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F Lederer

Publications and source records attributed to F Lederer.

At least 19 recordsLinked to original sources

Two-dimensional solitons in quasi-phase-matched quadratic crystals.

We study the existence and dynamics of two-dimensional spatial solitons in crystals that exhibit a periodic modulation of both the refractive index and the second-order susceptibility for achieving quasi-phase-matching. Far from resonances between the domain length of the periodic crystal and the diffraction length of the beams, it is demonstrated that the properties of the solitons in this quasi-phase-matched geometry are strongly influenced by the induced third-order nonlinearities. The stability properties of the two-dimensional solitons are analyzed as a function of the total power, the effective wave-vector mismatch between the first and second harmonics, and the relative strength between the induced third-order nonlinearity and the effective second-order nonlinearity. Finally, the formation of two-dimensional solitons from a Gaussian beam excitation is investigated numerically.

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Stable spatiotemporal spinning solitons in a bimodal cubic-quintic medium.

We investigate the formation of stable spatiotemporal three-dimensional (3D) solitons ("light bullets") with internal vorticity ("spin") in a bimodal system described by coupled cubic-quintic nonlinear Schrödinger equations. Two relevant versions of the model, for the linear and circular polarizations, are considered. In the former case, an important ingredient of the model are four-wave-mixing terms, which give rise to a phase-sensitive nonlinear coupling between two polarization components. Thresholds for the formation of both spinning and nonspinning 3D solitons are found. Instability growth rates of perturbation eigenmodes with different azimuthal indices are calculated as functions of the solitons' propagation constant. As a result, stability domains in the model's parameter plane are identified for solitons with the values of the spins of their components s=0 and s=1, while all the solitons with s> or =2 are unstable. The solitons with s=1 are stable only if their energy exceeds a certain critical value, so that, in typical cases, the stability region occupies approximately 25% of their existence domain. Direct simulations of the full system produce results that are in perfect agreement with the linear-stability analysis: stable 3D spinning solitons readily self-trap from initial Gaussian pulses with embedded vorticity, and easily heal themselves if strong perturbations are imposed, while unstable spinning solitons quickly split into a set of separating zero-spin fragments whose number is exactly equal to the azimuthal index of the strongest unstable perturbation eigenmode.

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Stable spatial solitons in semiconductor optical amplifiers.

The existence of stable dissipative spatial solitons at low intensities in patterned electrode semiconductor optical amplifiers (SOAs) is predicted theoretically. In contrast to conventional SOAs, this system may support stable solitons because the inherent saturating losses provide subcritical bifurcations for both the plane-wave and the soliton solution.

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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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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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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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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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Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities.

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, gives rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10% of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s=2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

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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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Stable spinning optical solitons in three dimensions.

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrödinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.

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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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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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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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The catalytic role of tyrosine 254 in flavocytochrome b2 (L-lactate dehydrogenase from baker's yeast). Comparison between the Y254F and Y254L mutant proteins.

