Based on the unified theory of coherence and polarization and the extended Huygens–Fresnel integral the free-space evolution of the recently introduced spectral degree of cross-polarization of a stochastic electromagnetic beam is studied. Unlike the spectral degree of coherence, the degree of cross-polarization is unbounded and exhibits non-monotonic changes with growing propagation distance and growing radial distance from the center of the beam, at fixed transverse cross-sections. Our numerical results pertain to the electromagnetic Gaussian Schell-model beams. We derive expressions for the cross-spectral density matrix of the EGSM beam for arbitrary transverse and longitudinal positions. The results show that the behavior of the degree of cross-polarization on propagation is determined by all of the parameters of the source radiating the beam. At sufficiently large distances from the source, the degree of cross-polarization stabilizes for all points within the beam independently of their radial positions.
Vectorial relations of field amplitudes are derived from the Lorentz lemma applied to electromagnetic fields at direct and reversed scenarios of a wave diffraction on a doubly-periodic planar array. Biorthogonality of polarization eigenstates of the waves propagating in opposite directions is shown with reference to a wave channel formed by an incident wave and a diffraction order. For a planar chiral array, an essential difference in polarization transformations of propagated waves is ascertained in the direct wave channel and in the reversed one. Numerical data are presented to demonstrate the polarization transformations by both transmitting and reflecting planar chiral arrays. A difference in polarization eigenstates inherent to a planar chiral array and a bulk chiral medium is noticed.
A comprehensive investigation of the optical properties of a composite metamaterial in which silver nanowires are aligned inside a finite-thickness dielectric host medium is presented. Using a rigorous finite-element based modelling approach, together with a self-consistent process for the extraction of effective-medium parameters, we find that this structure can enable an effective optical diamagnetic response that is orders of magnitude stronger compared to that of naturally occurring diamagnetic materials. Interestingly, our analysis reveals that there is a frequency region where the nanoforest exhibits a strong diamagnetic response while simultaneously allowing for high transmission of incident electromagnetic waves. We examine the physical origin behind the magnetic properties of this structure, as well as its resilience to fabrication imperfections. Our analysis shows that the structure is robust to the presence of disorder, in the occurrence of which it can still facilitate high figure-of-merit diamagnetic responses.
Recent experimental work on semiconductor-based harmonically mode-locked lasers geared toward low noise applications is reviewed. Active, harmonic mode-locking of semiconductor-based lasers has proven to be an excellent way to generate 10 GHz repetition rate pulse trains with pulse-to-pulse timing jitter of only a few femtoseconds without requiring active feedback stabilization. This level of timing jitter is achieved in long fiberized ring cavities and relies upon such factors as low noise rf sources as mode-lockers, high optical power, intracavity dispersion management and intracavity phase modulation. When a high finesse etalon is placed within the optical cavity, semiconductor-based harmonically mode-locked lasers can be used as optical frequency comb sources with 10 GHz mode spacing. When active mode-locking is replaced with regenerative mode-locking, a completely self-contained comb source is created, referenced to the intracavity etalon.
We report a camera system, associated motorized opto-mechanics, and data handling routines for imaging the three-dimensional structure of singularities within scalar and vector optical fields. Using Fourier techniques to analyse a series of cross-sectional images, we measure either the relative phase or state of polarization of monochromatic fields and analyse this for the identification and mapping of their associated singularities.
The increasing interest in the mechanical properties of complex systems at mesoscopic scale has recently fueled the development of new experimental techniques, collectively indicated as microrheology. Unlike bulk-based approaches (macrorheology), these new techniques make use of micrometric probes (usually microspheres) which explore the mechanical properties of the surrounding medium.In this paper we discuss the basic idea of microrheology and we will focus on one specific technique based on optical tweezers (OT). The discussion starts from Newtonian fluids to tackle the more general case of complex fluids, also showing results of these techniques on solutions of a relevant biomolecule: hyaluronic acid (HA). In particular, we study the viscoelastic properties of low molecular weight HA (155 kDa) at low ionic strength over an extended frequency range (0.1-1000 Hz) and in a wide range of concentrations (0.01-20 mg ml(-1)), which include both the dilute and semidilute regime. In the concentration range here explored and within the test frequencies covered by our techniques, samples prevalently exhibit a viscous behavior, the elastic contribution becoming significant at the highest concentrations. By comparing OT outcomes to those obtained by a traditional rheometer, we found that they were in good agreement in the overlapping frequency range of the two techniques, thus confirming the reliability of the microrheological approach.
Recent experiments (Kopp et al 2007 J. Opt. Soc. Am. B 24 A48) have demonstrated that the polarization sensitivity of chiral fiber gratings depends strongly on the grating symmetry: double-helix fibers are polarization sensitive while single-helix fibers are not. A coupled-mode perturbation theory is developed and used to explain the polarization properties of chiral fiber gratings. Features of the transmission spectrum such as multiple dips in the spectrum and circular dichroism are also derived and attributed to chiral Bragg scattering of the core modes into the cladding modes of the fiber.
A generalization of perturbation theory for weakly coupled optical waveguides beyond the scalar approximation is suggested that explicitly allows for the spin–orbit interaction embedded in the gradient term of the vector wave equation. The obtained perturbation theory is applied to study the problem of cross-talk in coupled ideal monomode fibres. We demonstrate the absence of cross-talk between orthogonal linear polarizations and the inversion of the circular polarization's sign caused by the spin–orbit interaction. The spin conversion length is determined.
