Observation of photon-photon thermodynamic processes under negative optical temperature conditions.

Statistical mechanics demands that the temperature of a system is positive provided that its internal energy has no upper bound. Yet if this condition is not met, it is possible to attain negative temperatures for which higher-order energy states are thermodynamically favored. Although negative temperatures have been reported in spin and Bose-Hubbard settings as well as in quantum fluids, the observation of thermodynamic processes in this regime has thus far remained elusive. Here, we demonstrate isentropic expansion-compression and Joule expansion for negative optical temperatures, enabled by purely nonlinear photon-photon interactions in a thermodynamic microcanonical photonic system. Our photonic approach provides a platform for exploring new all-optical thermal engines and could have ramifications in other bosonic systems beyond optics, such as cold atoms and optomechanics.

Propagative Oscillations in Codirectional Polariton Waveguide Couplers.

We report on novel exciton-polariton routing devices created to study and purposely guide light-matter particles in their condensate phase. In a codirectional coupling device, two waveguides are connected by a partially etched section that facilitates tunable coupling of the adjacent channels. This evanescent coupling of the two macroscopic wave functions in each waveguide reveals itself in real space oscillations of the condensate. This Josephson-like oscillation has only been observed in coupled polariton traps so far. Here, we report on a similar coupling behavior in a controllable, propagative waveguide-based design. By controlling the gap width, channel length, or propagation energy, the exit port of the polariton flow can be chosen. This codirectional polariton device is a passive and scalable coupler element that can serve in compact, next generation logic architectures.

Interaction of highly focused vector beams with a metal knife-edge.

We investigate the interaction of highly focused linearly polarized optical beams with a metal knife-edge both theoretically and experimentally. A high numerical aperture objective focuses beams of various wavelengths onto samples of different sub-wavelength thicknesses made of several opaque and pure materials. The standard evaluation of the experimental data shows material and sample dependent spatial shifts of the reconstructed intensity distribution, where the orientation of the electric field with respect to the edge plays an important role. A deeper understanding of the interaction between the knife-edge and the incoming highly focused beam is gained in our theoretical model by considering eigenmodes of the metal-insulator-metal structure. We achieve good qualitative agreement of our numerical simulations with the experimental findings.

Extraordinary low transmission effects for ultra-thin patterned metal films.

Thin metal films show a residual transmission for light in the visible and UV spectral range. This transmission can be strongly reduced by an appropriate sub-wavelength patterning of the metal film. Our investigation is focused on metal films with a thickness much below 100nm, where the transmission response is dominated by the individual posts acting like antennas and cannot be attributed to the excitation of surface plasmons. The almost complete suppression of transmission for ultra-thin metal films depends mainly on the absorber width, but not on the pitch of the pattern. The effect is robust with respect to imperfections of the geometry or larger features imprinted into the sub-wavelength pattern.

High numerical aperture imaging with different polarization patterns.

The modulation transfer function (MTF) is calculated for imaging with linearly, circularly and radially polarized light as well as for different numerical apertures and aperture shapes. Special detectors are only sensitive to one component of the electric energy density, e.g. the longitudinal component. For certain parameters this has advantages concerning the resolution when comparing to polarization insensitive detectors. It is also shown that in the latter case zeros of the MTF may appear which are purely due to polarization effects and which depend on the aperture angle. Finally some ideas are presented how to use these results for improving the resolution in lithography.

Discrete quadratic cavity solitons.

We predict the existence of various types of discrete solitons in arrays of coupled optical cavities endowed with a quadratic nonlinearity. We derive mean-field equations and determine their range of validity by comparing results with those from the original round-trip model. By using an analytical approach we identify domains in parameter space where solitons can potentially exist and describe their asymptotic behavior. Taking advantage of these results, we numerically find discrete solitons of different topologies. Some of them are unique to discrete models. Ultimately, we study the stability of these soliton solutions and find that discreteness appreciably influences this behavior.

Spatial ultrafast switching and frequency conversion in lithium niobate waveguide arrays.

We demonstrate phase-insensitive, ultrafast, all-optical spatial switching and frequency conversion in quadratically nonlinear waveguide arrays in periodically poled lithium niobate. Routing of milliwatt signals with wavelengths in the communication band (1550 nm) is achieved without pulse distortions by parametric interaction with a control beam with 10-W power and wavelengths near 775 nm.

An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings.

This paper describes in a very easy and intelligible way, how the diffraction efficiencies of binary dielectric transmission gratings depend on the geometrical groove parameters and how a high efficiency can be obtained. The phenomenological explanation is based on the modal method. The mechanism of excitation of modes by the incident wave, their propagation constants and how they couple into the diffraction orders helps to understand the diffraction process of such gratings and enables a grating design without complicated numerical calculations.

Mobility of discrete cavity solitons.

We investigate the mobility of discrete cavity solitons in arrays of coupled quadratic nonlinear resonators driven by an inclined holding beam. Unlike in transversely homogeneous cavities the inherent discreteness hinders or even prevents the soliton motion. As a consequence for the same system parameters one type of soliton may still be at rest, whereas others already move. This feature gives rise to collisions between these different types. To study the soliton dynamics in more detail we take advantage of a perturbation theory and derive soliton velocities semianalytically.

Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters.

