A temporal-coherence anisotropy of unpolarized light

We analyze the anisotropic behavior of unpolarized, temporally partially coherent light. We demonstrate that unpolarized light with different intrinsic degrees of coherence can present an anisotropic behavior which is experimentally observable while it is not the case if both intrinsic degrees are equal. This behavior is analyzed in comparison with the standard anisotropy property of partially polarized light.     

Coherent effects of multiple scattering for scalar and electromagnetic fields: Monte-Carlo simulation and Milne-like solutions

Based on an expansion of the Bethe-Salpeter equation in scattering orders a semi-analytic approach for simulation of coherent phenomena of multiple scattering in random media has been developed. We found that for scalar field the manifestation of these phenomena, observed as temporal field correlation function and coherent backscattering, are universal and well agreed with the results predicted by diffusion approximation. For the electromagnetic field the temporal correlation function and coherent backscattering are noticeably differ from those found for the scalar field, depending strongly on the scattering anisotropy. The obtained numerical results, for the first time to our knowledge, are compared directly with the known generalizations of the Milne solution.     

Changes in generalized Stokes parameters of stochastic electromagnetic beams on propagation through ABCD optical systems and in the turbulent atmosphere

Using the derived formulas for the transformation of 2 × 2 cross-spectral density matrix of the stochastic electromagnetic beams propagating through ABCD optical systems and in the turbulent atmosphere, the changes in the generalized Stokes parameters of the beams propagating under these conditions can be investigated directly. Some typical numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams passing through free space, focal system, dual-focus system, and the turbulent atmosphere with different structure parameters. Further extensions are also pointed out.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Spatial coherence properties of monochromatic electromagnetic beams and of laser modes

It is shown that, contrary to common belief, monochromatic light beams are, in general, not spatially completely coherent, i.e., they will, in general, not produce fringes of unit visibility in a Young's double pinhole interference experiment. We cite experiments with laser modes which confirm this result.     

Temperature Influence on Divergence Angles of Quartz Crystal Wollaston Prism

We propose a structural angle and main refractive indices as two key factors to understand the temperature influence on the divergence angles of the Wollaston prism. The temperature influence on the divergence angles of quartz crystal Wollaston prism is studied theoretically. The results show that divergence angles decrease with increasing temperature, while the divergence angle of e-light decrease more quickly than that of o-light. The testing system is established to verify the above results, and the experimental results are in agreement well with the theoretical analysis.     

Interference of conoscopic pictures of optical crystals

Nonconventional conoscopic pictures in poorly passing bunches of light, localized in a plane of uni-axial optical crystal are received. At usage of two crystal slabs with the optical axes oriented at angle to the plane of slab the interference conoscopic pictures are observed. The model explaining interference of conoscopic pictures is presented.     

Electromagnetic fields that remain totally polarized under propagation

It is remarked that, in general, a totally polarized field becomes partially polarized at the output of an optical system, even though the field propagates through non-polarizing devices. Two kinds of fields are shown in the present work, which maintain the totally-polarized character at the output of any (deterministic) non-polarizing first-order optical system. This property is satisfied by uniformly totally polarized beams and also by those fields whose electromagnetic degree of coherence [T. Setälä, J. Tervo, A.T. Friberg, Opt. Lett. 29 (2004) 328.] equals 1.     

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.     

Giant positive and negative lateral shifts from the Kretschmann-Raether configuration with a weakly absorbing left-handed slab

The lateral shift of a TE-polarized beam reflected from the Kretschmann-Raether structure with a weakly absorbing left-handed slab is studied theoretically. It is shown that the lateral shift can be very large negative as well as positive near the resonant condition. These large negative and positive shifts can be one order of magnitude much larger than the shift from the corresponding nonabsorbing slab. As the absorption factor increases, the incident angle of producing largest lateral shift increases when the thickness is kept unchanged but the thickness of the slab of producing largest lateral shift decreases when the incident angle is kept unchanged.     

