Abstract

It is presented a criteria for selecting the optimum aperture radius for the one beam Z-scan technique (OBZT), based on the analysis of the transmittance of the aperture. It is also presented a modification to the OBZT by directly measuring the beam radius in the far field with a rotating disk, which allows to determine simultaneously the non-linear absorptive coefficient and non-linear refractive index, much less sensitive to wave front distortions caused by inhomogeneities of the sample with a negligible loss of signal to noise ratio. It is demonstrated its equivalence to the OBZT.

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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. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
    [CrossRef]
  2. J. Wang, B. Gu, Y. M. Xu, and H. T. Wang, “Enhanced sensitivity of Z-scan technique by use of flat-topped beam,” Appl. Phys. B95(4), 773778 (2009).
    [CrossRef]
  3. T. Xia, D. J. Hagan, M. Sheik Bahae, and E. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett.19(5), 317–319 (1994).
    [CrossRef] [PubMed]
  4. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
    [CrossRef]
  5. P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. I. Bhattacharyya, S. Priyadarshi, and D. Goswami, “Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics,” Chem. Phys. Lett.469, 104–109, (2009).
    [CrossRef] [PubMed]
  16. A. Rogalski and Z. Bielecki, “Detection of optical radiation,” Bull. Pol. Ac.: Tech.52(1), 43–66 (2004).
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    [CrossRef]
  20. X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
    [CrossRef]

2009 (3)

J. Wang, B. Gu, Y. M. Xu, and H. T. Wang, “Enhanced sensitivity of Z-scan technique by use of flat-topped beam,” Appl. Phys. B95(4), 773778 (2009).
[CrossRef]

A. Nag, A. Kumar De, and D. Goswami, “Two-photon cross-section measurements using an optical chopper: z-scan and two-photon fluorescence schemes,” J. Phys. B: At. Mol. Opt. Phys.42(6), 065103, (2009).
[CrossRef]

I. Bhattacharyya, S. Priyadarshi, and D. Goswami, “Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics,” Chem. Phys. Lett.469, 104–109, (2009).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

A. Rogalski and Z. Bielecki, “Detection of optical radiation,” Bull. Pol. Ac.: Tech.52(1), 43–66 (2004).

2003 (1)

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
[CrossRef]

2001 (1)

X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
[CrossRef]

2000 (1)

J. Phillips and K. Kundert, “Noise in mixers, oscillators, samplers, and logic an introduction to cyclostationary noise,” Proceedings of the IEEE custom integrated circuits conference, 431–439, (2000).

1997 (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
[CrossRef]

1994 (2)

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
[CrossRef]

1986 (1)

S. Nemoto, “Determination of waist parameters of a Gaussian beam,” Appl. Opt.21(21), 3859–3863 (1986).
[CrossRef]

1984 (1)

1983 (1)

1978 (1)

1975 (1)

1971 (1)

Arnaud, J. A.

Bhattacharyya, I.

I. Bhattacharyya, S. Priyadarshi, and D. Goswami, “Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics,” Chem. Phys. Lett.469, 104–109, (2009).
[CrossRef] [PubMed]

Bielecki, Z.

A. Rogalski and Z. Bielecki, “Detection of optical radiation,” Bull. Pol. Ac.: Tech.52(1), 43–66 (2004).

Chapple, P. B.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
[CrossRef]

P. B. Chapple, “Beam waist and M2 measurement using a finite slit,” Opt. Eng.33(7), 2461–2466 (1994).
[CrossRef]

Connelly, J. A.

C. D. Motchenbacher and J. A. Connelly, Low-noise Electronic System Design (John Wiley & Sons Inc, 1993).

delaClaviére, B.

Fakis, M.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
[CrossRef]

Franke, E. A.

Franke, J. M.

Garetz, B. A.

Giannetas, V.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
[CrossRef]

Goswami, D.

A. Nag, A. Kumar De, and D. Goswami, “Two-photon cross-section measurements using an optical chopper: z-scan and two-photon fluorescence schemes,” J. Phys. B: At. Mol. Opt. Phys.42(6), 065103, (2009).
[CrossRef]

I. Bhattacharyya, S. Priyadarshi, and D. Goswami, “Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics,” Chem. Phys. Lett.469, 104–109, (2009).
[CrossRef] [PubMed]

Gu, B.

J. Wang, B. Gu, Y. M. Xu, and H. T. Wang, “Enhanced sensitivity of Z-scan technique by use of flat-topped beam,” Appl. Phys. B95(4), 773778 (2009).
[CrossRef]

Guo, S.

X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
[CrossRef]

Hagan, D. J.

T. Xia, D. J. Hagan, M. Sheik Bahae, and E. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett.19(5), 317–319 (1994).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
[CrossRef]

Hermann, J. A.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
[CrossRef]

Hou, L.

X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
[CrossRef]

Hubbard, W. M.

Khosrofian, J. M.

Kumar De, A.

A. Nag, A. Kumar De, and D. Goswami, “Two-photon cross-section measurements using an optical chopper: z-scan and two-photon fluorescence schemes,” J. Phys. B: At. Mol. Opt. Phys.42(6), 065103, (2009).
[CrossRef]

Kundert, K.

J. Phillips and K. Kundert, “Noise in mixers, oscillators, samplers, and logic an introduction to cyclostationary noise,” Proceedings of the IEEE custom integrated circuits conference, 431–439, (2000).

Liu, X.

X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
[CrossRef]

Mandeville, G. D.

McCally, R. L.

Mcduff, R. G.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
[CrossRef]

Mckay, T. J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
[CrossRef]

Ming, N.

X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
[CrossRef]

Motchenbacher, C. D.

C. D. Motchenbacher and J. A. Connelly, Low-noise Electronic System Design (John Wiley & Sons Inc, 1993).

Nag, A.

A. Nag, A. Kumar De, and D. Goswami, “Two-photon cross-section measurements using an optical chopper: z-scan and two-photon fluorescence schemes,” J. Phys. B: At. Mol. Opt. Phys.42(6), 065103, (2009).
[CrossRef]

Nemoto, S.

S. Nemoto, “Determination of waist parameters of a Gaussian beam,” Appl. Opt.21(21), 3859–3863 (1986).
[CrossRef]

Palpant, B.

Persephonis, P.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
[CrossRef]

Phillips, J.

J. Phillips and K. Kundert, “Noise in mixers, oscillators, samplers, and logic an introduction to cyclostationary noise,” Proceedings of the IEEE custom integrated circuits conference, 431–439, (2000).

Polyzos, I.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
[CrossRef]

Priyadarshi, S.

I. Bhattacharyya, S. Priyadarshi, and D. Goswami, “Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics,” Chem. Phys. Lett.469, 104–109, (2009).
[CrossRef] [PubMed]

Rogalski, A.

A. Rogalski and Z. Bielecki, “Detection of optical radiation,” Bull. Pol. Ac.: Tech.52(1), 43–66 (2004).

Ryasnyansky, I. A.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons Inc, 1991).
[CrossRef]

Shayler, P. J.

Sheik Bahae, M.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
[CrossRef]

Staromlynska, J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
[CrossRef]

Suzaki, Y.

Tachibana, A.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons Inc, 1991).
[CrossRef]

Tsigaridas, G.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
[CrossRef]

Van Stryland, E.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
[CrossRef]

Wang, H.

X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
[CrossRef]

Wang, H. T.

J. Wang, B. Gu, Y. M. Xu, and H. T. Wang, “Enhanced sensitivity of Z-scan technique by use of flat-topped beam,” Appl. Phys. B95(4), 773778 (2009).
[CrossRef]

Wang, J.

J. Wang, B. Gu, Y. M. Xu, and H. T. Wang, “Enhanced sensitivity of Z-scan technique by use of flat-topped beam,” Appl. Phys. B95(4), 773778 (2009).
[CrossRef]

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
[CrossRef]

Xia, T.

Xu, Y. M.

J. Wang, B. Gu, Y. M. Xu, and H. T. Wang, “Enhanced sensitivity of Z-scan technique by use of flat-topped beam,” Appl. Phys. B95(4), 773778 (2009).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. B (2)

J. Wang, B. Gu, Y. M. Xu, and H. T. Wang, “Enhanced sensitivity of Z-scan technique by use of flat-topped beam,” Appl. Phys. B95(4), 773778 (2009).
[CrossRef]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B76(1), 83–86 (2003).
[CrossRef]

Bull. Pol. Ac.: Tech. (1)

A. Rogalski and Z. Bielecki, “Detection of optical radiation,” Bull. Pol. Ac.: Tech.52(1), 43–66 (2004).

Chem. Phys. Lett. (1)

I. Bhattacharyya, S. Priyadarshi, and D. Goswami, “Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics,” Chem. Phys. Lett.469, 104–109, (2009).
[CrossRef] [PubMed]

IEEE J. Quant. Electron. (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quant. Electron.26(4), 760–769 (1990).
[CrossRef]

J. Nonlinear Opt. Phys. Mater (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-beam Z-scan: Measurement techniques and analysis,” J. Nonlinear Opt. Phys. Mater6(3), 251–293 (1997).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

X. Liu, S. Guo, H. Wang, N. Ming, and L. Hou, “Investigation of the influence of finite aperture size on the Z-scan transmittance curve,” J. Nonlinear Opt. Phys. Mater.10(4), 431–439 (2001).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

A. Nag, A. Kumar De, and D. Goswami, “Two-photon cross-section measurements using an optical chopper: z-scan and two-photon fluorescence schemes,” J. Phys. B: At. Mol. Opt. Phys.42(6), 065103, (2009).
[CrossRef]

Opt. Eng. (1)

P. B. Chapple, “Beam waist and M2 measurement using a finite slit,” Opt. Eng.33(7), 2461–2466 (1994).
[CrossRef]

Opt. Lett. (1)

Proceedings of the IEEE custom integrated circuits conference (1)

J. Phillips and K. Kundert, “Noise in mixers, oscillators, samplers, and logic an introduction to cyclostationary noise,” Proceedings of the IEEE custom integrated circuits conference, 431–439, (2000).

Other (2)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons Inc, 1991).
[CrossRef]

C. D. Motchenbacher and J. A. Connelly, Low-noise Electronic System Design (John Wiley & Sons Inc, 1993).

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Figures (12)

Fig. 1
Fig. 1

Front view of a slotted disk which rotates at a frequency Ω0 and eclipses a Gaussian beam shown in red. R is the distance from the rotation axis to the center of the beam, W is the beam width, and θ is the angle subtended by the spot beam.

Fig. 2
Fig. 2

Sensitivity of an aperture of radius (ρ0) to detect changes in its transmitted power (ΔP = P(W, ρ0) − P(WL, ρ0)), when the incident beam width changes from (WLW).

Fig. 3
Fig. 3

A) One beam Z-scan set up, B) Chopper Z-scan set up.

Fig. 4
Fig. 4

Establishment of the threshold voltages Vth1 and Vth2 using e−2 criteria for measuring the beam width W from Vph(t) (black line) and the beam profile (red line).

Fig. 5
Fig. 5

Set up for determining the optimum aperture radius for measuring transmitted power changes.

Fig. 6
Fig. 6

Z-scan curves free of nonlinear absorption for a bacteriorhodopsin sample, using different aperture radii (ρ0), WL = 3mm, the laser power was P0 = 40μW. In the inset is shown the normalized Vph measured without aperture, useful to obtain the free nonlinear absorption curves.

Fig. 7
Fig. 7

Rising part of Vph(t), notice the change of amplitude and slope as function of the sample position, the arrow indicates the increasing sample position z.

