Abstract

We report on the accurate measurement of nonlinear ellipse rotation (NER) by means of a phase-sensitive method employing a dual-phase lock-in. The magnitudes and signs of pure refractive electronic nonlinearities of silica and BK7 were determined with this new method using 150 femtosecond (fs) laser pulses at 775 nm. Experimental and theoretical analyses of the NER signal were carried out and the results were compared to those obtained with the Z-scan technique.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2013 (1)

2012 (1)

M. Kokhharov, S. A. Bakhromov, U. K. Makhmanov, R. A. Kokhkharov, and E. A. Zakhidov, “Self-induced polarization rotation of laser beam in fullerene (C70) solutions,” Opt. Commun. 285(12), 2947–2951 (2012).
[Crossref]

2011 (2)

2009 (1)

2007 (2)

2004 (1)

1998 (1)

1997 (2)

1990 (1)

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

1987 (1)

1973 (1)

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. 9(11), 1064–1069 (1973).
[Crossref]

1965 (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

1964 (1)

P. B. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependence change in the refractive index of liquids,” Phys. Rev. Lett. 12(18), 507–509 (1964).
[Crossref]

Adair, R.

Albert, O.

Bakhromov, S. A.

M. Kokhharov, S. A. Bakhromov, U. K. Makhmanov, R. A. Kokhkharov, and E. A. Zakhidov, “Self-induced polarization rotation of laser beam in fullerene (C70) solutions,” Opt. Commun. 285(12), 2947–2951 (2012).
[Crossref]

Barbano, E. C.

Burzler, J. M.

S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian-Bessel beams,” Phys. Rev. A 56(2), R1103–R1106 (1997).
[Crossref]

Chase, L. L.

De Boni, L.

I. Guedes, L. Misoguti, L. De Boni, and S. C. Zilio, “Heterodyne Z-scan measurements of slow absorbers,” J. Appl. Phys. 101(6), 063112 (2007).
[Crossref]

Etchepare, J.

Guedes, I.

I. Guedes, L. Misoguti, L. De Boni, and S. C. Zilio, “Heterodyne Z-scan measurements of slow absorbers,” J. Appl. Phys. 101(6), 063112 (2007).
[Crossref]

Hagan, D. J.

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

Hughes, S.

S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian-Bessel beams,” Phys. Rev. A 56(2), R1103–R1106 (1997).
[Crossref]

Kokhharov, M.

M. Kokhharov, S. A. Bakhromov, U. K. Makhmanov, R. A. Kokhkharov, and E. A. Zakhidov, “Self-induced polarization rotation of laser beam in fullerene (C70) solutions,” Opt. Commun. 285(12), 2947–2951 (2012).
[Crossref]

Kokhkharov, R. A.

M. Kokhharov, S. A. Bakhromov, U. K. Makhmanov, R. A. Kokhkharov, and E. A. Zakhidov, “Self-induced polarization rotation of laser beam in fullerene (C70) solutions,” Opt. Commun. 285(12), 2947–2951 (2012).
[Crossref]

Lefkir, M.

Liu, Z. B.

Maker, P. B.

P. B. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependence change in the refractive index of liquids,” Phys. Rev. Lett. 12(18), 507–509 (1964).
[Crossref]

Maker, P. D.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

Makhmanov, U. K.

M. Kokhharov, S. A. Bakhromov, U. K. Makhmanov, R. A. Kokhkharov, and E. A. Zakhidov, “Self-induced polarization rotation of laser beam in fullerene (C70) solutions,” Opt. Commun. 285(12), 2947–2951 (2012).
[Crossref]

Milam, D.

Minkovscki, N.

Misoguti, L.

Owyoung, A.

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. 9(11), 1064–1069 (1973).
[Crossref]

Payne, S. A.

Petrov, G. I.

Rivoire, G.

Said, A. A.

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

Satiel, S. M.

Savage, C. M.

P. B. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependence change in the refractive index of liquids,” Phys. Rev. Lett. 12(18), 507–509 (1964).
[Crossref]

Sheik-Bahae, M.

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

Shi, S.

Terhune, R. W.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

P. B. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependence change in the refractive index of liquids,” Phys. Rev. Lett. 12(18), 507–509 (1964).
[Crossref]

Tian, J. G.

Van Stryland, E. W.

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

Wei, T.

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

Yan, X. Q.

Zakhidov, E. A.

M. Kokhharov, S. A. Bakhromov, U. K. Makhmanov, R. A. Kokhkharov, and E. A. Zakhidov, “Self-induced polarization rotation of laser beam in fullerene (C70) solutions,” Opt. Commun. 285(12), 2947–2951 (2012).
[Crossref]

Zang, W. P.

Zhang, X. L.

Zhou, W. Y.

Zilio, S. C.

