Acceleration of ultra-thin electron layer.Analytical treatment compared with 1D-PIC simulation

In this paper, we apply an analytical model [V.V. Kulagin et al., Phys. Plasmas 14, 113101 (2007)] to describe the acceleration of an ultra-thin electron layer by a schematic single-cycle laser pulse and compare with one-dimensional particle-in-cell (1D-PIC) simulations. This is in the context of creating a relativistic mirror for coherent backscattering and supplements two related papers in this EPJD volume. The model is shown to reproduce the 1D-PIC results almost quantitatively for the short time of a few laser periods sufficient for the backscattering of ultra-short probe pulses.

Approximate analytical description for fundamental-mode fields of graded-index fibers: Beyond the Gaussian approximation

An approximate analytical description for fundamental-mode fields of graded-index fibers is explicitly presented by use of the power-series expansion method, the maximum-value condition at the fiber axis, the decay properties of fundamental-mode fields at large distance from the fiber axis, and the approximate modal parameters U obtained from the Gaussian approximation. This analytical description is much more accurate than the Gaussian approximation and at the same time keep the simplicity of the latter. As two special examples, we present the approximate analytical formulas for the fundamental-mode fields of a step profile fiber and a Gaussian profile fiber, and we find that they are both highly accurate in the single-mode range by comparing them with the corresponding exact solutions.

The analytical description and experiments of the optical bottle generated by an axicon and a lens

Based on the interferential theory, we deduce a new type of analytic expression suitable for describing the evolutions of the optical bottle beam generated from the axicon-lens optical system illuminated by the Gaussian beam for the first time. The theory does not use much approximation in the process of mathematical analysis and can better illustrate the optical bottle beam evolutions at any positions. With the derived expression, the three-dimensional (3D) longitudinal and transverse intensity profiles of the optical bottle beam are simulated numerically. The numerical calculations have been confirmed by the experimental results.

Analytical vectorial structure of hollow Gaussian beams in the far field

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation. (c) 2008 Optical Society of America.

Analytical model of spin filtering effect and its experimental verification in a forward-biased iron-metal-Al2O3-n-type GaAs tunneling structure under optical spin orientation

An analytical model for the spin filtering transport in a ferromagnetic-metal - Al2O3 - n-type semiconductor tunneling structure has been developed, and demonstrated that the ratio of the helicity-modulated photo-response to the chopped one is proportional to the sum of the relative asymmetry in conductance of two opposite spin-polarized tunneling channels and the MCD effect of the ferromagnetic metal film. The performed measurement in an iron-metal/Al2O3/n-type GaAs tunneling structure under the optical spin orientation has verified that all the aspects of the experimental results are very well in accordance with our model in the regime of the spin filtering. After the MCD effect of the iron film is calibrated by an independent measurement, the physical quantity of Delta G(t)/G(t) (Delta G(t) = G(t)(up arrow) - G(t)(down arrow) is the difference of the conductance between two opposite spin tunneling channels, G(t) =( G(t)(up arrow) + G(t)(down arrow))/2 the averaged tunneling conductance), which concerns us most, can be determined quantitatively with a high sensitivity in the framework of our analytical model. Copyright (c) EPLA, 2008.

Analytical study of the layered XY model with VCE method

Motivated by experiments on liquid-crystal films, we study the development of specific heat anomaly of finite layer system. With the VCE method, we introduce the strong surface interaction into the layered XY model and get the results of the forth-order analytical expansion. The results show that when the strong surface interaction becomes strong enough, the order trend defeats the quantum noise and the specific heat peak moves abnormally to the high temperature with the number of layers decreasing.

Analytical study of the antiferromagnetic Heisenberg films

With the variational cumulant expansion (VCE) method, the thermodynamic behaviors of S = 1/2 antiferromagnetic Heisenberg films in simple cubic lattices are studied analytically. From the analytic properties of the free energy, in principle we are able to calculate analytically the critical temperatures T-c(L) and the thermodynamic functions, to any order cumulant as the functions of the number of L (the hyperlayers in the hyperfilm). Explicit expressions for T-c(L) up to the fourth order are given. A comparison with the existing results for 3-dimensional system is given. The effective range of the interaction is obtained from numerical results.

