Refractive-Index Profiling of Buried Planar Waveguides by an Inverse Wentzel–Kramer–Brillouin Method

We propose an inverse Wentzel-Kramer-Brillouin (WKB) method for the construction of the refractive-index profiles of buried graded-index planar waveguides from the measured effective indexes of the guided modes. Our method involves experimental determination of the location of the peak index in the buried profile, measurement of the effective indexes in air, and an index-matching liquid, and application of a searching algorithm to find the best-fit profile through inverting the WKB equations. We present numerical examples and experimental results to demonstrate the performance of the method.     

Novel Nanostructures from Self‐Assembly of Chiral Block Copolymers

A diblock copolymer system constituting both achiral and chiral blocks, polystyrene‐block‐poly(L ‐lactide) (PS‐PLLA), was designed for the examination of chiral effects on the self‐assembly of block copolymers (BCPs). A unique phase with three‐dimensional hexagonally packed PLLA helices in PS matrix, a helical phase (H*), can be obtained from the self‐assembly of PS‐rich PS‐PLLA with volume fraction of PLLA f = 0.34, whereas no such phase was found in racemic polystyrene‐block‐poly(D .L ‐lactide) (PS‐PLA) BCPs. Moreover, various interesting crystalline PS‐PLLA nanostructures can be obtained by controlling the crystallization temperature of PLLA (T_c,PLLA), leading to the formation of crystalline helices (PLLA crystallization directed by helical confined microdomain) and crystalline cylinders (phase transformation of helical nanostructure dictated by crystallization) when T_c,PLLA < T_g,PS (the glass transition temperature of PS) and T_c,PLLA ≧ T_g,PS, respectively. As a result, a spring‐like behavior of the helical nanostructure can be driven by crystallization so as to dictate the transformation (i.e., stretching) of helices and to result in crystalline cylinders. For PS‐PLLA with PLLA‐rich fraction (f = 0.65), another unique phase, a hexagonally packed core‐shell cylinder phase with helical sense (CS*), in which the PS microdomains appear as shells and PLLA microdomains appear as matrix and cores, can be found in the self‐assembly of PLLA‐rich PS‐PLLA BCPs. The formation of those novel phases: helix and core‐shell cylinder is attributed to the chiral effect on the self‐assembly of BCPs, so we named this PS‐PLLA BCP as chiral BCP (BCP*). For potential applications of those materials, the spring‐like behavior with thermal reversibility might provide a method for the design of switchable nanodevices, such as nanoscale actuators. In addition, the PLLA blocks can be hydrolyzed. After hydrolysis, helical nanoporous PS bulk and PS tubular texture can be obtained and used as templates for the formation of nanocomposites.

     

Large-core single-mode channel waveguide based on geometrically shaped leaky cladding

We propose a leaky channel waveguide structure for large-mode-area single-mode operation. The proposed structure is characterized by a uniform rectangular core and a specially designed cladding, through which all the confined modes are leaky. Single-mode operation is ensured by choosing the waveguide parameters properly so that the differential leakage loss between the first two modes is sufficiently high. A general power-law cladding geometry profile is considered, which is solved by the effective-index method in conjunction with the transfer-matrix-method to obtain the effective indices and leakage losses of the modes. We show that, with a suitable choice of cladding parameters, the waveguide can demonstrate extended single-mode operation in the wavelength range 750–1600 nm with a core area as large as 100 μm². Such a large confinement area for mode propagation can effectively suppress nonlinear optical effects. The waveguide is expected to find applications in the design of high-power lasers and amplifiers. PACS 42.82.-m; 42.82.Et; 42.79.Gn; 42.55.-f; 42.82.Bq     

Optimizating the seats surrounding the platform in a recital hall when considering source directivity

The influence of source directivity can be significant for solo and chamber music performances, particularly for arena type halls that have improved visual intimacy for the audience. Computer simulation was performed to analyze the possibility of optimizing the acoustical qualities of a 4000-m³ recital hall with a significant portion of seats surrounding the platform when considering source directivity. The effects of surface treatments, length-to-width proportion, seating arrangement and platform location were evaluated. Most acoustical parameters derived from a baritone singer source were categorized as one factor that can be best represented by 2-kHz band early sound strength G_E. Regardless of room proportion, front-back 2-kHz band energy difference derived from optimized models can be controlled within 4 dB, a value much smaller than the difference in direct component.     

Geometric programming duals of channel capacity and rate distortion

We show that the Lagrange dual problems of the channel capacity problem with input cost and the rate distortion problem are simple geometric programs. Upper bounds on channel capacity and lower bounds on rate distortion can be efficiently generated from their duals. For channel capacity, the geometric programming dual characterization is shown to be equivalent to the minmax Kullback-Leibler (KL) characterization in Csiszar et al. (1981). For rate distortion, the geometric programming dual is extended to rate distortion with two-sided state information. A "duality by mapping" is then given between the Lagrange dual problems of channel capacity with input cost and rate distortion, which resolves several apparent asymmetries between their primal problems in the familiar form of mutual information optimization problems. Both the primal and dual problems can be interpreted in a common framework of free energy optimization from statistical physics.     

Explicit Time Marching Methods for the Time-Dependent Euler Computations

Four explicit type time marching methods, including one proposed by the authors, are examined. The TVD conditions of this method are analyzed with the linear conservation law as the model equation. Performance of these methods when applied to the Euler equations are numerically tested. Seven examples are tested, the main concern is the performance of the methods when discontinuities with different strengths are encountered. When the discontinuity is getting stronger, spurious oscillation shows up for three existing methods, while the method proposed by the authors always gives the results with satisfaction. The effect of the limiter is also investigated. To put these methods in the same basis for the comparison the same spatial discretization is used. Roe's solver is used to evaluate the fluxes at the cell interface; spatially second-order accuracy is achieved by the MUSCL reconstruction.     

Leaky optical fibre for large mode area singlemode operation

A novel optical fibre structure is introduced for large mode area singlemode operation. The fibre consists of a cladding index profile that increases monotonically in the radial direction. It is shown that the fibre can introduce exceedingly high leakage losses to the high-order modes, while maintaining a low loss to the fundamental mode. Numerical results are presented for power-law index profiles.     

Some observations on the accumulation potential in adsorptive stripping voltammetry

A newly named parameter, “initial scan potential”, the potential from which the voltammetric scan starts rather than the widely accepted accumulation potential, has been found to be responsible for some of the important features of voltammograms obtained in the adsorptive stripping voltammetry (AdSV) of some organochlorine compounds (DDT, Dieldrin, 2,4- dichlorophenoxyacetic acid, 2,4,5-trichlorophenoxyacetic acid). The experimental evidence reported strongly confirms the nonfaradaic nature of the preconcentration step in adsorptive stripping voltammetry.     

Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures

Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of layering as optimization decomposition, where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how layering as Optimization Decomposition provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures