Abstract

This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs.

© 2016 Optical Society of America

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References

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  1. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
    [Crossref]
  2. Jean-Michel Ménard, Markus Betz, Iliya Sigal, and Henry M. van Driel, “Single-beam differential z-scan technique,” Appl. Opt. 46(11), 2119–2122 (2007).
    [Crossref] [PubMed]
  3. Mauro Falconieri, Elia Palange, and Hugo L Fragnito, “Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique,” J. Opt. A: Pure Appl. Opt. 4, 404–407 (2002).
    [Crossref]
  4. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
    [Crossref]
  5. M. C. Fischer, H. C. Liu, I. R. Piletic, and W. S. Warren, “Simultaneous self-phase modulation and two-photon absorption measurement by a spectral homodyne Z-scan method,” Opt. Express 16(6), 4192–4205 (2008).
    [Crossref] [PubMed]
  6. D. Weaire, B. S. Wherrett, D. A. B. Miller, and S. D. Smith, “Effect of low-power nonlinear refraction on laser-beam propagation in InSb,” Opt. Lett. 4(10), 331–333 (1979).
    [Crossref] [PubMed]
  7. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
    [Crossref]
  8. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
    [Crossref]
  9. P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two dimentional z scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85(10), 7043–7050 (1999).
    [Crossref]
  10. J. A. DávilaPintle, E. Reynoso Lara, and M. D. Iturbe Castillo, “Sensitivity optimization of the one beam Z-scan technique and a z-scan technique immune to nonlinear absorption,” Opt. Express 21(13), 15350–15363, (2013).
    [Crossref]
  11. Standford Research Systems Inc., “Model SR540 optical chopper,” http://www.thinksrs.com/downloads/PDFs/Manuals/SR540m.pdf .
  12. J. A. Dávila, L. V. Reyes, and E. R. Lara, “A new technique to measure the width of Gaussian Beams,” in AIP Conference Proceedings, Niklaus Ursus Wetter and Jaime Frejlich (AIP Publishing, 2008), pp.628–631.
  13. R. S. Sirohi, A Course of Experiments with He-Ne Laser2 edition (New Age International (P) Limited, Publishers, 1991).
  14. F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
    [Crossref]

2013 (1)

2008 (1)

2007 (1)

2003 (3)

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
[Crossref]

2002 (1)

Mauro Falconieri, Elia Palange, and Hugo L Fragnito, “Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique,” J. Opt. A: Pure Appl. Opt. 4, 404–407 (2002).
[Crossref]

1999 (1)

P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two dimentional z scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85(10), 7043–7050 (1999).
[Crossref]

1995 (1)

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
[Crossref]

1979 (1)

Akkara, J. A.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Aranda, F. J.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Betz, Markus

Castillo, M. D. Iturbe

Chen, P.

P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two dimentional z scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85(10), 7043–7050 (1999).
[Crossref]

Chen, Z.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Dávila, J. A.

J. A. Dávila, L. V. Reyes, and E. R. Lara, “A new technique to measure the width of Gaussian Beams,” in AIP Conference Proceedings, Niklaus Ursus Wetter and Jaime Frejlich (AIP Publishing, 2008), pp.628–631.

DávilaPintle, J. A.

Fakis, M.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
[Crossref]

Falconieri, Mauro

Mauro Falconieri, Elia Palange, and Hugo L Fragnito, “Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique,” J. Opt. A: Pure Appl. Opt. 4, 404–407 (2002).
[Crossref]

Fischer, M. C.

Fragnito, Hugo L

Mauro Falconieri, Elia Palange, and Hugo L Fragnito, “Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique,” J. Opt. A: Pure Appl. Opt. 4, 404–407 (2002).
[Crossref]

Giannetas, V.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
[Crossref]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
[Crossref]

Kaplan, D. L.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Lara, E. R.

J. A. Dávila, L. V. Reyes, and E. R. Lara, “A new technique to measure the width of Gaussian Beams,” in AIP Conference Proceedings, Niklaus Ursus Wetter and Jaime Frejlich (AIP Publishing, 2008), pp.628–631.

Lara, E. Reynoso

Liu, H. C.

Ménard, Jean-Michel

Miller, D. A. B.

Oulianov, D. A.

