Comparison of uniform amplitude beam and intercepted Gaussian beam superresolution theories

The general superresolution theories for uniform amplitude beams and intercepted Gaussian beams are investigated. For these two types of incident beam, both two-zone amplitude and pure-phase filters are adopted to provide specific numerical descriptions of their differences in superresolution performances. Simulated results of comparisons between their performances indicate that, with the same spot size ratio, the intercepted Gaussian beam achieves a higher central image brightness ratio and significantly lower side-lobe effect irrespective of the filter used. (c) 2008 Elsevier Ltd. All rights reserved.

Non-rotating beams isospectral to a given rotating uniform beam

In this paper, we seek to find non-rotating beams with continuous mass and flexural stiffness distributions, that are isospectral to a given uniform rotating beam. The Barcilon-Gottlieb transformation is used to convert the fourth order governing equation of a non-rotating beam, to a canonical fourth order eigenvalue problem. If the coefficients in this canonical equation match with the coefficients of the uniform rotating beam equation, then the non-rotating beam is isospectral to the given rotating beam. The conditions on matching the coefficients leads to a pair of coupled differential equations. We solve these coupled differential equations for a particular case, and thereby obtain a class of non-rotating beams that are isospectral to a uniform rotating beam. However, to obtain isospectral beams, the transformation must leave the boundary conditions invariant. We show that the clamped end boundary condition is always invariant, and for the free end boundary condition to be invariant, we impose certain conditions on the beam characteristics. We also verify numerically that the frequencies of the non-rotating beam obtained using the finite element method (FEM) are the exact frequencies of the uniform rotating beam. Finally, the example of beams having a rectangular cross-section is presented to show the application of our analysis. Since experimental determination of rotating beam frequencies is a difficult task, experiments can be easily conducted on these rectangular non-rotating beams, to calculate the frequencies of the rotating beam. (c) 2012 Elsevier Ltd. All rights reserved.

Design and analysis of ARROW-based racetrack resonator vibration sensor for inertial navigation application

In this paper we propose and analyze a novel racetrack resonator based vibration sensor for inertial grade application. The resonator is formed with an Anti Resonance Reflecting Optical Waveguide (ARROW) structure which offers the advantage of low loss and single mode propagation. The waveguide is designed to operate at 1310nm and TM mode of propagation since the Photo-elastic co-efficient is larger than TE mode in a SiO2/ Si3N4/ SiO2. The longer side of the resonator is placed over a cantilever beam with a proof mass. A single bus waveguide is coupled to the resonator structure. When the beam vibrates the resonator arm at the foot of the cantilever experiences maximum stress. Due to opto-mechanical coupling the effective refractive index of the resonator changes hence the resonance wavelength shifts. The non uniform cantilever beam has a dimension of 1.75mm X 0.45mm X 0.020mm and the proof mass has a dimension of 3mm X 3mm X 0.380mm. The proof mass lowers the natural frequency of vibration to 410Hz, hence designed for inertial navigation application. The operating band of frequency is from DC to 100Hz and acceleration of less than 1g. The resonator has a Free Spectral Range (FSR) of 893pm and produces a phase change of 22.4mrad/g.

Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

Determination of Isospectral Nonuniform Rotating Beams

In this paper we look for nonuniform rotating beams that are isospectral to a given uniform nonrotating beam. A rotating nonuniform beam is isospectral to the given uniform nonrotating beam if both the beams have the same spectral properties, i.e., both the beams have the same set of natural frequencies under a given boundary condition. The Barcilon-Gottlieb type transformation is proposed that converts the governing equation of a rotating beam to that of a uniform nonrotating beam. We show that there exist rotating beams isospectral to a given uniform nonrotating beam under some special conditions. The boundary conditions we consider are clamped-free and hinged-free with an elastic hinge spring. An upper bound on the rotation speed for which isospectral beams exist is proposed. The mass and stiffness distributions for these nonuniform rotating beams which are isospectral to the given uniform nonrotating beam are obtained. We use these mass and stiffness distributions in a finite element analysis to show that the obtained beams are isospectral to the given uniform nonrotating beam. A numerical example of a beam having a rectangular cross section is presented to show the application of our analysis. DOI: 10.1115/1.4006460]

