Low-intensity Limit Research Articles

Induced absorption and stimulated emission in a driven two-level atom

We have considered the induced processes that occur in a driven two-level atom, where a laser photon is absorbed and emitted by the ground and by the excited states of the atom, respectively. In the low-intensity limit of the laser field, the induced spectra arising when a laser photon is absorbed by the ground state of the atom consist of two peaks describing induced-absorption and stimulated-emission processes, respectively, where the former prevails over the latter. Asymmetry of the spectral lines occurs at off-resonance and its extent depends on the detuning of the laser field. The physical, process where a laser photon is emitted by the excited state is the reverse of that arising from the absorption of a laser photon by the ground state of the atom. The former differs from the latter in that the emission of a laser photon by the excited state occurs in the low-frequency regime and that the stimulated-emission process prevails over that of the induced absorption. In this case, amplification of ultrashort pulses is likely to occur without the need of population inversion between the optical transitions. The computed spectra are graphically presented and discussed.

Resonant two-photon interference spectra induced by a bichromatic field in the excited state of a three-level atom

The interference spectra arising from the competition between a spontaneous process and an induced one by two laser fields, which interact on two-photon resonance with a three-level atom in the Lambda configuration have been considered. In the low intensity limit of both laser fields, the frequency profiles of the two peaks, which arise from the spontaneous and induced processes, respectively, cancel each other out completely at the centre of the line for zero detuning and at the finite values of the detuning as well. At those frequencies, the fluorescent light totally disappears. The interference spectra arising from the absorption of a laser photon by the ground state of the atom consists of two peaks describing the induced processes of absorption and stimulated emission, respectively.

Low-intensity limit of the laser cooling of a multistate atom.

We adapt an earlier semiclassical theory of laser cooling of an arbitrary multistate atom [J. Javanainen, Phys. Rev. A 44, 5857 (1991)] to the limit of low light intensity. The formal theory is implemented analytically on a computer using mathematica. Expressions of light-pressure force and diffusion are provided for ${\mathit{j}}_{1}$=1/2\ensuremath{\rightarrow}${\mathit{j}}_{2}$=3/2 and ${\mathit{j}}_{1}$=1\ensuremath{\rightarrow}${\mathit{j}}_{2}$=2 atoms in a one-dimensional optical confinement area in which the pair of counterpropagating waves has orthogonal polarizations. In our models the cooling temperature decreases as the level degeneracy increases.

Two-photon interference spectra induced by a bichromatic field in the excited state of a single three-level ion

We consider the interference spectra arising from the competition between a spontaneous process and two processes induced by two laser fields, which are coupled with a three-level atom in the "Λ" configuration. In the low-intensity limit of both laser fields and on two-photon resonance, the frequency profiles of the two peaks, which arise from the spontaneous and induced processes, cancel each other out completely at the center of the line for zero detuning and at the finite values of the detuning as well. At high intensities of the laser fields and on two-photon resonance, the dynamic Stark effect dominates the spectra of the excited state of the atom. Expressions for the interference spectra and correlation functions are derived, which describe the physical process of the absorption of a laser photon at two different times by the ground state of the atom. Interference spectra and correlation functions are calculated for the two-photon off-resonance and for the proces of the absorption of a photon by the ground state of the atom. In this case, the intensities of the frequency dips take negative values indicating that stimulated emission prevails for certain values of the detunings. Using values for the parameters involved close to those for Ba+, the computed two-photon resonance and off-resonance spectra are graphically presented and discussed.

A rotating ring-disc study of the photodissolution of n-Si in ammonium fluoride solutions

The extensive literature on the anodic dissolution of nand p-type silicon in fluoride solutions has been reviewed recently by Eddowes [l], who has also reexamined someof the earlier work of, for example, Memming and Schwandt [2]. It has been suggested that the photodissolution of n-Si corresponds to the formation of dimlent species unless the illumination intensity is sufficiently high that the process is no longer limited by the supply of holes, and Eddowes has confirmed this by coulometric and weight loss experiments. The photocorrosion of n-type silicon can in principle involve both hole capture and electron injection steps [3-61. Recently, we have reported results which agree with an earlier report by Matsumura and Morrison [5] that the photocurrent quantum efficiency for the dissolution of n-Si in ammonium fluoride solutions varies between four and two, depending on light intensity [4]. However, the quantum yield of 4 (photocurrent quadrupling) observed in the low intensity limit is consistent with the formation of tetruuafent silicon via a photocurrent quadrupling process in which the capture of a photogenerated hole is followed by the injection of three electrons into the conduction band. This conclusion appears to contradict the work discussed by Eddowes. We have proposed a simple reaction scheme [3,4] that explains the observed intensity dependence of the quantum yield in terms of competition between hole capture and electron injection by intermediate species. In this mechanism, divalent silicon appears only as a transient surface bound intermediate which can either inject an electron or, at higher intensities, capture a photogenerated hole to form

Anomalous optical transmission in homogeneous latex suspensions.

