Abstract

Dielectric multilayer coatings exhibiting steep reflectance in an extremely narrow transition zone, highly sensitive to any variations of layer refractive indices and therefore suitable for studying the nonlinear properties are produced and characterized. Increase of reflectance at growing intensity reveals the presence of the optical Kerr effect. A new method calculating intensity dependent spectral characteristics of multilayer optical coatings in the case of nonlinear interaction with high intensity laser pulses is developed. The method is based on the numerical solution of a boundary-value problem derived from the system of Maxwell equations describing the propagation of light through a multilayer system. The method opens a way to synthesis of optical coatings with predictable nonlinear properties. Comparison of our numerical modelling with experimental data enabled us to accurately determine the Kerr coefficients n2 of the widely-used thin-film materials Ta2O5 and Nb2O5.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (1)

2015 (3)

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

C. Rodríguez, S. Günster, D. Ristau, and W. Rudolph, “Frequency tripling mirror,” Opt. Express 23(24), 31594–31601 (2015).
[Crossref] [PubMed]

O. Razskazovskaya, T. T. Luu, M. Trubetskov, E. Goulielmakis, and V. Pervak, “Nonlinear absorbance in dielectric multilayers,” Optica 2(9), 803 (2015).
[Crossref]

2014 (3)

V. Pervak, O. Razskazovskaya, I. B. Angelov, K. L. Vodopyanov, and M. Trubetskov, “Dispersive mirror technology for ultrafast lasers in the range 220–4500 nm,” Adv. Opt. Technol. 3, 55–63 (2014).

I. Balasa, L. O. Jensen, and D. Ristau, “Laser calorimetric absorptance testing of samples with varying geometry,” Opt. Eng. 53(12), 122503 (2014).
[Crossref]

W. Schneider, A. Ryabov, C. Lombosi, T. Metzger, Z. Major, J. A. Fülöp, and P. Baum, “800-fs, 330-μJ pulses from a 100-W regenerative Yb:YAG thin-disk amplifier at 300 kHz and THz generation in LiNbO3,” Opt. Lett. 39(23), 6604–6607 (2014).
[Crossref] [PubMed]

2013 (2)

2011 (1)

2010 (1)

2009 (1)

2008 (2)

M. L. Gorodetsky, “Thermal noises and noise compensation in high-reflection multilayer coating,” Phys. Lett. A 372(46), 6813–6822 (2008).
[Crossref]

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

2007 (3)

T.-C. Chen, C.-J. Chu, C.-H. Ho, C.-C. Wu, and C.-C. Lee, “Determination of stress-optical and thermal-optical coefficients of Nb2O5 thin film material,” J. Appl. Phys. 101(4), 043513 (2007).
[Crossref]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007).
[Crossref] [PubMed]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87(1), 5–12 (2007).
[Crossref]

2005 (1)

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

2004 (2)

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

C.-Y. Tai, J. Wilkinson, N. Perney, M. Netti, F. Cattaneo, C. Finlayson, and J. Baumberg, “Determination of nonlinear refractive index in a Ta2O5 rib waveguide using self-phase modulation,” Opt. Express 12(21), 5110–5116 (2004).
[Crossref] [PubMed]

2003 (1)

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

2001 (1)

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

1999 (1)

T. A. Laine and A. T. Friberg, “Nonlinear thin-layer theory for stratified Kerr medium,” Appl. Phys. Lett. 74(22), 3248–3250 (1999).
[Crossref]

1996 (1)

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[Crossref]

1989 (1)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

1988 (1)

B. G. Bovard and H. A. Macleod, “Nonlinear behaviour of optical coatings subjected to intense laser irradiation,” J. Mod. Opt. 35(7), 1151–1168 (1988).
[Crossref]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

Amotchkina, T.

Amotchkina, T. V.

T. V. Amotchkina, A. V. Tikhonravov, M. K. Trubetskov, D. Grupe, A. Apolonski, and V. Pervak, “Measurement of group delay of dispersive mirrors with white-light interferometer,” Appl. Opt. 48(5), 949–956 (2009).
[Crossref] [PubMed]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

Angelov, I. B.

V. Pervak, O. Razskazovskaya, I. B. Angelov, K. L. Vodopyanov, and M. Trubetskov, “Dispersive mirror technology for ultrafast lasers in the range 220–4500 nm,” Adv. Opt. Technol. 3, 55–63 (2014).

