Non-singular Mueller matrices characterizing passive systems

We extended previous results and explained why it is necessary to work with SO(6,1)_e (sub-group of matrices with unit determinant and positive left upper corner element) in order to define a parametric form of an arbitrary non-singular Mueller matrix. The previously proposed solution in Devlaminck and Terrier [Definition of a parametric form of nonsingular Mueller matrices. J. Opt. Soc. Am. A 25 (2008) 2636-2643], was just a subset of this one. The issue of transmittance conditions for the matrices generated by this formalism is considered and conditions related to the elements of the polar decomposition are derived and give sufficient conditions to guarantee the transmittance conditions for the product matrix.     

Self-imaging of gratings with two roughness levels

In previous works, the authors have analyzed diffraction gratings with surface roughness on their strips. Appl. Opt. 46 (2007) 3668 determined the near field of a grating whose strips present two kinds of roughness, one of them so rough that the grating acts as an amplitude grating. On the other hand, in J. Opt. Soc. Am. A 25 (2008) 2390, a grating with roughness only in one of the grating levels is studied. In the present work, we extend our analysis to the general case where the strips of the grating present two finite roughness levels. As a consequence, the periodic modulation is only generated by random micro-topography of the strips. A statistical analysis is developed to obtain equations that predict the average intensity distribution after the grating. This general case presents differences with the previous works. For example, the maximum contrast of the self-images is given at a certain distance from the grating, that is, the contrast of the self images firstly increases with the distance of the observation plane and after, it decreases. Numerical simulations, based on Rayleigh–Sommerfeld approach, are performed which confirm the theoretical predictions.     

Wavelength-Multiplexing Diffractive Phase Element with Quantized Phase Structure

We have reported on the design algorithm of the wavelength-multiplexing diffractive phase element (WMDPE) capable of generating independent spot patterns for more than two wavelengths. [J. Opt. Soc. Am. A 18 (2001) 1082] In this paper, the stepwise quantization method proposed by F. Wyrowski [J. Opt. Soc. Am. A 7 (1990) 961] is built into the algorithm to design the WMDPE with quantized phase structure. Validity of the method is verified by the WMDPE for 7 wavelengths with 9 phase levels. The optical experiment demonstrates that the fabricated WMDPE generates correct patterns for different wavelengths. Performance dependence of the WMDPE on the number of quantized phase levels is discussed based on the simulation results.This paper was originally presented at the 2nd International Conference on Optical Design and Fabrication, ODF2000 which was held on November 15-17, 2000 at the International Conference Center, Tokyo, Waseda University, Japan.     

Photocurrent theory based on coordinate dependent lifetime

Recent work by Pejova [Mater. Res. Bull. 43, 2887 (2008)] showed that the widely cited classical photocurrent theory of DeVore [Phys. Rev. 102, 86 (1956)] does not necessarily apply for photocurrent experiments carried out on thin-film semiconductors. In this Letter, we theoretically and experimentally justify the successful use of the photocurrent model published by Bouchenaki et al. [J. Opt. Soc. Am. B 8, 691 (1991)].     

Coupling of volume and surface effects in scattering, and the "splitting rule"

Multiple scattering processes in a heterogeneous medium with rough boundaries lead inevitably to coupling of volume and surface effects. Our study of this problem using a statistical wave theory shows the nature of this coupling, brings forth the issues involved, and gives the approximations required to separate volume and surface effects. We hence understand that, only under rather special conditions, these two effects can be decoupled according to the "splitting rule" suggested by Guerin and Sentenac [J. Opt. Soc. Am. A24, 385 (2007)]. One situation where the two effects approximately separate is when the boundary roughness is small. In this case our results are in agreement with [J. Opt. Soc. Am. A24, 385 (2007)] and [Waves Random Media7, 303 (1997)]. Apart from this special situation, we find that volume and boundary effects always get coupled. Therefore, it is apparent that a splitting rule is a special property rather than a general law.     

