Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams

We present the first experimental observation of modulation instability of partially spatially incoherent light beams in non-instantaneous nonlinear media. We show that even in such a nonlinear partially coherent system (of weakly-correlated particles) patterns can form spontaneously. Incoherent MI occurs above a specific threshold that depends on the beams' coherence properties (correlation distance), and leads to a periodic train of one-dimensional (1D) filaments. At a higher value of nonlinearity, incoherent MI displays a two-dimensional (2D) instability and leads to self-ordered arrays of light spots.Comment: 16 pages, 4 figure

Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices

We investigate the interaction between a light beam and a two-dimensional photonic lattice that is photo-induced in a photorefractive crystal using partially coherent light. We demonstrate that this interaction process is associated with a host of new phenomena including lattice dislocation, lattice deformation, and creation of structures akin to optical polarons. In addition, two-dimensional discrete solitons are realized in such partially coherent photonic lattices.Comment: 12 pages, 4 figures (revised). accepted by Phys. Rev. Let

Molecular Containers for Anions Based on Triply-Linked Bis(Cyclopeptides)

The research presented in this PhD thesis is a contribution to the field of anion recognition in competitive aqueous solvent mixtures. Neutral anion receptors having a cage-type architecture have been developed on the basis of triply-linked bis(cyclopeptides) and their binding properties toward various inorganic anions have been studied. The synthetic approaches chosen to assemble the targeted container molecules rely on dynamic chemistry under the template effects of anions such as sulfate and halides. As reversible reactions metal-ligand exchange and thiol-disulfide exchange were used. Disulfide exchange has previously provided singly- and doubly-linked bis(cyclopeptide) receptors whose anion affinities in 2:1 acetonitrile/water mixtures approached the nanomolar range. Metal-ligand interactions have so far not been used to assemble bis(cyclopeptides) in our group. The cyclopeptide building blocks required for both approaches, namely cyclic hexapeptides containing alternating 6-aminopicolinic acid and either (2S,4S)-4-cyanoproline or (2S,4S)-4-thioproline subunits could be synthesized successfully. Self-assembly of the bis(cyclopeptide) held together by coordinative interactions has been attempted by treating the cyclopeptide trinitrile with square-planar palladium (II) complexes. The reaction was followed with different NMR spectroscopic techniques. Unfortunately, none of the experiments provides conclusive evidence that the targeted triply-linked cage was indeed formed. Bis(cyclopeptides) containing three dithiol derived linkers between the cyclopeptide rings could be synthesizes successfully. Two complexes were isolated, albeit in small amounts, one containing linkers derived from 1,2-ethanedithiol and the other one from 1,3-benzenedithiol that contain a sulfate anion incorporated in the cavity between the cyclopeptide rings. Formation of triply-linked bis(cyclopeptides) containing different types of linkers could be achieved by performing the synthesis in the presence of different dithiols. Unfortunately, the two C3 symmetrical bis(cyclopeptides) containing a single linker type could not be isolated in analytically pure form so that only qualitative binding studies could be performed. Investigations in this context indicate extraordinary sulfate affinity for these bis(cyclopeptides). In particular, affinity of the receptor containing the 1,2-ethanedithiol linkers for sulfate anions is so high that is even able to dissolve barium sulfate under appropriate conditions and presumably exceeds the sulfate affinity of the doubly-linked bis(cyclopeptides). The sulfate anion present in the cavity of this bis(cyclopeptide) can be replaced by a large number of other anions, i.e. by selenate, perrhenate, nitrate, tetrafluoroborate, hexafluorophosphate and halides. None of these complexes proved to be as stable as the corresponding sulfate complex. In addition, 1H-NMR spectroscopic investigations provided information about the solution structure of the bis(cyclopeptide) anion complexes. Sulfate release from the cavity of the receptor is a slow process while exchange of other anions is significantly faster. Another interesting feature that has been observed for sulfate and selenate complexes of the 1,2-ethanedithiol-containing bis(cyclopeptide) is the very slow H/D rate with which protons on amide groups located inside the cavity of the cage are replaced by deuterium atoms in protic deuterated solvents. This effect in combination with the observation that the different deuterated bis(cyclopeptide) species exhibit individual amide NH signals in the 1H-NMR spectrum are indicative for well defined complex geometries with strong hydrogen-bonding interactions between the anion and the amide NH groups of the receptor. Following the H/D exchange rate in the presence of various salts indicated that anion exchange proceeds via the dissociated complex and not by direct replacement of one anion by another one

Interlaced linear-nonlinear optical waveguide arrays

The system of coupled discrete equations describing a two-component superlattice with interlaced linear and nonlinear constituents is revisited as a basis for investigating binary waveguide arrays, such as ribbed AlGaAs structures, among others. Compared to the single nonlinear lattice, the interlaced system exhibits an extra band-gap controlled by the, suitably chosen by design, relative detuning. In more general physics settings, this system represents a discretization scheme for the single-equation-based continuous models in media with transversely modulated linear and nonlinear properties. Continuous wave solutions and the associated modulational instability are fully analytically investigated and numerically tested for focusing and defocusing nonlinearity. The propagation dynamics and the stability of periodic modes are also analytically investigated for the case of zero Bloch momentum. In the band-gaps a variety of stable discrete solitary modes, dipole or otherwise, in-phase or of staggered type are found and discussed

