Large Frequency Interval Research Articles

A femtosecond self-mode-locked Ti:sapphire laser with high stability of pulse-repetition frequency and its applications

The spectral characteristics and stability of a frequency of intermode beats of a fs self-mode-locked Ti:sapphire laser are investigated. An active method is used to obtain high stability. The frequency stability of intermode beats not lower than 1.27×10−12 rms in 50 s is achieved. Possible applications of the setup, such as measurement of large frequency intervals in the optical range, creation of optical frequency synthesizers, etc., are proposed. The physical principles for the creation of an optical clock of a new type using a highly stable fs Ti:sapphire laser are considered.

Combined Finite Element Analysis and Statistical Energy Analysis in Mechanical Intensity Calculations

Local and global energy e ow in structures built up by domains with different rigidities is studied. A combined e niteelementanalysis/statistical energy analysis (FEA/SEA)approach isadvanced wherestifferdomains (with low modal density ) are analyzed using FEA and weaker domains (with high modal density ) are analyzed using SEA. The approach proposed employs an energy-based iterative optimization procedure where the difference between externally supplied active power and the total power dissipated in the structure is minimized. Sectional forces in points connecting the stiff and weak domains are used as design variables. Dynamic substructuring is introduced to reduce the number of degrees of freedom in the e nite element domain during the optimization procedure. The potential to cover a large frequency interval is demonstrated in a numerical example in which the harmonic response of a truck is studied. Nomenclature As = source subsystem area C = damping matrix cg = group wave speed ci = mechanical intensity in direction i D(x ) = dynamic stiffness matrix E = Young’ s modulus Eor{E} = subsystem modal energy vector Ei = average total subsystem i energy F = force vector I = unity matrix

Combined finite element analysis and statistical energy analysis in mechanical intensity calculations

Local and global energy flow in structures built up by domains with different rigidities is studied. A combined finite element analysis/statistical energy analysis (FEA/SEA) approach is advanced where stiffer domains (with low modal density) are analyzed using FEA and weaker domains (with high modal density) are analyzed using SEA. The approach proposed employs an energy-based iterative optimization procedure where the difference between externally supplied active power and the total power dissipated in the structure is minimized. Sectional forces in points connecting the stiff and weak domains are used as design variables. Dynamic substructuring is introduced to reduce the number of degrees of freedom in the finite element domain during the optimization procedure. The potential to cover a large frequency interval is demonstrated in a numerical example in which the harmonic response of a truck is studied.

Efficient wide-band evaluation of mobile communications antennas using [Z] or [Y] matrix interpolation with the method of moments

The development of novel antennas for mobile communications often relies on performance simulations. The evaluation of the antenna surface currents for many frequencies using the method of moments (MoM) can take a long time since the impedance matrix must be computed for each new frequency. This paper investigates and compares two efficient methods for the computation of the broad-band performance of mobile communications antennas using frequency interpolation of either the MoM impedance matrix [Z] or admittance matrix [Y]. In either method, the elements of only a few matrices at relatively large frequency intervals are directly computed. These matrices are then used to interpolate the elements of the respective [Z] or [Y] matrices at the intermediate frequencies. Both methods reduce the time it takes to compute the antenna performance over a wide frequency band. The implementation of each method to evaluate the performance of several different antennas used for mobile communications is discussed. Examples with both frequency-domain and time-domain results are presented and both near-field and far-field quantities are considered. The accuracy, the simulation run times, and the computational requirements of direct MoM, [Z] matrix interpolation, and [Y] matrix interpolation are compared.

Acoustic nonlinearities in earth solids

Nonlinear elastic response in earth solids is a robust and representative physical characteristic. In this lecture the evidence leading to this conclusion is presented by providing an overview of theoretical and experimental developments in the domain. Illustrated measurements include those of nonlinear response in rock from a variety of dynamical wave experiments. The evidence leads to a pattern of unifying behavior. Nonlinear elasticity in earth solids is large relative to most materials; hysteresis and ‘‘discrete’’ memory play an important role in nonlinear properties of earth solids; nonlinear response is evident over a large frequency interval (dc to several MHz at least); and nonlinear response is significant, as is commonly appreciated, at large static and dynamic strain levels, but also at small strains where this behavior and the manifestations of this behavior are commonly disregarded. Recently, the methodology for extracting the nonlinear coefficients for a material have been proposed. Some theoretical models of structural nonlinearity of solid media and of wave propagation in such media are also described.