I. Guedes, L. Misoguti, L. De Boni, and S. C. Zilio, “Heterodyne Z-scan measurements of slow absorbers,” J. Appl. Phys. 101(6), 063112 (2007).
[Crossref]

Zílio, S. C.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

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

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. 9(11), 1064–1069 (1973).
[Crossref]

J. Appl. Phys. (1)

I. Guedes, L. Misoguti, L. De Boni, and S. C. Zilio, “Heterodyne Z-scan measurements of slow absorbers,” J. Appl. Phys. 101(6), 063112 (2007).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

M. Kokhharov, S. A. Bakhromov, U. K. Makhmanov, R. A. Kokhkharov, and E. A. Zakhidov, “Self-induced polarization rotation of laser beam in fullerene (C70) solutions,” Opt. Commun. 285(12), 2947–2951 (2012).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

Phys. Rev. A (1)

S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian-Bessel beams,” Phys. Rev. A 56(2), R1103–R1106 (1997).
[Crossref]

Phys. Rev. Lett. (1)

P. B. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependence change in the refractive index of liquids,” Phys. Rev. Lett. 12(18), 507–509 (1964).
[Crossref]

Other (2)

M. L. Miguez, E. C. Barbano, S. C. Zilio, L. Misoguti, and K. L. Vodopyanov, “New simple method for measuring nonlinear polarization ellipse rotation with high precision using a dual-phase lock-in,” in Nonlinear Frequency Generation and Conversion: Materials, Devices and Applications XIII, edited by Konstantin L. Vodopyanov, Proceedings of SPIE Vol. 8964 (SPIE, Bellingham, WA, 2014) 896446.

R. W. Boyd, Nonlinear Optics, 3rd edition (Academic, 2008).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram for nonlinear ellipse rotation measurements using a dual-phase lock-in adapted from a standard Z-scan method. We have used about 40 Hz for the rotation considering that the 1 kHz laser repetition rate is much higher.

Fig. 2
Fig. 2

(a) Z-scan normalized transmittance in silica obtained for linear (ϕ = 0°) and nearly circular (ϕ = 40°) polarized light. (b) ΔTpv obtained for different ellipticities. The solid lines are theoretical fits obtained for an instantaneous electronic nonlinearity.

Fig. 3
Fig. 3

(a) Phases measured with the lock-in amplifier in silica as a function of the sample position using different ϕ angles. The solid curves are theoretical fits based on Lorentzian curve (Eq. (12). (b) Phases measured at z = 0 as a function of ϕ.

Fig. 4
Fig. 4

(a) Z-scan normalized transmittance in BK7 obtained for linear (ϕ = 0°) and nearly circular (ϕ = 40°) polarized light. (b) ΔTpv obtained for different ellipticities. The solid lines are theoretical fits obtained for an instantaneous electronic nonlinearity.

Fig. 5
Fig. 5

(a) Phases measured with the lock-in amplifier in BK7 as a function of the sample position using different ϕ angles. The solid curves are theoretical fits based on Lorentzian curve (Eq. (12). (b) Phases measured at z = 0 as a function of ϕ.

Fig. 6
Fig. 6

(a) Phase measured in the lock-in amplifier as a function of sample z-position for silica using waveplate set to ϕ = 20°. The solid curves are the theoretical fits based on the Lorentzian curve. (b) Noise as a function of the sample z-position obtained by the difference between theoretical curve and the experimental data.

Equations (14)

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A = 6 χ 1122 ( or A = 3 χ 1122 + 3 χ 1212 ) ,
B = 6 χ 1221 .
( Δ n ) l i n = 1 2 n 0 ( A + B 2 ) | E | 2 ,
( Δ n ) c i r = 1 2 n 0 A | E | 2 ,
( Δ n ) l i n ( Δ n ) c i r = { 4 (orientational), 3/2 (pure nonresonant electronic), 1 (thermal, populational and electrostriction) .
Δ ϕ = k Δ n L = ω c [ 3 B 8 n 0 2 ε 0 c ] L I = ω c n 2 L I ,
Δ n = n n + = B 2 n 0 ( | E + | 2 | E | 2 ) .
| E ± | 2 = ( 1 ± θ ) 2 2 ( 1 + θ 2 ) | E | 2 ,
Θ = 1 2 ( k Δ n L ) = ω c ( θ 1 + θ 2 ) [ B 4 n 0 2 ε 0 c ] L I .
α = ω 2 c ( θ 1 + θ 2 ) [ B 4 n 0 2 ε 0 c ] L I = ω c ( θ 1 + θ 2 ) n 2 3 L I .
Δ ϕ = 3 ( 1 + θ 2 θ ) α .
Δ T p v = 0.406 Δ ϕ = 2.436 α max ,
Δ T p v = 1.218 α max l o c k i n .
α ( z ) = α ( 1 + ( z z R ) 2 ) ,

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