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Annual Meeting Optical Society of America

Stark shift/broadening by stimulated emission

Edward T. Dressler, Jon P. Davis

Published Jan 1, 1991• 0 citations
Publisher

Abstract

Previous experimental work by our group1 has shown that the two-photon excitation of the 6p[1/2,0] state of xenon has a fairly sharp threshold for the onset of amplified spontaneous emission (ASE) from the 6p[1/2,0] state to the excited 6s state. The excitation probability has the expected quadratic dependence on excitation intensity below the ASE threshold but an unexpected linear dependence above threshold. We hypothesize that the reduced excitation probability results from an ac Stark shift/broadening of 6p[1/2,0] state by the ASE field. We have numerically solved the coupled Maxwell-Bloch equations with and without the relevant Stark terms. The ASE threshold predicted by the numerical solutions occurs at an intensity about an order of magnitude higher than the experimental value. Because of uncertainties in some of the experimental parameters this difference is not unreasonable. Solution of the equations without Stark terms gives quadratic excitation dependence above the ASE threshold. Including the Stark terms reduces the dependence to a 1.2 power law. The change to a 1.2 power occurs ~50% above ASE threshold, whereas the experimental change occurs almost right at threshold.

DOI
10.1364/oam.1991.tubb5

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Previous experimental work by our group1 has shown that the two-photon excitation of the 6p[1/2,0] state of xenon has a fairly sharp threshold for the onset of amplified spontaneous emission (ASE) from the 6p[1/2,0] state to the excited 6s state. The excitation probability has the expected quadratic dependence on excitation intensity below the ASE threshold but an unexpected linear dependence above threshold. We hypothesize that the reduced excitation probability results from an ac Stark shift/broadening of 6p[1/2,0] state by the ASE field. We have numerically solved the coupled Maxwell-Bloch equations with and without the relevant Stark terms. The ASE threshold predicted by the numerical solutions occurs at an intensity about an order of magnitude higher than the experimental value. Because of uncertainties in some of the experimental parameters this difference is not unreasonable. Solution of the equations without Stark terms gives quadratic excitation dependence above the ASE threshold. Including the Stark terms reduces the dependence to a 1.2 power law. The change to a 1.2 power occurs ~50% above ASE threshold, whereas the experimental change occurs almost right at threshold.
We have numerically solved a simplified set of Maxwell-Bloch equations for a two-field, three-level model. Excitation from the ground state to the upper state is a two-photon process with a nonresonant intermediate state. Amplified spontaneous emission can occur from the upper excited state of the model system to the intermediate state. The equations can contain terms corresponding to the dynamic Stark effect resulting from the amplified spontaneous-emission field. Inclusion of these terms significantly reduces the excitation probability when the irradiance of the exciting field is above the threshold for occurrence of amplified spontaneous emission from the upper excited state. These theoretical results qualitatively explain a recent experimental observation of the decreased excitation probability for such a process in gas-phase xenon.
Excitation of xenon near the two-photon resonance between the ground state and the 6p(1/2,0) state produces forward conical emission at a wavelength close to the 828-nm 6p(1/2,0)—6s(3/ 2,1) excited-state transition. We describe experimental features of this process as excited by 600-ps pulses of 250-nm radiation from a frequency-doubled dye laser with intensity up to 1.3 × 108 W/ cm2 in xenon at pressures of 1-20 Torr. The conical emission occurs most prominently when the driving field is a few gigahertz above the frequency at which spontaneous emission from the excited 6p state peaks. The cone angle increases with xenon pressure in the 1-10-Torr range. The dependence appears consistent with the predictions based on noncollinearly phase-matched four-wave mixing. In this interpretation, the fourth wave would be near resonance with the 146.9-nm first resonance transition of xenon and detuned to the low-frequency side. The conical emission co-exists (and may compete with) an axial stimulated process which may be either two-photon driven amplified spontaneous emission or stimulated hyper-Raman scattering. The different tuning characteristics for the two processes make the extent of their competition unclear.
Both on-axis and conical emissions have been observed following two-photon pumping of the 5p states of krypton and the 6p', 7p, 8p, and 4f states of xenon. In the former case, coherent emissions from the 5p states to the 5s are observed, and in the latter case, many p..-->..s, d..-->..p, and f..-->..d cascade emissions are observed. By analogy to the well-studied alkali and alkaline earth examples, the emissions are discussed in terms of amplified spontaneous emission (ASE), stimulated hyper-Raman scattering, and parametric four-wave mixing. The physical processes responsible for the conical emission and for intensity anomalies in the xenon p..-->..s emissions are not understood at present. Interference effects due to coherent cancellation between competing excitation pathways may be occurring. 4 refs., 3 figs.
A new, simple method for the generation of Xe(6s[3/2]1) and Xe(6s′[1/2]1) atoms is described. The method involves resonant two-photon excitation of Xe(6p[1/2]0 and 6p′[3/2]2) states followed by amplified spontaneous emission (ASE) to the Xe(6s[3/2]1 and 6s′[1/2]1) states. The vacuum ultraviolet transitions, Xe(6s[3/2]1→5p6(1S0)) at 147 nm and Xe(6s′[1/2]1→5p6(1S0)) at 129.6 nm, were used to monitor the time dependence of the resonance state atom concentrations. The quenching rate constants of these resonance atoms with ten molecules were measured at 300 K. The quenching cross-sections of the Xe(6s and 6s′) resonance atoms are compared to the cross-sections of the metastable Xe(6s[3/2]2) atoms and Xe(6p[3/2]2) atoms. The correlation between quenching cross-sections and photoabsorption cross-section of the molecules predicted by the resonance dipole–dipole energy transfer model is discussed. The applicability of the two-photon driven ASE method for the generation of other resonance state atoms is considered.
In order to perform multi-photon ionization experiments at a particular light intensity, the AC Stark-shift of the xenon 6s level is used as a probe to select that intensity from the range of intensities present in the laser focus. Our analysis provides an accurate, wide-range distribution function of the intensities in our multi-mode laser pulses. Using this method we determined there al order of non-linearity of the resonant ionization process and the probability for additional photon absorption.
In the literature one finds several conflicting accounts of the phase difference of stimulated and spontaneous emission, as well as absorption, with respect to an existing (triggering) electromagnetic field. One of these approaches proposes that stimulated emission and absorption occur in phase and out of phase with their driving field, respectively, whereas spontaneous emission occurs under an arbitrary phase difference with respect to an existing field. It has served as a basis for explaining quantum-mechanically the laser linewidth, its narrowing by a factor of 2 around the laser threshold, as well as its broadening due to amplitude-phase coupling, resulting in Henry’s α-factor. Assuming the validity of Maxwell’s equations, all three processes would, thus, violate the law of energy conservation. In semi-classical approaches, we investigate stimulated emission in a Fabry-Pérot resonator, analyze the Lorentz oscillator model, apply the Kramers-Kronig relations to the complex susceptibility, understand the summation of quantized electric fields, and quantitatively interpret emission and absorption in the amplitude-phase diagram. In all cases, we derive that the phase of stimulated emission is 90o in lead of the driving field, and the phase of absorption lags 90o behind the transmitted field. Also spontaneous emission must obey energy conservation, hence it occurs with 90o phase in lead of an existing field. These semi-classical findings agree with recent experimental investigations regarding the interaction of attosecond pulses with an atom, thereby questioning the physical explanation of the laser linewidth and its narrowing or broadening.