Rate Equation Theory Research Articles

Measurements of atomic sodium in flames by asynchronous optical sampling: theory and experiment

Asynchronous optical sampling (ASOPS) is a pump-probe method for the measurement of species concentrations in turbulent high-pressure flames. We show that rapid measurement of species number density can be achieved in a highly quenched environment by maintaining a constant beat frequency between the mode-locking frequencies of the pump and the probe lasers. A model for the ASOPS method based on rate equation theory for three- and four-level atoms is presented. A number of improvements are made to the basic ASOPS instrument, which result in a greatly enhanced signal-to-noise ratio. Atomic sodium is aspirated into an atmospheric pressure C(2)H(4)/O(2)/N(2) flame and detected with the ASOPS instrument. When excited-state lifetimes are fitted by using the ASOPS theory, a 3P((1/2),3/2) ? 3S((1/2)) quenching-rate coefficient of 1.72 x 10(9) s(-1) and a 3P(3/2) ? 3P((1/2)) doublet-mixing rate coefficient of 3.66 x 109 s(-1) are obtained, in excellent agreement with literature values. ASOPS signals obtained over a wide range of pump and probe beam powers validate the rate equation theory. Improvements are suggested to improve the signal-to-noise ratio, since the present results are limited to laminar flows.

A reassessment of standard rate equations for low facet reflectivity semiconductor lasers using traveling wave rate equations

A set of traveling wave equations, which are a simple extension of the common rate equations, is used to study the effect of longitudinal gain saturation in Fabry-Perot semiconductor lasers. Analytical solutions are derived which are valid for both low and high Q cavities. A comparison is made to a theory with no spatial dependence. The maximum longitudinal carrier density deviation from the threshold value under lasing conditions is calculated for arbitrary facet reflectivities. It is shown that this deviation leads to linear equations for the emitted output power when compared to a standard rate equation theory. Improved designs for semiconductor lasers are suggested from this analysis. >

J=1 to J=0 D2 conversion in solid D-T.

{ital J}=1 to {ital J}=0 molecular rotational time constants for {ital J}=1 D{sub 2} in solid D-T at 1.8 to 14 K have been obtained by analyzing the longitudinal relaxation times {ital T}{sub 1} of the tritons in the same sample. The inherent time constant in the electric quadrupole theory of {ital T}{sub 1} is a function of both the {ital J}=1 T{sub 2} and {ital J}=1 D{sub 2} concentrations. By subtracting out the {ital J}=1 T{sub 2} behavior as obtained from pure T{sub 2} samples, the {ital J}=1 to {ital J}=0 D{sub 2} time constants remain. From 10 to 14 K, the D{sub 2} time constants are longer than those for T{sub 2} at constant temperature by the ratio of the nuclear magnetic moments. From 1.8 to 5.3 K, the two time constants are identical at about 5 h. A time-constant minimum occurs at about 10 K for both hydrogens. A rate-equation theory of rotational catalysis by free hydrogen atoms created by the tritium radioactivity is presented.

Atoms in coherent and incoherent fields: I. Microscopic theory of Einstein's rate equation

A fundamental investigation of the problem of an incoherently driven two-level atom is presented. In the case of a black body (thermal) broad band field the Einstein radiation rate equation is derived once a statistical decorrelation between matter and field variables is made. This is also shown to be true for N #62; 1 independent (non-cooperative) atoms. The normalised second order correlation function g (2)(0) = 2 for N ⪢ 1, characterising the chaotic nature of the scattered field. We also investigate the hierarchy of approximations to the rate equation. To first order in the coupling constant e 2 ( e is the electron charge) a generalised (correlated) rate equation, for a single atom, is derived. The statistical correlation of field and matter has its effect on the atomic saturation as well as on the scattered radiation where g (2)(∞) #62; 1 (partial coherence) compared with full coherent radiation, g (2)(∞) = 1, in the decorrelated case.

Tribological properties of unidirectional polyphenylene sulfide-carbon fiber laminate composites

The effect of carbon fiber orientation on the friction-wear properties of uniaxial polyphenylene sulfide matrix-carbon fiber composites has been investigated by means of mechanical wear testing, microscopy and phenomenological models. Qualitative conclusions have been reached to explain the experimental findings, utilizing a semiempirical wear rate equation and mechanomolecular friction theory.

