We report the observation of unidirectional plasmon propagation in metallic nanowires over distances >10 μm. Through control of the incident excitation wavelength and rod composition, we demonstrate the selective coupling of photons into the plasmon mode of a 20 nm diameter nanowire. This mode then propagates in a nonemissive fashion down the wire length before being emitted as an elastically scattered photon at the distal end. As expected from previous studies of plasmon excitation in nanoparticles and thin films, we observe a strong wavelength and material dependence of this phenomenon. This metal-dependent plasmon propagation is exploited to produce a wire through which plasmons propagate unidirectionally. A bimetallic wire with a sharp Au/Ag heterojunction is shown to display both wavelength dependence and unidirectionality with respect to plasmon propagation across the heterojunction. It is expected that these results will contribute to the growing interest in optical energy transport in molecular-le...

Unidirectional Plasmon Propagation in Metallic Nanowires

Neural networks

The Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples.

Numerical solution of fractional differential equations using the generalized block pulse operational matrix

The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.

A new set of orthogonal functions and its application to the analysis of dynamic systems

Solving nonlinear mixed Volterra-Fredholm integral equations with two dimensional block-pulse functions using direct method

It is established that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983). The superiority is mainly due to the most elemental nature of BPFs in comparison to any other PCBF function. It is also proved that the operational matrix for integration in the BPF domain is connected to the integration operational matrix in the DUSF domain by simple linear transformation involving invertible Toeplitz matrices. The transformation appears to be transparent because the integration operational matrices are found to match exactly. The reason for such transparency is explained mathematically. Finally, Hwang claimed superiority of DUSFs compared to Walsh functions in obtaining the solution of functional differential equations using a stretch matrix in the DUSF domain. It is shown that the stretch matrices of Walsh and DUSF domains are also related by linear transformation and use of any of these two matrices leads to exactly the same result. This is supported by a...

Block pulse functions, the most fundamental of all piecewise constant basis functions

The present work searches for a suitable set of orthogonal functions for the analysis of control systems with sample-and-hold ( S/H ). The search starts with the applicability of the well known block pulse function (BPF) set and uses an operational technique by defining a block pulse operational transfer function ( BPOTF ) to analyse a few control systems. The results obtained are found to be fairly accurate. But this method failed to distinguish between an input sampled system and an error sampled system. To remove these limitations, another improved approach was followed using a sample-and-hold operational matrix, but it also failed to come up with accurate results. Further, the method needed a large number of component block pulse functions leading to a much larger amount of storage as well as computational time. To search for a more efficient technique, a new set of piecewise constant orthogonal functions, termed sample-and-hold functions (SHF), is introduced. The analysis, based upon a similar operational technique, in the SHF domain results in the same accuracy as the conventional z -transform analysis. Here, the input signal is expressed as a linear combination of sample-and-hold functions; the plant having a Laplace transfer function G(s) is represented by an equivalent sample-and-hold operational transfer function ( SHOTF ), and the output in the SHF domain is obtained by means of simple matrix multiplication. This technique is able to do away with the laborious algebraic manipulations associated with the z -transform technique without sacrificing accuracy. Also, the accuracy does not depend upon m and the presented method does not need any kind of inverse transformation. A few linear sample-and-hold SISO control systems, open loop as well as closed loop, are analysed as illustrative examples. The results are found to match exactly with the z -transform solutions. Finally, an error analysis has been carried out to estimate the upper bound of the mean integral squared error (m.i.s.e.) of the SHF approximation of a function f(t) of Lebesgue measure.

A new set of piecewise constant orthogonal functions for the analysis of linear siso systems with sample-and-hold

A modification to conventional block pulse functions (BPF) is proposed by describing a set of linearly pulse-width modulated block pulse functions (LPWM-BPF) that has been utilised to develop a generalised convolution matrix of operational nature. This matrix is used to determine convolution of time-varying functions and is also employed to solve linear feedback system identification problem. Also, a recursive technique for solving the identification problem in the conventional BPF domain has been derived. Numerical examples are treated to establish the validity of the proposal. The representational error analysis has also been carried out for the LPWM-BPF to show that this kind of BPF set introduces less error than the conventional equal-width BPF.

Linearly pulse-width modulated block pulse functions and their application to linear SISO feedback control system identification

The present work makes use of the block pulse domain operational matrix for differentiation D1(m) to find out an operational transfer function. Analysis of simple control systems using this Block Pulse Operational Transfer Function (BPOTF) shows that the results are not so accurate when compared with the direct expansion of the exact solution in the BPF domain. To remove this defect, one shot operational matrices for repeated integration (OSOMRI) are obtained and these matrices are used to develop a Modified Block Pulse Operational Transfer Function (MBPOTF) for linear SISO control system analysis in the block pulse function domain. A few linear SISO control systems are analysed using the developed MBPOTF s as illustrative examples. The results are found to match exactly with the direct BPF expansions of the exact solutions.

All-integrator approach to linear SISO control system analysis using block pulse functions (BPF)

A new capacitor array structure which is both energy and area efficient is presented for a 4 bit successive approximation register (SAR) analog-to-digital converter (ADC). The proposed circuit consumes zero energy in the second and third comparison cycles. Significant lowering of energy in the different charge redistribution steps is ensured by applying different voltages in the switching scheme of the various comparison cycles. Besides energy saving to the extent of 98%, a 75% reduction in capacitance is achieved compared to the conventional method.

Sunit K. Sen

Papers

Block pulse functions, the most fundamental of all piecewise constant basis functions

A new set of piecewise constant orthogonal functions for the analysis of linear siso systems with sample-and-hold

Linearly pulse-width modulated block pulse functions and their application to linear SISO feedback control system identification

All-integrator approach to linear SISO control system analysis using block pulse functions (BPF)

An energy and area efficient SC SAR ADC structure based on multi level capacitor switching technique