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Biomedical subjects

U Peschel

Publications and source records attributed to U Peschel.

At least 19 recordsLinked to original sources
PubMed2005

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.

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PubMed2005

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.

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PubMed2005

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.

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PubMed2004

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.

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PubMed2004

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.

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PubMed2004

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.

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PubMed2004

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.

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PubMed2003

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.

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PubMed2003

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.

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PubMed2003

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.

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PubMed2002

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.

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PubMed2002

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.

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PubMed2002

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.

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PubMed2001

Perturbation theory for domain walls in the parametric Ginzburg-Landau equation.

We demonstrate that in the parametrically driven Ginzburg-Landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion. These differences originate from singular rotation of the eigenvector governing the transition. We present analytical results on the stability of Ising walls, deriving explicit expressions for the critical eigenvalue responsible for the transition from rest to motion. We then develop a weakly nonlinear theory to characterize the singular character of the transition and analyze the dynamical effects of spatial inhomogeneities.

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PubMed2001

Effects of spatial inhomogeneities on the dynamics of cavity solitons in quadratically nonlinear media.

We study the dynamics of cavity solitons under the influence of spatial inhomogeneities and derive generalized equations of motions. For perturbations large compared to the soliton size we find the modulus of the soliton velocity to be proportional to the gradient of the respective perturbation and that the proportionality coefficient changes sign when the soliton peak power drives the cavity beyond the resonance. For short scale perturbations solitons may be trapped at the extrema of the inhomogeneities. Shape and stability of these trapped solitons can be quasianalytically described by means of a perturbation theory. If both types of perturbations act solitons are either trapped or move depending on the strength of the respective perturbation. In the framework of a quasiparticle approach this dynamics is governed by a differential equation that holds for particle motion in a strongly viscous fluid under the action of a constant and harmonically varying force. We also show that in addition to acquiring a velocity the very existence conditions of the solitons (hysteresis curve) are affected by both kinds of perturbations. We find good quantitative agreement between our analytical results and numerical findings, which were obtained for a two wave interaction in a cavity filled with a quadratically nonlinear material.

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PubMed2001

Universal criterion and amplitude equation for a nonequilibrium Ising-Bloch transition.

We identify a universal criterion for the onset of a nonequilibrium Ising-Bloch (NIB) transition, and describe the behavior near the bifurcation by a generic amplitude equation. We found that a NIB transition is caused by an antisymmetric eigenvector passing the translational mode of the system at a critical point. In this context we discuss Hamiltonian and dissipative systems. We report on a NIB in nonlinear optics, manifesting itself in a transition from static to moving polarization fronts.

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