I. B. Angelov, M. von Pechmann, M. K. Trubetskov, F. Krausz, and V. Pervak, “Optical breakdown of multilayer thin-films induced by ultrashort pulses at MHz repetition rates,” Opt. Express 21(25), 31453–31461 (2013).
[Crossref] [PubMed]

Apolonski, A.

T. V. Amotchkina, A. V. Tikhonravov, M. K. Trubetskov, D. Grupe, A. Apolonski, and V. Pervak, “Measurement of group delay of dispersive mirrors with white-light interferometer,” Appl. Opt. 48(5), 949–956 (2009).
[Crossref] [PubMed]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87(1), 5–12 (2007).
[Crossref]

Balasa, I.

I. Balasa, L. O. Jensen, and D. Ristau, “Laser calorimetric absorptance testing of samples with varying geometry,” Opt. Eng. 53(12), 122503 (2014).
[Crossref]

Ballmer, S.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

Baudach, S.

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Baum, P.

Baumberg, J.

Beygi Azar Aghbolagh, F.

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

Bonse, J.

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Bovard, B. G.

B. G. Bovard and H. A. Macleod, “Nonlinear behaviour of optical coatings subjected to intense laser irradiation,” J. Mod. Opt. 35(7), 1151–1168 (1988).
[Crossref]

Cattaneo, F.

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

Chen, T.-C.

T.-C. Chen, C.-J. Chu, C.-H. Ho, C.-C. Wu, and C.-C. Lee, “Determination of stress-optical and thermal-optical coefficients of Nb2O5 thin film material,” J. Appl. Phys. 101(4), 043513 (2007).
[Crossref]

Chirkin, A. S.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

Chu, C.-J.

T.-C. Chen, C.-J. Chu, C.-H. Ho, C.-C. Wu, and C.-C. Lee, “Determination of stress-optical and thermal-optical coefficients of Nb2O5 thin film material,” J. Appl. Phys. 101(4), 043513 (2007).
[Crossref]

DeBell, G. W.

Dimitrov, V.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[Crossref]

Emmert, L. A.

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

Ernst, A. R.

Evans, M.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

Fedulova, E.

Fejer, M.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

Finlayson, C.

Friberg, A. T.

T. A. Laine and A. T. Friberg, “Nonlinear thin-layer theory for stratified Kerr medium,” Appl. Phys. Lett. 74(22), 3248–3250 (1999).
[Crossref]

Fritsch, K.

Fritschel, P.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

Fuentes-Hernandez, C.

Fülöp, J. A.

Gao, J.

Gorodetsky, M. L.

M. L. Gorodetsky, “Thermal noises and noise compensation in high-reflection multilayer coating,” Phys. Lett. A 372(46), 6813–6822 (2008).
[Crossref]

Goulielmakis, E.

Gross, T.

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Grupe, D.

Günster, S.

C. Rodríguez, S. Günster, D. Ristau, and W. Rudolph, “Frequency tripling mirror,” Opt. Express 23(24), 31594–31601 (2015).
[Crossref] [PubMed]

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

Hales, J. M.

Harry, G.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

Haus, J. W.

Ho, C.-H.

T.-C. Chen, C.-J. Chu, C.-H. Ho, C.-C. Wu, and C.-C. Lee, “Determination of stress-optical and thermal-optical coefficients of Nb2O5 thin film material,” J. Appl. Phys. 101(4), 043513 (2007).
[Crossref]

Hsu, J.

Jasapara, J. C.

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Jensen, L. O.

I. Balasa, L. O. Jensen, and D. Ristau, “Laser calorimetric absorptance testing of samples with varying geometry,” Opt. Eng. 53(12), 122503 (2014).
[Crossref]

Katte, N.

Kautek, W.

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Kippelen, B.

Krausz, F.

Krueger, J.

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Laine, T. A.

T. A. Laine and A. T. Friberg, “Nonlinear thin-layer theory for stratified Kerr medium,” Appl. Phys. Lett. 74(22), 3248–3250 (1999).
[Crossref]

Lee, C.-C.

