Linear and nonlinear properties of multicomponent glass photonic crystal fibers

Processes resulting in supercontinuum generation in multicomponent glass photonic crystal fibers are reviewed in this paper. Multicomponent glass photonic crystal fibers are shown to have a broad transmission range, extending up to 4.5 μm in selected cases. Pumping with a 1240-nm femtosecond pulse at very low sub-nJ energies resulted in soliton formation and dispersive wave generation in a multicomponent PCF sample having a double-core square-lattice structure. These processes were described using a phase-matching model derived from the simulated dispersive properties of the fiber. Third-harmonic generation was observed in the radiation modes of a different cobweb sample with the simultaneous formation of a soliton in the NIR.     

Combining directional light output and ultralow loss in deformed microdisks

A drawback of optical modes in microdisk cavities is their isotropic light emission. Here we report a novel, robust, and general mechanism that results in highly directional light emission from high-quality modes. This surprising finding is explained by a combination of wave phenomena (wave localization along unstable periodic ray trajectories) and chaotic ray dynamics in open systems (escape along unstable manifolds) and applies even to microlasers operating in the common multimode regime. We demonstrate our novel mechanism for the lima?on cavity and find directional emission with narrow angular divergence for a significant range of geometries and material parameters.     

Modal dispersion phase-matched frequency doubling in composite planar waveguide using ion-exchanged glass and optically nonlinear poled polymer

We report on the fabrication and characterization of composite planar waveguides for frequency doubling. Modal dispersion phase matching is obtained for TM₀ fundamental and (TM₁, TM₂) harmonic wavelength. The experimental conversion efficiency was η=0.45% with an SH wavelength of 0.516 μm for TM₀^ω–TM₂^2ω mode conversion. The phase-matching condition can be fulfilled by adjusting the diffusion time of ion-exchange and the thickness of the polymer layer.     

Linear and nonlinear intersubband optical absorptions in an asymmetric rectangular quantum well

The linear and nonlinear intersubband optical absorptions in Al_xlGa_1-xlAs/GaAs/Al_xr Ga_1-xrAs asymmetric rectangular quantum well are studied within the framework of the density matrix formalism. We have calculated the electron energy levels and the envelope wave functions using the effective mass approach. In addition, we have obtained an expression for saturation intensity. It is shown that the parameters such as asymmetry and width of potential well not only shift the peak positions in absorption spectrum but also considerably modify their height. These results suggest that the absorption process can be easily controlled by the structure parameters of an asymmetric rectangular quantum well. Also, the incident optical intensity has a great effect on the total absorption spectrum. We have seen that the absorption peak is reduced by half when the optical intensity is approximately 0.8 MW/cm² for well width L=90 ? and β=0.5. Moreover, it is seen that the saturation intensity is quite sensitive to the structure parameters of an asymmetric rectangular quantum well. Thus, the results presented here can be useful for electro-optical modulators and photodetectors in the infrared region.     

Linear superposition in nonlinear equations

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions.     

Linear and nonlinear Dirac equation

Using the usual matrix representation of Clifford algebra of spacetime, quantities independent of the choice of a representation in the Dirac theory are examined, relativistic invariance of the theory is discussed, and a nonlinear equation is proposed. The equation presents no negative energy waves and gives the same results as the linear theory for hydrogen atom.     

Chiral ordering in the four-dimensional planar spin glass

The chiral glass behaviour of the nearest-neighbour random-bond XY spin glass in four dimensions is studied by Monte Carlo simulations. A chiral glass transition at T _cg = 0:90 ± 0:05 is found by a finite-size scaling analysis of the results. The associated chiral correlation-length exponent is estimated to be gv _cg = 0:6±0:1. Both values are very similar to those reported recently for the spin glass transition in this model. The results strongly suggest a simultaneous ordering of spin and chirality in four dimensions.     

Strong self-phase modulation in planar chalcogenide glass waveguides

Single-mode planar waveguides were fabricated from chalcogenide glass compounds with large Kerr nonlinearities. Strong self-phase modulation of subpicosecond pulses along with low linear and nonlinear absorption losses demonstrates the potential for ultrafast, low-power, all-optical processing applications.     

Linear and nonlinear optical absorption coefficients in an asymmetric graded ridge quantum wire

In this article, the optical absorption coefficients in an asymmetric ridge quantum wire within the framework of the density matrix formalism are studied. The energy spectrum and wave functions of a quantum wire with graded confinement potential using the effective mass approximation are analytically calculated. The results show that parameters such as the asymmetry and width of the potential well change the position and magnitude of the absorption peak and saturation intensity. The incident optical intensity also has a great effect on the total absorption.     

Improved method for loss measurements in planar waveguides

A method employing an isosceles prism and a right-angle one is developed for loss measurement in planar waveguides. During the measuring process, the isosceles prism is fixed and the right-angle prism fixed on the waveguide slides by following the waveguide. Only by adjusting the gap thickness we can realize the loss measurement in planar waveguides. The method is demonstrated with an Ag/Na ion-exchanged waveguide fabricated on BK7 glass from AgNO₃ melt diluted with NaNO₃ (mass ratio 1:9), with the condition of 4 h and . The experimental results show that the method has the advantages on convenient operation, accurate results and no required end polishing.     