Fig. 8
Fig. 8

Rising time (τ) of Vph(t) as function of the sample position (z), in the inset it is shown the amplitude of Vph(t) versus z (which represents the nonlinear transmitance of the sample).

Fig. 9
Fig. 9

Z-scan curves of the physical variables of the two techniques when P0 = 10μW, for the OBZT ρ0 = 0.1WL and a lock-in amplifier was needed, PL and τL are the values measured for OBZT and chopper techniques respectively when the sample was located far from the focus.

Fig. 10
Fig. 10

Picture of a Gaussian beam profile distorted by an inhomogeneous sample, the graph shows the detected signal Vph(t), since the chopper technique works with the integral of the Gaussian profile and thanks to the limited bandwidth of the trans-impedance amplifier, the speckle affects little to the measurement.

Fig. 12
Fig. 12

Equivalence in W measurements given by the calibrated chopper and knife edge techniques.

Fig. 11
Fig. 11

Calibration of the chopper width measurement.

Equations (41)

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

τ 2 W ( ζ ) Ω 0 R
T ( z ) = P ( W ( z ) , ρ 0 ) P ( W ( ) , ρ 0 )
P ( W , ( z ) , ρ 0 ) = P 0 ( 1 exp ( 2 ρ 0 2 W ( z ) 2 ) )
Δ T ( z ) T ( ) = Δ P P 0 S 1
Δ P P 0 = P ( W , ρ 0 ) P ( W L , ρ 0 ) P 0
S = 1 exp ( 2 ρ 0 2 W L 2 )
Δ W = W W L
2 ρ 0 W P ( W , ρ 0 ) = 0
ρ 0 = W L 2
Δ P P 0 = exp ( 1 ) exp ( W L 2 W 2 )
Δ P P 0 2 exp ( 1 ) ( Δ W W L )
Δ T ( z ) T ( ) 1.16 ( Δ W W L )
Δ T p v 0.406 ( 1 S ) 0.25 | Δ Φ 0 |
Δ W p v W L 0.273 | Δ Φ 0 |
Δ τ = 2 Ω 0 R Δ W
V p h = R L P
S N = R L ( P ) 4 k T R L Δ f
Δ f = 1.57 2 π R L C L
Δ P min = 2 4 k T R L Δ f R L
| Δ W min OB W L | = exp ( 1 ) 4 k T R L Δ f R L P 0
| Δ W min O B W L | = 2.72 P n R L P 0
P ch ( t ) = P 0 2 ( 1 erf ( 2 R sin ( Ω 0 t ) W ) )
β = R W
P ch ( t ) P 0 2 ( 1 erf ( 2 β Ω 0 t ) )
P ch ( t ) = 1 2 2 π m = 0 1 2 m + 1 exp ( 1 8 ( 2 m + 1 β ) 2 ) sin ( ( 2 m + 1 ) Ω 0 t )
Δ f c = 4 β f 0
Δ f c Δ f
Δ f c 1 τ = Ω 0 β 2
Δ f π β f 0
var ( j ( t c ) ) var ( n ( t c ) ) ( d V p h ( t c ) d t ) 2
V ph ( t ) R L P ch ( t )
var ( j ( t c ) ) P n ( d v ph ( t c ) dt ) 2
var ( W ) Ω 0 R 2 P n | d V ph ( t c ) d t |
t c = ± 2 W L 3 Ω 0 R
| d d t V ph ( ± t c ) | = 2 π e 8 9 β Ω 0 ( R L P 0 )
Δ W min Ch W L = 3 P n R L P 0
Δ τ p v τ L 0.273 | Δ Φ 0 |
Δ P P 0 ( 4 ρ 0 2 W L 2 exp ( 2 ρ 0 2 W L 2 ) ) Δ W W L
Δ P P L = 1.98 ( Δ τ ) τ L
Δ f Δ f c
W k n = 0.8 W c h + 74.8 μ m

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