The filamentation of ultrashort pulses in air is investigated theoretically and experimentally. From the theoretical point of view, beam propagation is shown to be driven by the interplay between random nucleation of small-scale cells and relaxation to long waveguides. After a transient stage along which they vary in location and in amplitude, filaments triggered by an isotropic noise are confined into distinct clusters, called "optical pillars," whose evolution can be approximated by an averaged-in-time two-dimensional (2D) model derived from the standard propagation equations for ultrashort pulses. Results from this model are compared with space- and time-resolved numerical simulations. From the experimental point of view, similar clusters of filaments emerge from the defects of initial beam profiles delivered by the Teramobile laser facility. Qualitative features in the evolution of the filament patterns are reproduced by the 2D reduced model.

Discrete cavity solitons.

We derive evolution equations describing light propagation in an array of coupled-waveguide resonators and predict the existence of discrete cavity solitons. We identify stable, unstable, and oscillating solitons by varying the coupling strength between the anticontinuous and the continuous limit.

Interaction of femtosecond light filaments with obscurants in aerosols.

The interaction of ultrashort laser pulses with opaque droplets in the atmosphere is examined numerically. Intense filaments resulting from the balance between self-focusing and ionization of air molecules are shown to be robust against obscurants sized up to 2/3 of the filament diameter. (3D+1)-dimensional numerical simulations confirm recent experimental data [F. Courvoisier et al., Appl. Phys. Lett. 83, 213 (2003)]. The filament is rapidly rebuilt with minimal loss of energy over a few cm after the interaction region. The replenishment of the pulse mainly proceeds from the nonlinear attractor responsible for the formation of a spatial soliton modeling the filament core.

Stability of weakly nonlinear localized states in attractive potentials.

We analyze the stability of bound states to the nonlinear Schrödinger equation with an "attractive" linear potential and a cubic nonlinearity of arbitrary sign. A sufficient stability criterion is derived, which only requires knowledge of the linear modes of the potential. The results are double-checked numerically for the step-index optical fiber. An estimate of the growth rate versus nonlinearity is established in the limit of weak power.

Discrete solitons in inhomogeneous waveguide arrays.

The existence and dynamical properties of discrete solitons in inhomogeneous waveguide arrays with a Kerr nonlinearity are studied in two different configurations. First we investigate the effect of a longitudinal periodic modulation of the coupling strength on the dynamics of discrete solitons. It is shown that resonances of internal modes of the soliton with the longitudinal structure may lead to soliton oscillations and decay. Second we study the existence and stability of discrete solitons in arrays exhibiting a linear variation of the waveguide effective index in the transverse direction. We find that resonant coupling between conventional discrete solitons and linear Wannier-Stark states leads to the formation of so-called hybrid discrete solitons.

Dynamics and stability of solitary waves in optical-microwave interaction.

We study the dynamics and the stability of localized bound states of optical and microwave fields, which are linked together by a quadratic nonlinearity. The system is an example of an intense interaction between low and high frequency waves, as appears in many areas of physics. Perturbed solitary waves show a number of regular but damped oscillations with strong radiation from the microwave. It is demonstrated that these oscillations are caused by the excitation of several quasibound asymmetric linear modes of the solitary wave. The associated eigenvalues are found to be complex leading to a decay of the oscillations as observed numerically. Additional quasibound linear modes with a complex eigenvalue corresponding to exponential growth also exist, but due to physical constraints cannot be excited. Therefore, in contrast to systems solely with high frequency waves, the stability of the solutions is retained.

Highly efficient waveguide bends in photonic crystal with a low in-plane index contrast.

We report on the realization and characterization of highly efficient waveguide bends in photonic crystals made of materials with a low in-plane index contrast. By applying an appropriate bend design photonic crystal bends with a transmission of app. 75 % per bend were fabricated.

Reciprocity theorem and perturbation theory for photonic crystal waveguides.

Starting from Maxwell's equations we derive a reciprocity theorem for photonic crystal waveguides. A set of strongly coupled discrete equations results, which can be applied to the simulation of perturbed photonic crystal waveguides. As an example we analytically study the influence of the dispersion of a two level system on the band structure of a photonic crystal waveguide. In particular, the formation of polariton gaps is discussed.

Modulational instability in optical-microwave interaction.

The stability of continuous optical and microwave fields is studied in the presence of dispersion and second order nonlinearity. The cascade combination of optical rectification and the electro-optic effect induces modulational instability (MI) in a wide range of system parameters. It is demonstrated that MI can lead potentially to filamentation of high power optical pulses as well as the generation of terahertz radiation.

Anomalous refraction and diffraction in discrete optical systems.

We experimentally prove that light propagation in a discrete system, i.e., an array of coupled waveguides, exhibits striking anomalies. We show that refraction is restricted to a cone, irrespective of the initial tilt of the beam. Diffraction can be controlled in size and sign by the input conditions. Diffractive beam spreading can even be arrested and diverging light can be focused. The results can be thoroughly theoretically explained.

Hybrid discrete solitons.

The existence and stability of discrete solitons in waveguide arrays exhibiting a linear variation of the effective index and a Kerr nonlinearity is studied. We find that the resonant coupling of the conventional discrete soliton to a linear Wannier-Stark state does not entail soliton decay. We rather observe the formation of a bound state where the Wannier-Stark state gets nonlinearly modified. This results in an infinite number of isolated branches of hybrid discrete solitons.