Evaluation of thermal radiation dependent performance of GaSb thermophotovoltaic cell based on an analytical absorption coefficient model

Applying the model dielectric function method, we have expressed the absorption coefficient of GaSb analytically at room temperature relating to the contribution of various critical points of its electronic band structure. The calculated absorption spectrum shows good agreement with the reported experimental data obtained by spectral ellipsometry on nominally undoped sample. Based on this analytical absorption spectrum, we have qualitatively evaluated the response of active absorbing layer structure and its photoelectric conversion properties of GaSb thermophotovoltaic device on the perturbation of external thermal radiation induced by the varying radiator temperature or emissivity. Our calculation has demonstrated that desirable thickness to achieve the maximum conversion efficiency should be decreased with the increment of radiator temperature and the performance degradation brought by any structure deviation from its optimal one would be stronger meanwhile. For the popular radiator temperature, no more than 1500 K in a real solar thermophotovoltaic system, and typical doping profile in GaSb cell, a reasonable absorbing layer structure parameter should be controlled within 100-300 nm for the emitter while 3000-5000 nm for the base.

Evaluating 0.53 eVGaInAsSbthermophotovoltaic diode based on an analytical absorption model

Radiant heat conversion performance dominated by the active layer of Ga0.84In0.16As0.14Sb0.86 diode has been systematically investigated based on an analytic absorption spectrum, which is suggested here by numerically fitting the limited experimental data. For the concerned diode configuration, our calculation demonstrates that the optimal base doping is 3-4 x 10(17) cm(-3), which is less sensitive to the variation of the external radiation spectrum. Given the scarcity of the alloy elements, an economical device configuration of the 0.2-0.6 mu m emitter and the 4-6 mu m base would be particularly acceptable because the corresponding conversion efficiency cannot exhibit discouraging degradation in comparison to the one for the optimal structure, the thickness of which may be up to 10 mu m. More importantly, the method we suggested here to calculate alloy absorption can be easily transferred to other composition, thus bringing great convenience for design or optimization of the optoelectronic device formed by these alloys.

A three-dimensional analytical solution of the microheater temperature before bubble nucleation

A three-dimensional analytical solution of the microheater temperature based on heat diffusion equation is developed and compared with experimental results. Dimensionless parameters are introduced to analyze the temperature rise time and the distribution under steady state. To study the microheater temperatures before bubble nucleation, a set of working fluids and microheaters are considered. It is shown that the dimensionless time xi(-)(0) required for the temperature rise from room to 95% of the steady state temperature is about 75, not dependent on working fluids and microheaters. Heat transfer to the surrounding liquid is mainly caused by conduction, not by convection and radiation mechanisms. The microheater length affects the surface temperature uniformity, while its width influences the steady temperatures significantly, yielding the transition from heterogeneous to homogeneous nucleation mechanism from square microheaters to narrow line microheaters. 

Density Gradient Ultracentrifugation of Nanotubes: Interplay of Bundling and Surfactants Encapsulation

Density gradient ultracentrifugation (DGU) has emerged as a promising tool to prepare chirality enriched nanotube samples. Here, we assess the performance of different surfactants for DGU. Bile salts (e.g., sodium cholate (SC), sodium deoxycholate (SDC), and sodium taurodeoxycholate (TDC)) are more effective in individualizing Single Wall Carbon Nanotubes (SWNTs) compared to linear chain surfactants (e.g., sodium dodecylbenzene sulfonate (SDBS) and sodium dodecylsulfate (SDS)) and better suited for DGU. Using SC, a narrower diameter distribution (0.69-0.81 nm) is achieved through a single DGU step on CoMoCAT tubes, when compared to SDC and TDC (0.69-0.89 nm). No selectivity is obtained using SDBS. due to its ineffectiveness in debundling. We assign the reduce selectivity of dihydroxy bile salts (S DC and TDC) in comparison with trihydroxy SC to the formation of secondary micelles. This is determined by the number and position of hydroxyl ( OH) groups on the a-side of the steroid backbone. We also enrich CoMoCAT SWNT in the 0.84-0.92 nm range using the Pluronic F98 triblock copolymer. Mixtures of bile salts (SC) and linear chain surfactants (SOS) are used to enrich metallic and semiconducting laser-ablation grown SWNTs. We demonstrate enrichment of a single chirality, (6,5), combining diameter and metallic versus semiconductillg separation on CoMoCAT samples.

Approximate analytical optical transfer function for a wavefront-coded imaging system with two-dimensional rectangularly separable phase masks

Wavefront coding can be used to extend the depth of field of incoherent imaging systems and is a powerful system-level technique. In order to assess the performance of a wavefront-coded imaging system, defocused optical transfer function (OTF) is the metric frequently used. Unfortunately, to the best of our knowledge, among all types of phase masks, it is usually difficult to obtain the analytical OTF except the cubic one. Although numerical computation seems good enough for performance evaluation, the approximate analytical OTF is still indispensable because it can reflect the relationship between mask parameters and system frequency response in a clearer way. Thus, a method is proposed to derive the approximate analytical OTF for two-dimensional rectangularly separable phase masks. The analytical results are well consistent with the direct numerical computations, but the proposed method can be accepted only from engineering point of view and needs rigorous proof in future. (c) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3485759]

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.