Stimulated emission cross sections

ESA and stimulated emission cross sections at the fluorescence wavelength Af. Note that ESA spectra strongly overlap the entire fluorescence region of 3 and 11 (Eig. 11, curves V, 2 ). 

The output is thus a continuous train of pulses separated by the dye cavity round-trip time. Even though the pump laser pulses may be of the order of 200 ps long, dye laser pulses of less than 10 ps can be achieved by synchronous pumping. This is because the dye molecules have extremely large stimulated emission cross-sections and the dye laser pulse passing through the dye stream immediately de-excites the dye molecule, in a few picoseconds, by stimulated emission [13]. 

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. 

Figure 7.8 Dependence of stimulated emission cross section for the P(20) line of the (001)-(100) laser transition in COa on gas temperature and pressure for 1-1-8 laser mixture [8].

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. 

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). 

The spectroscopic properties and chemistry of aprotic Nd + laser liquids plus references to earlier studies are discussed by Brecher and French (V7). The oscillator strengths and fluorescence lifetimes are comparable to those in solids with quantum efficiencies near unity. Since fluorescence line-widths are smaller than in glasses, the stimulated emission cross sections are larger (1 8), although still less than in crystals. Aprotic liquid laser materials and references are listed in Ref. 19. Thus far only Nd3+ has been used as the laser ion although other lanthanide ions could also be used. 

Saiki T, Motokoshi S, Imasaki K, Fujioka K, Fujita H, Nakatsuka M et al (2008) Effective fluorescence lifetime and stimulated emission cross-section of Nd/Cr YAG ceramics under CW lamplight pumping. Jpn J Appl Phys 47 7896-7902... 

Optical gain is usually defined in terms of a stimulated emission cross-section, cr, which can be calculated from readily measmable quantities ... 

The B X transition has a larger stimulated-emission cross section than that of the C —> A transition, indicating that the B X transition usually gives intense lasing. The C -> A band consists of relatively broad continua, which is attributed to the repulsive structure of the A state. 

The stimulated-emission cross section of the B X bands of RGHs like XeCl and KrF may be written as... 

Large stimulated emission cross section (narrow fluorescence linewidth)... 

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. 

X 60 cm. The total volume of Nd laser glass for multiple beam lasers can be >10 cm . Important materials properties for these high-power lasers are the nonlinear refractive index which governs the deliverable focusable power to a fusion target, the gain coefficient with affects the overall efficiency, and the stimulated emission cross section which determines the gain saturation behavior (Weber, 1976). 

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