Nonlinear refractive index of porcine cornea studied by z-scan and self-focusing during femtosecond laser processing

doi:10.1364/OE.18.003700

Nonlinear refractive index of porcine cornea studied by z-scan and self-focusing during femtosecond laser processing

M. Miclea, U. Skrzypczak, S. Faust, F. Fankhauser, H. Graener, and G. Seifert »View Author Affiliations

Optics Express, Vol. 18, Issue 4, pp. 3700-3707 (2010)
http://dx.doi.org/10.1364/OE.18.003700

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Abstract

We have investigated the nonlinear refractive index of ex-vivo pig cornea by a combined approach using the standard z-scan technique on extracted corneas or corneal slices, as well as studying the deviations caused by self-focusing during femtosecond laser processing of the pig eyes. The experiments yield consistently an upper limit of 1.2 MW for the critical power of self-focusing in porcine cornea, and a value of 2·10⁻¹⁹ m²/W for its nonlinear refractive index. We also demonstrate that due to this nonlinear refraction the cutting depth of typical fs-laser surgery processing in cornea may depend considerably, albeit in a well controllable way, on the laser parameters.

OCIS Codes
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(190.0190) Nonlinear optics : Nonlinear optics

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: November 17, 2009
Revised Manuscript: January 11, 2010
Manuscript Accepted: January 11, 2010
Published: February 5, 2010

Virtual Issues
Vol. 5, Iss. 5 Virtual Journal for Biomedical Optics

Citation
M. Miclea, U. Skrzypczak, S. Faust, F. Fankhauser, H. Graener, and G. Seifert, "Nonlinear refractive index of porcine cornea studied by z-scan and self-focusing during femtosecond laser processing," Opt. Express 18, 3700-3707 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-4-3700

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References

H. Lubatschowski, “Overview of Commercially Available Femtosecond Lasers in Refractive Surgery,” J. Refract. Surg. 24(1), 102–107 (2008).
H. K. Soong and J. B. Malta, “Femtosecond lasers in ophthalmology,” Am. J. Ophthalmol. 147(2), 189–197, e2 (2009). [CrossRef]
T. Juhasz, F. H. Loesel, R. M. Kurtz, C. Horvath, J. F. Bille, and G. Mourou, ““Corneal Refractive Surgery with Femtosecond Lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (1999). [CrossRef]
H. Lubatschowski, G. Maatz, A. Heisterkamp, U. Hetzel, W. Drommer, H. Welling, and W. Ertmer, “Application of ultrashort laser pulses for intrastromal refractive surgery,” Graefes Arch. Clin. Exp. Ophthalmol. 238(1), 33–39 (2000). [CrossRef] [PubMed]
R. W. Boyd, Nonlinear Optics (Elsevier Inc. - 2008), Chapter 7.
J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35(8), 1156–1167 (1999). [CrossRef]
C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80(2), 247–253 (2005). [CrossRef]
C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Computational model for nonlinear plasma formation in high NA micromachining of transparent materials and biological cells,” Opt. Express 15(16), 10303–10317 (2007). [CrossRef] [PubMed]
A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74(4-5), 419–425 (2002). [CrossRef]
K. Plamann, V. Nuzzo, D. Peyrot, F. Deloison, M. Savoldelli, and J. M. Legeais, “Laser parameters, focusing optics and side effects in femtosecond laser corneal surgery”, Proc. SPIE 6844, W0–W10 (2008)
M. P. Poudel, “Study of self-focusing effect induced by femtosecond photodisruption on model substances,” Opt. Lett. 34(3), 337–339 (2009). [CrossRef] [PubMed]
E. W. Van Stryland, M. Sheik-Bahae, Characterization Techniques and Tabulations for Organic Nonlinear Materials, M. G. Kuzyk and C. W. Dirk eds., (Marcel Dekker, Inc. 1998) 655–692.
M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A, Pure Appl. Opt. 1(6), 662–667 (1999). [CrossRef]
J. Kampmeier, B. Radt, R. Birngruber, and R. Brinkmann, “Thermal and biomechanical parameters of porcine cornea,” Cornea 19(3), 355–363 (2000). [CrossRef] [PubMed]
S. Venkatesh, S. Guthrie, F. R. Cruickshank, R. T. Bailey, W. S. Foulds, and W. R. Lee, “Thermal lens measurements in the cornea,” Br. J. Ophthalmol. 69(2), 92–95 (1985). [CrossRef] [PubMed]
M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70(4), 587–591 (2000). [CrossRef]
W. Liu and S. L. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13(15), 5750–5755 (2005). [CrossRef] [PubMed]
E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119(5-6), 479–484 (1995). [CrossRef]
P. P. Ho and R. R. Alfano, “Optical Kerr effects in liquids,” Phys. Rev. A 20(5), 2170–2187 (1979). [CrossRef]
H. Sun, M. Han, M. H. Niemz, and J. F. Bille, “Femtosecond laser corneal ablation threshold: dependence on tissue depth and laser pulse width,” Lasers Surg. Med. 39(8), 654–658 (2007). [CrossRef] [PubMed]
L. M. Liu, Photonic devices (Cambridge University Press, 2005), Chapter 9.

