Stimulated emission level crossing

The laser scheme is modified when neodymium is placed in other host environments in that the electronic levels have slightly different energies with different stimulated emission cross sections which may vary with the polarization of the stimulating radiation. As an example, Nd in lanthanum beryllate host (Nd BeL), the major laser transition is at 1079 nm and 1070 nm for two different polarizations. YAG is the most common and versatile host for neodymium but glass has advantages for high energy applications such as fusion research. Other crystal hosts such as YAP, YLF and BeL have some unique features. 

Here (Tabs,i is the cross-section for an absorption from the Si -level to higher lying states, Nt is the density of triplet excitations and (Tt is the corresponding cross-section for absorption into higher lying triplet levels. Since the first two terms on the right hand side both depend linearly on the density N xc of excited Si-states an effective stimulated emission cross-section iVsc,cn = sc- ahs,i can be defined. A quantitative treatment of the triplet absorption is more complicated since the density of molecules in the 7 -stale has to be known. 

In Eq. (3), 039 and 023 are the cross sections for stimulated emission and absorption. For narrow-line absorption and emission spectra, these two cross sections are equal. For broadband spectra with emission bandwidth greater than kT, the cross sections are connected by a generalized Einstein relation (6J. The final term in Eq. (3) accounts for possible excited-state absorption from the upper laser level to higher excited-states indicated by the dashed level in Fig. 1. If aesa > a32> absorption from level 3 dominates stimulated emission and laser action is not possible. 

The gain, from Eq. (3), is governed by a product of the stimulated emission cross section and the population inversion (N3-N2). The latter is dependent upon the absorption spectrum and its spectral match with the pump source, the lifetime of the metastable level 3 which determines the pumping rate required, and the quantum efficiency. The last quantity includes the fluorescence conversion efficiency (the number of ions excited to the fluorescing level per incident pump photon) and the quantum efficiency of the fluorescing state (the fractional number of photons emitted per excited ion in the upper laser level). 

Optical spectroscopy of Er " doped into bulk AIN ceramics has been reported [296]. The material was prepared by using hot press sintering of AIN with Et203 and (NH4)(ErE4), which yielded fully dense, translucent, hexagonal AIN. The Er concentration was a small fraction of a percent, and resided in multiple sites, with one type of center dominant. A number of the energy levels of Er " were identified for this center. The temperature dependent fluorescence lifetime was probably radiative, with which the stimulated emission and absorption cross section spectra were derived for the " I... 

In the right hand side of these equations, the first term nj /x represents the loss or gain by spontaneous emission from the excited level to the ground level Eq the second term, proportional to the light intensity P/S, represents the joint action of absorption and of stimulated emission (the coefficient a is proportional to the cross section of the interaction between photons and atoms). 

So far we have considered level crossing monitored through spontaneous emission. A level-crossing resonance can also manifest itself as a change in absorption of an intense monochromatic wave tuned to the molecular transition when the absorbing levels cross under the influence of external fields. The physical origin of this stimulated level-crossing spectroscopy is based on saturation effects and may be illustrated by a simple example [845]. 

J.S. Levine, R Boncyk, A. Javan Observation of hyperfine level crossing in stimulated emission. Rhys. Rev. Lett. 22, 267 (1969)... 

An attractive feature of the Judd-Ofelt approach is that once the intensity parameters are determined, they can be used to calculate the probability of transitions between any 4f" levels of interest for laser action. This includes absorption and fluorescence intensities, excited-state absorption, radiative lifetimes and branching ratios, and, combined with fluorescence spectra, stimulated emission cross sections (Krupke, 1974a). Best results are obtained for the lower-lying levels of 4f" which are well separated from the opposite-parity configurations and thus in keeping with the approximations made by Judd and Ofelt. Since the Judd-Ofelt parameters are not expected to differ greatly for adjacent ions in the lanthanide series, estimates can be made using extrapolated n values. 

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