Threshold condition

In practice the laser can operate only when n, in Equation (9.2), takes values such that the corresponding resonant frequency v lies within the line width of the transition between the two energy levels involved. If the active medium is a gas this line width may be the Doppler line width (see Section 2.3.2). Figure 9.3 shows a case where there are twelve axial modes within the Doppler profile. The number of modes in the actual laser beam depends on how much radiation is allowed to leak out of the cavity. In the example in Figure 9.3 the output level has been adjusted so that the so-called threshold condition allows six axial modes in the beam. The gain, or the degree of amplification, achieved in the laser is a measure of the intensity. 

Changes in polarization may be caused by either the input stress profile or a relaxation of stress in the piezoelectric material. The mechanical relaxation is obviously inelastic but the present model should serve as an approximation to the inelastic behavior. Internal conduction is not treated in the theory nevertheless, if electrical relaxations in current due to conduction are not large, an approximate solution is obtained. The analysis is particularly useful for determining the signs and magnitudes of the electric fields so that threshold conditions for conduction can be established. 

As we shall see immediately, this condition, together with the linearity of the neuronal excitations in the threshold condition, allows us to determine a finite system s fate almost entirely) analytically. 

Note that equations 8.105 and 8.106 effectively define a simple discrete diffusion process in one dimension the presence of a threshold condition also makes the diffusion process a nonlinear one (see below). 

This implies a threshold condition (G = y) for the population difference zlA th = (N2 - A i)th = y/2aL. If the population inversion, AN, is larger than ZiiVth, a wave reflected back and forth in the resonator will be amplified and its intensity will increase, in spite of the losses. 

In order to realize the extremely small linewidths, attainable because of the temporal coherence of induced emission, care must be taken to ensure that the threshold condition for induced oscillation is fulfilled for only one mode. The transverse modes can be eliminated by an appropriate choice of the cavity dimensions, introducing... 

The observation of the induced emission, its time behavior and threshold conditions allow to study with new techniques details of chemical reactions which lead to specific states of the molecular or atomic reaction product A quantitative study of such laser systems will also yield information about collisional deactivation rates of the excited states (see also Section 111.4). 

An important result bearing on the influence of applied fields on gaseous systems detonating at their threshold conditions is the observation that a flame in a uniform electrical field is always bent toward the negative electrode, as was first observed by Lewis (Ref 3). 

Although a population inversion for the two states of the bromine atom has been observed following the vacuum ultraviolet photolysis of CF3Br,76 it has not yet proved possible to meet the threshold conditions for stimulated emission. The work reported in Ref. 76 showed that the intensity of the... 

Non-equilibrium excitation in flames has been discussed from the point of view of possible inversions286. The possibility of laser action on several transitions of CN excited in active nitrogen has been discussed292 in terms of relevant rate equations and the threshold condition for oscillation. A chemical laser is of course a physical phenomenon, the performance of which depends critically on the rate... 

Calculations of anthropogenic (greenhouse) climate change show that thermohaline circulation (THC) in NH oceans may weaken in the future. However, even the models that show this weakening still demonstrate that greenhouse warming in Europe will persist. So far, no one knows whether irreversible collapse of THC is a possibility or which threshold conditions correspond to such a collapse. No existing model predicts total cessation of THC for the next 60 years. 

Estimate the temperature of laser torch plasma corresponding to the threshold of capillary instability of liquid 100 nm copper drop. This estimate can be done using the instability threshold condition (1) rewritten in the form ... 

Since it has been shown that in many exothermic reactions a large part of the energy liberated enters the vibration of the newly formed molecule, there has been considerable interest in developing vibrational lasers pumped by chemical reaction. Although a total inversion between vibrational states is not required [223], it is difficult to reach the threshold condition for lasing action if relaxation is faster than excitation by reaction. These effects can be reduced where a light flash (or pulsed discharge) initiates reaction, and stimulated emission has now been observed from a number of systems [224]. 

Determination of the threshold conditions for melting and sublimation under realistic tokamak conditions with mixed materials. Development of methods to calculate the melt layer loss in case of transient excess heat loads. 

Fig. 11. Time resolved I emission signals obtained from the apparatus shown in Fig. 10. Trace a was recorded under subthreshold conditions. Above threshold conditions were used to record traces b and c. The sharp spikes in these tr2ices indicate bursts of lasing. Reproduced with permission from Ref. 9.

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