Flavocytochrome b2 catalyses the oxidation of L-lactate to pyruvate in yeast mitochondrial intermembrane space. Its flavoprotein domain is a member of a family of FMN-dependent 2-hydroxy-acid-oxidizing enzymes. Numerous solution studies suggest that the first step of the reaction consists of proton abstraction from lactate C2, leading to a carbanion that subsequently yields electrons to FMN. The crystal structure suggests that the enzyme base is His373, and that Tyr254 may be hydrogen bonded to the substrate hydroxyl. Studies carried out with the Y254F mutant [Dubois, J., Chapman, S.K., Mathews, F.S., Reid, G.A. & Lederer, F. (1990) Biochemistry 29, 6393-6400] showed that Tyr254 does not act as a base but stabilizes the transition state. As the mutation did not induce any change in substrate affinity, the question of the existence of the hydrogen bond in the Michaelis complex remained open. Similar results with glycolate oxidase, mutated at the same position, led to the suggestion that these enzymes actually operate via a hydride transfer mechanism [Macheroux, P., Kieweg, V., Massey, V., Soderlind, E., Stenberg, K. & Lindqvist, Y. (1993) Eur. J. Biochem. 213, 1047-1054]. In the present work, we have re-investigated the matter by analysing the properties of a Y254L mutant flavocytochrome b2, as well as the behaviour of the Y254F enzyme with two substrates other than lactate, and a series of inhibitors. The Y254L protein is less efficient with L-lactate than the wild-type enzyme by a factor of 500, but the substrate affinity is unchanged. In contrast, L-phenyllactate and mandelate, poor substrates (the latter acting more as an inhibitor), exhibit an increased affinity. In addition, the Y254L mutant enzyme is more efficient with phenyllactate than lactate as a substrate. In order to rationalize these observations, we have modelled phenyllactate and mandelate in the active site, using previously described modelling experiments with lactate as a starting point. The results indicate that mandelate cannot bind in an orientation allowing proton abstraction by His373, due to steric interference by the side chains of Ala198 and Leu230. It might possibly adopt a binding mode as proposed previously for lactate, which leads to a hydride transfer and with which the 198 and 230 side chains do not interfere. However, other researchers [Sinclair, R., Reid, G.A. & Chapman, S.K. (1998) Biochem. J. 333, 117-120] showed that A198G, L230A and A198G/L230A mutant enzymes exhibit a strongly improved mandelate dehydrogenase activity. These results indicate that relief of the steric crowding facilitates catalysis by enabling a better mandelate orientation at the active site, suggesting that its productive binding mode is similar to that proposed for lactate in the carbanion mechanism. The modelling studies therefore support the hypothesis of a carbanion mechanism for all substrates. In addition, we present the effect of the two mutations at position 254 on the binding of a number of competitive inhibitors (such as sulfite, D-lactate, propionate) and of inhibitors that are known to bind at the active site both when the flavin is oxidized and when it is in the semiquinone state (propionate, oxalate and L-lactate at high concentrations). Unexpectedly, the results indicate that the integrity of Tyr254 is necessary for the binding of these inhibitors at the semiquinone stage.

Amino Acid Substitution↗

Limits for interchannel frequency separation in a soliton wavelength-division multiplexing system.

We identify the required interchannel frequency separation of the input field for a soliton wavelength-division multiplexing (WDM) system. It is found that the critical frequency separation above which WDM with solitons is feasible increases with the number of transmission channels. Moreover, it is shown that a combination of time- and wavelength-division multiplexing yields the largest transmission capacity. Finally, the structure of the soliton spectra which correspond to the frequency separation smaller than the critical frequency is discussed.

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Kinetic and crystallographic studies on the active site Arg289Lys mutant of flavocytochrome b2 (yeast L-lactate dehydrogenase).