T.-C. Chen, C.-J. Chu, C.-H. Ho, C.-C. Wu, and C.-C. Lee, “Determination of stress-optical and thermal-optical coefficients of Nb2O5 thin film material,” J. Appl. Phys. 101(4), 043513 (2007).
[Crossref]

Liu, J.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

Lombosi, C.

Luu, T. T.

Macleod, H. A.

B. G. Bovard and H. A. Macleod, “Nonlinear behaviour of optical coatings subjected to intense laser irradiation,” J. Mod. Opt. 35(7), 1151–1168 (1988).
[Crossref]

Major, Z.

McIver, J. K.

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

Menoni, C. S.

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

Mero, M.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

Metzger, T.

Naumov, S.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87(1), 5–12 (2007).
[Crossref]

Netti, M.

Ogin, G.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

Owens, D. T.

Patel, D.

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

Perney, N.

Perry, J. W.

Pervak, V.

Powers, P.

Pronin, O.

Razskazovskaya, O.

O. Razskazovskaya, F. Krausz, and V. Pervak, “Multilayer coatings for femto- and attosecond technology,” Optica 4(1), 129 (2017).
[Crossref]

O. Razskazovskaya, T. T. Luu, M. Trubetskov, E. Goulielmakis, and V. Pervak, “Nonlinear absorbance in dielectric multilayers,” Optica 2(9), 803 (2015).
[Crossref]

V. Pervak, O. Razskazovskaya, I. B. Angelov, K. L. Vodopyanov, and M. Trubetskov, “Dispersive mirror technology for ultrafast lasers in the range 220–4500 nm,” Adv. Opt. Technol. 3, 55–63 (2014).

Ristau, D.

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

C. Rodríguez, S. Günster, D. Ristau, and W. Rudolph, “Frequency tripling mirror,” Opt. Express 23(24), 31594–31601 (2015).
[Crossref] [PubMed]

I. Balasa, L. O. Jensen, and D. Ristau, “Laser calorimetric absorptance testing of samples with varying geometry,” Opt. Eng. 53(12), 122503 (2014).
[Crossref]

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Rodriguez, C.

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

Rodríguez, C.

Rudolph, W.

C. Rodríguez, S. Günster, D. Ristau, and W. Rudolph, “Frequency tripling mirror,” Opt. Express 23(24), 31594–31601 (2015).
[Crossref] [PubMed]

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

Rudolph, W. G.

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Ryabov, A.

Sabbah, A.

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

Sakka, S.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[Crossref]

Sarangan, A.

Scalora, M.

Schneider, W.

Starke, K.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Sun, Z.

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

Tai, C.-Y.

Tikhonravov, A. A.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

Tikhonravov, A. V.

Trubetskov, M.

E. Fedulova, M. Trubetskov, T. Amotchkina, K. Fritsch, P. Baum, O. Pronin, and V. Pervak, “Kerr effect in multilayer dielectric coatings,” Opt. Express 24(19), 21802–21817 (2016).
[Crossref] [PubMed]

O. Razskazovskaya, T. T. Luu, M. Trubetskov, E. Goulielmakis, and V. Pervak, “Nonlinear absorbance in dielectric multilayers,” Optica 2(9), 803 (2015).
[Crossref]

V. Pervak, O. Razskazovskaya, I. B. Angelov, K. L. Vodopyanov, and M. Trubetskov, “Dispersive mirror technology for ultrafast lasers in the range 220–4500 nm,” Adv. Opt. Technol. 3, 55–63 (2014).

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

Trubetskov, M. K.

Vodopyanov, K. L.

V. Pervak, O. Razskazovskaya, I. B. Angelov, K. L. Vodopyanov, and M. Trubetskov, “Dispersive mirror technology for ultrafast lasers in the range 220–4500 nm,” Adv. Opt. Technol. 3, 55–63 (2014).

von Pechmann, M.

Welling, H.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

Welsch, E.

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

Wilkinson, J.

Wu, C.-C.

T.-C. Chen, C.-J. Chu, C.-H. Ho, C.-C. Wu, and C.-C. Lee, “Determination of stress-optical and thermal-optical coefficients of Nb2O5 thin film material,” J. Appl. Phys. 101(4), 043513 (2007).
[Crossref]

Adv. Opt. Technol. (1)

V. Pervak, O. Razskazovskaya, I. B. Angelov, K. L. Vodopyanov, and M. Trubetskov, “Dispersive mirror technology for ultrafast lasers in the range 220–4500 nm,” Adv. Opt. Technol. 3, 55–63 (2014).

