Abstract

We investigated the magnitude and origin of the nonlinear refraction in several solvents with the nonlinear ellipse rotation measurements as a function of the pulse duration in the range from 60fs to 2ps. Due to the presence of non-instantaneous nuclear contributions concurrently with the nearly instantaneous electronic nonlinearity, solvents present effective refractive nonlinearities that depend on the pulse duration. By proposing an empirical model where the nonlinearity grows exponentially with the pulse duration normalized to the response time, we could separate contributions from fast isotropic and slow nuclear reorientational nonlinearities. Z-scan measurements were also carried out to support our model.

© 2017 Optical Society of America

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References

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

2016 (2)

2015 (3)

K. Iliopoulos, D. Potamianos, E. Kakkava, P. Aloukos, I. Orfanos, and S. Couris, “Ultrafast third order nonlinearities of organic solvents,” Opt. Express 23(19), 24171–24176 (2015).
[Crossref] [PubMed]

K. Polok, W. Gadomski, and B. Ratajska-Gadomska, “Femtosecond optical Kerr effect setup with signal “live view” for measurements in the solid, liquid, and gas phases,” Rev. Sci. Instrum. 86(10), 103109 (2015).
[Crossref] [PubMed]

M. L. Miguez, E. C. Barbano, J. A. Coura, S. C. Zilio, and L. Misoguti, “Nonlinear ellipse rotation measurements in optical thick samples,” Appl. Phys. B 120(4), 653–658 (2015).
[Crossref]

2014 (2)

2013 (1)

M. B. M. Krishna and D. N. Rao, “Influence of solvent contribution on nonlinearities of near infra-red absorbing croconate and squaraine dyes with ultrafast laser excitation,” J. Appl. Phys. 114(13), 133103 (2013).
[Crossref]

2012 (1)

2011 (1)

2009 (2)

2008 (1)

2005 (1)

J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear susceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005).
[Crossref]

2004 (1)

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

2001 (1)

2000 (1)

P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ(3) in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4–6), 459–472 (2000).
[Crossref]

1998 (1)

1997 (1)

1996 (1)

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

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]

1988 (1)

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24(2), 443–454 (1988).
[Crossref]

1973 (1)

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

Aloukos, P.

Baba, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Barbano, E. C.

Boudebs, G.

Burgin, J.

J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear susceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005).
[Crossref]

Chang, S.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Chia, C.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Coura, J. A.

M. L. Miguez, E. C. Barbano, J. A. Coura, S. C. Zilio, and L. Misoguti, “Nonlinear ellipse rotation measurements in optical thick samples,” Appl. Phys. B 120(4), 653–658 (2015).
[Crossref]

Couris, S.

de Souza, T. G. B.

Ensley, T. R.

Ferdinandus, M. R.

Fishman, D. A.

Freysz, E.

P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ(3) in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4–6), 459–472 (2000).
[Crossref]

Gadomski, W.

K. Polok, W. Gadomski, and B. Ratajska-Gadomska, “Femtosecond optical Kerr effect setup with signal “live view” for measurements in the solid, liquid, and gas phases,” Rev. Sci. Instrum. 86(10), 103109 (2015).
[Crossref] [PubMed]

Ganeev, R. A.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Gu, B.

Gu, X.

Guillon, C.

J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear susceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005).
[Crossref]

Hagan, D. J.

Hsu, C. C.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Hu, H.

Huang, T. H.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Iliopoulos, K.

Ishizawa, N.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Ji, W.

Kajzar, F.

Kakkava, E.

Kenney-Wallace, G. A.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24(2), 443–454 (1988).
[Crossref]

Kimmel, M.

Krishna, M. B. M.

M. B. M. Krishna and D. N. Rao, “Influence of solvent contribution on nonlinearities of near infra-red absorbing croconate and squaraine dyes with ultrafast laser excitation,” J. Appl. Phys. 114(13), 133103 (2013).
[Crossref]

Kuo, C. T.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Kuroda, H.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Langot, P.

J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear susceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005).
[Crossref]

P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ(3) in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4–6), 459–472 (2000).
[Crossref]

Lefkir, M.

