I heard somewhere the ablation threshold is proportional to the square root of the pulse length but I was not able to find a reference.
Is that an empirical relationship? which is the validity range? Does it works only for nanosecond lasers?
Dear Diego,
On the surface and in the bulk optical materials always contain laser absorbing foreign inclusions and impurities, the origin of which has a different nature (abrasive material, the particles of the crucible; dirt contained in the feed, and so on). Usually, the dependence of the ablation threshold of real materials is determined by the presence of such defects.
In general, this relationship has an empirical character. Because of the complexity of the phenomenon of ablation it can be described only approximately. The same applies to own breakdown in pure materials. Of course, it works not only in the range of nanosecond pulses.
At the same time dependence of the ablation threshold has a characteristic shape. In the simplest case for imperfect materials, calculations show that when the pulse duration τp > τ0 (τ0 ≈ l2/a, l - the characteristic size of the "most dangerous" defect, a - thermal switching) power density threshold Pth ~ (tp )1/2. At a pulse duration τp < τ0 threshold power density Pth ~ (tp )-1.
Actually dependence of a threshold of an ablation on duration of an impulse can be characterized by other power dependence that is connected as with existence of defects of various sizes (a polymodality of thresholds of an ablation), and their nature. However on this dependence there will be a characteristic inflection point.
More information can be found in a number of publications survey character, which contains extensive information on selected aspects of laser damage (ablation): a series of summaries (see 1 and references therein) papers presented at a symposium on optical materials for high-power lasers 2; review of work on the laser strength of thin-film optical coatings 3, as well as numerous other reviews4 and original articles5,6.
For pure materials a theoretical model is developed to describe the process of ultrashort-pulse laser-induced damage to dielectrics. In the model, multiphoton ionization, avalanche ionization, electron-ion recombination, and the electron diffusion are taken into account (see for example7).
1. Bennet t H. E., G u e n t h e г A. H.,Milam D., N e w m a n В. Е.— Ibidem, 1983, v. 22, p. 3276.
2. This symposium annually since 1962, is held in the United States (Boulder, Colorado), and his works are published by the National Bureau of Standards; see: Index of Papers: Laser Induced Damage in Optical Materials, Proceedings of the Boulder Damage Symposium (U.S. Department of the Commerce, National Institute of Standards, 1969-95), Vol. 1-27.
3. W a 1 k e r T. W., Guenther A. H., Nielsen P. E.— IEEE J. Quantum Electron., 1981, v. QE-17, p. 2041
4. http://ufn.ru/ufn86/ufn86_1/Russian/r861h.pdf
5.https://www.researchgate.net/publication/252740760_Influence_of_the_surface_layer_on_the_optical_strength_of_lithium_niobate
6. http://iopscience.iop.org/1063-7818/32/4/A13
7. Dalwoo Kim, Guo-Bin Ma, and Gang-Yao Xiao. Theoretical Studies on the Threshold Dependence of Laser-Induced Damage. Journal of the Korean Physical Society, Vol. 32, No. 1, January 1997, pp. 60-63
Advice: when you search for articles on the theme you must type "laser damage" (but not "laser ablation")
Regards, Leonid A. Skvortsov
Article Influence of the surface layer on the optical strength of li...
Let
t - laser pulse duration
F - laser pulse fluence ~ intensity*t
Energy of laser pulse is distributed over the depth L depending on the absorption depth La as well as the length of thermal diffusion during the laser pulse Ld
approximately Ld= (4*D*t)1/2
D is thermal diffusivity equal
D = (thermal_conductivity)/(mass_density*specific_heat)
When Ld >> La we have roughly L = Ld~ t 1/2.
The threshold is achieved when density of absorbed energy proportional to F/L is equal to some critical energy density Wc. Hence threshold fluence Fc = Wc*L ~ t 1/2
I hope I wrote it clearly.
I meant laser ablation as used in Pulsed Laser Deposition (PLD) of materials, not the laser damage. In nanosecond regime the ablation mechanism is mostly thermal. Hence, the above considerations may be repeated more exact using formulas for time-dependent distribution of heat in the target.