Volume 80A, number 4 PHYSICS LETTERS 8 December 1980

SELF-FOCUSING OF A GAUSSIAN LASER BEAM REFLECTED

FROM A THERMOCAPILLARY LIQUID SURFACE

German Da COSTA Departamento de Fisica, Universidad Sim6n Bolivar, Caracas, Venezuela

Received 14 August 1980

Self-focusing of laser radiation reflected from the surface of liquid heavy hydrocarbons is reported. Close agreement of experimental data with theoretical previsions suggests that thermocapillarity is the main physical phenomenon involved. The focus appears at 40 cm of the sample surface after 1 s of irradiation at 350 mW.

A bell-shaped depression develops in a liquid sur- face irradiated by a gaussian laser beam [1]. Thermo- capillarity was proposed as the main physical pheno- menon involved [2]. This theory correctly describes qualitative aspects of the steady-state development of the experiment. The early stage of interaction is studied now. In that case, a straightforward calcula- tion [3] derived from the theory of ref. [2] previews

A F ~ A'

Fig. 1.

that the reflected laser beam is self-focused at any observation plane ~0 (placed at a distance L from the liquid surface in fig. 1) at a time instant:

t s = ( 2 ~ ) - l ( a / L ) t 0 , (1)

after the beginning of the irradiation. The time con- stant t O and the other parameters involved here are defined in ref. [2]. The diameter D(t , L) of the caustic light cone reflected from the inflexion points G, G' (fig. 1)is also given in ref. [3]:

D(t, L) = a ~ [ 1 - 2a(t/to) (L/a)], (2)

at the observation plane ~(L). c~ is a dimensionless parameter depending on the physical properties of the liquid sample. From eqs. (1), (2) one obtains also [3],

vt s = a ~ , (3)

where v = OD/Otlt=o and a is the radius of the laser beam at the 1/e point of the gaussian power distribu- tion. Eq. (3) is a striking theoretical prevision, for it implies that the product of the self-focusing time t s and the initial caustic growth rate v does not depend on the position of the observation plane nor on the material properties. The corresponding experiment was performed with an argon laser emitting 350 mW at 5145 A. The beam radius at the output mirror was 0.8 mm, the beam divergence 1 mrad and the distance from the output mirror to the sample 3 m. So we have a = 2.3 mm at the sample surface, and the theoretical previ- sion from eq. (3) is ot s = 3.24 mm. The samples were

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Volume 80A, number 4 PHYSICS LETTERS 8 Deeembor 1980

strongly light-absorbing heavy oils from the Orinoco Belt (Venezuela). A photographic sequence of the reflected light distribution at an observation plane ~b placed at L = 40 cm is presented in fig. 2. The re- cording frequency is 4 frames/s. The first enlarged photograph (fig. 3) corresponds to t = 0 (beginning of the irradiation). No light caustics appear here. A

Fig. 2.

light caustic proceeding from the lateral hills E, E' appears at t = 0.25 s (fig. 4). This early caustic is not previewed by the theory of ref. [2]. At this time in. stant, light coming from the central depression is still focused well above the observation plane. The focus F is formed over ~ at the self-focusing time t s = 1 s (fig. 5). Afterwards, another light caustic coming from the internal inflexion points G, G' develops (figs. 6, 7, corresponding to t = 1.5 s andt = 2 s, respectively). The interference pattern accompanying this new caustic

Fig. 3. Fig. 4.

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Volume 80A, number 4 PHYSICS LETTERS 8 December 1980

Fi~. 5.

r

i i

Fig. 6.

was studied in refs. [1,2]. The dimension of the refer- ence grid in the enlarged photographs is d = 1 mm. As D(t = 1 s) = 0 and D (t = 2s) = 3 mm one has t s = 1 s, o = 3 mm/s. So the experimental result is o t s = 3 mm,

Fig. 7.

in close agreement with the theoretical prevision. Similar results are obtained for other laser power levels. This reinforces the hypothesis that thermocapillarity is the main phenomenon involved in the early stage of the interaction of low-power laser beams and liquid materials. It is pointed out that the preceding interpre- tation of the experiment considers the focal region as being formed only by the point F. In a deeper analysis the complex light distribution existing in the focal re- gion of the central depression may also be taken into account.

This research is supported by the University Simon Bolivar and the National Agency FONINVES.

References

[1] G. Da Costa and J. Calatroni, Appl. Opt. 17 (1978) 2381. [2] G. Da Costa and J. Calatroni, Appl. Opt. 18 (1979) 233. [3] G. Da Costa, Phys. Lett. 80A (1980) 323.

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