Abstract

In this letter we report a novel technique to measure small laser beam spot sizes. We use the open aperture z-scan technique as a tool to measure the laser beam spot size. This technique measures small spot sizes with accuracy better than 10%.

© 1999 Optical Society of America

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References

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  1. Photon Inc., BeamScan manual for model 1180 optical profiler.
  2. M. Sheik-Bahae et al., “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26,760–769 (1990).
    [CrossRef]
  3. E.W. Van Stryland, M. Sheik-Bahae, “Z-scan technique for nonlinear materials characterization,” Critical reviews of optical science and technology, SPIE CR69,501–524 (1997).
  4. H.S. Loka et al., “Two-photon absorption coefficient and refractive index changes in low-temperature-grown GaAs,” Proc. CLEO ’98 6,536 (1998).

1998

H.S. Loka et al., “Two-photon absorption coefficient and refractive index changes in low-temperature-grown GaAs,” Proc. CLEO ’98 6,536 (1998).

1997

E.W. Van Stryland, M. Sheik-Bahae, “Z-scan technique for nonlinear materials characterization,” Critical reviews of optical science and technology, SPIE CR69,501–524 (1997).

1990

M. Sheik-Bahae et al., “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26,760–769 (1990).
[CrossRef]

Loka, H.S.

H.S. Loka et al., “Two-photon absorption coefficient and refractive index changes in low-temperature-grown GaAs,” Proc. CLEO ’98 6,536 (1998).

Sheik-Bahae, M.

E.W. Van Stryland, M. Sheik-Bahae, “Z-scan technique for nonlinear materials characterization,” Critical reviews of optical science and technology, SPIE CR69,501–524 (1997).

M. Sheik-Bahae et al., “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26,760–769 (1990).
[CrossRef]

Van Stryland, E.W.

E.W. Van Stryland, M. Sheik-Bahae, “Z-scan technique for nonlinear materials characterization,” Critical reviews of optical science and technology, SPIE CR69,501–524 (1997).

Critical reviews of optical science and technology, SPIE

E.W. Van Stryland, M. Sheik-Bahae, “Z-scan technique for nonlinear materials characterization,” Critical reviews of optical science and technology, SPIE CR69,501–524 (1997).

IEEE J. Quantum Electron.

M. Sheik-Bahae et al., “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26,760–769 (1990).
[CrossRef]

Proc. CLEO ’98

H.S. Loka et al., “Two-photon absorption coefficient and refractive index changes in low-temperature-grown GaAs,” Proc. CLEO ’98 6,536 (1998).

Other

Photon Inc., BeamScan manual for model 1180 optical profiler.

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Figures (4)

Figure 1
Figure 1

Open aperture z-scan experimental setup where the ratio of power defined by detectors D2 and D1 is measured as a function of the sample position z with respect to the focal plane.

Figure 2
Figure 2

The coordinate system used in calculating the transmission of a Gaussian beam through a sample of thickness d.

Figure 3
Figure 3

The effect of the beam spot size on the calculated normalized transmittance.

Figure 4
Figure 4

The dotted line represents the measured normalized transmittance as a function of sample position (z-scan data) at λ = 900 nm fer a sample grown at (a) 270°C and annealed for 30 s at 700°C with average power ~13 µW, spot size ~1.6 µm and β = 35 cm/GW and (b) 220°C and annealed for 30 s at 900°C with average power ~8 mW, spot size ~2.1 µm end β = 30 cm/GW using a 150 fs pulse. The solid lines show the different theoretical fits using different beam spot sizes.

Equations (6)

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d I ( z ,   z ) / d z = β   I ( z ,   z ) 2
I ( z ) = I ( z = 0 ) / [ 1 + I ( z = 0 ) β z ]
T ( z ) = P z = d ( z ) / P z = 0 ( z )
P z = d ( z ) = t r = 0 θ = 0 2 π I ( z ) exp ( ( t / τ p ) 2 exp ( 2 ( r / w 0 ) 2 ) 1 + I ( z ) β   d exp ( ( t / τ p ) 2 exp ( 2 ( r / w 0 ) 2 ) r d r   d θ   d t .
P z = 0 ( z ) = t r = 0 θ = 0 2 π I ( z ) exp ( ( t / τ p ) 2 exp ( 2 ( r / w o ) 2 ) r d r   d θ   d t .
T ( z ) = 2 π I ( z ) β d τ p 0 ln ( 1 + I ( z ) β   d exp ( ( t / τ p ) 2 ) ) d t .

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