Abstract

A four-dimensional spatiotemporal nonlinear Schrödinger equation coupled with a plasma equation is solved for anisotropic crystal of MgO doped lithium niobate. The modeling is performed for x-cut and z-cut lithium niobate crystals commonly used for waveguide writing by femtosecond lasers. The effect of various parameters such as energy, duration, and polarization of the incident laser pulse on distribution of the plasma density in the vicinity of focus is studied. Our simulations reveal that the maximum plasma density in the vicinity of the focus is higher for longer pulse durations and higher pulse energies. Furthermore, it is observed that for the same peak powers of the incident pulse, the plasma density generated inside the crystal is higher for linear polarization as compared to circular polarization.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007).
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2012 (1)

2010 (1)

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron. 40, 966–985 (2010).
[CrossRef]

2007 (9)

J. Thomas, M. Heinrich, J. Burghoff, and S. Nolte, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[CrossRef]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Optical and structural properties of waveguides in LiNbO3 fabricated by ultrashort laser pulses,” Proc. SPIE 6460, 64600W (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A 86, 165–170 (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Waveguide in lithium niobate fabricated by focused ultrashort laser pulses,” Appl. Surf. Sci. 253, 7899–7902 (2007).
[CrossRef]

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

A. H. Nejadmalayeri and Peter R. Herman, “Rapid thermal annealing in high repetition rate ultrafast laser waveguide writing in lithium niobate,” Opt. Express 15, 10842 (2007).
[CrossRef]

2006 (4)

A. H. Nejadmalayeri and P. R. Herman, “Ultrafast laser waveguide writing: lithium niobate and the role of circular polarization and picosecond pulse width,” Opt. Lett. 31, 2987–2989 (2006).
[CrossRef]

R. R. Thomson, S. Campbell, I. J. Blewett, A. K. Kar, and D. T. Reid, “Optical waveguide fabrication in z-cut lithium niobate (LiNbO3) using femtosecond pulses in the low repetition rate regime,” Appl. Phys. Lett. 88, 111109 (2006).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89, 081108 (2006).
[CrossRef]

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

2004 (1)

L. Gui, B. X. Xu, and T. C. Chong, “Microstructure in lithium niobate by use of focused femtosecond laser pulses,” IEEE Photon. Technol. Lett. 16, 1337–1339 (2004).
[CrossRef]

2003 (1)

D. Hovhannisyan and K. Stepanyan, “Femtosecond laser pulse propagation in a uniaxial crystal,” J. Mod. Opt. 50, 2201–2211 (2003).
[CrossRef]

Berge, L.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Blewett, I. J.

R. R. Thomson, S. Campbell, I. J. Blewett, A. K. Kar, and D. T. Reid, “Optical waveguide fabrication in z-cut lithium niobate (LiNbO3) using femtosecond pulses in the low repetition rate regime,” Appl. Phys. Lett. 88, 111109 (2006).
[CrossRef]

Bookey, Henry T.

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2007), Chap. 1.

Bulgakova, N. M.

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron. 40, 966–985 (2010).
[CrossRef]

Burghoff, J.

J. Thomas, M. Heinrich, J. Burghoff, and S. Nolte, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Waveguide in lithium niobate fabricated by focused ultrashort laser pulses,” Appl. Surf. Sci. 253, 7899–7902 (2007).
[CrossRef]

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Optical and structural properties of waveguides in LiNbO3 fabricated by ultrashort laser pulses,” Proc. SPIE 6460, 64600W (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A 86, 165–170 (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89, 081108 (2006).
[CrossRef]

Campbell, S.

R. R. Thomson, S. Campbell, I. J. Blewett, A. K. Kar, and D. T. Reid, “Optical waveguide fabrication in z-cut lithium niobate (LiNbO3) using femtosecond pulses in the low repetition rate regime,” Appl. Phys. Lett. 88, 111109 (2006).
[CrossRef]

Cerullo, G.

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

Chiodo, N.

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

Choi, S. C.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Chong, T. C.

L. Gui, B. X. Xu, and T. C. Chong, “Microstructure in lithium niobate by use of focused femtosecond laser pulses,” IEEE Photon. Technol. Lett. 16, 1337–1339 (2004).
[CrossRef]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Diels, J. C.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsewier, 2006), Chap. 1, p. 32.

Gong, Q.

Grebing, C.

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Waveguide in lithium niobate fabricated by focused ultrashort laser pulses,” Appl. Surf. Sci. 253, 7899–7902 (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89, 081108 (2006).
[CrossRef]

Gui, L.