We have observed a deviation from the law of exponential attenuation of a 633-nm optical beam in a homogeneous scattering medium in the low-intensity limit, where nonlinear optical effects or thermal effects are insignificant (Bouguer's law). This deviation occurs when the spatial correlation length is comparable to or larger than the asymptotic attenuation length, whence the assumption of independent scattering events is violated. We develop a statistical model for the optical dielectric fluctuations which fits well our nonexponential beam-transmission data in homogeneous suspensions of 1-\ensuremath{\mu}m latex spheres. We use this to determine the correlation lengths (7 to 12 \ensuremath{\mu}m) of the dielectric fluctuations in these suspensions. These correlation lengths are consistent with values that we deduce from the observed angular spreads of forward light scattering.

Laser-assisted electron transitions

General formulae of differential transition probabilites per unit time of laser-as-sisted, bound-free and free-bound processes from inner shells such as laser-assisted X-ray absorption, recombination, internal conversion processes are given for cases of linearly and circularly polarized lasers of intermediately high intensities in a nonrelativistic, one-electron model. The low frequency and low intensity limits of the transition rate are discussed. The laser-assisted processes near their threshold are also investigated. It is also shown that the method can be extended to other laser-assisted processes, e.g. to laser-assisted Auger and heavy ion Coulomb scattering (or ionization) processes.

Interference spectra in a two-level atom

We have considered the interference spectra arising from the competition between a spontaneous process and one induced by a laser field in a two-level atom. Expressions for the spectral functions have been derived describing the spectra of the excited and ground states of the atom in the low- and high-intensity limit of the laser field. For the excited-state spectra in the low-intensity limit, the frequency profiles of the two peaks, which arise from the spontaneous and the induced processes, cancel each other out completely near the center of the line, while for the ground state the induced process dominates. For finite values of the detuning, the spectra of the excited state consist of two peaks, which have positive and negative frequency profiles, respectively. The computed spectra have been graphically presented and discussed. In the high-intensity limit, the dynamic Stark effect dominates the spectra of the excited and ground states of the atom. Expressions for the correlation functions have been derived that describe the emission or the absorption of a laser photon at two different times. The derived expressions for the corresponding delay functions in the low- and high-intensity limits have been found to be identical to those recently proposed in the literature. The laser field has been treated as a classical as well as a quantized entity.

A laser-excited three-level atom

We considered the excitation spectra for the excited states of a three-level atom, where the strong and the weak atomic transitions are driven by resonant and nonresonant laser fields, respectively. The spectral functions describing the excitation spectra for the electric dipole allowed excited state and for the metastable state of the atom have been derived when both laser fields are quantized as well as when they are treated as classical entities. In the low-intensity limit of the laser field operating in the strong transition, there are two short-lifetime excitations, the spontaneous one and the induced one, which appear at the same frequency, and a long-lifetime excitation induced by the weak laser field. These excitations compete with each other at resonance as well as at finite detunings of the weak laser field. In the high-intensity limit of the laser field operating in the strong transition, the competition is between the short- and the long-lifetime side bands, which are induced by the strong and the weak laser fields, respectively. The ratio of the maximum intensities of the peaks describing the long- and the short-lifetime excitations exhibits a resonance variation with the detuning of the weak laser field. Comparison between the results obtained when the laser fields are treated as quantized and as classical entities is made.

Transmission and reflection of transverse-magnetic-polarized optical fields at stratified nonlinear media.

For the first time we study the transmission and the reflection of transverse-magnetic-polarized optical fields which impinge obliquely on diverse multilayer systems showing distinct resonances of geometrical origin in the low-intensity limit. The individual layers are endowed with nonlinear materials, the complex dielectric functions of which depend on the local intensity of the optical wave. The field propagation is described by a straightforward algorithm that reduces the final field calculation to a standard Runge-Kutta procedure. With respect to varying input fluxes we discuss in detail the response characteristic of a single nonlinear film near the angle of total internal reflection, a nonlinear periodic multilayer system near the edges of its stop gap, and a nonlinear Fabry-P\'erot \'Etalon, coated with linear or nonlinear dielectric mirrors, near an Airy resonance, respectively. For all configurations under investigation, a bistable input-output flux characteristic is predicted. We compare also the response behavior as it depends on the state of polarization. A clear advantage of transverse electric polarized fields with respect to lower switching intensities could be identified. There are indications for optical bistability with respect to the polarization angle.

Theory of the Optical Stark Effect in Semiconductors under Ultrashort‐Pulse Excitation

AbstractThe optical Stark effect is computed for femtosecond excitation of the electron–hole‐pair states in semiconductors. The theory is based on the effective Bloch equations for semiconductors and is evaluated for the large detuning, low intensity limit. For the example of CdS, good agreement with recent femtosecond experiments is found. It is shown that the coherent interaction of the pulses and the medium polarization dominates the semiconductor response as long as the pulse duration is of the order of, or less than, the coherence decay time of the medium.

Measurements of Ultrafast Optical Nonlinearities in Semiconductors

AbstractThe response of a bulk semiconductor platelet under the influence of nonresonant pulse excitation below the band gap is measured using femtosecond laser techniques. These optical Stark effect measurements are analyzed using the effective Bloch equations for semiconductors. These equations are solved (i) dynamically in the large detuning, low intensity limit and (ii) for arbitrary intensities in the adiabatic limit.