Linear and nonlinear excitations in warm dense matter

Small and large amplitude linear and nonlinear ion acoustic and Langmuir waves are investigated for plasma with the generalized equation of state (EoS). This EoS covers a wide range of energy-density conditions from dilute classical regime up to the relativistically degenerate matter. Investigation shows that the linear dispersion and localized excitations of ion acoustic waves are significantly affected by the plasma parameters. It is also found that the criterion for ordinary soliton existence is significantly different for fully degenerate and nondegenerate plasma regimes with given electron temperature. In the nondegenerate regime, bright solitons form only for Mach numbers above a critical value which is only a function of the fluid temperature.     

Linear and nonlinear photoexcitation dynamics in pi-conjugated polymers

Linear and nonlinear recombination kinetics with various lifetime distributions were identified for long-lived photoexcitations in a series of pi-conjugated polymer films using modulation frequency and excitation intensity dependencies of the photoinduced absorption. This includes monomolecular, bimolecular, and defect-limited recombination processes that lead to saturation. Using generalized kinetics parameters, we found characteristic plots for all recombination processes. Specifically, the bimolecular recombination process shows superlinear intensity dependence away from the steady state; on the contrary, dispersive bimolecular recombination leads to sublinear dependence.     

Self-induced nonlinear polarization change of femtosecond laser pulse propagation in an optically isotropic glass

The self-induced polarization change of femtosecond laser pulses passing through an isotropic optical glass is investigated. It is shown that supercontinuum generations from femtosecond lasers tend to be identical for the incident beam with different polarizations ranging from a large-ellipticity to a linear state when the incident laser power increases. Theoretical analysis reveals that a transient intensity-dependent birefringence is induced in the glass sample by the laser pulse itself, and the accumulated nonlinear phase shift leads to a change in polarization ellipticity. Simulation results are consistent with the experimental observations. PACS 42.50.Md; 42.65.Jx; 42.81.Gs; 77.22.Ej     

Linear and nonlinear rheology of wormlike micelles

Several surfactant molecules self-assemble in solution to form long, cylindrical, flexible wormlike micelles. These micelles can be entangled with each other leading to viscoelastic phases. The rheological properties of such phases are very interesting and have been the subject of a large number of experimental and theoretical studies in recent years. We shall report our recent work on the macrorheology, microrheology and nonlinear flow behaviour of dilute aqueous solutions of a surfactant CTAT (Cetyltrimethylammonium Tosilate). This system forms elongated micelles and exhibits strong viscoelasticity at low concentrations (∼0.9 wt%) without the addition of electrolytes. Microrheology measurements of G(θ) have been done using diffusing wave spectroscopy which will be compared with the conventional frequency sweep measurements done using a cone and plate rheometer. The second part of the paper deals with the nonlinear rheology where the measured shear stress σ is a nonmonotonic function of the shear rate . In stress-controlled experiments, the shear stress shows a plateau for larger than some critical strain rate, similar to the earlier reports on CPyCl/NaSal system. Cates et al have proposed that the plateau is a signature of mechanical instability in the form of shear bands. We have carried out extensive experiments under controlled strain rate conditions, to study the time-dependence of shear stress. The measured time series of shear stress has been analysed in terms of correlation integral and Lyapunov exponent to show unambiguously that the behaviour is typical of low dimensional dynamical systems.     

Low radiation loss Y-junctions in planar dielectric optical waveguides

A simple structure is proposed to reduce radiation losses of Y-junctions in planar optical waveguides by decreasing refractive indices near the branching regions. The losses of the properly designed Y-junctions can be reduced by around an order of magnitude compared with those of conventional ones when the branching angles are large.     

Linear and nonlinear Schrödinger equations

The Schrödinger equation for a point particle in a quartic potential and a nonlinear Schrödinger equation are solved by the decomposition method yielding convergent series for the solutions which converge quite rapidly in physical problems involving bounded inputs and analytic functions. Several examples are given to demonstrate use of the method.     

Linear integral equations and nonlinear difference-difference equations

This paper studies the dynamics of members of the two-parameter family of maps x → μx(1 ? x^v), emphasizing the evolution from snapback repeller to crisis bifurcations. The example of the square root map $\text{v =}\text{1}\text{2}$ is taken to represent the subfamily where v is fixed and taken from the range $\text{1}\text{2}\text{≤ v ≤ 1}$. A map from such a subfamily is shown to be conjugate with a map with negative Schwarzian derivative. This allows a characterization of crisis as the demise of a snapback repeller on a proper subinterval.     

Linear and nonlinear photoinduced deformations of cantilevers

Glassy and elastomeric nematic networks with dye molecules present can be very responsive to illumination, huge reversible strains being possible. If absorption is appreciable, strain decreases with depth into a cantilever, leading to bend that is the basis of micro-opto-mechanical systems (MOMS). Bend actually occurs even when Beer's law suggests a tiny penetration of light into a heavily dye-doped system. We model the nonlinear opto-elastic processes behind this effect. In the regime of cantilever thickness giving optimal bending for a given incident light intensity, there are three neutral surfaces. In practice such nonlinear absorptive effects are very important since heavily doped systems are commonly used.