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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Non-linear excitation of atoms by ultrashort electromagnetic pulses

Valery Alexandrovich Astapenko, Sergey V. Sakhno

Published Apr 27, 2016• 0 citations
Publisher

Abstract

The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter [1]. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration (τ) [2] as well as the dependence on the carrier phase with respect to the pulse envelope (φ) [3-4]. It should be noted that if the dependence of the probability W on the phase φ manifests itself either only for very short pulses, when ωτ < 1 (ω is carrier frequency of the pulse), or in case of a nonlinear photoprocess [3], the function W(τ) can differ from a linear function in the limit ωτ> 1 too for fields of moderate strength, when the perturbation theory is applicable [2].

DOI
10.1117/12.2227335

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The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter [1]. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration (τ) [2] as well as the dependence on the carrier phase with respect to the pulse envelope (φ) [3-4]. It should be noted that if the dependence of the probability W on the phase φ manifests itself either only for very short pulses, when ωτ < 1 (ω is carrier frequency of the pulse), or in case of a nonlinear photoprocess [3], the function W(τ) can differ from a linear function in the limit ωτ> 1 too for fields of moderate strength, when the perturbation theory is applicable [2].
At the present time suopicosecond pulses of laser light as short as 0.5·10−12 s have been generated and detected and the possssibility of 50·10−15 s pulses generation as a limit is predicted [1]. Nothing has been said about the fundamental physical reasons that determine this limit. The aim of our work is to throw some light upon the generate mechanisms that govern the generation of ultrashort photon pulses and other pulses of physical fields of limited short duration. It is also obvious that the pulse duration Δt cann't be shorter than the elementary time length Δto if if it exists. So let us search for possicis candidates for Δto and look for methods of their generation. There is only one general method availaole to get automatically snortened pluses of boson fields - the method of boson avalanches [2]. It consists of the following: take an excited particle and put it into a physical resonator for a boson field for getting a boson by means of the sneous boson emission process in the resonator in a time τ. If we put N > 1 equel excited particles into the resonator we shall get a pulse of boson radiation consisting of ∼N bosons in a time (τ/N)·η, where η is an interference factor of the order η (λ2/Ao) for a radiating disk of square section Ao and for bosons of wavelength λ. This law was well established for photons generated by solids for which τ = 10−3 s, Ao = 1 cm2, λ2 = 10−10 cm2 and N = 1019 and Δt = 10−12 s. But these numbers are not the limited ones and we could pose for instance N = 1023 and τ = 10−10s. The result Δ t =10−21 will be wrong because in 10−11 s photons can travel only through a distance Δ1 ∼ 3·10−11 cm and a sphere of diameter Δ1 = 3·10−11 led with ordinary matter cann't contain 1023 particies. It must be said that particles outside of this sphere cann't interact to produce a motor, ava-_anche. So we see thatboson avalancnes can generate pulses as shot as needed if the material is as dense as to fulfill the new condition.
The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration as well as the dependence on the carrier phase with respect to the pulse envelope. It should be noted that if the dependence of the probability W on the phase manifests itself either only for very short pulses, when ωt 1 too for fields of moderate strength, when the perturbation theory is applicable. The present work is dedicated to the theoretical analysis of two-photon excitation of hydrogen atom in a discrete energy spectrum by ultrashort electromagnetic pulses of femto- and subfemtosecond ranges of durations. As examples, excitation of hydrogen atom from the ground state to excited states with a zero orbital moment is considered.
Abstract The time dependence (on the pulse duration and on current time) of resonant photoprocesses induced by electromagnetic pulses of various durations (including ultrashort and quasi-monochromatic pulses) is analyzed using perturbation theory. Pulses with the Gaussian and exponential envelopes, as well as the Lorentzian and Gaussian spectral profiles of a photoprocess cross section are considered. Simple analytic expressions are obtained for the probability in the long-time limit. The time dependence for a given pulse duration is investigated analytically in the monochromatic and ultrashort limits and numerically for intermediate values of parameters. Specific features of the temporal dynamics, which are common for resonant photoprocesses and depend on the pulse shape and the spectral cross section profile are established.