Practical guide for 7S resonant frequency mixing in mercury: generation of light in the 230–185-and 140–120-nm ranges

We present recent measurements of refractive indices, nonlinear susceptibilities, and isotope shifts important for sum- and difference-frequency mixing through the 71,3S two-photon resonances of Hg. These data are presented in a form that makes it possible to make quick and accurate calculations of index-matching and mixing efficiencies in the low-intensity limit.

Quantum measurements of position, detection of weak classical forces, and interferometric noise

We discuss quantum measurements of position and repeated-measurement schemes for monitoring free-mass position to an arbitrary accuracy. Using these schemes, weak classical forces can be monitored to an arbitrary accuracy. To illustrate various measurement uncertainties and intrinsic uncertainties, we consider the case of a Michelson interferometer. In the low-intensity limit, two measurement uncertainties, photon counting error and radiation pressure error, are independent of the intrinsic uncertainty. The uses of squeezed states and number eigenstates are discussed.

Many-electron dynamics of heavy atoms in intense laser fields: effects of screening and correlation

We discuss the role of many-electron interactions in multiphoton multielectron ionization of heavy atoms and try to indicate the relative importance of collective effects and screening, relaxation and shakeup, and Fermi sea correlations. The purpose of the work is to look for approximations in which the photoemission processes have been renormalized in consistent ways with respect to the field and the electron–electron interaction. This involves effective shift and broadening of energy levels, effective matrix elements for ionization by the field, effective field-induced density of states for the photoelectron, etc. In an application, we consider the low-intensity limit and discuss two-photon one-electron ionization of the 5p shell of Xe using a zero-field atomic basis set. This calculation demonstrates important ways in which collective effects may enter, and it also represents the first reported calculation of its kind. Finally, we apply the scheme for dressing the many-electron processes to a discussion of time scales in two-step double ionization, introducing the laser pulse duration in an intuitive way.

Resonance fluorescence of a laser-cooled trapped ion in the Lamb-Dicke limit.

The resonance fluorescence spectrum of a laser-cooled trapped ion is theoretically studied in the Lamb-Dicke limit. Angular averaged spectrum around the elastic peak and the motional sidebands is calculated. The widths of the sidebands are shown to be given by the cooling rate of the ion in the trap. In the limit when the trapping force is strong a possibility of dispersive line shapes is predicted. The spectrum derived is also shown to reproduce in the low-intensity limit the earlier perturbative results.

Collision-enhanced Hanle resonances and transverse optical pumping in four-wave light mixing in Na vapor.

Collision-enhanced Hanle resonances in the 3 $^{2}S_{1/2}$ electronic ground state of Na atoms have been studied in a phase-conjugate four-wave light-mixing geometry. Narrow resonances in zero magnetic field have been observed at very high inert-buffer-gas pressures, with a width of 21 mG, or less than 10 kHz, full width at half-maximum. The intensity and the width of these resonances has been studied as a function of buffer-gas pressure, of alkali-metal vapor pressure, of detuning from the ${D}_{1}$ and ${D}_{2}$ Na resonances, and of the intensity of the incident light beams. Saturation phenomena and power broadening are observed. The results are explained theoretically in terms of transversely pumped optical gratings. The equivalence of this description with collision-induced coherence gratings in the limit of low light intensities is demonstrated.

Velocity-selective optical pumping and collision effects

Optical pumping performed with a quasi monochromatic laser beam in an atomic gas introduces a redistribution of Zeeman populations selectively in a single velocity class. In the limit of low pumping intensity the rate theory is valid for a description of velocity-selective optical pumping (V.S.O.P.). Well-defined atomic observables (population, orientation, alignment) and their velocity-correlated collisional relaxation can be studied. Also, a modified scheme for the detection of second order effects of optical pumping allows one to observe light shift induced signals. In particular, V.S.O.P. and its combination with modulated pumping, magnetic depolarization (level crossing), and magnetic resonance techniques provide information about the atomic collision characteristics such as collision rates and kernels for velocity-changing collisions.

Transit-time effects in a strong field inverted lamb dip theory

The inverted Lamb dip theory for a spatially-bounded plane laser beam is presented, valid for arbitrary gas pressure levels and field intensities. Line shape, power-broadening, contribution of transit-time and gas pressure effects to the dip linewidth have been computed and are found to be in perfect agreement with experimental data. In the limit of low pressure and intensity, the dip linewidth is found to depend only on the beam radius and the mean thermal velocity of molecules.

Transient four-wave mixing and coherent transient optical phenomena

The general formalism of transient four-wave mixing is developed using the diagrammatic technique of Yee and Gustafson, and applied systematically to two-, three-, and four-level systems. The results predict all possible photon-echo phenomena including free-induction decay in the low-intensity limit. Connections to transient saturation spectroscopy and other coherent transient effects can also be made. The treatment can be readily extended to the more general problem of coherent transient optical effects with $n$ waves.