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].     

On definition and measurement of extinction cross section

Following the recent analyses of extinction by Berg et al. [J Opt Soc Am A 2008;25:1504–1513; J Opt Soc. Am A 2008;25:1514–1520], we show that although it is possible to define and measure the extinction cross section for a single particle using a detector of light facing the incident beam, this requires certain theoretical assumptions and experimental precautions.     

Halo Reduction Technique in Phase Contrast Microscopy

A new phase contrast microscopy technique has been developed which achieves halo reduction by applying an apodization to the Zernike phase contrast method. In this technique, a new apodized phase plate is placed at the back focal plane of the objective. This plate consists of a quarter wave phase shift ring conjugated of the illuminating aperture, which has a 25#x0025; transmittance, and a pair of adjacent rings having 50#x0025; transmittance. The developed technique yields the highest resolution images without a bluish hue effect ever achieved in phase contrast microscopy.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.     

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.     

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.     

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.     

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.     

Experimental evidence of zero forward scattering by magnetic spheres

Magnetically induced diffraction patterns by micron sized magnetic spheres dispersed in a ferrofluid disappear at a certain critical magnetic field. This critical field is found to depend on the concentration of the ferrofluid and on the volume of the magnetic spheres. We attribute this effect to the zero forward scattering by magnetic spheres as predicted by Kerker, Wang, and Giles [J. Opt. Soc. Am. 73, 765 (1983)]. We suggest that such a dispersion can be used to study the optical analogues of localization of electrons in condensed matter, the Hall effect, and the anisotropic diffusion, etc. The combination of the micron sized magnetic spheres and the ferrofluid will also be useful to design magnetically tunable photonic devices.     

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.     

On the resolving power of high-contrast saturated absorption spectroscopy

Recently Svanberg et al. [Optics Lett. 11 (1986) 138; J. Opt. Soc. Am. B 4 (1987) 462] obtained saturated absorption resonances with subnatural linewidth by working in the regime of high pumping intensities and optically thick atomic samples. We analyze here this new spectroscopic regime, within the formalism of Maxwell-Bloch-type equations, in the case of a Doppler broadened medium having two nearly degenerate but uncoupled resonances. We show that even in this most favourable case it is not possible to resolve spectral features that lie within the natural linewidth.     

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.     

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)].     

Precision measurement of the refractive index of carbon dioxide with a frequency comb

We report a higher precision measurement of the refractive index of carbon dioxide using a frequency comb as the light source in a Mach-Zehnder interferometer setup. The experimental sensitivity can reach the level of 8.8x10(-9). Taking into account the measurement accuracy of temperature and pressure, the experimental accuracy has a value of 1.2x10(-8). The measurement result has a deviation from the commonly quoted result [Old , J. Opt. Soc. Am.61, 89 (1971)] by 6.4x10(-7) at 800 nm.     

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)].     

Phase behavior and selectivity of DNA-linked nanoparticle assemblies

We propose a model that can account for the experimentally observed phase behavior of DNA-nanoparticle assemblies [J. Am. Chem. Soc. 125, 1643 (2003)]; Science 289, 1757 (2000)]]. The binding of DNA-coated nanoparticles by dissolved DNA linkers can be described by exploiting an analogy with quantum particles obeying fractional statistics. In accordance with experimental findings, we predict that the phase-separation temperature of the nanocolloids increases with the DNA coverage of the colloidal surface. Upon the addition of salt, the demixing temperature increases logarithmically with the salt concentration. Our analysis suggests an experimental strategy to map microscopic DNA sequences onto the macroscopic phase behavior of the DNA-nanoparticle solutions. Such an approach should enhance the efficiency of methods to detect (single) mutations in specific DNA sequences.     

Phase aberration correction in medical ultrasound using speckle brightness as a quality factor

Medical ultrasonic images are degraded by tissues with inhomogeneous acoustic velocities. The resulting phase aberration raises the off-peak response of the imaging system's point spread function (PSF), decreasing dynamic range. In extreme cases, multiple images of a single target are displayed. Phase aberration may become a limiting factor to image quality as ultrasonic frequency and aperture size are increased in order to improve spatial resolution. A method is proposed to correct for unknown phase aberration, which uses speckle brightness as a quality factor. The phase delays of a phased array transducer are modified, element by element, to maximize mean speckle brightness in a region of interest. The technique proposed is analogous to the correction technique used by Muller and Buffington [J. Opt. Soc. Am. 64 (9), 1200-1209 (1974)] to adaptively focus incoherent optical telescopes. The method is demonstrated using a computer model with several different simulated aberration profiles. With this model, mean speckle brightness is calculated using the two-dimensional PSF. Experiments have also been conducted in which speckle brightness is shown to increase as the phase delays of an ultrasonic scanner are modified in order to compensate for a rippled aberrating layer made of silicone rubber. The characteristics of the proposed method, and the possibility of employing it clinically to correct for unknown inhomogeneities in acoustic velocity, are discussed.     

Unfolding of an unstable singularity point into a ring

It is well known that phase singularities, in general lines in space, are topologically stable features of a wave field. An exception is a pointlike singularity, which is unstable and deforms into a ring or disappears when a small perturbation is applied. Recently, Nye showed how such an event can be understood as an unfolding of a higher-order dislocation [J. Opt. Soc. Am. A (to be published)]. We present an optical implementation of this model and show experimentally that the focal region of a lens contains points of zero intensity on the optical axis that deform into rings when a small amount of spherical aberration is applied to the system.     

Extraction of optical scattering parameters and attenuation compensation in optical coherence tomography images of multilayered tissue structures

A recently developed analytical optical coherence tomography (OCT) model [Thrane et al., J. Opt. Soc. Am. A 17, 484 (2000)] allows the extraction of optical scattering parameters from OCT images, thereby permitting attenuation compensation in those images. By expanding this theoretical model, we have developed a new method for extracting optical scattering parameters from multilayered tissue structures in vivo. To verify this, we used a Monte Carlo (MC) OCT model as a numerical phantom to simulate the OCT signal for heterogeneous multilayered tissue. Excellent agreement between the extracted values of the optical scattering properties of the different layers and the corresponding input reference values of the MC simulation was obtained, which demonstrates the feasibility of the method for in vivo applications. This is to our knowledge the first time such verification has been obtained, and the results hold promise for expanding the functional imaging capabilities of OCT.     

Quantization of Kähler manifolds and the asymptotic expansion of Tian–Yau–Zelditch

In this paper we study the link between the asymptotic expansion of Tian–Yau–Zelditch [J. Diff. Geom. 32 (1990) 99] and the quantization of compact Kähler manifolds carried out in [J. Geophys. 7 (1990) 45; Trans. Am. Math. Soc. 337 (1993) 73].     

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.