Laser 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. 

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). 

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... 

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]. 

It was shown that for semiconductor lasers based on InGaN/GaN heterostructures, at optical excitation by the laser pulses of the femtosecond duration ( 150fs) the laser threshold exceed 2 0 GW/cm. It is caused most probably by non-steady excitation conditions. FWHM of the laser spectra alters from 13 to 25 nm. Amplification occurs in a wide interval of 60-80 nm and the gain at maximum reaches 85-153 cm . 

Let us now ask what is the value of the inversion AN which effects the stimulated emission rate. The inversion in a laser cavity cannot build up to more than a threshold inversion ANo which can be obtained from the threshold condition of Schawlow and Townes. 

The relevance of the superposition integral of the laser mode and the pumped volume t]y is determined by the regime of laser emission. The material factors that influence the laser threshold and thus the laser emission efficiency rii, in the case of CW emission, have been evaluated. Several of these factors, such as the emission quantum efficiency and the effective lifetime, can be influenced by the conditions of the experiment (concentration of the doping ions, temperature), whereas the quantum defect ratio is influenced by the pump wavelength. 

The condition for the laser effect is simply given by the threshold condition corresponding to the balance between gains and losses... 

The peculiar case of fibers for 3-level amplifiers and lasers In sect. 2.2.3 we briefly recalled the threshold flux condition for 4-level systems (eq. 118). In the 3-level case, when the final state for laser emission is the ground state or has noticeable population, the threshold condition becomes... 

The total amplification /t//o has maxima for cp — lqn, which corresponds to the condition (5.53) for the eigenfrequencies of the resonator with the modification (5.57). For G(v) 1, the total amplification Ij/h becomes infinite for (j) = 2qn. This means that even an infinitesimally small input signal results in a finite output signal. Sueh an input is always provided, for instance, by the spontaneous emission of the excited atoms in the active medium. For G(v) = 1 the laser amplifier converts to a laser oscillator. This condition is equivalent to the threshold condition (5.7). Because of gain saturation (Sect. 5.3), the amplification remains finite and the total output power is determined by the pump power rather than by the gain. 

According to (5.8) the gain factor Go(v) = exp[—2a(y)L] depends on the line profile g v — vq) of the molecular transition Ei E. The threshold condition can be illustrated graphically by subtracting the frequency-dependent losses from the gain profile. Laser oscillation is possible at all frequencies vl where this subtraction gives a positive net gain (Fig. 5.22). 

When the threshold condition for lasing Ai > A2 -f- 1 is fulfilled, where Ai = G A plq, A2 = —G2A2p/q, the spatially homogeneous steady-state solutions /o, A/o of Equations (44) correspond to single-mode CW laser operation. They have the form... 

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