electron avalanche theory for relatively small photon energies, h/10.2 (is laser fre-uency, I is ionization potential). Fig.2. Temperature dependence of critical field predicted /12/ T=1/2 vg (2mI)1/2 (see text for denotetions). n Fig.3. Frequency dependence of critical field predicted/17/ by electron avalanche the ory for picosecond and nanosecond pulse width regions (is laser radiation fre uency, I is ionization potential). NE 2 versus 7971 Fig.4. Critical field parameter, qc pulse width for NaCl predicted tiphoton (curves 1,2,3) and electron ava by mul Fig.5. Damage threshold versus temperature in NaCl at various wave lengths/33,34/ Frequency, 1015sec-1 30.6 2.76 1.06 0.69 0.53 Wavelength, um Fig.6. Frequency dependence of damage threshold in NaCl at 300 K /33,34/. THE THEORY OF INCLUSION-INITIATED LASER DAMAGE IN OPTICAL M.F. Koldunov, A.A. Manenkov, and I.L. Pokotilo Academy of Sciences A model of laser induced damage based on the mechanism of thermal explosion of absorbing inclusions is analyzed. Conditions for occurrence of the thermal explosion are formulated. The influence of saturation of the absorption of laser radiation and the role of photoionization of a dielectric matrix by absorbing inclusion on thermal radiation in explosion development are considered. The kinetics of the thermal explosion are analyzed, and the pulse width dependence of the damage threshold is found. Numerical estimates of the damage thresholds for typical cases are presented, showing that the thermal explosion model considered is a rather realistic one for describing the laser-induced damage in optical materials containing absorbing inclusions. Key words: absorbing inclusions, damage threshold, laser induced damage, photoionization, pulse-duration dependence, thermal explosion, thermal radiation. The important result of the numerous experimental investigations which have been carried out until recently consists of the fact that absorbing inclusions strongly affect the laser-induced damage in dielectric materials /I/. Many laser damage features (low damage threshold of the dielectric surface as compared with its bulk, variation of the damage threshold in a sample and from one sample to another, damage statistics and so on) are explained from this standpoint. The pioneering theoretical investigations of laser damage due to absorbing inclusion were carried out in papers /2,3/ where laser heating of the absorbing inclusion was analyzed under the assumption that the material parameters, such as absorption and thermal conductivity coefficients, are independent of temperature. Expressions were found for a laser damage threshold in terms of different criteria of the critical temperature, T, corresponding to the melting point /2/ and the mechanical breakdown /3/. The models considered in papers /2,3/ qualitatively explain some important regularities of laser induced damage, such as the dependence of the damage threshold on pulse duration /2/, but they do not sufficiently correspond to physical processes of laser damage. First of all, the assumption that the material parameters are independent of temperature cannot be correct, since the temperature in an inclusion region can reach 10" 'K, when the intensity is equal to the damage threshold /I/. Besides, in a framework of the thermoelastic model /3/ the value and physical sense of the critical temperature remain indefinite because of difficulty in estimating critical stresses at which the mechanical breakdown occurs. Finally, from the viewpoint of the thermoelastic stress model a correlation between the damage threshold of the materials and their physicalmechanical parameters should take place, which does not agree with the experimental data. A substantially new approach to the laser damage problem has been proposed in paper /4/, where it was shown that an allowance for the temperature dependence of the material parameters yields a qualitative change in the character of laser-produced heating of the absorbing inclusions. In this case there is a threshold intensity q2 (or an associated critical temperature T2) which if exceeded, leads to thermal explosion of the absorbing inclusion. The thermal explosion model explains the catastrophic character of laserinduced damage with a strictly defined damage threshold. If the energy absorbed by the inclusion is not sufficient to produce a macrodamage in the material (it can take place for inclusions of very small submicron size), the thermal explosion can serve as a source of absorption in the surrounding material through photoionization by thermal radiation. This mechanism was proposed in Ref. /5/ and developed in detail in Ref. /6/. Another mechanism of additional absorption is associated with thermal-ionization /7/ but it, obviously, may be effective only for the narrow bandgap materials. |