L. Gui, B. X. Xu, and T. C. Chong, “Microstructure in lithium niobate by use of focused femtosecond laser pulses,” IEEE Photon. Technol. Lett. 16, 1337–1339 (2004).
[CrossRef]

Hartung, H.

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A 86, 165–170 (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Optical and structural properties of waveguides in LiNbO3 fabricated by ultrashort laser pulses,” Proc. SPIE 6460, 64600W (2007).
[CrossRef]

Heinrich, M.

J. Thomas, M. Heinrich, J. Burghoff, and S. Nolte, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[CrossRef]

Herman, P. R.

Herman, Peter R.

Hovhannisyan, D.

D. Hovhannisyan and K. Stepanyan, “Femtosecond laser pulse propagation in a uniaxial crystal,” J. Mod. Opt. 50, 2201–2211 (2003).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962), Chap. 6.

Ji, W.

H. P. Li, J. K. Liao, X. G. Tang, and W. Ji, “Three-photon absorption in MgO-doped LiNbO3 crystal,” in Proceedings of CLEO/QELS (Optical Society of America, 2008), paper JWA35.

Jiang, H.

Jung, C.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Kar, A. K.

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

R. R. Thomson, S. Campbell, I. J. Blewett, A. K. Kar, and D. T. Reid, “Optical waveguide fabrication in z-cut lithium niobate (LiNbO3) using femtosecond pulses in the low repetition rate regime,” Appl. Phys. Lett. 88, 111109 (2006).
[CrossRef]

Kasparian, J.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Kim, W. K.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Ko, D. K.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Lee, H. M.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Lee, H. Y.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Lee, Y. L.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Li, H. P.

H. P. Li, J. K. Liao, X. G. Tang, and W. Ji, “Three-photon absorption in MgO-doped LiNbO3 crystal,” in Proceedings of CLEO/QELS (Optical Society of America, 2008), paper JWA35.

Liao, J. K.

H. P. Li, J. K. Liao, X. G. Tang, and W. Ji, “Three-photon absorption in MgO-doped LiNbO3 crystal,” in Proceedings of CLEO/QELS (Optical Society of America, 2008), paper JWA35.

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Nejadmalayeri, A. H.

Noh, Y. C.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Nolte, S.

J. Thomas, M. Heinrich, J. Burghoff, and S. Nolte, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Optical and structural properties of waveguides in LiNbO3 fabricated by ultrashort laser pulses,” Proc. SPIE 6460, 64600W (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A 86, 165–170 (2007).
[CrossRef]

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Waveguide in lithium niobate fabricated by focused ultrashort laser pulses,” Appl. Surf. Sci. 253, 7899–7902 (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89, 081108 (2006).
[CrossRef]

Nuter, R.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Osellame, R.

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

Psaila, N. D.

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

Reid, D. T.

R. R. Thomson, S. Campbell, I. J. Blewett, A. K. Kar, and D. T. Reid, “Optical waveguide fabrication in z-cut lithium niobate (LiNbO3) using femtosecond pulses in the low repetition rate regime,” Appl. Phys. Lett. 88, 111109 (2006).
[CrossRef]

Rosenfeld, A.

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron. 40, 966–985 (2010).
[CrossRef]

Rudolph, W.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsewier, 2006), Chap. 1, p. 32.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Chap. 6.

Skupin, S.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Sohn, I. B.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Stepanyan, K.

D. Hovhannisyan and K. Stepanyan, “Femtosecond laser pulse propagation in a uniaxial crystal,” J. Mod. Opt. 50, 2201–2211 (2003).
[CrossRef]

Stoian, R.

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron. 40, 966–985 (2010).
[CrossRef]

Strikwerda, J.

J. Strikwerda, Finite Difference Scheme and Partial Differential Equations (Society for Industrial and Applied Mathematics, 2004), Chap. 3, pp. 88–93.

Tang, X. G.

H. P. Li, J. K. Liao, X. G. Tang, and W. Ji, “Three-photon absorption in MgO-doped LiNbO3 crystal,” in Proceedings of CLEO/QELS (Optical Society of America, 2008), paper JWA35.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Chap. 6.

Thomas, J.

J. Thomas, M. Heinrich, J. Burghoff, and S. Nolte, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[CrossRef]

Thomson, R. R.

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

R. R. Thomson, S. Campbell, I. J. Blewett, A. K. Kar, and D. T. Reid, “Optical waveguide fabrication in z-cut lithium niobate (LiNbO3) using femtosecond pulses in the low repetition rate regime,” Appl. Phys. Lett. 88, 111109 (2006).
[CrossRef]

Tunnermann, A.

