Lasing condition

The above treatment is valid quite generally, even if f2 — fi > huj. when the denominator in (4.17) is negative. Under the same conditions, the absorption coefficient in (4.15) is also negative, and the spontaneous emission rate in (4.17) remains positive. When the absorption coefficient is negative, stimulated emission overcompensates the rate of upward transitions and the 2-level system amplifies the incident light exactly as in a laser. The condition f2 — fi > tko is also known as the lasing condition and is called inversion. 

Since the rate of stimulated emission can be very much faster than the spontaneous emission rate, the time resolution of chemical laser measurements can be quite high. In a very crude way one might say that the rate of emission under lasing conditions can be deliberately increased by a sufficiently intense stimulating field so as to exceed any other collisional rate in... 

S. Longhi, Non-markovian decay and lasing condition in an optical microcavity coupled to a structured reservoir, Phys. Rev. A 74 (2006) 063826. 

Fig. 9.39 Dependences of depolarization on Nd " concentration under nonlasing at an absorbed pump power of 1 W. The solid line represents the calculated depolarization, while the dotted line indicates the calculation under the ideal lasing condition. Reproduced with permission from [285]. Copyright 2007, Elsevier...

Gainov, V.V., Shaidullin, R.I., Ryabushkin, O.A., 2010. Temperature measurements in the core of active optical fibers under lasing conditions. Instrum. Exp. Tech. 53 (6), 853-859. 

Fundamentally, the conditions for lasing are detemiined unambiguously once the populations and coherences of the system density matrix are known. Yet, we have been unable to find in the literature any simple criterion for lasing in multilevel systems in temis of the system density matrix alone. Our conjecture is that entropy, as... 

It has been said tliat anytliing will lase if pumped witli enough energy, but tire efficiency of tire pumping process is important for practical, economical devices. In tliis regard two-level lasers are of little interest because, except under extraordinary pumping conditions, one can only equalize tire populations of tire upper and lower levels. A... 

The light emitted in the spontaneous recombination process can leave tire semiconductor, be absorbed or cause additional transitions by stimulating electrons in tire CB to make a transition to tire VB. In tliis stimulated recombination process anotlier photon is emitted. The rate of stimulated emission is governed by a detailed balance between absorjDtion, and spontaneous and stimulated emission rates. Stimulated emission occurs when tire probability of a photon causing a transition of an electron from tire CB to VB witli tire emission of anotlier photon is greater tlian that for tire upward transition of an electron from tire VB to tire CB upon absorjDtion of tire photon. These rates are commonly described in tenns of Einstein s H and 5 coefficients [8, 43]. For semiconductors, tliere is a simple condition describing tire carrier density necessary for stimulated emission, or lasing. This carrier density is known as... 

If the temperature were raised, more molecules would attain the excited state, but even at 50,000°C there would be only one excited-state atom for every two ground-state atoms, and stimulated emission would not produce a large cascade effect. To reach the excess of stimulated emissions needed to build a large cascade (lasing), the population of excited-state molecules must exceed that of the ground state, preferably at normal ambient temperatures. This situation of an excess of excited-state over ground-state molecules is called a population inversion in order to contrast it with normal ground-state conditions. 

Excitation conditions and threshold vulues for lasing in different conjugated polymers. Different resonator structures are used to achieve real lasing. Note that it is in some cases difficult to compare the values due to the different laser pulse duration used in the experiments. indicates the wavelength for excitation, r(,u< is the pulse duration of the exciting laser pulse atu A the urea of the spot on the sample. 

Reference Material and resonator Excitation conditions Threshold for lasing... 

Fig. 3.2.5 Profiles of acylcarnitines as their butyl esters in plasma (precursor of m/z 85 scan) of a normal control (a) and patients with various organic acidemias. Propionylcarnitine (C> m/z 274 peak 3) is the primary marker for both propionic acidemia (b) and methylmalonic acidemias (c). Note that an elevation of methylmalonylcarnitine (C4-UC m/z 374) is not typically found in patients with methylmalonic acidemias. In the three cases of ethylmalonic encephalopathy (d) analyzed in our laboratory, elevations of ,- (m/z 288 peak 4) and C5-acylcarnitine (m/z 302 peak 5) species were noted. Isolated C5-acylcarnitine elevations are encountered in patients with isovaleric acidemia (e), where it represents isovalerylcarnitine. Cs-Acylcarnitine is also elevated in patients with short/branched chain acyl-CoA dehydrogenase deficiency, where it represents 2-methylbutyrylcarnitine (see Fig. 3.2.4), and in patients treated with antibiotics that contain pivalic acid, where it represents pivaloylcarnitine [20, 59, 60]. Patients with /3-ketothio-lase deficiency (f) present with elevations of tiglylcarnitine (C5 i m/z 300 peak 6) and C5-OH acylcarnitine (m/z 318 peak 7). In most cases of 3-methylcrotonyl-CoA carboxylase deficiency (g) Cs-OH acylcarnitine is the only abnormal acylcarnitine species present. The differential diagnosis of C5-OH acylcarnitine elevations includes eight different conditions (Table 3.2.1). Also note that C5-OH acylcarnitine represents 3-hydroxy isovalerylcarnitine in 3-methylcrotonyl-CoA carboxylase deficiency (g), and 2-methyl 3-hydroxy butyrylcarnitine in / -ketothiolase deficiency...

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