Liu, R. T.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Liu, Z. B.

Lotshaw, W. T.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24(2), 443–454 (1988).
[Crossref]

Luc, J.

McMorrow, D.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24(2), 443–454 (1988).
[Crossref]

Miguez, M. L.

M. L. Miguez, E. C. Barbano, J. A. Coura, S. C. Zilio, and L. Misoguti, “Nonlinear ellipse rotation measurements in optical thick samples,” Appl. Phys. B 120(4), 653–658 (2015).
[Crossref]

M. L. Miguez, E. C. Barbano, S. C. Zilio, and L. Misoguti, “Accurate measurement of nonlinear ellipse rotation using a phase-sensitive method,” Opt. Express 22(21), 25530–25538 (2014).
[Crossref] [PubMed]

Milam, D.

Misoguti, L.

Montant, S.

P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ(3) in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4–6), 459–472 (2000).
[Crossref]

O’Shea, P.

Orfanos, I.

Owyoung, A.

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

Peceli, D.

Polok, K.

K. Polok, W. Gadomski, and B. Ratajska-Gadomska, “Femtosecond optical Kerr effect setup with signal “live view” for measurements in the solid, liquid, and gas phases,” Rev. Sci. Instrum. 86(10), 103109 (2015).
[Crossref] [PubMed]

Potamianos, D.

Rao, D. N.

M. B. M. Krishna and D. N. Rao, “Influence of solvent contribution on nonlinearities of near infra-red absorbing croconate and squaraine dyes with ultrafast laser excitation,” J. Appl. Phys. 114(13), 133103 (2013).
[Crossref]

Ratajska-Gadomska, B.

K. Polok, W. Gadomski, and B. Ratajska-Gadomska, “Femtosecond optical Kerr effect setup with signal “live view” for measurements in the solid, liquid, and gas phases,” Rev. Sci. Instrum. 86(10), 103109 (2015).
[Crossref] [PubMed]

Rau, I.

Reed, J. M.

Reichert, M.

Rivoire, G.

Ryasnyansky, A. I.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Sahraoui, B.

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]

Sakakibara, S.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Seidel, M.

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.

Suzuki, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Tian, J. G.

Trebino, R.

Tsai, C. P.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Tse, W. S.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Turu, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Van Stryland, E. W.

Wang, H. T.

Webster, S.

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]

Wei, T. H.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Yan, X. Q.

Yen, S. M.

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

Zhang, X. L.

Zhao, P.

Zhou, W. Y.

Zilio, S. C.

Appl. Opt. (1)

Appl. Phys. B (2)

M. L. Miguez, E. C. Barbano, J. A. Coura, S. C. Zilio, and L. Misoguti, “Nonlinear ellipse rotation measurements in optical thick samples,” Appl. Phys. B 120(4), 653–658 (2015).
[Crossref]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3–4), 433–438 (2004).
[Crossref]

Appl. Phys. Lett. (1)

J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear susceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005).
[Crossref]

IEEE J. Quantum Electron. (3)

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24(2), 443–454 (1988).
[Crossref]

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]

IEEE J. Sel. Top. Quantum Electron. (1)

T. H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2(3), 756–768 (1996).
[Crossref]

J. Appl. Phys. (1)

M. B. M. Krishna and D. N. Rao, “Influence of solvent contribution on nonlinearities of near infra-red absorbing croconate and squaraine dyes with ultrafast laser excitation,” J. Appl. Phys. 114(13), 133103 (2013).
[Crossref]

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

Opt. Commun. (1)

P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ(3) in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4–6), 459–472 (2000).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Opt. Mater. Express (1)

Optica (2)

Rev. Sci. Instrum. (1)

K. Polok, W. Gadomski, and B. Ratajska-Gadomska, “Femtosecond optical Kerr effect setup with signal “live view” for measurements in the solid, liquid, and gas phases,” Rev. Sci. Instrum. 86(10), 103109 (2015).
[Crossref] [PubMed]

Other (1)

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

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Figures (9)

