A Reply to the Comment by C. M. Soukoulis et al.

We report single-photon interference in the sidebands of modulated light. The relative phase of interacting quantum states is reliably controlled by the phase of a low-frequency modulating signal. We show how this type of interference can be used to build a robust system for quantum cryptography. An experiment was implemented at 1540 nm, over a 20-km-long standard single-mode fiber, using a germanium singlephoton avalanche photodiode.

We present an exact calculation of the cross-spectral density tensor of the near field thermally emitted into free space by an opaque planar surface. The approach, based on fluctuational electrodynamics and the fluctuation-dissipation theorem, yields novel near-field correlation properties. We show that the spatial coherence length of the field close to the surface at a given wavelength $\lambda$ may be much smaller than the well-known $\lambda /2$ of blackbody radiation. We also show that a long-range correlation may exist, when resonant surface waves, such as surface-plasmon or surface-phonon polaritons, are excited. These results should have important consequences in the study of coherence in thermal emission and in the modeling of nanometer scale radiative transfer.

We report the first observation of self-modified optical diffraction, beam ellipticity recovery and conservation, and intensity independent self-focusing in an anisotropic diffusion-type nonlinearity realized in ferroelectrics heated above the centrosymmetric transition. The interaction, a photorefractive diffusion-driven quadratic nonlinearity, constitutes the first known natural realization of a higher-order logarithmic nonlinearity and allows an analytical description of the observed phenomena and the prediction of a class of noncircular solitons with no characteristic length scale.

We study high-order harmonic generation in the general case of absorbing and dispersive atomic gas media. For ultrashort laser pulses, the harmonic conversion efficiency tends to a limit mainly imposed by the harmonic reabsorption in the gas. This limit, independent on the gas density, is the same for both the case of a loosely focused beam or a beam guided in a gas-filled hollow-core fiber. Under optimum conditions, we measured the highest conversion efficiency to date $(4\times {10}^{-5\mathrm{}})$ for the 15th harmonic generated in xenon using a 40 fs, 1.5 mJ, 800 nm pulse at a 1 kHz repetition rate.

The thermally restorable photoswitching between the spectroscopically distinct two phases has been observed for thin films of poly(3-alkylthiophene) with regioregular alkyl sidegroups. The primary process of the photoinduced phase transition is completed within a duration of the exciting laser pulse (5 ns), in which photogenerated electron-hole pairs on the polymer backbone with the density above a critical value appear to trigger a self-activated process for the phase conversion. Such a fast photoswitching of the electronic and/or structural state may be applied as well to many other conjugated polymers with optoelectronic functionality.

We measure attenuation and phase velocity of sound waves in suspensions of colloidal silica spheres. As the concentration of colloids increases, the dependence of the attenuation changes from linear to at least quadratic in volume fraction. This change is attributed to a viscous coupling of neighboring scatterers. When the wavelength is comparable to the sphere size, the sound velocity decreases with increasing volume fraction and falls below that of the pure liquid.

We derive the Kramers-Moyal equation for the conditional probability density of velocity increments from the theoretical model recently proposed by V. Yakhot [Phys. Rev. E 57, 1737 (1998)] in the limit of the high Reynolds number. We show that the higher order ( $n\ge 3$ ) Kramers-Moyal coefficients tend to zero and the velocity increments are evolved by the Fokker-Planck operator. Our results are compatible with the phenomenological description, developed for explaining recent experiments by R. Friedrich and J. Peinke [Phys. Rev. Lett. 78, 863 (1997)].

An operator approach to two-beam coupling in photorefractive media for which each beam is composed of information that varies in both space and time reduces the problem to a single differential equation: $d\rho /dz=\left[\right[{\sigma }_0,\rho ],\rho ]/4\mathrm{}$. $[A,B]=AB-BA$ is the commutator of two operators, $\rho$ is a density operator that embodies the state of the optical field, and ${\sigma }_0$ is a coupling operator. A solution exists in closed form for specific cases and is amenable to numerical integration in general. The evolution of $\rho$ is unitary and approaches a block diagonal in a representation that diagonalizes ${\sigma }_0$.

We demonstrate a phase-matched high-harmonic generation of 100 fs Ti:sapphire laser pulses by a self-guided beam in 30 Torr of neon gas. Phase matching of high harmonics is experimentally examined by changing the propagation length up to 7 mm. Phase-matched propagation over 7 mm magnifies the conversion efficiency around the 49th harmonic (in the cutoff region) by 40 times. On the other hand, harmonics around the 25th order (in the plateau region) peak at 4 mm, resulting in an enhancement of 4. This scheme enhances the conversion efficiencies in the cutoff region up to ${10}^{-6\mathrm{}}$, corresponding to a few nJ per high-harmonic pulse in the 76 eV region.

We investigate the theory of a nonlinear magneto-optic Fabry-Pérot interferometer, filled with an isotropic dielectric that possesses linear and nonlinear artificial gyrotropy. We show that the nonreciprocity leads to specific multistable transmission patterns and, in particular, to a polarization controlled multistability at constant input intensity. We also show that the reciprocity of the cavity can be restored effectively for certain parameter regimes.

We present a scenario of $\left(3+1\right)$-dimensional spatiotemporal dynamics of femtosecond laser pulses in a nonlinear media with normal dispersion. The sequence of events at progressively higher powers can be characterized as single splitting, multiple splitting, and coalescence. Self-focusing and splitting events are in general spatially separated. Experimental data confirm the above scenario, with measurements at the highest powers corresponding to the regime of continuum generation.

We experimentally investigate pattern formation in a single-wavelength long laser cavity with a large Fresnel number. Near the laser threshold, we observe a single frequency spatially periodic structure corresponding to titled waves theoretically predicted by the Maxwell-Bloch equations. We also show the presence of secondary instabilities at other wavelengths and polarization instabilities at the same wavelength for different parameter values.

We present the first demonstration of an optically written waveguide in an atomic vapor. By strongly pumping one rubidium transition, we are able to “waveguide” a weak probe beam at a different rubidium transition. These effects can be understood with reference to a model of the refractive index for a $V$ system.

We report both experimentally and analytically a transition from a convective to an absolute regime for a Kelvin-Helmholtz unstable sheared interface between two fluids in parallel flow in a Hele-Shaw cell. Experimental evidence is obtained by measurements from both sides of this transition, via two independent tests. The results are in good agreement with the nonlinear transition recently described in a theoretical analysis [Couairon and Chomaz, Physica (Amsterdam) 108D, 236 (1997)].

The results of an experimental study of flow in a small aspect ratio liquid crystal cell are presented where the dimensions of the device are on the same scale as the width of a human hair. This system is found to display wide ranging dynamical behavior, from simple oscillations to seemingly homogeneous turbulence. Through a systematic study of the low-dimensional behavior we uncover an organizing center for the dynamics.

We report the analysis of branched manifolds through homologies, in order to extend the range of applicability of the topological approach to the analysis of human speed data. Analytic and experimental cases are discussed.

Crutchfield et al. observed that noise truncates period-doubling cascade and induces chaos. To date, however, very little low-dimensional chaos has been unambiguously identified experimentally. This discrepancy stimulates us to reexamine the noisy logistic map. We find that noise can indeed induce chaos. However, this is not associated with the main $2^n$ cascade. We identify three basic conditions for noise to induce chaos. We also show that when noise induces chaos the complete period-doubling cascade is inhibited, otherwise the cascade is simply masked by noise.

Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by Lévy stable laws. The classical limit of these dynamics can be related to fractional kinetic equations. In particular, we derive a fractional extension of Kramers equation.