result in contributions to both the spin and orbital terms of the angular momentum. To illustrate this, a particular example with a vortex beam is considered.     

Global parameters for characterizing the radial and azimuthal polarization content of totally polarized beams

Several global parameters are proposed to characterize the radial and azimuthal polarization content of non-uniformly totally polarized beams. Such figures of merit can be written and measured in terms of two Stokes parameters, and also from the data at the output of either a radial or an azimuthal dichroic polarizer, integrated throughout the beam profile. The measurability of the proposed parameters has also been experimentally checked.     

Rotations of eigenvibration direction in anisotropic crystals

The electric field of incident light induces dipoles in anisotropic media, vibrating in two perpendicular directions of the principal axes. Because of the tensor property of the dielectric constant, an induced dipole is subject to a torque, tending to rotate it about the axis parallel to the propagation direction. The directions of eigenvibration of the ordinary (o-ray) and extraordinary (e-ray) waves are no longer perpendicular in this sense. We propose here the relationships to describe the rotation of the induced dipole in the perpendicular electric fields. The rotation angles are found to increase with increasing dielectric constants and electric field strength of the incident light, exhibiting large values near the resonance frequencies in the infrared range at the azimuth angle /4 of the polarized incident light. Piezoelectric and ferroelectric crystals have a large value of the dielectric constant in the infrared frequency range. Rotations of the vibration direction of the o-ray and the e-ray waves are shown in the infrared transmission spectra recorded by incidence of the polarized light and transmission through piezoelectric and ferroelectric crystals (-quartz, LiNbO₃, and LiTaO₃). Interference of the o-ray and the e-ray waves transmitted through the crystals confirms the rotations of the vibration directions, a self-modulation effect of light in piezoelectric and ferroelectric crystals induced by the electric field of the propagating light.     

Smallest focal hole

We study theoretically routes toward the most confined dark channel that can be obtained using high angular aperture focusing. One possible solution is to use a radially polarized beam combined with an optical singularity. Another possibility is to use an azimuthally polarized light beam combined with an annular aperture or a phase filter. Our results suggest that a focal hole of full-width at half maximum of approximately 0.3λ₀/NA is achievable, where λ₀ is the wavelength in vacuum and NA is the numerical aperture of the focusing system. Finally, we show that by letting a phase-shifted plane wave and a focused scalar wave interfere only one point in the focal plane will exhibit zero intensity. Advantages and disadvantages of the schemes are discussed.     

Giant optical activity and circular dichroism in the terahertz region based on bi-layer Y-shaped chiral metamaterial

We present a bi-layer Y-shaped chiral metamaterial (CMM) that can realize a giant optical activity and circular dichroism (CD) effect to the incident linear polarization wave in the terahertz (THz) region. Numerical simulation results exhibit that the pronounced CD effect with a great difference between the transmission coefficients for the circularly polarized waves can be obtained at 5.06 THz, meanwhile the 90°-polarization rotation can be observed at 5.2 THz when a y-polarized wave is incident to this CMM propagating along the −z-axis. The mechanism of the optical activity and giant CD effect is illustrated by simulated surface current distributions. Further, the influences of the structural parameters of the proposed CMM to the optical activity and CD effect have been investigated numerically.     

Self-mixing interference effects in orthogonally polarized dual-frequency Nd:YAG lasers at different feedback levels

The self-mixing interference effects are investigated in birefringence dual-frequency Nd:YAG lasers at different optical feedback levels. For weak feedback level, both of the intensities of the two modes are sinusoidally modulated by external cavity length with a feedback period of half laser wavelength. While these two modes can only coexist in a part of feedback period at moderate feedback level, i.e., one mode reaches its maximum intensity, the other one extinguishes. At high feedback level, complete polarization switching (one mode oscillating, the other one extinguishing) between two polarized modes is observed, and every switching corresponds to quarter-wavelength variation of external cavity length. Furthermore, two feedback schemes, i.e., isotropic optical feedback (IOF) and polarized optical feedback (POF) are taken into account. The theoretical analysis based on a model of two-mode-coupled laser is presented, which is in good agreement with experimental results. Our results can advance the research of self-mixing interferometer of orthogonally polarized dual-frequency lasers.     