Flavocytochrome b(2) from Saccharomyces cerevisiae couples L-lactate dehydrogenation to cytochrome c reduction. The crystal structure of the native yeast enzyme has been determined [Xia, Z.-X., and Mathews, F. S. (1990) J. Mol. Biol. 212, 837-863] as well as that of the sulfite adduct of the recombinant enzyme produced in Escherichia coli [Tegoni, M., and Cambillau, C. (1994) Protein Sci. 3, 303-313]; several key active site residues were identified. In the sulfite adduct crystal structure, Arg289 adopts two alternative conformations. In one of them, its side chain is stacked against that of Arg376, which interacts with the substrate; in the second orientation, the R289 side chain points toward the active site. This residue has now been mutated to lysine and the mutant enzyme, R289K-b(2), characterized kinetically. Under steady-state conditions, kinetic parameters (including the deuterium kinetic isotope effect) indicate the mutation affects k(cat) by a factor of about 10 and k(cat)/K(M) by up to nearly 10(2). Pre-steady-state kinetic analysis of flavin and heme reduction by lactate demonstrates that the latter is entirely limited by flavin reduction. Inhibition studies on R289K-b(2) with a range of compounds show a general rise in K(i) values relative to that of wild-type enzyme, in line with the elevation of the K(M) for L-lactate in R289K-b(2); they also show a change in the pattern of inhibition by pyruvate and oxalate, as well as a loss of the inhibition by excess substrate. Altogether, the kinetic studies indicate that the mutation has altered the first step of the catalytic cycle, namely, flavin reduction; they suggest that R289 plays a role both in Michaelis complex and transition-state stabilization, as well as in ligand binding to the active site when the flavin is in the semiquinone state. In addition, it appears that the mutation has not affected electron transfer from fully reduced flavin to heme, but may have slowed the second intramolecular ET step, namely, transfer from flavin semiquinone to heme b(2). Finally, the X-ray crystal structure of R289K-b(2), with sulfite bound at the active site, has been determined to 2.75 A resolution. The lysine side chain at position 289 is well-defined and in an orientation that corresponds approximately to one of the alternative conformations observed in the structure of the recombinant enzyme-sulfite complex [Tegoni, M., and Cambillau, C. (1994) Protein Sci. 3, 303-313]. Comparisons between the R289K-b(2) and wild-type structures allow the kinetic results to be interpreted in a structural context.

Arginine↗

Flavin-protein interactions in flavocytochrome b2 as studied by NMR after reconstitution of the enzyme with 13C- and 15N-labelled flavin.

A new procedure was devised for reversibly removing the flavin from flavocytochrome b2. It allowed reconstitution with selectively enriched 13C- and 15N-labelled FMN for an NMR analysis of the chemical shifts of the enriched positions as well as that of 31P. From these measurements, it was possible to deduce information about the hydrogen-bonding pattern of FMN in the protein, the hybridization states of the nitrogen atoms and (in part) the pi-electron distribution. The carbonyl groups at C(2) and C(4) and the nitrogen atoms N(1) and N(5) form hydrogen bonds to the apoenzyme in both redox states. Nevertheless, according to 15N-chemical shifts, the bond from the protein to N(3) is very weak in both redox states, whereas that to N(5) is strong for the oxidized state, and is weakened upon flavin reduction. On the other hand, the 13C-NMR results indicate that the C(2) and C(4) carbonyl oxygens form stronger hydrogen bonds with the enzyme than most other flavoproteins in both redox states. From coupling constant measurements it is shown that the N(3) proton is not solvent accessible. Although no N-H coupling constant could be measured for N(5) in the reduced state due to lack of resolution, N(5) is clearly protonated in flavocytochrome b2 as in all other known flavoproteins. With respect to N(10), it is more sp3-hybridized in the oxidized state than in free FMN, whereas the other nitrogen atoms show a nearly planar structure. In the reduced state, N(5) and N(10) in bound FMN are both more sp3-hybridized than in free FMN, but N(5) exhibits a higher degree of sp3-hybridization than N(10), which is only slightly shifted out of the isoalloxazine plane. In addition, two-electron reduction of the enzyme leads to anion formation on N(1), as indicated by its 15N-chemical shift of N(1) and characteristic upfield shifts of the resonances of C(2), C(4) and C(4a) compared to the oxidized state, as observed for most flavoproteins. 31P-NMR measurements show that the phosphate geometry has changed in enzyme bound FMN compared to the free flavin in water, indicating a strong interaction of the phosphate group with the apoenzyme.

Binding Sites↗

Three-dimensional spinning solitons in the cubic-quintic nonlinear medium.

We find one-parameter families of three-dimensional spatiotemporal bright vortex solitons (doughnuts, or spinning light bullets), in bulk dispersive cubic-quintic optically nonlinear media. The spinning solitons display a symmetry-breaking azimuthal instability, which leads to breakup of the spinning soliton into a set of fragments, each being a stable nonspinning light bullet. However, in some cases the instability is developing so slowly that the spinning light bullets may be regarded as virtually stable ones, from the standpoint of an experiment with finite-size samples.

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