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A 86, 165–170 (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Optical and structural properties of waveguides in LiNbO3 fabricated by ultrashort laser pulses,” Proc. SPIE 6460, 64600W (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Waveguide in lithium niobate fabricated by focused ultrashort laser pulses,” Appl. Surf. Sci. 253, 7899–7902 (2007).
[CrossRef]

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007).
[CrossRef]

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89, 081108 (2006).
[CrossRef]

Wolf, J. P.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Xu, B. X.

L. Gui, B. X. Xu, and T. C. Chong, “Microstructure in lithium niobate by use of focused femtosecond laser pulses,” IEEE Photon. Technol. Lett. 16, 1337–1339 (2004).
[CrossRef]

Yang, H.

Yang, W. S.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Yu, B. A.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Yu, J.

Yu, N. E.

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

Appl. Phys. A (2)

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007).
[CrossRef]

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A 86, 165–170 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89, 081108 (2006).
[CrossRef]

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[CrossRef]

J. Thomas, M. Heinrich, J. Burghoff, and S. Nolte, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[CrossRef]

R. R. Thomson, S. Campbell, I. J. Blewett, A. K. Kar, and D. T. Reid, “Optical waveguide fabrication in z-cut lithium niobate (LiNbO3) using femtosecond pulses in the low repetition rate regime,” Appl. Phys. Lett. 88, 111109 (2006).
[CrossRef]

Appl. Surf. Sci. (1)

J. Burghoff, C. Grebing, S. Nolte, and A. Tunnermann, “Waveguide in lithium niobate fabricated by focused ultrashort laser pulses,” Appl. Surf. Sci. 253, 7899–7902 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Henry T. Bookey, R. R. Thomson, N. D. Psaila, A. K. Kar, N. Chiodo, R. Osellame, and G. Cerullo, “Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate,” IEEE Photon. Technol. Lett. 19, 892–894 (2007).
[CrossRef]

L. Gui, B. X. Xu, and T. C. Chong, “Microstructure in lithium niobate by use of focused femtosecond laser pulses,” IEEE Photon. Technol. Lett. 16, 1337–1339 (2004).
[CrossRef]

J. Mod. Opt. (1)

D. Hovhannisyan and K. Stepanyan, “Femtosecond laser pulse propagation in a uniaxial crystal,” J. Mod. Opt. 50, 2201–2211 (2003).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Proc. SPIE (1)

J. Burghoff, H. Hartung, S. Nolte, and A. Tunnermann, “Optical and structural properties of waveguides in LiNbO3 fabricated by ultrashort laser pulses,” Proc. SPIE 6460, 64600W (2007).
[CrossRef]

Quantum Electron. (1)

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron. 40, 966–985 (2010).
[CrossRef]

Rep. Prog. Phys. (1)

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Other (7)

J. Strikwerda, Finite Difference Scheme and Partial Differential Equations (Society for Industrial and Applied Mathematics, 2004), Chap. 3, pp. 88–93.

http://www.fabrinet.co.th/custappl/casix/aa/product/prod_cry_linbo3.html .

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsewier, 2006), Chap. 1, p. 32.

H. P. Li, J. K. Liao, X. G. Tang, and W. Ji, “Three-photon absorption in MgO-doped LiNbO3 crystal,” in Proceedings of CLEO/QELS (Optical Society of America, 2008), paper JWA35.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962), Chap. 6.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Chap. 6.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2007), Chap. 1.

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Figures (6)

Fig. 1.
Fig. 1.

Geometries of pulse focusing inside (a) x-cut MgO-LN and (b) z-cut MgO-LN crystal.

Fig. 2.
Fig. 2.

Spatial and temporal distribution of the propagating pulse at entrance (a), (b) and focus (c), (d), under linear focusing condition, inside x-cut LiNbO3 crystal. The incident pulse has duration of 200 fs and energy of 5 μJ and is circularly polarized.

Fig. 3.
Fig. 3.

Variation of maximum plasma density along propagation axis at the vicinity of focus inside x-cut MgO-LN for pulse energy of 5 μJ and different pulse durations for circular (a) and linear (b) polarizations. Variation of maximum plasma density along propagation axis for pulse duration of 250 fs and different pulse energies for circular (c) and linear (d) polarizations.

Fig. 4.
Fig. 4.

