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International Conference on Pulsed Lasers and Laser Applications (AMPL)

Computer simulation of the helium line profiles under laser excitation in near-resonance regions

Elena Vladimirovna Koryukina

Published Nov 2, 2023• 0 citations
Publisher

Abstract

The spectral line profiles of helium atoms in laser fields are simulated within the framework of the method based on the numerical solution of the non-stationary Schrödinger equation. The proposed method is free from limitations of perturbation theory and makes it possible to calculate the emission spectra of atoms both under non-resonant and resonant excitation by the electric field. The algorithm of this method is implemented in the StarkD software package written in FORTRAN and Maple. Within the framework of the proposed method, the behavior of the helium spectral line profiles is studied under changing electric field frequency in the range of 105 – 107 MHz, which is typical of lasers. A comparative analysis of the behavior of the helium spectral line profiles in resonances and interresonance regions is carried out. Practical applications of the obtained theoretical results are proposed.

DOI
10.1117/12.3007347

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The spectral line profiles of helium atoms in laser fields are simulated within the framework of the method based on the numerical solution of the non-stationary Schrödinger equation. The proposed method is free from limitations of perturbation theory and makes it possible to calculate the emission spectra of atoms both under non-resonant and resonant excitation by the electric field. The algorithm of this method is implemented in the StarkD software package written in FORTRAN and Maple. Within the framework of the proposed method, the behavior of the helium spectral line profiles is studied under changing electric field frequency in the range of 105 – 107 MHz, which is typical of lasers. A comparative analysis of the behavior of the helium spectral line profiles in resonances and interresonance regions is carried out. Practical applications of the obtained theoretical results are proposed.
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The prediction of the energy level shifts and intensity transfer in atomic hydrogen and helium spectra caused by an external electric field was one of the first applications of wave mechanics. Early measurements relied on electrical discharge sources for excited atoms; since discharge processes will not produce excited states with n > 7 in observable densities, very large (10s to 100s kV cm) electric fields were required to resolve spectral modifications. The development of high peak power lasers enabled excitation to high n (Rydberg) states, increasing field sensitivity down to millivolts/cm and allowing comparison of experiment and theory in well-defined conditions. Field modified selection rules can be used to measure the field direction as well as magnitude. Analysis of line shape simulations of Stark modified Rydberg spectra reveals pitfalls in commonly used field measurement techniques. An ambiguity in defining series termination results in a factor of 2 discrepancy in field measurements based on Inglis Teller line merging. Field-induced line broadening (unresolved manifold splitting) in triplet and singlet helium are shown to differ significantly, with triplet broadening nonlinear with field.
In the present work, the influence of an alternating circularly polarized electric field on the energy spectrum of the He atom is studied. The calculations are performed by the method of the energy matrix diagonalization of an atom in the electric field. This method has allowed us to study the behaviour of the helium energy spectrum from the same numerical procedure under resonant and non-resonant excitations by the electric field. Based on the calculation results, we have found that the resonance effects take place not only in the vicinity of resonance, but they influence the shift directions of the Stark states even under non-resonant excitation. Additionally, we have established that the helium energy spectrum behaves consistently in the electric field. The results obtained have allowed us to clarify mechanisms of the influence of the resonance effects on the radiative characteristics of helium plasma.
Several calculations have been carried out using the transition operator technique. The radiative decay in a two-level quantum system with excited state coupled by an external perturbation has been investigated and an expression obtained for P(t), the probability of finding the atom in its excited state at time t. This is seen to possess a steady value for yt >> 1 and a third term which decays at nearly half the rate of its second. Next radiative decay of an atom with two close-lying excited states is considered and |bq| 2 , the spectral density for spontaneous emission from the uppermost level, calculated. This shows that the proximity of the upper two levels makes the line-shape non-Lorentxian. Heisenberg equations of motion were then derived for the transitions operators of an ℓ-level atom undergoing radiative decay, the possibility of overlapping pairs of levels being ignored. These master equations were then used to obtain the spectral profiles of certain atomic lines, employing the so-far avoided Markoff approximation. First the spectral density of the scattered radiation was found for transitions between levels 5P3/2 and 4S (ground state), and 6S and 5P 3/2, in the potassium atom when driving fields of arbitrary strength coupled levels 6S and 4P3/2, and 4P 3/2 and 4S. Triple-peaked profiles were obtained. Spectral profiles for emission were then derived for transitions between levels 3P and (ground state), and 3P and in the hydrogen atom when a driving field of arbitrary strength coupled levels The former profile was double the latter quadruple-peaked. Lastly master equations were derived for an atom, with two excited levels undergoing radiative decay, when allowance was made for thepossibility of their overlapping. A driving field of arbitrary magnitude coupled the uppermost and ground states. The spectrum for the scattered light resulting from transitions between the uppermost and ground state was found and graphs computed for various field strengths and separations of the excited states.
The fluorescence intensities for the D lines in non-resonant excitation of the alkali-helium pairs under single-collision conditions were obtained from calculations of the optical collision spectra by the quantum coupled-channels method. The close relation of the non-adiabatic transition probability from a molecular level to an atomic state during the final stage of an optical collision and the spectral dependence of the relative fluorescence intensities is investigated. An analysis of the impact region in terms of line-broadening and fine-structure cross sections calculated separately for all systems confirms the factorisation approximation.