Radiance backscattered by a strongly scattering medium in the high spatial frequency limit.

We study the radiative transfer of a spatially modulated plane wave incident on a half-space composed of a uniformly scattering and absorbing medium. For spatial frequencies that are large compared to the scattering coefficient, we find that first-order scattering governs the leading behavior of the radiance backscattered by the medium. The first-order scattering approximation reveals a specific curve on the backscattered hemisphere where the radiance is concentrated. Along this curve, the radiance assumes a particularly simple expression that is directly proportional to the phase function. These results are inherent to the radiative transfer equation at large spatial frequency and do not have a strong dependence on any particular optical property. Consequently, these results provide the means by which spatial frequency domain imaging technologies can directly measure the phase function of a sample. Numerical simulations using the discrete ordinate method along with the source integration interpolation method validate these theoretical findings.

Radiative transport theory for light propagation in luminescent media.

We propose a generalization of radiative transport theory to account for light propagation in luminescent random media. This theory accounts accurately for the multiple absorption and reemission of light at different wavelengths and for anisotropic luminescence. To test this theory, we apply it to model light propagation in luminescent solar concentrators (LSCs). The source-iteration method is used in two spatial dimensions for LSCs based on semiconductor quantum dots and aligned nanorods. The LSC performance is studied in detail, including its dependence on particle concentration and the anisotropy of the luminescence. The computational results using this theory are compared with Monte Carlo simulations of photon transport and found to agree qualitatively. The proposed approach offers a deterministic methodology, which can be advantageous for analytic and computational modeling. This approach has potential for more efficient and cost-effective LSCs, as well as in other applications involving luminescent radiation.

Demonstration of nondegenerate spectrum reversal in optical-frequency regime.

This Letter reports theoretical and experimental studies of spectrum reversal with tunable wavelength offset in the optical-frequency regime-two widely separated spectral sidebands can always behave as mirror images of one another with respect to the center frequency of the controlling pump pulse. We call this interesting physical phenomenon "spectral mirror imaging."

A quantitative approach to soliton instability.

We present an approach for instabilities of solitons that is based on the spectrum of a fourth-order linearized operator. Unlike the standard approach which is based on the slope (Vakhitov-Kolokolov) condition, this approach provides the quantitative value of the instability rate and the qualitative nature of the instability dynamics.

Scanning tunneling microscopy images of alkane derivatives on graphite: role of electronic effects.

Scanning tunneling microscopy (STM) images of self-assembled monolayers of close-packed alkane chains on highly oriented pyrolitic graphite often display an alternating bright and dark spot pattern. Classical simulations suggest that a tilt of the alkane backbone is unstable and, therefore, unlikely to account for the contrast variation. First principles calculations based on density functional theory show that an electronic effect can explain the observed alternation. Furthermore, the asymmetric spot pattern associated with the minimum energy alignment is modulated depending on the registry of the alkane adsorbate relative to the graphite surface, explaining the characteristic moiré pattern that is often observed in STM images with close packed alkyl assemblies.

Charge delocalization in proton channels, II: the synthetic LS2 channel and proton selectivity.

In this study, the minimalist synthetic LS2 channel is used as a prototype to examine the selectivity of protons over other cations. The free-energy profiles along the transport pathway of LS2 are calculated for three cation species: a realistic delocalized proton (including Grotthuss shuttling)--H(+), a classical (nonshuttling) hydronium--H(3)O(+), and a potassium cation--K(+). The overall barrier for K(+) is approximately twice as large as that for H(+), explaining the >100 times larger maximal ion conductance for the latter, in qualitative agreement with the experimental result. The profile for the classical hydronium is quantitatively intermediate between those of H(+) and K(+) and qualitatively more similar to that of H(+), for which the locations of the peaks are well correlated with the troughs of the pore radius profile. There is a strong correlation between the free-energy profiles and the very different characteristic hydration structures of the three cation species. This work suggests that the passage of various cations through ion channels cannot always be explained by simple electrostatic desolvation considerations.

Charge delocalization in proton channels, I: the aquaporin channels and proton blockage.

The explicit contribution to the free energy barrier and proton conductance from the delocalized nature of the excess proton is examined in aquaporin channels using an accurate all-atom molecular dynamics computer simulation model. In particular, the channel permeation free energy profiles are calculated and compared for both a delocalized (fully Grotthuss shuttling) proton and a classical (nonshuttling) hydronium ion along two aquaporin channels, Aqp1 and GlpF. To elucidate the effects of the bipolar field thought to arise from two alpha-helical macrodipoles on proton blockage, free energy profiles were also calculated for computational mutants of the two channels where the bipolar field was eliminated by artificially discharging the backbone atoms. Comparison of the free energy profiles between the proton and hydronium cases indicates that the magnitude of the free energy barrier and position of the barrier peak for the fully delocalized and shuttling proton are somewhat different from the case of the (localized) classical hydronium. The proton conductance through the two aquaporin channels is also estimated using Poisson-Nernst-Planck theory for both the Grotthuss shuttling excess proton and the classical hydronium cation.

Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures.

Localized nonlinear modes, or solitons, are obtained for the two-dimensional nonlinear Schrödinger equation with various external potentials that possess large variations from periodicity, i.e., vacancy defects, edge dislocations, and quasicrystal structure. The solitons are obtained by employing a spectral fixed-point computational scheme. Investigation of soliton evolution by direct numerical simulations shows that irregular-lattice solitons can be stable, unstable, or undergo collapse.

Noise-induced linewidth in frequency combs.

Frequency combs generated by trains of pulses emitted from mode-locked lasers are analyzed when the center time and phase of the pulses undergo noise-induced random walk, which broadens the comb lines. Asymptotic analysis and computation reveal that, when the standard deviation of the center-time jitter of the nth pulse scales as n(p/2) where p is a jitter exponent, the linewidth of the kth comb line scales as k(2/p). The linear-dispersionless (p=1) and pure-soliton (p=3) dynamics in lasers are derived as special cases of this time-frequency duality relation. In addition, the linewidth induced by phase jitter decreases with power P(out), as (P(out))(-1/p).

Self-focusing Distance of Very High Power Laser Pulses.

We show numerically for continuous-wave beams and experimentally for femtosecond pulses propagating in air, that the collapse distance of intense laser beams in a bulk Kerr medium scales as 1/P;1/2 for input powers P that are moderately above the critical power for self focusing, but that at higher powers the collapse distance scales as 1/P.

Control of multiple filamentation in air.

In this Letter we provide what is believed to be the first experimental evidence of suppression of the number of filaments for high-intensity laser pulses propagating in air by beam astigmatism. We also show that the number, pattern, and spatial stability of the filaments can be controlled by varying the angle that a focusing lens makes with the axial direction of propagation. This new methodology can be useful for applications involving atmospheric propagation, such as remote sensing.

Carrier-envelope phase slip of ultrashort dispersion-managed solitons.

The carrier-envelope phase slip of an ultrashort pulse circulating in a mode-locked Ti:sapphire laser is analyzed. The laser cavity is modeled by a dispersion- and nonlinearity-managed nonlinear Schrödinger equation. The combined contributions to the phase slip induced by nonlinear phase and nonlinear dispersion are found to approach zero for strong dispersion maps. The dependence of the slip on third-order dispersion is found as well. The analytical results are verified using numerical simulations.

Multiple filamentation induced by input-beam ellipticity.

We provide what is to our knowledge the first experimental evidence that multiple filamentation (MF) of ultra-short pulses can be induced by input beam ellipticity. Unlike noise-induced MF, which results in complete beam breakup, the MF pattern induced by small input beam ellipticity appears as a result of nucleation of annular rings surrounding the central filament. Moreover, our experiments show that input beam ellipticity can dominate the effect of noise (transverse modulational instability), giving rise to predictable and highly reproducible MF patterns. The results are explained with a theoretical model and simulations.

Optical light bullets in a pure Kerr medium.

We show that small negative fourth-order dispersion can arrest spatiotemporal collapse of ultrashort pulses with anomalous dispersion in a planar waveguide with pure Kerr nonlinearity, resulting in (2 + 1)D optical bullets. Similarly to solitons, these bullets undergo elastic collisions. Since these bullets can self-trap from noisy Gaussian input beams and propagate without any power losses, this result may be used to realize experimentally stable, nondissipative optical bullets.

The mechanism of proton exclusion in aquaporin channels.

The mechanism of proton exclusion in aquaporin channels is elucidated through free energy calculations of the pathway of proton transport. The second generation multistate empirical valence bond (MS-EVB2) model was applied to simulate the interaction of an excess proton with the channel environment. Jarzynski's equality was employed for rapid convergence of the free energy profile. A barrier sufficiently high to block proton transport is located near the channel center at the NPA motif-a site involved in bi-orientational ordering of the embedded water-wire in absence of the excess proton. A second and lower barrier is observed at the selectivity filter near the periplasmic outlet where the channel is narrowest. This secondary barrier may be essential in filtering other large solutes and cations.

Self-focusing of circularly polarized beams.

We present a systematic study of propagation of circularly polarized beams in a Kerr medium. In contrast to previous studies, vectorial effects (i.e., coupling to the axial component of the electric field and the grad-div term) and nonparaxiality are not neglected in the derivation. This leads to a system of equations that takes into account nonparaxiality, vectorial effects, and coupling to the opposite circular component (i.e., the one rotating in the opposite direction). Using this system we show that the standard model in the literature for self-focusing of circularly polarized beams can lead to completely wrong results, that circular polarization is stable during self-focusing, and that nonparaxiality and vectorial effects arrest collapse, leading instead to focusing-defocusing oscillations. We also show that circularly polarized beams are much less likely to undergo multiple filamentation than linearly polarized beams.