The steady-state response of multidegree-of-freedom systems with a spatially localized nonlinearity

This thesis is concerned with the dynamic response of a General multidegree-of-freedom linear system with a one dimensional nonlinear constraint attached between two points. The nonlinear constraint is assumed to consist of rate-independent conservative and hysteretic nonlinearities and may contain a viscous dissipation element. The dynamic equations for general spatial and temporal load distributions are derived for both continuous and discrete systems. The method of equivalent linearization is used to develop equations which govern the approximate steady-state response to generally distributed loads with harmonic time dependence.

The qualitative response behavior of a class of undamped chainlike structures with a nonlinear terminal constraint is investigated. It is shown that the hardening or softening behavior of every resonance curve is similar and is determined by the properties of the constraint. Also examined are the number and location of resonance curves, the boundedness of the forced response, the loci of response extrema, and other characteristics of the response. Particular consideration is given to the dependence of the response characteristics on the properties of the linear system, the nonlinear constraint, and the load distribution.

Numerical examples of the approximate steady-state response of three structural systems are presented. These examples illustrate the application of the formulation and qualitative theory. It is shown that disconnected response curves and response curves which cross are obtained for base excitation of a uniform shear beam with a cubic spring foundation. Disconnected response curves are also obtained for the steady-state response to a concentrated load of a chainlike structure with a hardening hysteretic constraint. The accuracy of the approximate response curves is investigated.

On the Hartman-Grobman Theorem with Parameters

The Hartman-Grobman Theorem of linearization is extended to families of dynamical systems in a Banach space X, depending continuously on parameters. We prove that the conjugacy also changes continuously. The cases of nonlinear maps and flows are considered, and both in global and local versions, but global in the parameters. To use a special version of the Banach-Caccioppoli Theorem we introduce equivalent norms on X depending on the parameters. The functional setting is suitable for applications to some nonlinear evolution partial differential equations like the nonlinear beam equation.

Collimation of deuterium / 3-helium fusion products for advanced spacecraft propulsion and power