Variation of maximum plasma density along propagation axis at the vicinity of focus inside z-cut MgO-LN crystal for pulse with circular polarization and (a) energy of 5 μJ and different pulse durations, (b) pulse duration of 250 fs and different pulse energies.

Fig. 5.
Fig. 5.

Spatial distributions of plasma density (a), (c) and electric field intensity (b), (d) along propagation axis for a femtosecond pulse with circular polarization, energy of 5 μJ, and duration of 250 fs inside x-cut crystal (a), (b) and z-cut crystal (c), (d).

Fig. 6.
Fig. 6.

Temporal evolution of pulse intensity along propagation axis inside x-cut crystal for femtosecond pulse with circular polarization, energy of 5 μJ and duration of 250 fs.

Tables (1)

Tables Icon

Table 1. Physical Constants and Parameters for MgO Doped LiNbO3 Crystal

Equations (42)

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E(y,z,t)=Ey0e^y+Ez0e^z,
Ey0(y,z,t)=(2Pinπr02)1/2exp((y2+z2)(1r02+ik0o2f)t2/tp2)Ez0(y,z,t)=iEy0(y,z,t).
2E+εc22Et2=1ε0c2[2PNLt2+Jt],
ε=(εo000εo000εe).
Ey(x,y,z,t)x=iko22Ey(x,y,z,t)t2+i2k0oT2Ey(x,y,z,t)+ik0o2no2ε0PyNL12ε0nocJy
Ez(x,y,z,t)x=ike22Ez(x,y,z,t)t2+i2k0eT2Ez(x,y,z,t)+ik0e2ne2ε0PzNL12ε0necJz,
T=/y+/z.
Pi(ω)=3ε0jklχijkl(3)(ω;ω,ω,ω)Ej(ω)Ek(ω)El(ω).
[PxNLPyNLPzNL]=3ε0[χ11000χ31χ16χ311/3χ11000χ110χ1600001/3χ11χ31χ310χ330χ160χ16χ3100][0|Ey|2Ey|Ez|2EzEy|Ez|2+Ey|Ez|2+Ez2Ey*Ey2Ez*+|Ey|2Ez+|Ey|2Ez00000].
J⃗t=e2meρE⃗J⃗τc.
Jy=σoε0noc(1+iωτc)ρEyJz=σeε0nec(1+iωτc)ρEz,
σo=e2meε0nocτc(1+ω2τc2)σe=e2meε0necτc(1+ω2τc2).
Jy=cε0noβ(K)(|Ey|2+|Ez|2)(K1)EyJz=cε0neβ(K)(|Ey|2+|Ez|2)(K1)Ez.
Eyx=iko22Eyt2+i2k0oT2Ey+ik0o2no2ε0{3ε0(χ11|Ey|2Ey+χ16(2Ey|Ez|2+Ez2Ey*)}12σo(1+iωτc)ρEy12β(K){(|Ey|2+|Ez|2)K1}Ey
Ezx=ike22Ezt2+i2k0eT2Ez+ik0e2ne2ε0{3ε0(χ33|Ez|2Ez+χ16(Ey2Ez*+2|Ey|2Ez))}12σe(1+iωτc)ρEz12β(K){(|Ey|2+|Ez|2)K1}Ez.
no(λ)=4.8762+0.11554(λ20.04674)0.033119λ2ne(λ)=4.5469+0.094779(λ20.04439)0.026721λ2.
t=t/tp,x=x/4xfo,y=y/wfo,z=z/wfoT2=wfo2T2,ρ=ρ/ρBD,ey=Ey/(2Pin/πwfo2)1/2ez=Ez/(2Pin/πwfo2)1/2
eyx=iδo2eyt2+iT2ey+icmo{(χ11|ey|2ey+χ16(2ey|ez|2+(ez)2ey*))}γo(1+iωτc)ρeyμo{(|ey|2+|ez|2)K1}ey,