Alfano, R. R.
Arnold, C. L.
Bailey, R. T.
Bille, J. F.
Birngruber, R.
Brinkmann, R.
Chin, S. L.
Cruickshank, F. R.
Drommer, W.
Ertmer, W.
Falconieri, M.
Foulds, W. S.
Franco, M. A.
Grillon, G.
Guthrie, S.
Han, M.
Heisterkamp, A.
Hetzel, U.
Ho, P. P.
Horvath, C.
Ji, W.
Juhasz, T.
Kampmeier, J.
Kurtz, R. M.
Le Blanc, C.
Lee, W. R.
Li, H. P.
Liu, W.
Loesel, F. H.
Lubatschowski, H.
Maatz, G.
Malta, J. B.
Mamom, T.
Mourou, G.
Mysyrowicz, A.
Nibbering, E. T. J.
Niemz, M. H.
Noack, J.
Poudel, M. P.
Prade, B. S.
Radt, B.
Ripken, T.
Soong, H. K.
Sun, H.
Tang, S. H.
Venkatesh, S.
Vogel, A.
Welling, H.
Yin, M.

Am. J. Ophthalmol.

H. K. Soong and J. B. Malta, “Femtosecond lasers in ophthalmology,” Am. J. Ophthalmol. 147(2), 189–197, e2 (2009). [CrossRef]

Appl. Phys. B

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80(2), 247–253 (2005). [CrossRef]
A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74(4-5), 419–425 (2002). [CrossRef]
M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70(4), 587–591 (2000). [CrossRef]

Br. J. Ophthalmol.

S. Venkatesh, S. Guthrie, F. R. Cruickshank, R. T. Bailey, W. S. Foulds, and W. R. Lee, “Thermal lens measurements in the cornea,” Br. J. Ophthalmol. 69(2), 92–95 (1985). [CrossRef] [PubMed]

Cornea

J. Kampmeier, B. Radt, R. Birngruber, and R. Brinkmann, “Thermal and biomechanical parameters of porcine cornea,” Cornea 19(3), 355–363 (2000). [CrossRef] [PubMed]

Graefes Arch. Clin. Exp. Ophthalmol.

H. Lubatschowski, G. Maatz, A. Heisterkamp, U. Hetzel, W. Drommer, H. Welling, and W. Ertmer, “Application of ultrashort laser pulses for intrastromal refractive surgery,” Graefes Arch. Clin. Exp. Ophthalmol. 238(1), 33–39 (2000). [CrossRef] [PubMed]

IEEE J. Quantum Electron.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35(8), 1156–1167 (1999). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. Juhasz, F. H. Loesel, R. M. Kurtz, C. Horvath, J. F. Bille, and G. Mourou, ““Corneal Refractive Surgery with Femtosecond Lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (1999). [CrossRef]

J. Opt. A, Pure Appl. Opt.

M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A, Pure Appl. Opt. 1(6), 662–667 (1999). [CrossRef]

J. Refract. Surg.

H. Lubatschowski, “Overview of Commercially Available Femtosecond Lasers in Refractive Surgery,” J. Refract. Surg. 24(1), 102–107 (2008).

Lasers Surg. Med.

H. Sun, M. Han, M. H. Niemz, and J. F. Bille, “Femtosecond laser corneal ablation threshold: dependence on tissue depth and laser pulse width,” Lasers Surg. Med. 39(8), 654–658 (2007). [CrossRef] [PubMed]

Opt. Commun.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119(5-6), 479–484 (1995). [CrossRef]

Opt. Express

Opt. Lett.