Current space exploration has transpired through the use of chemical rockets, and they have served us well, but they have their limitations. Exploration of the outer solar system, Jupiter and beyond will most likely require a new generation of propulsion system. One potential technology class to provide spacecraft propulsion and power systems involve thermonuclear fusion plasma systems. In this class it is well accepted that d-He3 fusion is the most promising of the fuel candidates for spacecraft applications as the 14.7 MeV protons carry up to 80% of the total fusion power while ‘s have energies less than 4 MeV. The other minor fusion products from secondary d-d reactions consisting of 3He, n, p, and 3H also have energies less than 4 MeV. Furthermore there are two main fusion subsets namely, Magnetic Confinement Fusion devices and Inertial Electrostatic Confinement (or IEC) Fusion devices. Magnetic Confinement Fusion devices are characterized by complex geometries and prohibitive structural mass compromising spacecraft use at this stage of exploration. While generating energy from a lightweight and reliable fusion source is important, another critical issue is harnessing this energy into usable power and/or propulsion. IEC fusion is a method of fusion plasma confinement that uses a series of biased electrodes that accelerate a uniform spherical beam of ions into a hollow cathode typically comprised of a gridded structure with high transparency. The inertia of the imploding ion beam compresses the ions at the center of the cathode increasing the density to the point where fusion occurs. Since the velocity distributions of fusion particles in an IEC are essentially isotropic and carry no net momentum, a means of redirecting the velocity of the particles is necessary to efficiently extract energy and provide power or create thrust. There are classes of advanced fuel fusion reactions where direct-energy conversion based on electrostatically-biased collector plates is impossible due to potential limits, material structure limitations, and IEC geometry. Thermal conversion systems are also inefficient for this application. A method of converting the isotropic IEC into a collimated flow of fusion products solves these issues and allows direct energy conversion. An efficient traveling wave direct energy converter has been proposed and studied by Momota , Shu and further studied by evaluated with numerical simulations by Ishikawa and others. One of the conventional methods of collimating charged particles is to surround the particle source with an applied magnetic channel. Charged particles are trapped and move along the lines of flux. By introducing expanding lines of force gradually along the magnetic channel, the velocity component perpendicular to the lines of force is transferred to the parallel one. However, efficient operation of the IEC requires a null magnetic field at the core of the device. In order to achieve this, Momota and Miley have proposed a pair of magnetic coils anti-parallel to the magnetic channel creating a null hexapole magnetic field region necessary for the IEC fusion core. Numerically, collimation of 300 eV electrons without a stabilization coil was demonstrated to approach 95% at a profile corresponding to Vsolenoid = 20.0V, Ifloating = 2.78A, Isolenoid = 4.05A while collimation of electrons with stabilization coil present was demonstrated to reach 69% at a profile corresponding to Vsolenoid = 7.0V, Istab = 1.1A, Ifloating = 1.1A, Isolenoid = 1.45A. Experimentally, collimation of electrons with stabilization coil present was demonstrated experimentally to be 35% at 100 eV and reach a peak of 39.6% at 50eV with a profile corresponding to Vsolenoid = 7.0V, Istab = 1.1A, Ifloating = 1.1A, Isolenoid = 1.45A and collimation of 300 eV electrons without a stabilization coil was demonstrated to approach 49% at a profile corresponding to Vsolenoid = 20.0V, Ifloating = 2.78A, Isolenoid = 4.05A 6.4% of the 300eV electrons’ initial velocity is directed to the collector plates. The remaining electrons are trapped by the collimator’s magnetic field. These particles oscillate around the null field region several hundred times and eventually escape to the collector plates. At a solenoid voltage profile of 7 Volts, 100 eV electrons are collimated with wall and perpendicular component losses of 31%. Increasing the electron energy beyond 100 eV increases the wall losses by 25% at 300 eV. Ultimately it was determined that a field strength deriving from 9.5 MAT/m would be required to collimate 14.7 MeV fusion protons from d-3He fueled IEC fusion core. The concept of the proton collimator has been proven to be effective to transform an isotropic source into a collimated flow of particles ripe for direct energy conversion.

Dependence of residual amplitude noise in electro-optic phase modulators on the intensity distribution of the incident field

Our results demonstrate that photorefractive residual amplitude modulation (RAM) noise in electro-optic modulators (EOMs) can be reduced by modifying the incident beam intensity distribution. Here we report an order of magnitude reduction in RAM when beams with uniform intensity (flat-top) profiles, generated with an LCOS-SLM, are used instead of the usual fundamental Gaussian mode (TEM00). RAM arises from the photorefractive amplified scatter noise off the defects and impurities within the crystal. A reduction in RAM is observed with increasing intensity uniformity (flatness), which is attributed to a reduction in space charge field on the beam axis. The level of RAM reduction that can be achieved is physically limited by clipping at EOM apertures, with the observed results agreeing well with a simple model. These results are particularly important in applications where the reduction of residual amplitude modulation to 10^-6 is essential.

A uniform 290 nm periodic square structure on ZnO fabricated by two-beam femtosecond laser ablation

A uniform submicron periodic square structure was fabricated on the surface of ZnO by a technique of two linearly polarized femtosecond laser beams with orthogonal polarizations ablating material alternately. The formed two-dimensional ordering submicron structure consists of close-packed submicron squares with a spacial periodicity of 290 nm, which arises from the intercrossing of two orthogonal submicron ripple structures induced by the two beams respectively. The result demonstrates a noninterference effect of two-beam ablation based on the alternate technique, which should come from the polarization-dependent enhancement of the subwavelength ripple structure and the large interval of two alternate pulses. This two-beam alternate ablation technique is expected to open up prospects for the submicron fabrication of wide-bandgap materials.

Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.