Product decompositions of depolarizing Mueller matrices with negative determinants

We show that the product decomposition of a depolarizing Mueller matrix (S.-Y. Lu, R.A. Chipman, J. Opt. Soc. Am. A 13 (1996) 1106) as well as the recently proposed reverse decomposition (R. Ossikovski, A. De Martino, Opt. Lett. 32 (2007) 689) need to be extended in order to account for Mueller matrices with negative determinants. The necessity of such an extension of the formalism is illustrated on experimentally determined Mueller matrices. The procedure of the modified decomposition formalism is explicitly described.     

Generalized wavefront phase for non-Kolmogorov turbulence

We introduce the Lévy fractional Brownian field family to model the turbulent wavefront phase. This generalized model allows us to overcome the limitations found in a previous approach [Perez et al., J. Opt. Soc. Am. A 21, 1962 (2004)]. More precisely, our new model provides stationary phase increments over the full inertial range. Thus it successfully extends classical results to non-Kolmogorov turbulence without any approximation.     

A Teleportation with Two Quantum Channels

Recently a quantum teleportation scheme has been analyzed by Wangner et al. (J. Opt. Soc. Am. B 27:A73–A80, 2010) which is based on spatially and temporarily resolved collective spontaneous emission. We study a similar model, which has the two atoms trapped in a resonant cavity instead of in the free vacuum space. It is found that the quantum channel experiences entanglement of sudden death (ESD), yet every time this channel can recover after an interval of time. Surprisingly, we demonstrate there exits another channel to assist the initial channel to complete the teleportation, and the fidelity can be well beyond the classical limit of 2/3, with the increase of dipole-dipole interaction.     

A variant on eigenmode method in periodic crossed gratings

The eigenvalue problem discussed in Noponen and Turunen [Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles, J. Opt. Soc. Am. A 11 (1994) 2494–2502] for crossed gratings is analyzed in a different way using the three components of the electric field instead of the components E_x,y, H_x,y. As a result, half as many eigenvectors are needed.     

Determination of surface profile statistics from electromagnetic scattering data

A new reverse Monte Carlo method for the determination of the surface profile statistics from differential reflection data for the scattering of electromagnetic radiation from rough surfaces is presented. The method is used to extract the power spectrum of the surface profile from scattering data recently measured by West and O'Donnell [J. Opt. Soc. Am. A 12, 390 (1995)]. Excellent agreement with the power spectrum of the surface profile measured by contact profilometry is obtained.     

Multilayer Anisotropic Bi-periodic Diffraction Gratings

The formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73 (1983) 901] treating the diffraction on planar multilayered 1D anisotropic gratings is extended to the diffraction on anisotropic 2D multilayer grating structures bi-periodic in the plane parallel to the interfaces. In addition to the oblique incidence of plane waves, the case of normal incidence is also treated. The goal of the paper is to provide a basis for the formal analysis of 2D patterned multilayers with natural or induced anisotropies. For example, such structures are of interest in the design of new magnetic and magneto-optic devices. In view of the fact that the anisotropies have often a negligible effect on the energy distribution among diffracted modes with respect to the isotropic case the optical response is alternatively expressed in terms of the ellipsometric parameters of diffracted waves. The present analysis represents generalization of the problem of electromagnetic wave interactions in planar multilayers consisting of layers characterized by a general permittivity tensor treated by Yeh [J. Opt. Soc. Am. 69 (1979) 742].     

Unification of radar phenomena as spacetime curvature: prediction and observation of an affine-phase effect

The many properties of radar echoes and other radiative systems were recently described by Gabriel [J. Opt. Soc. Am. A 19, 946 (2002)] as lower-dimensional projections of simple forms in special relativity. A broader treatment including coherent phenomena is summarized, in which the phase properties of radar images and interferograms are also shown to have a simple unified structure. Their apparent complexity is a result of projection onto the lower dimension(s) of the observation. A predicted new property, locally scalable (affine) phase, is observed in a radar interferogram.     