Manifestation of nonlinear elasticity in rock: convincing evidence over large frequency and strain intervals from laboratory studies

Abstract. Nonlinear elastic response in rock is established as a robust and representative characteristic rock rather than a curiosity. We show measurements of this behaviour from a variety of experiments on rock taken over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behaviour in rock: (1) Nonlinear response in rock is ubiquitous. (2) The response takes place over a large frequency interval (dc to 105 kHz at least). (3) The response not only occurs, as is commonly appreciated, large strains but also at small strains where this behaviour and the manifestations of this behaviour are commonly disregarded.

Manifestation of nonlinear elasticity in rock: Convincing evidence over large frequency and strain intervals from laboratory studies

Nonlinear elastic response in rock is established as a robust and representative characteristic of rock rather than a curiosity. This behavior is illustrated from a variety of experiments conducted over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behavior in rock: (1) Nonlinear response in rock is enormous; (2) the response takes place over a large frequency interval (dc–106 Hz at least); (3) the response not only occurs, as is commonly appreciated, at large strains but also at small strains where nonlinear response and the manifestations of this behavior are commonly disregarded. Nonlinear response may manifest itself in a variety of manners, including a nonlinear stress−strain relation (hysteretic/discrete memory), nonlinear dissipation, harmonic generation, and resonant peak shift, all of which are related. The experiments described include: quasistatic stress−strain tests (strains of 10-4–10-1 at frequencies near dc-1Hz); torsional oscillator experiments (strains of 10−4–10−7, frequencies between 0.1 and 100Hz); resonant bar experiments (strains of 10−4–10−8, frequencies between 103 and 104 Hz); and dynamic, propagating wave experiments (strains of 10−6–10−9, frequencies between 103 and 106 Hz). [Work supported by OBES/DOE through the University of California and the Institut Français du Pétrole.]

Acoustic waves in bubbly liquids: (1) Can strong localization of waves be attained by internal resonances? (2) Acoustic wave propagation in one-dimensional stratified gas–liquid media: The different regimes

An inhomogeneous medium with scatterers presenting internalresonances has been suggested to be an efficient system to localize classical waves. Within a mean-field approach describing the internal degrees of freedom of the scatterers and their strong interactions in the near field regime, the existence of two longitudinal modes associated with the scatterers and embedding medium degrees of freedom is found. Anderson localization is shown to be reached in a rather large frequency interval for the ‘‘slow’’ mode, above the single scatterer resonant frequency, whereas the ‘‘fast’’ mode is never localized. An experimental situation is discussed where the localization of the ‘‘slow’’ mode could be observed. This work appeared in J. Phys. I France 2, 1861–1867 (1992). Also considered is the problem of the propagation of acoustic waves in a one-dimensional bubbly liquid, either periodic or random. The response of the bubbly liquid to an incident wave in any range of concentrations, bubble size polydispersity, and frequency range has been computed exactly. Three main regimes are found, depending on the average value of the bubble radius R, average distance d between bubbles, and wavelength λ in the liquid: (1) ‘‘phonon’’ or ‘‘mass-spring’’ regime; (2) ‘‘bubble’’ regime; and (3) ‘‘stratified’’ regime. In the random systems, the Anderson localization length is computed both numerically and analytically in the limit of uncorrelated disorder, for various system realizations.

Can strong localization of waves be attained by internal resonances ?