Large-amplitude fluctuations due to longitudinal mode coupling in diode-pumped intracavity-doubled Nd:YAG lasers

The output of a laser-diode-pumped Nd:YAG laser with an intravcavity-doubling crystal exhibits large-amplitude fluctuations and longitudinal-mode instabilities. The results of an experimental and theoretical investigation of these instabilities are described. The instabilities arise from coupling of the longitudinal modes of the laser oscillator by sum-frequency generation in the nonlinear crystal. A rate-equation theory of a multilongitudinal-mode laser oscillator with an intracavity-doubling crystal is presented that includes terms modeling the sum-frequency and frequency-doubling processes.

Bistability and passive Q-switching of a CO2 laser with saturable absorber

The coexistence of bistability and repetitive passive Q-switching of a CO2 laser with a gaseous saturable absorber has been investigated experimentally. With CH3F as the saturable absorber bistability has been observed simultaneously with passive Q-switching, whereas with CH3OH either one of these phenomena can only exist, as demonstrated for the first time. The measured features of both systems can be explained qualitatively by rate-equation theory.

Analysis of AC and DC hopping conductivity in impurity bands and amorphous semiconductors

The extended pair approximation is used to compare the predictions of the Miller-Abrahams rate equation theory (1960) for AC and DC hopping conductivity with experiment. For an analysis of impurity conduction the authors consider data for n-type silicon and gallium arsenide. In both cases the theory accurately predicts the DC conductivity when reasonable assumptions concerning the density of states are made. In the AC regime the theory provides a good description of the data on silicon but in the case of the gallium arsenide data the theory predicts an onset of AC behaviour at a frequency about six orders of magnitude higher than that observed. Data for amorphous germanium are also analysed. The theory fits the DC conductivity which follows a T-1/4 law, with a characteristic frequency R0, of 1021 Hz. The AC conductivity is qualitatively in agreement but the onset of AC behaviour is two orders of magnitude higher in frequency than is observed.

Operating characterics of an optically pumped waveguide fir laser

We report measurements of the effect of resonator length changes, 13CO 2 laser frequency and 13CO 2 laser intensity on the FIR power emitted by an optically pumped waveguide FIR laser operating on the exceptionally strong 15NH 3 laser line at 152.9 μm. The Doppler-splitting of the FIR output frequency shows a CO 2 power-dependent deviation from the linear dependence on 13CO 2 laser frequency expected from rate equation theory. Similar, but weaker, effects are also reported using the less strong CH 3OH FIR line at 118.8 μm.

Pulse compression in continuously pumped dye lasers with a slow saturable absorber

Conditions for pulse compression and stability in a system of spatially separated amplifier and absorber contained in a ring or a common two-mirror cavity are investigated theoretically. The width of the pulse that travels in the cavity is assumed to be short compared to the longitudinal but long to the transversal relaxation times of the amplifier and the absorber (rate-equation theory). Especially the smallest ratios of the cross sections of the absorption and the stimulated emission needed for pulse shortening are calculated by analytical and numerical treatment.

Fim observation of defect clusters in tungsten irradiated with 200 KeV C+ion

Abstract Dose dependence of the size distribution of vacancy clusters in tungsten irradiated with 200 KeV C+ ions at 65 and 800°C was obtained with Field Ion Microscopy (FIM). At 65°C all of the vacancy clusters were below 15 A in diameter. At 800°C the density of vacancy clusters below 15 A was saturated, but the density of those above 15 A increased with dose. The results at both temperatures imply that the nuclei of voids would be the vacancy clusters below 15 A which come from depleted zones and that depleted zones play an important role in the genesis of voids in ion and neutron irradiation, kinetic analysis of the point defect behaviour based on rate equation theory has explained the experimental results at 65°C that total vacancy concentration and single vacancy concentration is proportional to t 1/2 (t is irradiation time).

On the rate-equation formulations of hopping conductivity in amorphous semiconductors: quantum transport approach

The present controversy regarding the validity of the AC and DC rate-equation formulations of hopping conductivity is examined within the exact resolvent theoretic framework of quantum transport theory. It has been argued that terms representing field-induced charges in the local value of the chemical potential which appear in rate-equation theory should not be present: this would destroy the percolation theoretic interpretations of the DC conductivity. The present theory, based on the Kubo formalism, demonstrates the validity of the rate equations in the weak-coupling, low-frequency and DC limits. The controversy is resolved by the observation that the anti-rate-equation theories have neglected an infinite sequence of terms appearing in perturbation theory which restore the disputed chemical potential terms to the rate-equation formulation.