Perturbation-induced radiation by the Ablowitz-Ladik soliton

An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are calculated for linear damping and quintic perturbations.Comment: 13 pages, 4 figures, Phys. Rev. E (in press

Elliminating The Transverse Instabilities of Kerr Solitons

We show analytically, numerically, and experimentally that a transversely stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk medium. The transverse instability of the soliton is completely eliminated if it is made sufficiently incoherent along the transverse dimension. We derive a criterion for the threshold of transverse instability that links the nonlinearity to the largest transverse correlation distance for which the 1D soliton is stableComment: 14 pages, 2 figure

All-optical routing and switching for three-dimensional photonic circuitry

The ability to efficiently transmit and rapidly process huge amounts of data has become almost indispensable to our daily lives. It turned out that all-optical networks provide a very promising platform to deal with this task. Within such networks opto-optical switches, where light is directed by light, are a crucial building block for an effective operation. In this article, we present an experimental analysis of the routing and switching behaviour of light in two-dimensional evanescently coupled waveguide arrays of Y- and T-junction geometries directly inscribed into fused silica using ultrashort laser pulses. These systems have the fundamental advantage of supporting three-dimensional network topologies, thereby breaking the limitations on complexity associated with planar structures while maintaining a high dirigibility of the light. Our results show how such arrays can be used to control the flow of optical signals within integrated photonic circuits

Elliptical optical solitary waves in a finite nematic liquid crystal cell

2015 Elsevier B.V. The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the chirp variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation

Molecular Containers for Anions Based on Triply-Linked Bis(Cyclopeptides)

The research presented in this PhD thesis is a contribution to the field of anion recognition in competitive aqueous solvent mixtures. Neutral anion receptors having a cage-type architecture have been developed on the basis of triply-linked bis(cyclopeptides) and their binding properties toward various inorganic anions have been studied. The synthetic approaches chosen to assemble the targeted container molecules rely on dynamic chemistry under the template effects of anions such as sulfate and halides. As reversible reactions metal-ligand exchange and thiol-disulfide exchange were used. Disulfide exchange has previously provided singly- and doubly-linked bis(cyclopeptide) receptors whose anion affinities in 2:1 acetonitrile/water mixtures approached the nanomolar range. Metal-ligand interactions have so far not been used to assemble bis(cyclopeptides) in our group. The cyclopeptide building blocks required for both approaches, namely cyclic hexapeptides containing alternating 6-aminopicolinic acid and either (2S,4S)-4-cyanoproline or (2S,4S)-4-thioproline subunits could be synthesized successfully. Self-assembly of the bis(cyclopeptide) held together by coordinative interactions has been attempted by treating the cyclopeptide trinitrile with square-planar palladium (II) complexes. The reaction was followed with different NMR spectroscopic techniques. Unfortunately, none of the experiments provides conclusive evidence that the targeted triply-linked cage was indeed formed. Bis(cyclopeptides) containing three dithiol derived linkers between the cyclopeptide rings could be synthesizes successfully. Two complexes were isolated, albeit in small amounts, one containing linkers derived from 1,2-ethanedithiol and the other one from 1,3-benzenedithiol that contain a sulfate anion incorporated in the cavity between the cyclopeptide rings. Formation of triply-linked bis(cyclopeptides) containing different types of linkers could be achieved by performing the synthesis in the presence of different dithiols. Unfortunately, the two C3 symmetrical bis(cyclopeptides) containing a single linker type could not be isolated in analytically pure form so that only qualitative binding studies could be performed. Investigations in this context indicate extraordinary sulfate affinity for these bis(cyclopeptides). In particular, affinity of the receptor containing the 1,2-ethanedithiol linkers for sulfate anions is so high that is even able to dissolve barium sulfate under appropriate conditions and presumably exceeds the sulfate affinity of the doubly-linked bis(cyclopeptides). The sulfate anion present in the cavity of this bis(cyclopeptide) can be replaced by a large number of other anions, i.e. by selenate, perrhenate, nitrate, tetrafluoroborate, hexafluorophosphate and halides. None of these complexes proved to be as stable as the corresponding sulfate complex. In addition, 1H-NMR spectroscopic investigations provided information about the solution structure of the bis(cyclopeptide) anion complexes. Sulfate release from the cavity of the receptor is a slow process while exchange of other anions is significantly faster. Another interesting feature that has been observed for sulfate and selenate complexes of the 1,2-ethanedithiol-containing bis(cyclopeptide) is the very slow H/D rate with which protons on amide groups located inside the cavity of the cage are replaced by deuterium atoms in protic deuterated solvents. This effect in combination with the observation that the different deuterated bis(cyclopeptide) species exhibit individual amide NH signals in the 1H-NMR spectrum are indicative for well defined complex geometries with strong hydrogen-bonding interactions between the anion and the amide NH groups of the receptor. Following the H/D exchange rate in the presence of various salts indicated that anion exchange proceeds via the dissociated complex and not by direct replacement of one anion by another one