An inhomogeneous medium with scatterers presenting internal resonances has been suggested to be an efficient system to localize classical waves. Within a mean-field approasch describing the internal degrees of freedom of the scatterers and their strong interactions in the near field regime, we find the existence of two longitudinal modes associated with the scatterers and embedding medium degrees of freedom.Anderson localization is shown to be reached in a rather large frequency interval for the «slow»mode,above the single scatterer resonant frequency,whereas the «fast»mode is never localized.We discuss an experimental situation where the localization of the «slow»mode could be observed.

Neutron-spectroscopy measurement of a fracton density of states.

Inelastic neutron scattering, combined with Brillouin and elastic small-angle neutron scattering, were used to test universality in the spectral dimension d\ifmmode \tilde{}\else \~{}\fi{}. The fracton density of states, obtained here on a new fractal silica aerogel and over a large frequency interval, now gives d\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\simeq}1.8. This suggests that d\ifmmode \tilde{}\else \~{}\fi{} is a sensitive function of the fractal structure.

Generation of wide-band data from the method of moments by interpolating the impedance matrix (EM problems)

The method of moments (MM) requires computation of the impedance matrix at each frequency. Since the computation can be a very time-consuming process, its performance over a wide frequency range can require a prohibitive amount of CPU time. A method is described whereby the impedance matrix is computed at relatively large frequency intervals and then interpolated to approximate its values at intermediate frequencies. Basically, the method trades reduced computer CPU time for increased storage. >

Two-Photon Spectroscopy with an FM Laser

Two-photon excitation of gas atoms by two counter-propagating frequency modulated laser beams is investigated with the help of second order perturbation theory. Simple spectra nearly free of Doppler broadening can be obtained from a region of the sample where the sum frequency of the two beams is constant. The comb of equally spaced laser modes can thus be locked to a resonant two-photon transition, providing calibration markers for the measurement of large optical frequency intervals.

Intermode calibration of diode-laser spectra using tandem étalons

The paper deals with an approach which can improve the accuracy of etalon calibration of tunable diode-laser (TDL) spectra in the IR and extend absolute calibration among several isolated modes. Two etalons placed in the laser beam produce a combined fringe pattern that, with the aid of a monochromator mode selector, can be used to establish the number of fringes between any two spectral points separated by a large frequency interval. This technique has been applied to several similar cases for calibration of isolated modes or verification of the identity of lines of known frequency.

A subpicosecond dye laser directly pumped by a mode-locked argon laser

We report on a mode-locked cw dye laser which reliably produces light pulses as short as 850 fsec. Short-pulse operation depends critically on the stability and spectral purity of a frequency synthesizer which generates the radio-frequency signal for the acousto-optic mode locker of the argon pump laser. The regular axial mode spectrum of the dye laser extends over 500 GHz and can provide an accurate calibration scale for the spectroscopic measurement of large frequency intervals. The high stability of the locked modes has been demonstrated by observing Doppler-free multiple-pulse two-photon spectra of the sodium 3S-5S transition linewidths as narrow as 4MHz.

High-Resolution Two-Photon Spectroscopy with Picosecond Light Pulses

We have demonstrated the feasibility of Doppler-free two-photon spectroscopy with a train of picosecond standing-wave light pulses from a synchronously pumped mode-locked cw dye laser. The actively controlled mode spectrum provides a means for accurate measurements of large frequency intervals. From a multipulse spectrum of the sodium $3s\ensuremath{-}4d$ transition we have determined a new value of the $4d$ fine-structure splitting, 1028\ifmmode\pm\else\textpm\fi{}0.4 MHz.

Determination of Strengths and Widths for Non-Lorentzian Lines

A new expression for semi-empirical non-Lorentzian line shape has been obtained. The absorptances in NH 3 –H 2 , HCl–CO 2 and NO–NO collisions are better represented by a line shape varying as |ν-ν 0 | -η with η=1.6 at frequencies greater than ∼1 cm -1 from the line center. For CO 2 lines, however, the Lorentzian shape seems to be valid within a large frequency interval from the line center. A method for determining the strengths and widths of non-Lorentzian lines from the equivalent width data is discussed. This method has been applied to the rotational lines of CO.