Файл: Antsiferov V.V., Smirnov G.I. Physics of solid-state lasers (ISBN 1898326177) (CISP, 2005)(179s).pdf

Physics of Solid-State Lasers

both roots are real and negative and

In this case, small deviations from the stationary state are accompanied by a smooth return to this state, and the inversion tracks the field almost completely. The transition process of this type is characteristic of gas lasers and, in some cases, of solid-state lasers.

At a high density of radiation in stationary regime Uc, when the equality

2 Nc

Here ν is the frequency of damping pulsations of radiation density U and the inversion of populations N. The damping of the pulsations is characterised by the real part of the roots of the characteristic equation ~γ . The solution of the system of equations (6.33), (6.34) in this situation can be written in the following approximate form:

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Equation (6.51) for the frequency of pulsations indicates that they are determined by the dynamic Stark effect with the resonance effect of strong radiation on the working levels of the active medium. In fact, in the limiting case of high radiation density

the frequency of slightly damping pulsations

is, as indicated by equation (6.31) for the Einstein coefficient Bmn = B/ 2, proportional to the Raby frequency

chatacterising the light splitting of the working levels by the resonance field.

The realisation of the condition of existence of pulsations (6.48) depends on the ratio of the constants characterising the main relaxation processes in the system (the losses of radiation in the resonator µ σ 0, the relaxation of the inversion of populations γ ), and also the pumping determining the degree of excitation of the active system N0. In particular, a ruby laser is characterised by the following values of the parameters of the

the stationary regime Uc corresponds in this case to intensity Ic = cUc ~ 104 W/cm2, and the conditions of existence of the pulsations (6.47), determined by the dynamic Stark effect, are fulfilled. The frequency of pulsations and the damping constant of the pulsations in accordance with equations (6.50), (6.51) are evaluated as follows: ν ~ 1.2 × 10 6 s–1;

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Physics of Solid-State Lasers

γ ~ 1500 s–1. Consequently, the period of pulsations is T = 2π /γ ~ 5 × 10 –6 s, and approximately 102 oscillations take place during the characteristic time of damping of the pulsations ~γ −1 . This is in complete agreement with the experimental results.

For a laser on aluminium–yttrium garnet, activated by Nd ions, we

have γ = γ mn + γ mg ~ 4400 s–1 ~ µ BUs; σ 0 ~ 3 × 10 8 s–1; µ ~ Nc/N0 ~ 10–1. In this laser, inequality (6.48) is not fulfilled as efficiently as in

sations is unchanged. Therefore, in the laser with the active medium of this type, the pulsations regime changes very rapidly to the stationary generation regime. This weakening of the effect of the dynamic Stark effect on the generation process is associated with the screening of the working levels by external electron shells.

6.5 THE GIANT PULSE REGIME

Single powerful lasing pulses can be induced by means of a sharp change of the gain or losses in the laser resonator. For rapid active changes of the losses in the laser resonators, it is recommended to use mechanical or electroand magneto-optical Q-factor modulators with the switching time of the losses from microseconds to fractions of microseconds.

The lasing behaviour of a laser with active disconnection of the losses can be described by the system of equations (6.33) and (6.34). The initial inversion of the populations N (t) at the moment of disconnection of

After a rapid decrease of the losses to the value σ 0 <σ ~0 which can be carried out using sufficiently powerful and long-term pumping at the moment when the inversion reaches the value σ~0 /β , when the gain becomes equal to the initial losses, the radiation of the inversion in lasing of the giant pulse is almost completely independent of the pumping and spontaneous transitions. Therefore, in equation (6.33) only the term BNU, describing the forced transitions, will remain for the inversion of the populations, and the development of lasing in the giant pulse regime is described by the following system of equations

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Principles of lasing of solid-state lasers

This system is reduced to the following differential equation

The maximum of the giant pulse corresponds to the values U = 0, N = σ 0/β , and radiation density is

Taking into account the coefficient of inactive losses σ , the power of the radiation passing outside the limits of the resonator is

where S is the cross-sectional area of the active medium, l is its length. Substituting (6.64) into (6.65) makes it possible to determine the maximum power of radiation passing outside the limits of the resonator.

The lasing of the giant pulse is accompanied by the release of the energy

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Physics of Solid-State Lasers

inside the active medium.

The value of the minimum inversion of populations Nmin remaining after the lasing of a giant single pulse, can be determined from equation (6.61) taking into account the fact that at the minimum N(t) we have dN/dt = 0 and U >> 0 in accordance with (6.56):

This energy is lower than the total energy stored in the active medium

since the fraction W(0)g is used as a result of the inactive losses in the resonator, and the other part, expressed by the equation

remains in the medium because of incomplete scintillation.

The mean duration of the giant single pulse ∆ t is evaluated by the following equation, taking equations (6.62), (6.65) into account:

The estimates for ruby and Nd glass lasers with active media with the length l ~ 10 cm, cross-section S ~ 1 cm2 and the resonators with the length l ~ 102 cm show that the maximum value of the power of

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