Effect of rotational and intramode vibrational coupling on short-pulse amplification in CO<inf>2</inf>

The extraction of stored energy from a CO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -laser amplifier by a short-duration input pulse is described using a rate-equation theory. The influence of rotational and intramode vibrational energy-transfer processes is studied as a function of the energy density E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</inf> and width τ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> of the input pulse. By a suitable choice of normalized variables δ and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{in}/E_{sat}</tex> for the extracted-energy and input-energy density, it is found that the results for different values of τ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> are interrelated by simple translations in a δ versus <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{in}/E_{sat}</tex> diagram. The characteristic curves in this diagram are nearly independent of the amplifier gain factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\exp (\alpha_{0}L)</tex> for high-gain systems. A comparison of the theory with experimental results of Figueira et al. shows satisfactory agreement and leads to an estimate of (1.0-3.5) 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> torr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> for the rate of intra-mode vibrational-vibrational (VV) energy transfer in CO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> .

Comparison of theory and experiment for nanosecond-pulse amplification in high-gain CO2 amplifier systems

Short-pulse energy extraction measurements have been made on the Los Alamos Scientific Laboratory three-stage amplifier system. The energy extraction from one, two, and all three stages was found to be in excellent agreement with a rate equation theory including rotational relaxation and beam expansion. Amplified pulse energies of up to 20 J in 1.5 nsec were obtained.

Mode-locking of quasi-continuous lasers

A simple rate-equation theory is developed which indicates that the combination of nonlinear amplification and nonlinear absorption may be responsible for ultrashort pulse generation in a mode-locked quasi-continuous laser system in the absence of commensurately short relaxation times. It is tentatively proposed that this mechanism is responsible for picosecond pulse generation in the mode-locked dye laser.

Theory and Operation of a Proton-Spin Refrigerator

By rotating a crystal of (Yb, Y) ${({\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{S}{\mathrm{O}}_{4})}_{3}$\ifmmode\cdot\else\textperiodcentered\fi{}9${\mathrm{H}}_{2}$O (abbreviated as Yb: YES) at 60 rps in a magnetic field of 10 kOe at 1.4\ifmmode^\circ\else\textdegree\fi{}K, nuclear polarizations as large as 19% are observed for the protons in the ${\mathrm{H}}_{2}$O and ${\mathrm{C}}_{2}$${\mathrm{H}}_{5}$ groups. This comes about because the ${\mathrm{Yb}}^{3+}$ ions have both an anisotropic $g$ factor (${g}_{\ensuremath{\parallel}}=3.35,{g}_{\ensuremath{\perp}}\ensuremath{\approx}0$) and an anisotropic spin-lattice relaxation rate $\ensuremath{\propto}{cos}^{2}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$, allowing the ${\mathrm{Yb}}^{3+}$ polarization at $\ensuremath{\theta}={45}^{\ensuremath{\circ}}$ to be transferred to the protons by cross relaxation at $\ensuremath{\theta}={90}^{\ensuremath{\circ}}$; cyclic repetition of this is a refrigerator, which can, in principle, maintain a nuclear-spin polarization comparable to an electron-spin polarization. The paramagnetic and relaxation properties of Yb: YES are discussed in detail. Proton relaxation is studied and found to agree approximately with theoretical expectations. A general rate-equation theory of spin refrigerators is developed and used to interpret the measurements in Yb: YES. Although the present polarizations are limited by insufficient rotation speed and multiple spin flips, it is apparent that Yb: YES is a favorable substance, and that polarizations of \ensuremath{\sim}50% might be achieved at higher fields and higher speeds; application to polarized targets is suggested.

4A2 - The utilization of semiclassical and rate equations for design of steady-state lasers

Semiclassical equations are used to determine the output power of steady-state optical maser as a function of various parameters (pumping level, crystal losses, cavity length, and mirror transparancy). The results obtained are compared with those given by the rate equations theory (as applied to a ruby crystal). It is shown that the difference between these two methods from the technical point of view is insignificant and did not appear in ordinary experiments.

Some aspects of infra-red quantum counter action in Er-doped SrF 2

Measurements are presented of the optical properties and strength of quantum counter action in Er3+-doped SrF2 which demonstrate the validity of a simple rate equation theory of quantum counter action. This analysis is used to assess the quantum counter as a potential narrow band infra-red detector. An extension of the theory to the case of modulated input radiation is shown to provide a method for measuring lifetimes of excited states which may not be accessible by conventional techniques, e.g. non-fluorescent levels. Some results obtained by this method are reported.