P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two dimentional z scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85(10), 7043–7050 (1999).
[Crossref]

Palange, Elia

Mauro Falconieri, Elia Palange, and Hugo L Fragnito, “Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique,” J. Opt. A: Pure Appl. Opt. 4, 404–407 (2002).
[Crossref]

Persephonis, P.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
[Crossref]

Piletic, I. R.

Polyzos, I.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
[Crossref]

Rao, D. V. G. L. N.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Rentzepis, P. M.

P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two dimentional z scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85(10), 7043–7050 (1999).
[Crossref]

Reyes, L. V.

J. A. Dávila, L. V. Reyes, and E. R. Lara, “A new technique to measure the width of Gaussian Beams,” in AIP Conference Proceedings, Niklaus Ursus Wetter and Jaime Frejlich (AIP Publishing, 2008), pp.628–631.

Roach, J. F.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
[Crossref]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
[Crossref]

Sigal, Iliya

Sirohi, R. S.

R. S. Sirohi, A Course of Experiments with He-Ne Laser2 edition (New Age International (P) Limited, Publishers, 1991).

Smith, S. D.

Tomov, I. V.

P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two dimentional z scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85(10), 7043–7050 (1999).
[Crossref]

Tsigaridas, G.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
[Crossref]

van Driel, Henry M.

VanStryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
[Crossref]

Warren, W. S.

Weaire, D.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
[Crossref]

Wherrett, B. S.

Wong, C.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Zhou, P.

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B-Lasers O (2)

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B-Lasers O 76, 83–86 (2003).
[Crossref]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique for elliptic Gaussian beams,” Appl. Phys. B-Lasers O 77, 71–75 (2003).
[Crossref]

IEEE J. Quantum Elect. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. VanStryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Elect. 26, 760–769 (1990).
[Crossref]

J. Appl. Phys. (1)

P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two dimentional z scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85(10), 7043–7050 (1999).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

Mauro Falconieri, Elia Palange, and Hugo L Fragnito, “Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique,” J. Opt. A: Pure Appl. Opt. 4, 404–407 (2002).
[Crossref]

Opt. Comm. (1)

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan analysis for high order nonlinearities through Gaussian decomposition,” Opt. Comm. 225, 253–268 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Rev. (1)

F. J. Aranda, D. V. G. L. N. Rao, C. Wong, P. Zhou, Z. Chen, J. A. Akkara, D. L. Kaplan, and J. F. Roach, “Non linear optical interactions in bacteriorhodopsin using z-scan,” Opt. Rev. 2 (3), 204–206 (1995).
[Crossref]

Other (3)

Standford Research Systems Inc., “Model SR540 optical chopper,” http://www.thinksrs.com/downloads/PDFs/Manuals/SR540m.pdf .

J. A. Dávila, L. V. Reyes, and E. R. Lara, “A new technique to measure the width of Gaussian Beams,” in AIP Conference Proceedings, Niklaus Ursus Wetter and Jaime Frejlich (AIP Publishing, 2008), pp.628–631.

R. S. Sirohi, A Course of Experiments with He-Ne Laser2 edition (New Age International (P) Limited, Publishers, 1991).

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Figures (7)

Fig. 1
Fig. 1 Processing of the detected signal (Vph) into a square signal (Vsq).
Fig. 2
Fig. 2 Experimental setup of the chopper z-scan technique, P: Polarizer, L1: Lens, S: Sample, Ch: Chopper, PD: Photodetector, EC: Electronic circuit, DAQ: Data acquisition card and PC: Personal computer.
Fig. 3
Fig. 3 Eclipsing time as a function of the rotation period of the chopper.
Fig. 4
Fig. 4 Duty cycle versus rotation period.
Fig. 5
Fig. 5 Colocation of the chopper in order to sweep along (a) minor axis and (b) major axis.
Fig. 6
Fig. 6 Characterization of the elliptic beam to establish the origin where the minimum waist along the minor axis occurs.
Fig. 7
Fig. 7 z-scan curves obtained along major and minor axes. The Rayleigh range and astigmatism differences can be seen in both curves.

Equations (8)

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τ 2 w Ω 0 R
τ w π R T
δ = w π R
Δ z m Δ z M = r M r m
n 2 = Δ ϕ 0 k I 0 L e f f
Δ ϕ 0 Δ τ p v 0.273 τ L
n 2 = 1 0.273 k I 0 L e f f Δ δ p v δ L .
n 2 = 1.79 × 10 4 c m 2 W .

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