Fig. 1
Fig. 1 Pulse width as function of the grating pair micrometer reading obtained with the silica NER signal. The line is the parabolic fitting curve given in Eq. (12).
Fig. 2
Fig. 2 (a) NER signals for acetone for three different pulse widths at the same pulse energy. (b) The NER signals normalized to a scale where the side shoulders (silica signal) are equals. The points are the experimental data and the lines are numerically calculated using the Eq. (11).
Fig. 3
Fig. 3 Effective refractive nonlinearity for linear and circular polarization determined by the Z-scan technique in CS2. The lines are the numerically calculated by Eq. (4) using the data of Table 1.
Fig. 4
Fig. 4 (a) Nonlinear susceptibilities determined from nonlinear refraction of CS2. The experimental Z-scan points of Aeff + Beff/2 and Aeff were obtained with linear and circular polarizations, respectively. The experimental Beff points were determined indirectly from Aeff + Beff/2 and Aeff points. The theoretical lines were calculated with Eq. (4). (b) Ratio between ΔTpv(linear)/ΔTpv(circular) obtained with Z-scan measurements. The theoretical ratio (line) was obtained with Eq. (4).
Fig. 5
Fig. 5 Experimental points of Beff for CS2 obtained with NER measurements. The nonlinear susceptibility curves were determined with Eq. (4) (dashed lines) and with our empirical model (solid lines). We did not use error bars in the experimental points just to help to see the lines.
Fig. 6
Fig. 6 Experimental Beff values of the 8 solvents obtained with NER measurements (points). The lines are theoretical curves given by Eq. (9).
Fig. 7
Fig. 7 Effective n2 values obtained with our model, Eq. (5) using the data of Table 2, for the solvents of Fig. 6. The points in the graph are just to help to distinguish the solvents, they are not experimental measurements.
Fig. 8
Fig. 8 Experimental Beff values of all 8 solvents obtained with NER measurements (points). By fitting the experimental Beff data with Eq. (9) (black solid lines) other nonlinear susceptibilities can be obtained, Aeff (blue dash lines) and Aeff + Beff/2 (red dashed lines).
Fig. 9
Fig. 9 The ratio n2,efflin/n2,effcirc for all solvents obtained with the Z-scan technique. The lines are the theoretical fittings based on our model, n2,efflin/n2,effcirc = (Aeff + Beff/2)/Aeff.

Tables (2)

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Table 1 Values of the third-order response of CS2 from [6]. The B values were determined from Eqs. (7) and (8)

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Table 2 Fitting parameters of third-order response of all solvents. Some data from literature, Ref [24]. a [11], b [23], c and [6]d. Here, B is in 10−21m2/V2 and n2 is in 10−20m2/W and τ is in ps

Equations (12)

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Δn( t )= n 2,el I( t )+ R ( tt' )I( t' )dt',
R( t )= m n 2,m r m ( t ) ,
Δn( t ) = Δn( t )I( t )dt I( t )dt ,
n 2,eff = n 2,el + I( t ) R( tt' )I( t' )dt'dt I 2 ( t )dt .
n 2,eff = n 2,fast + n 2,slow ( 1exp( τ τ 0 ) ),
n 2 = 3 χ 1111 4 n 0 2 ε 0 c = 3 4 n 0 2 ε 0 c ( A 3 + B 6 )= 1 4 n 0 2 ε 0 c ( A+ B 2 ),
n 2,fast = 3 8 B fast n 0 2 ε 0 c = 3 8 A fast n 0 2 ε 0 c ,
n 2,slow = 1 6 B slow n 0 2 ε 0 c = A slow n 0 2 ε 0 c ,
B eff = B fast + B slow ( 1exp( τ τ 0 ) ).
A eff = A fast + A slow ( 1exp( τ τ 0 ) )= B fast + B slow 6 ( 1exp( τ τ 0 ) ).
α( z ) lockin = ωsin2ϕB 8 n 0 2 ε 0 c 2 ( n 0 z R ) I 0 2 [ tan 1 ( z b / z R ) tan 1 ( z a / z R ) ],
τ( ps )= ( d 10.5 ) 2 +0.06,

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