Pure Gaussian Distributions Research Articles

Single- and multi-photon-induced ultraviolet excitation and photodissociation of CH3I probed by coincident ion momentum imaging.

The UV-induced photodissociation dynamics of iodomethane (CH3I) in its A-band are investigated by time-resolved coincident ion momentum imaging using strong-field ionization as a probe. The delay-dependent kinetic energy distribution of the photofragments resulting from double ionization of the molecule maps the cleavage of the carbon-iodine bond and shows how the existence of a potential well in the di-cationic potential energy surfaces shapes the observed distribution at small pump-probe delays. Furthermore, the competition between single- and multi-photon excitation and ionization of the molecule is studied as a function of the intensity of the UV-pump laser pulse. Two-photon excitation to Rydberg states is identified by tracking the transformation of the delay-dependent singly-charged iodomethane yield from a pure Gaussian distribution at low intensity to a Gaussian with an exponentially decaying tail at higher intensities. Dissociative ionization induced by absorption of three UV photons is resolved as an additional delay-dependent feature in the kinetic energy of the fragment ions detected in coincidence.

A comprehensive analysis of a TE11 to HE11 mode converter for an oversized F-band corrugated waveguide

We have investigated the mode transition behavior from approximately half- to quarter-wavelength in typical F-band (90–140 GHz) TE11 to HE11 converters of varying corrugation depths. Simulations in which the number of slots in the corrugation is varied indicate that the optimal number of slots should be greater than two, which is in excellent agreement with the experimental results. The mode content was also analyzed with and without a quarter-wavelength depth-corrugated tapered section. The electric field pattern at the exit of a quarter-wavelength tapered transition connected to a half-wavelength to quarter-wavelength TE11 to HE11 mode converter is compared with that without a converter. Electric field patterns both with and without a half- to quarter-wavelength TE11 to HE11 mode converter show a highly Gaussian field pattern with less than 35 dB of cross-polarization. Simulated field patterns are in good agreement with the experimentally measured field patterns, with the measured and simulated electric field distributions matching approximately 96.5 and 97.5%, respectively, to a pure Gaussian distribution.

Approximations of impulse response curves based on the generalized moving Gaussian distribution function

We derive approximations (in time) for impulse response curves not based on the Gaussian distribution (like the well-known Edgeworth expansions), but based on other suitable distribution functions. In general, we derive the full expansion for such an approximation based on an approximative function, the derivatives and the cumulants of this approximative function and on the cumulants of the impulse response curve itself, see formula (39). Suitable distribution functions exhibit a skewed profile which offers better opportunities for approximations of typical impulse response curves than approximations based on the symmetrical Gaussian distribution. As an example of such a suitable approximative distribution function we study more in detail the Generalized Moving Gaussian distribution Z t = 1 M 0 t ν exp − α t − β / t 2 , 0 < t < ∞ , α > 0 , β > 0 , − ∞ < ν < ∞ , with the normalization M 0 = 2 β α ν + 1 / 2 exp 2 α β K ν + 1 2 α β . A common feature in convection–diffusion problems is that the Laplace transform of an impulse response curve can be described by a single exponential as a( s) exp ( xb( s)). We characterize the first four cumulants in terms of the Taylor coefficients of the functions a( s) and b( s). Moreover, it is shown that the temporal cumulants are linear in the spatial variable. This material is applied to several examples and it is shown that the proposed approximative Generalized Moving Gaussian distributions for impulse responses in the field of convection–diffusion type cases perform in general better than the expansions based on the pure Gaussian distribution. Based on this type of approximation other properties based on the original impulse response curve can be found along analytical ways.

Intracavity coherent addition of 16 laser distributions

The efficient intracavity coherent addition of 16 separate laser Gaussian mode distributions is presented. The coherent addition is achieved in a multichannel pulsed Nd:YAG laser resonator by use of four intracavity interferometric beam combiners. The results reveal 88% combining efficiency with a combined output beam of nearly pure Gaussian distribution.

Deconvolution of seismic data using adaptive Gaussian mixtures

Based on a Gaussian mixture model for the reflectivity sequence, the authors present a new technique for blind deconvolution of seismic data. The method obtains a deconvolution filter that maximizes at its output a measure of the relative entropy between the proposed Gaussian mixture and a pure Gaussian distribution. A new updating procedure for the mixture parameters is included in the algorithm: it allows one to apply the algorithm without any prior knowledge about the signal and noise. A simulation example illustrates the performance of the proposed method.

The analysis of ensembles of moderately saturated interstellar lines

It is shown that the combined equivalent widths for a large population of Gaussian-like interstellar line components, each with different central optical depths tau(0) and velocity dispersions b, exhibit a curve of growth (COG) which closely mimics that of a single, pure Gaussian distribution in velocity. Two parametric distributions functions for the line populations are considered: a bivariate Gaussian for tau(0) and b and a power law distribution for tau(0) combined with a Gaussian dispersion for b. First, COGs for populations having an extremely large number of nonoverlapping components are derived, and the implications are shown by focusing on the doublet-ratio analysis for a pair of lines whose f-values differ by a factor of two. The consequences of having, instead of an almost infinite number of lines, a relatively small collection of components added together for each member of a doublet are examined. The theory of how the equivalent widths grow for populations of overlapping Gaussian profiles is developed. Examples of the composite COG analysis applied to existing collections of high-resolution interstellar line data are presented.

Analysis of Hollow-Cathode-Discharge-Excited Ar i, Ar ii, and Au i Spectral-Line Profiles Measured with a Fabry–Perot Interferometer*

Spectral profiles of Au i, Ar i, and Ar ii lines obtained with a scanning Fabry–Perot spectrometer from a low-current, 3.2-mm-diam Au hollow-cathode discharge in ~6 torr of Ar are fitted with Voigt functions to determine the apparent lorentzian half-widths, ΔLs, and apparent Doppler temperatures, Ts, as functions of the discharge current. Ts values of the Au i 4792-A line are approximately equal to those of the Ar i lines, whereas for the Au i 3123-A line, the Ts values are much greater. Arguments are presented to show that these high Ts values result from the high initial ejection energy of the sputtered atoms and the short lifetime of the upper state. Typically, Ts = 1010, 1180, and 1760 K for the Ar i 4511, Au i 4792, and Au i 3123-A lines, respectively. The Ts values of the Ar ii doublet-state lines equal those of the Ar i lines, whereas for the Ar ii quartet-state lines, the Ts values are significantly lower. The ΔLs values of the Ar i lines, whose transitions terminate on resonance states, are predicted by resonance-broadening theory. The ΔLs values of the Ar ii lines range from 0.010 to 0.031 cm−1 and far exceed the calculated resonance- and Stark-broadening terms. A proposed model of the Ar ii spectral-line profile consists of a superposition of two pure gaussian distributions, which represent one group of high-energy ions accelerated by axial electric fields in an electrical double layer (DL) at the end of the cathode, and a second group in equilibrium with Ar atoms. The sum closely approximates a Voigt function whose analysis yields apparent values, ΔLc and Tc, which equal the corresponding observed quantities. The ΔLs values are found to vary with discharge conditions, presumably depending upon the completion of the DL formation.