Transient and steady-state electrostrictive laser beam trapping

Damage in Laser Materials

“…-C,g (n )X^/At. (21) a^o Equations (20) and (21) predict a constant total power threshold [34] for At »t and an energy density threshold varying inversely with At for At « T. To illustrate this behavior, curves based on calculations for ruby laser radiation in BK-7 glass [40] are plotted as solid lines in figure 5 along with a data point for damage accompanied by self-focusing from a 40ij, initial beam radius [41]. The exact agreement between this measurement and the calculations is probably fortuitous since the damage level should exceed the trapping threshold in order to reduce the beam cross-section significantly The beam must also travel a finite distance in the material for self-focusing to have a notable effect An approximate focusing length can be defined by equating the optical path length (n^+ An)L£ along the beam axis with the path length n^(L^^+^h^^^^from the beam perimeter to the axis, where An is the change in refractive index on axis [42].…”

“…The exact agreement between this measurement and the calculations is probably fortuitous since the damage level should exceed the trapping threshold in order to reduce the beam cross-section significantly The beam must also travel a finite distance in the material for self-focusing to have a notable effect An approximate focusing length can be defined by equating the optical path length (n^+ An)L£ along the beam axis with the path length n^(L^^+^h^^^^from the beam perimeter to the axis, where An is the change in refractive index on axis [42]. Using appropriate limiting forms for An [40] and requiring to equal the sample length L, gives Large local intensity variations over the beam cross-section can cause localized self-focusing resulting in the formation of multiple filaments 2,2 ---•°= At/L (22) d b^'…”

Pulse duration dependence of laser damage mechanisms

“…For At ~ z the acoustic wave does not have time to develop fully, and trapping requires an increased energy density given by Equations 20 and 21 predict a constant total power threshold [36] for At >> 9 and an energy density threshold varying inversely with At for At ~ "c. To illustrate this behaviour, curves based on calculations for ruby laser radiation in BK-7 glass [43] are plotted as solid lines in fig. 5 along with a data point for damage accompanied by self-focusing from a 40 /~m initial beam radius [44].…”

“…An approximate focusing length Lf can be defined by equating the optical path length (no +An) Lf along the beam axis with the path length no(LZ+ r2) 1/2 from the beam perimeter to the axis, where An is the change in refractive index on axis [45]. Using appropriate limiting forms for An [43] and requiring Lf to equal the sample length L, gives e a ~: r 2 A t/L 2 (22) forAt >> zand ed oc r~/(L 2 A t) (23) for At ~ z. When a sample is irradiated by a sharply focused beam, the length which is useful for development of self-focusing is less than L.…”

Optical and mechanical properties of some neodymium-doped laser glasses

“…( an) Data on p -:-are needed to calc ulate th e selfrip T focusin g induced by e lec trostriction [33]. Calcula tion s…”