M. P. Poudel, “Study of self-focusing effect induced by femtosecond photodisruption on model substances,” Opt. Lett. 34(3), 337–339 (2009). [CrossRef] [PubMed]

Phys. Rev. A

P. P. Ho and R. R. Alfano, “Optical Kerr effects in liquids,” Phys. Rev. A 20(5), 2170–2187 (1979). [CrossRef]

Other

L. M. Liu, Photonic devices (Cambridge University Press, 2005), Chapter 9.
E. W. Van Stryland, M. Sheik-Bahae, Characterization Techniques and Tabulations for Organic Nonlinear Materials, M. G. Kuzyk and C. W. Dirk eds., (Marcel Dekker, Inc. 1998) 655–692.
K. Plamann, V. Nuzzo, D. Peyrot, F. Deloison, M. Savoldelli, and J. M. Legeais, “Laser parameters, focusing optics and side effects in femtosecond laser corneal surgery”, Proc. SPIE 6844, W0–W10 (2008)
R. W. Boyd, Nonlinear Optics (Elsevier Inc. - 2008), Chapter 7.

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[1] H. Lubatschowski, “Overview of Commercially Available Femtosecond Lasers in Refractive Surgery,” J. Refract. Surg. 24(1), 102–107 (2008).

[2] H. K. Soong and J. B. Malta, “Femtosecond lasers in ophthalmology,” Am. J. Ophthalmol. 147(2), 189–197, e2 (2009). [CrossRef]

[3] T. Juhasz, F. H. Loesel, R. M. Kurtz, C. Horvath, J. F. Bille, and G. Mourou, ““Corneal Refractive Surgery with Femtosecond Lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (1999). [CrossRef]

[4] H. Lubatschowski, G. Maatz, A. Heisterkamp, U. Hetzel, W. Drommer, H. Welling, and W. Ertmer, “Application of ultrashort laser pulses for intrastromal refractive surgery,” Graefes Arch. Clin. Exp. Ophthalmol. 238(1), 33–39 (2000). [CrossRef] [PubMed]

[5] R. W. Boyd, Nonlinear Optics (Elsevier Inc. - 2008), Chapter 7.

[6] J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35(8), 1156–1167 (1999). [CrossRef]

[7] C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80(2), 247–253 (2005). [CrossRef]

[8] C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Computational model for nonlinear plasma formation in high NA micromachining of transparent materials and biological cells,” Opt. Express 15(16), 10303–10317 (2007). [CrossRef] [PubMed]

[9] A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74(4-5), 419–425 (2002). [CrossRef]

[10] K. Plamann, V. Nuzzo, D. Peyrot, F. Deloison, M. Savoldelli, and J. M. Legeais, “Laser parameters, focusing optics and side effects in femtosecond laser corneal surgery”, Proc. SPIE 6844, W0–W10 (2008)

[11] M. P. Poudel, “Study of self-focusing effect induced by femtosecond photodisruption on model substances,” Opt. Lett. 34(3), 337–339 (2009). [CrossRef] [PubMed]

[12] E. W. Van Stryland, M. Sheik-Bahae, Characterization Techniques and Tabulations for Organic Nonlinear Materials, M. G. Kuzyk and C. W. Dirk eds., (Marcel Dekker, Inc. 1998) 655–692.

[13] M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A, Pure Appl. Opt. 1(6), 662–667 (1999). [CrossRef]

[14] J. Kampmeier, B. Radt, R. Birngruber, and R. Brinkmann, “Thermal and biomechanical parameters of porcine cornea,” Cornea 19(3), 355–363 (2000). [CrossRef] [PubMed]

[15] S. Venkatesh, S. Guthrie, F. R. Cruickshank, R. T. Bailey, W. S. Foulds, and W. R. Lee, “Thermal lens measurements in the cornea,” Br. J. Ophthalmol. 69(2), 92–95 (1985). [CrossRef] [PubMed]

[16] M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70(4), 587–591 (2000). [CrossRef]

[17] W. Liu and S. L. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13(15), 5750–5755 (2005). [CrossRef] [PubMed]

[18] E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119(5-6), 479–484 (1995). [CrossRef]

[19] P. P. Ho and R. R. Alfano, “Optical Kerr effects in liquids,” Phys. Rev. A 20(5), 2170–2187 (1979). [CrossRef]

[20] H. Sun, M. Han, M. H. Niemz, and J. F. Bille, “Femtosecond laser corneal ablation threshold: dependence on tissue depth and laser pulse width,” Lasers Surg. Med. 39(8), 654–658 (2007). [CrossRef] [PubMed]

[21] L. M. Liu, Photonic devices (Cambridge University Press, 2005), Chapter 9.

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Nonlinear refractive index of porcine cornea studied by z-scan and self-focusing during femtosecond laser processing