Process and waveguide parameter relationships for the design of planar silver ion-exchanged glass waveguides

In this paper the experimental results of diffusion studies and modal characterization of Ag⁺-Na⁺exchanged glass waveguides are presented. Empirical relations between the process and the device parameters are derived and subsequently used to formulate a systematic procedure for fabricating single- and multimode waveguides.     

Zero-Sum Differential Games Involving Hybrid Controls

We study a zero-sum differential game with hybrid controls in which both players are allowed to use continuous as well as discrete controls. Discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, an autonomous jump set A or a controlled jump set C, where one controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. One player uses all the three types of controls, namely, continuous controls, autonomous jumps, and controlled jumps; the other player uses continuous controls and autonomous jumps. We prove the continuity of the associated lower and upper value functions V⁻ and V⁺. Using the dynamic programming principle satisfied by V⁻ and V⁺, we derive lower and upper quasivariational inequalities satisfied in the viscosity sense. We characterize the lower and upper value functions as the unique viscosity solutions of the corresponding quasivariational inequalities. Lastly, we state an Isaacs like condition for the game to have a value This work was partially supported by Grants DRDO 508 and ISRO 050 to the Non-linear Studies Group, Indian Institute of Science. The first author is a University Grant Commission Research Fellow and the financial support is gratefully acknowledged. The authors thank Prof. M.K. Ghosh, Department of Mathematics, Indian Institute of Science, for introducing the problem and thank the referee for useful suggestions.     

Dynamical signatures of ‘phase transitions’: Chaos in finite clusters

Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article.     

Screening the optical properties of Ag-Au alloy gradients formed by bipolar electrodeposition using surface enhanced Raman spectroscopy

We report the synthesis of Ag-Au alloy gradients on stainless steel substrates using bipolar electrodeposition (BP-ED), a technique based on the existence of a potential gradient at the interface of a bipolar electrode (BPE) and an electrolytic solution. The interfacial potential gradient causes the rates of electrodeposition of Ag and Au to vary along the length of the BPE, leading to the electrodeposition of a chemical concentration gradient. The surface morphology of the electrodeposits was characterized using scanning electron microscopy (SEM), and their chemical composition was determined using energy dispersive X-ray spectroscopy (EDX). Self-assembled monolayers of a Raman-active probe molecule (benzene thiol) were allowed to form on the surface of the alloy gradients, and confocal Raman microscopy was employed to determine the alloy composition that resulted in the maximum surface enhanced Raman scattering (SERS) intensity. An alloy composition of ca. 70% Ag/30% Au was found to be optimum for SERS excited using 514.5 nm radiation, and it is explained on the basis of composition-dependent changes in the local surface plasmon resonance (LSPR) of the electrodeposited Ag-Au alloy.     

Determination of 77Se-77Se and 77Se-13C J-coupling parameters for the clusters [Re5OsSe8(CN)6]3- and [Re4Os2Se8(CN)6]2-

We have investigated rarely observed 77Se J-couplings (spin-spin couplings) in the mixed-metal face-capped octahedral clusters [Re5OsSe8(CN)6]3- and [Re4Os2Se8(CN)6]2- at natural abundance. To the best of our knowledge, these are the first observations of Se-Se spin-spin interactions between mu3-Se sites, important for stereochemical assignments in hexarhenium analogues, Chevrel phase materials, and similar cluster materials. NMR techniques such as COSY, INADEQUATE, and 2D J-resolved spectroscopy have been used in conjunction to study these interactions. The two isomers (cis and trans) of [Re4Os2Se8(CN)6]2- were distinguishable, and selective isotopic labeling of [Re5OsSe8(CN)6]3- with 13CN ligands enabled resonances to be assigned by observing the 2J (Se-M-C) couplings. For [Re5OsSe8(CN)6]3-, two different 2J (Se-M-Se) couplings were measurable on a single cluster, and these are related to one another through spin-spin interactions across a face diagonal or along an edge of the cube of inner selenium ligands. A rigorous analysis based on combinatorial math has been invoked to assign the couplings on the basis of the probability of multiple-spin interactions. The face diagonal association is found to result in a J-coupling interaction larger in magnitude than that from coupling along an edge of the cube-information critical for making stereochemical assignments of selenium sites.     

Symmetry breaking in quantum chaotic systems

We show, using semiclassical methods, that as a symmetry is broken, the transition between universality classes for the spectral correlations of quantum chaotic systems is governed by the same parametrization as in the theory of random matrices. The theory is quantitatively verified for the kicked rotor quantum map. We also provide an explicit substantiation of the random matrix hypothesis, namely that in the symmetry-adapted basis the symmetry-violating operator is random.     

Tapered, both in dimension and in index, velocity coupler: theoryand experiment

The authors consider a tapered velocity coupler (TVC) that meets the adiabatic invariance condition with sufficiently strong coupling between the fundamental modes of individual guides in the middle region of the coupler while permitting individual excitation at the input end and sorting of the modes at the output end. This approach helps reduce the device length considerably by permitting much higher taper angle. A TVC consisting of one tapered and another straight, graded index waveguide is modeled using the normal modes of the entire, composite TVC structure. The analytical results are in excellent agreement with experimental results for a TVC fabricated in Ti:LiNbO₃. It is shown that the representation of the local normal modes as the superposition of the modes of the uncoupled guides leads to erroneous results     

Broad-band distributed Bragg reflectors with photorefractive Ti : Cu : LiNbO/sub 3/ waveguide gratings

We have realized broad-band distributed Bragg reflectors with photorefractive gratings recorded at 441.6 nm in channel Ti : Cu : LiNbO/sub 3/ waveguides. Proton-assisted copper exchange is used to enable a high level of copper doping and, thereby, achieve an extremely large modulation of refractive index (/spl ges/ 5/sup */10/sup -4/) within a photorefractive grating. Experimental structures demonstrate reflectivities up to 17% with full-width at half-maximum bandwidths in excess of 1.2 nm at center wavelengths around 1.55 /spl mu/m.