Appl. Opt. (2)

Appl. Phys. B (1)

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87(1), 5–12 (2007).
[Crossref]

Appl. Phys. Lett. (1)

T. A. Laine and A. T. Friberg, “Nonlinear thin-layer theory for stratified Kerr medium,” Appl. Phys. Lett. 74(22), 3248–3250 (1999).
[Crossref]

J. Appl. Phys. (2)

T.-C. Chen, C.-J. Chu, C.-H. Ho, C.-C. Wu, and C.-C. Lee, “Determination of stress-optical and thermal-optical coefficients of Nb2O5 thin film material,” J. Appl. Phys. 101(4), 043513 (2007).
[Crossref]

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[Crossref]

J. Mod. Opt. (1)

B. G. Bovard and H. A. Macleod, “Nonlinear behaviour of optical coatings subjected to intense laser irradiation,” J. Mod. Opt. 35(7), 1151–1168 (1988).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Eng. (1)

I. Balasa, L. O. Jensen, and D. Ristau, “Laser calorimetric absorptance testing of samples with varying geometry,” Opt. Eng. 53(12), 122503 (2014).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Optica (2)

Phys. Lett. A (1)

M. L. Gorodetsky, “Thermal noises and noise compensation in high-reflection multilayer coating,” Phys. Lett. A 372(46), 6813–6822 (2008).
[Crossref]

Phys. Rev. B (1)

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

Phys. Rev. B Condens. Matter (1)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter 39(5), 3337–3350 (1989).
[Crossref] [PubMed]

Phys. Rev. D Part. Fields Gravit. Cosmol. (1)

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78(10), 102003 (2008).
[Crossref]

Proc. SPIE (4)

J. Bonse, S. Baudach, J. Krueger, W. Kautek, K. Starke, T. Gross, D. Ristau, W. G. Rudolph, J. C. Jasapara, and E. Welsch, “Femtosecond laser damage in dielectric coatings,” Proc. SPIE 4347, 24 (2001).
[Crossref]

M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202 (2003).
[Crossref]

L. A. Emmert, C. Rodriguez, Z. Sun, F. Beygi Azar Aghbolagh, S. Günster, D. Ristau, D. Patel, C. S. Menoni, and W. Rudolph, “Optical coatings excited by femtosecond lasers near the damage threshold: challenges and opportunities,” Proc. SPIE 9632, 96320K (2015).
[Crossref]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses (Best Oral Presentation),” Proc. SPIE 5273, 501 (2004).
[Crossref]

Other (5)

H. A. Macleod, Thin-Film Optical Filters, 4th ed. (Taylor and Francis, 2010).

T. Amotchkina, M. K. Trubetskov, E. Fedulova, K. Fritsch, O. Pronin, F. Krausz, and V. Pervak, “Characterization of nonlinear effects in edge filters,” in Optical Interference Coatings 2016, OSA Technical Digest (online) (Optical Society of America, 2016), paper ThD.3.

M. Sheik-Bahae and P. Michael, Hasselbeck, “Third-order optical nonlinearities” in Handbook of Optics Vol. IV, M. Bass, ed. (McGraw-Hill, 2010).

S. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontières, 1992).

A. V. Tikhonravov and M. K. Trubetskov, “OptiLayer software,” http://www.optilayer.com .

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Figures (7)

