Abstract

A simple technique for in situ measurements of pulsed Gaussian-beam spot sizes is reported. This technique is particularly useful for measurements on highly focused beam spots. It can also be used for absolute calibration of the threshold-energy fluences for pulsed-laser-induced effects. The thresholds for several effects in picosecond-laser-induced phase transformation on silicon-crystal surfaces are calibrated with this technique.

© 1982 Optical Society of America

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References

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  1. For example, a multilens camera technique: I. M. Winer, “A self-calibrating technique measuring laser beam intensity distributions,” Appl. Opt. 5, 1437 (1966).
    [CrossRef] [PubMed]
  2. See, for example, A Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 110–117.
  3. J. M. Liu, R. Yen, H. Kurz, N. Bloembergen, “Phase transformation on and charged particle emission from a silicon crystal surface, induced by picosecond laser pulses,” Appl. Phys. Lett. 39, 755 (1981). Photographs of the amorphous ring patterns can be found in this reference.
    [CrossRef]

1981

J. M. Liu, R. Yen, H. Kurz, N. Bloembergen, “Phase transformation on and charged particle emission from a silicon crystal surface, induced by picosecond laser pulses,” Appl. Phys. Lett. 39, 755 (1981). Photographs of the amorphous ring patterns can be found in this reference.
[CrossRef]

1966

Bloembergen, N.

J. M. Liu, R. Yen, H. Kurz, N. Bloembergen, “Phase transformation on and charged particle emission from a silicon crystal surface, induced by picosecond laser pulses,” Appl. Phys. Lett. 39, 755 (1981). Photographs of the amorphous ring patterns can be found in this reference.
[CrossRef]

Kurz, H.

J. M. Liu, R. Yen, H. Kurz, N. Bloembergen, “Phase transformation on and charged particle emission from a silicon crystal surface, induced by picosecond laser pulses,” Appl. Phys. Lett. 39, 755 (1981). Photographs of the amorphous ring patterns can be found in this reference.
[CrossRef]

Liu, J. M.

J. M. Liu, R. Yen, H. Kurz, N. Bloembergen, “Phase transformation on and charged particle emission from a silicon crystal surface, induced by picosecond laser pulses,” Appl. Phys. Lett. 39, 755 (1981). Photographs of the amorphous ring patterns can be found in this reference.
[CrossRef]

Winer, I. M.

Yariv, A

See, for example, A Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 110–117.

Yen, R.

J. M. Liu, R. Yen, H. Kurz, N. Bloembergen, “Phase transformation on and charged particle emission from a silicon crystal surface, induced by picosecond laser pulses,” Appl. Phys. Lett. 39, 755 (1981). Photographs of the amorphous ring patterns can be found in this reference.
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. M. Liu, R. Yen, H. Kurz, N. Bloembergen, “Phase transformation on and charged particle emission from a silicon crystal surface, induced by picosecond laser pulses,” Appl. Phys. Lett. 39, 755 (1981). Photographs of the amorphous ring patterns can be found in this reference.
[CrossRef]

Other

See, for example, A Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 110–117.

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Figures (4)

Fig. 1
Fig. 1

Transverse spatial profile of the unfocused second-harmonic laser beam, taken with a Reticon photodiode array.

Fig. 2
Fig. 2

Semilog plots of the energy dependence of the outer radii (○) and inner radii (•) of the amorphous ring patterns on a (111) silicon surface and the radii of the burn spots (X) on a Polaroid film, induced by 20-psec pulses at 532 nm. ρ is the experimentally determined (1/e) intensity radius of the green beam at the focal spot.

Fig. 3
Fig. 3

Semilog plots of the energy dependence of the outer radii of the amorphous patterns on a (111) silicon surface (○) and a (100) silicon surface (Δ) and the radii of the burn spots (X) on a Polaroid film, induced by 15-psec pulses at 266 nm. ρ is the experimentally determined (1/e) intensity radius of the UV beam at the focal spot.

Fig. 4
Fig. 4

Comparison between the measured (○) and calculated (solid curve) spatial-profile characteristics around the waist of the second-harmonic beam focused by a lens with focal length f: d is the distance from the lens, d0 is the position of the beam waist, ω0 is the beam waist size, and θ is the divergence of the focused beam.

Tables (1)

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Table 1 Threshold-Energy Fluences for Picosecond-Laser-Induced Phase Transformation on Silicon-Crystal Surfaces

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I ( r , t ) = I 0 exp ( r 2 / ρ 2 ) exp ( t 2 / τ 2 ) ,
E ( r ) = d tI ( r , t ) = E 0 exp ( r 2 / ρ 2 ) ,
E ( r a ) = E 0 exp ( r a 2 / ρ 2 ) = E a ,
E ( r c ) = E 0 exp ( r c 2 / ρ 2 ) = E c .
r a 2 = ρ 2 ( ln E 0 ln E a ) ,
r c 2 = ρ 2 ( ln E 0 ln E c ) .

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