The effect of impedance boundary conditions on the potential function of the boundary diffraction wave theory

A novel potential function of the boundary diffraction wave theory is obtained for the impedance surfaces by the asymptotic reduction of the modified theory of physical integrals. The function is expressed in terms of the direction vectors of the incident and scattered rays. The application of the method is performed on the problem of diffraction of plane waves by an impedance half plane for oblique incidence.     

Experimental observation of focal shifts in focused partially coherent beams

We report the experimental observation of focal shifts in partially coherent beams of Gaussian Schell-model (GSM) type focused by a circularly apertured thin lens. The relative focal shift increases as the aperture radius or the state of coherence of the GSM source decrease. The experimental results agree well with theoretical predictions.     

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.     

Tightly Focusing of Circularly Polarized Vortex Beams through a Uniaxial Birefringent Crystal

Under the approximation of small birefringence, the properties of circularly polarized vortex beams tightly focused through a uniaxial birefringent crystal are studied. With the proper combination of the topological charge and the birefringence, the small focus, the small bottle beam and the inverse c-shaped intensity profile can be obtained. The effects of the focal shift and the Strehl ratio on the birefringence are analysed. A relation between angular momentum （included spin and orbital） and topological Pancharatnam charge is also presented.     

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.     

Scattering from a Multi-Layered Sphere Located in a High-Order Hermite-Gaussian Beam

Scattering of a high-order Hermite-Gaussian beam by a multi-layered sphere is analyzed. The incident high- order Hermite-Gaussian beam field is expressed by the complex-source-point method and expanded in terms of spherical vector wave functions. The beam shape coefficients of the Hermite-Gaussian beam are obtained. Under electromagnetic field boundary conditions, coefficients in the expressions of scattering fields are derived. Results of the numerical calculation of scattering intensity are presented. The effects of the particle parameters and beam parameters on scattering intensity are discussed in detail.     

Flat-topped spectrum obtained from partially coherent hollow Gaussian Schell-model beams passing through a slit

The anomalous spectral behaviors of partially coherent polychromatic hollow Gaussian Schell-model beams (HGSMBs) diffracted by a slit are investigated. Besides spectral switches, asymmetrical dual-peak spectral split and multi-peak spectral split are observed. In the vicinity of the positions where spectral switches occur, flat-topped spectrum can be obtained, the bandwidth of which is adjustable by changing the transverse coherence width and the observation position. The flat-topped spectrum has potential application for creating probe beams in optical metrology systems and generating broadband optical sources in fiber optic sensor interface systems.     

Spectral anomalies in supercontinuum focused waves

The diffraction-induced spectral anomalies in the focal plane of an apertured spherical wave with supercontinuum flat-top power spectrum are investigated. Coherent broadband radiation (also incoherent white light) demonstrates a strong blue shift in the vicinity of the optical axis, and discrete spectral gaps with overall red shift arise out of this central region. Unlike narrow-band light, the spectral switch effect fades away with ultra-broad spectra.     

Prevailing effects of interference or diffraction by multiple apertures

The effects of interference and diffraction produced by a bidimensional structure composed of multiple and identical apertures are studied. Such effects are competitive during the propagation, that is, in some planes the interference effects are more visible, while in others prevail the diffraction ones. Using the number of Fresnel zones, the spatial domains where the interference or diffraction effects prevail are defined and parameterized. Simulation and experimental results are further introduced to verify the proposed method.     

Fast calculation technique for scattering in T-matrix method

In scattering calculations using the T-matrix method, the calculation of the T-matrix involves multiplication and inversion of matrices. These two types of matrix operations are time-consuming, especially for the matrices with large size. Petrov et al. [D. Petrov, Y. Shkuratov, G. Videen, Opt. Lett. 32 (2007) 1168] proposed an optimized matrix inversion technique, which suggests the inversion of two matrices, each of which contains half the number of rows. This technique reduces time-consumption significantly. On the basis of this approach, we propose another fast calculation technique for scattering in the T-matrix method, which obtains the scattered fields through carrying out only the operations between matrices and the incident field coefficient. Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al.