Showing papers in "Journal of the Optical Society of America in 2007"

Phase retrieval and saddle-point optimization

Abstract: Iterative algorithms with feedback are among the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase retrieval problems, escaping local minima and producing images at resolutions beyond the capabilities of lens-based optical methods. Here the input-output iteration is improved by a lower-dimensional subspace saddle-point optimization.

A three-dimensional degree of polarization based on Rayleigh scattering

Abstract: A measure of the degree of polarization for the three-dimensional polarization matrix (coherence matrix) of an electromagnetic field is proposed, based on Rayleigh scattering. The degree of polarization at a point is defined as an average, over all scattering directions, of an imagined dipole scattering of the three-dimensional state of polarization. This gives a well-defined purity measure, which, unlike other proposed measures of the three-dimensional degree of polarization, is not a unitary invariant of the matrix. This is demonstrated and discussed for several examples, including a partially polarized transverse beam.

Texton-based segmentation of retinal vessels

Abstract: With improvements in fundus imaging technology and the increasing use of digital images in screening and diagnosis, the issue of automated analysis of retinal images is gaining more serious attention. We consider the problem of retinal vessel segmentation, a key issue in automated analysis of digital fundus images. We propose a texture-based vessel segmentation algorithm based on the notion of textons. Using a weak statistical learning approach, we construct textons for retinal vasculature by designing filters that are specifically tuned to the structural and photometric properties of retinal vessels. We evaluate the performance of the proposed approach using a standard database of retinal images. On the DRIVE data set, the proposed method produced an average performance of 0.9568 specificity at 0.7346 sensitivity. This compares well with the best-published results on the data set 0.9773 specificity at 0.7194 sensitivity [Proc. SPIE5370, 648 (2004)].

Solitons in Bragg gratings with saturable nonlinearities

Abstract: We introduce two different systems of coupled-mode equations to describe the interaction of two waves coupled by the Bragg reflection in the presence of saturable nonlinearity. The basic model assumes the ordinary linear coupling between the modes. It may be realized as a photorefractive waveguide, with a Bragg lattice permanently written in its cladding. We demonstrate the presence of a cutoff point in the system's bandgap, with gap solitons existing only on one side of it. Close to this point, the soliton's norm diverges with power −3/2. The soliton family between the cutoff point and the edge of the bandgap is stable. In this model, stationary bound states of two in-phase solitons are found too, but they are unstable, transforming themselves into breathers. Another model assumes a photoinduced longitudinal bulk grating, with the corresponding intermode coupling subject to saturation along with the nonlinearity. In that model, another cutoff point is found, with the soliton's norm diverging near it with power −2. Solitons are stable in this model too (while it does not give rise to two-soliton bound states). Collisions between moving solitons are always quasi-elastic, in either model.

Electro-optical investigations of holographic-polymer-dispersed ferroelectric liquid crystals

Abstract: Uniform alignment of ferroelectric liquid-crystal domains encapsulated by a polymer binder was established through a holographic exposure process. The refractive index modulation in these thin films is modeled as a phase grating that can be electrically addressed to erase the optical diffractive properties. A phenomenological model is developed to take into account a distribution of domain sizes and an effective field that stabilizes the ferroelectric liquid-crystal domains. A diffraction model successfully predicts changes in normalized intensities for first-order diffraction with applied field. These gratings demonstrate microsecond-scale response and relaxation times for various grating pitch sizes between approximately 3 and approximately 12 microm.

Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities: erratum

Abstract: We present a detailed study of soliton compression of ultrashort pulses based on phase-mismatched second-harmonic generation (SHG) (i.e., the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role; we define an effective soliton number—related to the difference between the SHG and the Kerr soliton numbers—and show that it has to be larger than unity for successful pulse compression to take place. This requires that the phase mismatch be below a critical level, which is high in a material where the quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through extensive numerical simulations we find dimensionless scaling laws, expressed through the effective soliton number, that control the behavior of the compressed pulses. These laws hold in the stationary regime, in which group-velocity mismatch effects are small, and they are similar to the ones observed for fiber soliton compressors. The numerical simulations indicate that clean compressed pulses below two optical cycles can be achieved in a β-barium borate crystal at appropriate wavelengths, even for picosecond input pulses.