Fig. 1
Fig. 1 (a) Sensitivity of the NMC reflection to a small increase of refractive index (see the text for details); (b) Angular reflectance sensitivity of the designed and produced NMCs.
Fig. 2
Fig. 2 Structures of the designed NMCs: F502 (a), F504 (b).
Fig. 3
Fig. 3 Comparison of the experimental, nominal and model transmittance curves of F502 (a) and F504 (b) samples. Inset: comparison of measured and nominal group delay at AOI = 8°.
Fig. 4
Fig. 4 Schematic of the setup for studying the nonlinear effects of the NMC samples. Yb:YAG thin-disk regenerative amplifier: 1030 nm central wavelength, 50 kHz repetition rate, 1 ps pulse duration [30].
Fig. 5
Fig. 5 Comparison of experimental modulation depths values measured with optical chopper at increasing intensities and model values calculated with the help of the developed method (see the details in Section 4): F502 (a), F504 (b).
Fig. 6
Fig. 6 Comparison of the experimental modulation depth values measured at different R 0 levels and modulation depths calculated based on the developed model (see Sections 4 and 5 for details).
Fig. 7
Fig. 7 Nonlinear addition to the refractive index Δn( z ) (Eq. (9)) calculated for F502 design at the intensity of 30.9 GW/cm2, reflectance levels R 0 of 50% and 80% (a) and for F504 design at the intensity of 75.9 GW/cm2, reflectance levels R 0 of 40% and 70% (b).

Tables (1)

Tables Icon

Table 1 Cauchy coefficients and thermo-optic parameters of layers’ refractive indices and substrate.

Equations (21)

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n ˜ H = n H + n 2 I
n( λ )= A 0 + A 1 ( λ 0 λ ) 2 + A 2 ( λ 0 λ ) 4 ,
M F 2 = j=1 134 ( R (p) ( X; λ j )100% ) 2 + i=1 66 ( R (p) ( X; λ i ) ) 2 ,
M F 2 = j=1 134 ( R (p) ( X; λ j )100 ) 2 + i=1 66 ( R (p) ( X; λ i ) ) 2 + k=1 200 [ GD D (p) ( X; λ k )+5000 5000 ] 2 ,
DF( Δ H , Δ L )= j=1 L [ T( d 1 ( 1+ Δ H ), d 2 ( 1+ Δ L ),...; λ j ) T ^ ( λ j ) ] 2 min,
R= P ref P inc , T= P tr P inc .
I= 2 P inc f rep τ p πab ,
R ch = P ref,ch P inc,ch , T ch = P tr,ch P inc,ch .
Δn( z )= n 2 I( z ), I= | E( z ) | 2 2 η 0 ,
du dz =ik[ 1 α 2 n ˜ 2 ( z,| Ε( z ) | ) ]v, dv dz =ik n ˜ 2 ( z,| Ε( z ) | )u, 0<z< z a , n ˜ ( z,| Ε( z ) | )=n( z )+ n 2 | Ε( z ) | 2 , Ε( z )={ u( z ); αv( z ) n ˜ 2 ( z,| Ε( z ) | ) }, u( 0 )= E T , v( 0 )= q s E T ,
E R = q a u( z a ,k )v( z a ,k ) 2 q a , E A = q a u( z a ,k )+v( z a ,k ) 2 q a .
R( E A ,k )= | q a u( z a ,k )v( z a ,k ) q a u( z a ,k )+v( z a ,k ) | 2 .
E A =f( E T ),
φ i ( k ) = 2πh λ ( n i,av (k) ) 2 α 2 , n i,av (k) = 1 2 ( n( ξ i1 )+ n ( k ) ( ξ i ) ), q i ( k ) = ( n i,av (k) ) 2 ( n i,av (k) ) 2 α 2 ,
( u ( k ) ( ξ i ) v ( k ) ( ξ i ) )=( cos φ i ( k ) ( i/ q i ( k ) )sin φ i ( k ) i q i ( k ) sin φ i ( k ) cos φ i ( k ) )( u( ξ i1 ) v( ξ i1 ) ).
| E ( k ) ( ξ i ) |= | u ( k ) ( ξ i ) | 2 + | v ( k ) ( ξ i ) | 2 α 2 ( n ( k ) ) 4 , n ( k ) ( ξ i )= n H + n 2 | E ( k1 ) ( ξ i ) | 2 2 η 0 .
E( ξ i )= E ( k ) ( ξ i ), n( ξ i )= n ( k ) ( ξ i )
E( z )E( z ) E T , E T =| 2 q a u( z a ) 2 q a u( z a )+v( z a ) |cosθ.
σ 2 =( 1 7 i=2 8 [ Δ R nl ( θ i )Δ R ch ( θ i ) ] 2 )
ΔR( I )Δ R nl ( I )+Δ R Thermal ( P,Δt )
Δ R Thermal =R( d 1 + α H Δt, d 2 + α L Δt,...; n H + β H Δt, n L + β L Δt ) R 0

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