An instrument for rapidly and non-invasively sorting different cell specimens is a valuable tool in biological and medical research. Parallel identification of target specimens through image analysis can sort based on highly tuneable selection criteria and can enable high-speed optical sorting when matched with a rapidly reconfigurable optical sorting field. We demonstrate the potential of such a system using colloidal polystyrene microspheres. By combining machine vision with a parallel add-on optical manipulation scheme, we were able to move identified particles over a distance of several hundred micrometres at velocities that exceed 800 mu m s(-1) and are easily scalable to higher velocities.
In its original formulation the Fourier modal method provides a very fast convergence for one- and two-dimensional dielectric structures, but owing to the Gibbs phenomenon the convergence is poor for a high contrast of the permittivity function, especially for metal-dielectric structures. The scheme has been improved by methods such as factorization rules and adaptive spatial resolution. We are going to discuss the combination of these methods in a covariant formulation, including a new method to calculate the homogeneous sub- and superstrates in the adaptive coordinate system. We use it to obtain the optical properties of split-ring resonators. Additionally, we will show how the spectra of stacked structures can be derived very efficiently.
We study theoretically the propagation of higher-order two-dimensional spatial solitons in optical media with nonlocal thermal nonlinear response. We show that these localized states experience complex dynamics including transformations between solitons of different symmetries which depend strongly on the geometry of a nonlinear sample. Boundaries exert repulsive forces on a soliton and, depending on its initial position relative to the boundaries, we observe transverse motion of a beam as a whole across the sample, effectively facilitating transformations.
For an electromagnetic stochastic beam, the choice of the mathematical structure of the cross-spectral density matrix is limited by the constraint of non-negative definiteness. We present a sufficient condition for building these matrices in such a way that this constraint is automatically satisfied. This allows us to put into evidence that electromagnetic beams can exhibit very peculiar correlation properties, some of which would not be encountered in scalar treatments. These results are illustrated by means of a number of examples.
The performance of Fresnel zone plates having a polygonal boundary between zones has been studied. The contribution of the complex amplitude of each zone is calculated analytically and numerically solved. The case of a continuous phase plate is considered as the limit case in performance for each polygonal shape. This performance is compared with respect to the circular case. Also four different methods to define a polygonal FZP having discrete phase shift are analyzed and compared.
Nonlinearities are becoming more and more important for a variety of applications in nanosciences, bio-medical sciences, information processing and photonics. For applications at the crossings of these fields, especially microscopic and nanoscopic imaging and manipulation, nonlinearities play a key role. They may range from simple nonlinear parameter changes up to applications in manipulating, controlling and structuring material by light, or the manipulation of light by light itself.
Averaged coupled wave equations are derived for a fibre Bragg grating with Gaussian noise added to the refractive index. The corrections to reflection and transmission coefficients are expressed in terms of a Green matrix of the unperturbed grating. The explicit formula for the Green matrix is derived for the uniform grating. The average reflectivity is calculated analytically. The noise is shown to increase reflectivity outside the Bragg reflection band and to smooth out the oscillations in the spectrum.
Diffraction gratings have been proposed as core elements in future laser-interferometric gravitational wave detectors. In this paper, we use a steady-state technique to derive coupling of lateral grating displacement to the output ports of a diffractive Fabry-Perot cavity. By introducing a signal to noise ratio (SNR) for each of the three cavity output ports, the magnitudes of the noise sidebands originating from lateral grating displacement are compared to the magnitude of a potential gravitational wave signal. For the example of a 3 km long Fabry-Perot cavity featuring parameters similar to the planned Advanced Virgo instrument, we found that the forward-reflecting grating port offers the highest SNR at low frequencies. Furthermore, for this example suspension requirements for lateral isolation were computed, and a factor of 20 relaxation at a frequency of 10 Hz can be gained over the transmitted port by observing the forward-reflected port.
Various types of optical fibres have been investigated and compared for delivering high power laser beams to an optical plug (comprising of lenses and an optical window) for the application of laser-induced ignition of gasoline and air mixtures in an automotive internal combustion engine. Three main types of optical fibre were examined: multi-mode step index silica, sapphire and photonic crystal. The fibres had various core sizes ranging from 35 to 600 mu m and numerical apertures between 0.046 and 0.64. A Q-switched Nd:YAG laser operating at the fundamental wavelength 1064 nm with a pulse length of 15 ns was used for the testing. Fibre output beam properties, including beam mode quality, output divergence, transmission losses, beam energy thresholds and effects of engine vibration were investigated. These fibre beam properties were compared with known beam parameters for laser ignition to assess the suitability of such fibres for a laser ignition system. Online fibre delivery laser ignition engine tests were performed with the most suitable fibres, which showed that combustion could be achieved with this system despite a relatively large percentage of misfires.
The first comprehensive exact theory of strongly nonlinear guided waves in a double-negative planar metamaterial waveguide is developed. The theoretical consequences are that novel surface and guided waves are predicted because of the special relationship of the boundary fields to each other. The analysis leads smoothly to tunability with power and direct access to group velocity control.
We reveal that the reduction of the group velocity of light in periodic waveguides is generically associated with the presence of vortex energy flows. We show that the energy flows are gradually frozen for slow-light at the Brillouin zone edge, whereas vortices persist for slow-light states having non-vanishing phase velocity inside the Brillouin zone. We also demonstrate that presence of vortices can be linked to the absence of slow-light at the zone edge, and present calculations illustrating these general results.
We present a parallel writing method in silica glass by multiple femtosecond laser beams. Collinear femtosecond laser beams with different wavefront curvature were incident on an objective lens and focused at different depths below the surface of silica glass. Hence multiple focal points exist in the glass simultaneously and parallel writing on multiple layers is realized. By adjusting the beam wavefront, the layer distance and the layer alignment can be changed. Our parallel writing method is useful to shorten the fabrication time of femtosecond laser direct writing.