Topological and morphological transformations of developing singular paraxial vector light fields

The paper is devoted to establishment of the real-time topological and morphological dynamics of generic developing paraxial elliptic speckle fields generated and driven by the system ‘laser beam + photorefractive crystal LiNbO₃:Fe’. Generic space-time development of full gamut of polarization ellipse parameters (ellipticity, azimuth, morphology of C points, optical diabolos and handedness) and their combination in fixed beam cross-section was measured in details by the elaborated quick-action real-time Stokes-polarimetry. Whole field irreversible evolution is fulfilled through totality of random space/time C point pair nucleation/annihilation. The ‘life-story’ of C point and optical diabolo pairs is realized through ‘local topological/morphological transition’ with fully reversible scenario. It starts from smooth fragment of speckle field by formation of pre-nucleation local structure and finishes by after-annihilation local structure which decays to another smooth structure. Scenarios of star-monstar pair nucleation/annihilation and monstar  ↔  lemon transformation were established. Measured statistics of C point and diabolo morphological forms was in excellent agreement with theory predictions. All allowed scenarios of diabolo pair ‘life-story’ started/finished as star-hyperbolic monstar-hyperbolic pair were measured. Evolution of polarization ellipses handedness is implemented through L contours movement and reconnection with a saddle as the catalyst. Reconnection of L contour peninsula leads to birth of closed L contour delimiting island of fixed handedness ellipses with/without C points. Elaborated approach and presented results start the dynamic singular optics of time-dependent vector light fields.     

Polarization-resolved analysis of the characteristics of a Raman laser made with a polarization maintaining fiber

We derive a simple model describing steady characteristics of Raman fiber lasers made with polarization maintaining fibers. We show both theoretically and experimentally that this kind of laser simply consists of two independent Raman lasers linearly polarized along the fiber birefringence axes. The output power characteristics of the laser are shown not to be influenced by optical Kerr effect. Finally, we use our model to propose answers to questions recently raised about efficiency of Raman lasers made with polarization maintaining fibers.     

Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

Depolarization characteristics of incompletely polarized and partially coherent laser beams in slant atmospheric turbulence

Based on the cross-spectral density function of transmission theory and the unified theory of coherence and polarization, the depolarization characteristics of incompletely polarized and partially coherent laser propagation in slant atmospheric turbulence are investigated. According to extended Huygens–Fresnel principle, the analytical expressions for intensity and degree of polarization in the slant path are derived. The effects of the wavelength, the initial spot size and the transmission distance on the intensity and degree of polarization are described. The results show that a more stable distribution of the degree of polarization at the receiver is obtained with increasing wavelength for a certain receiver height. The conclusions play an important role in optical communications and target recognition.     

Propagation characteristics of the rectangular flattened Gaussian beams through circular apertured and misaligned optical systems

Based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expression for the output field distribution of a rectangular flattened Gaussian beam passing through a circular apertured and misaligned paraxial ABCD system is derived. The result brings more convenient for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of a rectangular flattened Gaussian beam through a circular apertured and misaligned optical system.     

The focus of light – theoretical calculation and experimental tomographic reconstruction

We present numerical calculations on the field distribution in the focus of an optical system with high numerical aperture. The diffraction integrals which are based on the Debye approximation are derived and evaluated for a radially polarized input field with a doughnut-shaped intensity distribution. It is shown that this mode focusses down to a spot size significantly smaller as compared to the case of linear polarization. An experimental setup to measure the three-dimensional intensity distribution in the focal region is presented, which is based on the knife-edge method and on tomographic reconstruction. Received: 14 July 2000 / Published online: 30 November 2000     

Focus shaping of cylindrically polarized vortex beams by a high numerical-aperture lens

The focus-shaping technique of a cylindrically polarized vortex beam by a high numerical-aperture lens is reported. Such a polarized vortex beam is decomposed into radial and azimuthal polarization. It is shown that the total intensity distribution in the focal region is dependent not only on the numerical-aperture maximal angle and the polarization rotation angle but also on the topological charge. By choosing the proper combination of parameters, the adjustably confined flat-topped focus and focal hole can be obtained. The focus-shaping technique may find wide applications, such as optical tweezers, laser printing and material processing.