Reduction of quantum noise in optical interferometers using squeezed light

We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so-called “dark port case,” when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (“dark port”). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R. Barak and Y. Ben-Aryeh, J. Opt. Soc. Am. B 25, 361 (2008)]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.     

Realizable differential matrices for depolarizing media

The evolution of a Stokes vector through depolarizing media is considered. A general form for the differential matrix is found that is appropriate in the presence of depolarization and it is parameterized in a manner that ensures that it yields, upon integration, a valid Mueller matrix for any choice of parameters. The form expands the more limited form for a nondepolarizing matrix given by Azzam [J. Opt. Soc. Am. 68, 1756 (1978)] and which was extended recently by others to include depolarization. A Mueller matrix decomposition is proposed that is based upon the new parameterization.     

Pulse characteristics of an optical parametric oscillator pumped by sub-30-fs light pulses

We obtained nearly transform-limited light pulses of 34 fs near 1.2 microm by pumping an optical parametric oscillator with a 2-mm-long KTP crystal by 26-fs pulses from a Ti:sapphire laser. The average power of the pulses that were obtained was greater than 50 mW, at an 80-MHz repetition rate. Attempts to downscale the pulse duration by decreasing the pump-pulse duration revealed remarkable limitations of the attainable pulse length for sub-30-fs pump pulses, in accordance with a recent theoretical study [J. Opt. Soc. Am. B 17, 741 (2000)].     

Self-imaging with finite energy

General solutions and conditions are presented for paraxial waves that image themselves with different scales through free propagation. These waves, represented as superpositions of Gauss-Laguerre modes, have finite energy and thus finite effective width. The self-imaging wave fields described by Montgomery [J. Opt. Soc. Am. 57, 772 (1967)], which possess a Fourier transform that is confined to a ring structure, are obtained as a specific limiting case of an infinite aperture.     

Forward and reverse product decompositions of depolarizing Mueller matrices

Because of the noncommutativity of the matrix product, the three factors into which a depolarizing Mueller matrix is decomposed, i.e., the diattenuator, the retarder, and the depolarizer, form six possible products grouped into two families, as already pointed out [J. Opt. Soc. Am. A13, 1106 (1996); Opt. Lett.29, 2234 (2004)]. We show that, apart from the generalized polar decomposition generating the first family of products, there exists a dual decomposition belonging to the second family. The mathematical procedure for this dual decomposition is given, and the symmetry existing between the two decompositions is pointed out. The choice of the most appropriate decomposition for a given practical optical arrangement is likewise discussed and illustrated by simple examples.     

Quasi-Gaussian beam analytical basis and comparison with an alternative approach (L)

A superposition of propagating Bessel beams was recently numerically demonstrated to approximate a Gaussian beam and was used to evaluate the scattering by a sphere centered on the focal point of the beam. An analytical beam synthesis used in optics by Agrawal and Pattanayak [J. Opt. Soc. Am. 69, 575-578 (1979)] is found here to be recovered as the weak focusing limit of the quasi-Gaussian beam when evanescent contributions are omitted from the analytical synthesis. The propagating-wave part of the analytical synthesis has similarities to, and differences from, the recent quasi-Gaussian approximation.     

Angle-of-arrival variance’s dependence on the aperture size for indoor convective turbulence

We analyze the angle-of-arrival variance of an expanded and collimated laser beam once it has traveled through an indoor convective turbulence. A continuous position detector is set at the focus of a lens collecting the laser beam. The effect of the different turbulent scales, between the inner and the outer scales, is studied by changing the diameter of a circular pupil before the collector lens. The experimental optical setup follows the design introduced by Masciadri and Vernin [Appl. Opt., 36(6) (1997) 1320]. Tilt data measurements are studied using the fractional Brownian motion model for the turbulent wave-front phase introduced in a previous paper [Pérez et al., J. Opt. Soc. Am. A 21(10) (2004) 1962]. The Hurst exponents associated to different strengths of turbulence are obtained from the here proposed D^2H−2 dependence.