ezx=iδe2ezt2+ik0ok0eT2ez+icme{(χ33|ez|2ez+χ16((ey)2ez*+2|ey|2ez))}γe(1+iωτc)ρezμe{(|ey|2+|ez|2)K1}ez,
δo=2koxfotp2,δe=2kexfotp2,xfo=k0owfo22,cmo=k0o12xfo(Pin/πwfo2)no2,cme=k0e12xfo(Pin/πwfo2)ne2,γo=2xfoσoρBD,γe=2xfoσeρBDμo=μe=2xfoβ(K)(2Pin/πwfo2)K1.
12Re(J·E*)=UiρIt.
ρt=ρEg(σo|Ey|2+σe|Ez|2)+β(K)(|Ey|2+|Ez|2)(K)Kω0,
ρt=ρ(vo|ey|2+ve|ez|2)+(|ey|2+|ez|2e0)K,
e0=(KωρBDβ(K)tp)1/Kπwfo22Pin,vo=σotpEg2Pinπwfo2,ve=σetpEg2Pinπwfo2.
E(x,y,z,t)=Exe^x+Eye^y.
(PxNLPyNLPzNL)=3ε0[χ11000χ31χ16χ311/3χ11000χ110χ1600001/3χ11χ31χ310χ330χ160χ16χ3100](|Ex|2Ex|Ey|2Ey000002|Ey|2Ex+(Ey)2Ex*(Ex)2Ey*+2|Ex|2Ey0).
Exz=iko22Ext2+i2k0oT2Ex+ik0o2no2ε0{3ε0χ11{(|Ex|2+23|Ey|2)Ex+13(Ex*Ey)Ey}12σo(1+iωτc)ρEx12β(K){(|Ex|2+|Ey|2)K1}Ex,
Eyz=iko22Eyt2+i2k0oT2Ey+ik0o2no2ε0{3ε0χ11{(|Ey|2+23|Ex|2)Ey+13(ExEy*)Ex}12σo(1+iωτc)ρEy12β(K){(|Ex|2+|Ey|2)K1}Ey,
ρt=ρEgσo(|Ex|2+|Ey|2)+β(K)(|Ex|2+|Ey|2)(K)Kω0,
T=/x+/y.
t=t/tp,z=z/4zfo,x=x/wfo,y=y/wfo,T2=wfo2T2,ρ=ρ/ρBD,ex=Ex/(2Pin/πwfo2)1/2ey=Ey/(2Pin/πwfo2)1/2
exz=iδ2ext2+iT2ex+icSF{(|ex|2+23|ey|2)ex+13(ex*ey)ey}γo(1+iωτc)ρexμ{(|ex|2+|ey|2)K1}ex,
eyz=iδ2eyt2+iT2ey+icSF{(|ey|2+23|ex|2)ey+13(ey*ex)ex}γo(1+iωτc)ρeyμ{(|ex|2+|ey|2)K1}ey,
ρt=voρ(|ex|2+|ey|2)+(|ex|2+|ey|2e0)K,
μ=2zfβ(K)(2Pin/πwf2)(K1)andγo=2σoρBDzf,δ=2zfk/tp2,cSF=(12k0ozf/no2)χ11(Pin/πwf2),e0=(KωρBDβ(K)tp)1/Kπwf22Pin,vo=σotpEg2Pinπwf2.
Qabs(W/m3)=σoρ(|Ey|2+σeρ|Ez|2)+β(K)(|Ey|2+|Ez|2)Kforx-cut crystal.
Qabs(W/m3)=σoρ(|Ex|2+|Ey|2)+β(K)(|Ex|2+|Ey|2)Kforz-cut crystal.
Aeyi,j,tmy+1/2eyi+1,j,tmy+1/2eyi1,j,tmy+1/2=Beyi,j,tm+C1(eyi,j,t+1m+eyi,j,t1m)=hi,j,tmCeyi,j,tmz+1/2eyi,j+1,tmz+1/2eyi,j1,tmz+1/2=Deyi,j,tmy+1/2+C2(eyi+1,j,tmy+1/2+eyi1,j,tmy+1/2)=gi,j,tmy+1/2Eeyi,j,tm+1eyi,j,t+1m+1eyi,j,t1m+1=Feyi,j,tmz+1/2+C3(eyi,j+1,tmz+1/2+eyi,j1,tmz+1/2)=di,j,tmz+1/2,
el,j,tmy+1/2(l=i1,i,i+1)=(el,j,tm+el,j,tm+1)/2ei,l,tmz+1/2(l=j1,j,j+1)=(ei,l,tm+ei,l,tm+1)/2.
A=2i(Δy)2Δx+2,B=2(Δy)2δo(Δt)2+iγo(1+iω0τc)ρ(Δy)22i(Δy)2Δx,C=2i(Δz)2Δx+2D=2i(Δz)2Δx2(Δz)2(Δy)2,E=2i(Δt)2δoΔx+2+iγo(1+iω0τc)ρ(Δt)2/δo,F=+2(Δt)2δo(Δz)2+2i(Δt)2δoΔxC1=(Δy)2δo(Δt)2,C2=((Δz)2(Δy)2),C3=(Δt)2δo(Δz)2.
Aezi,j,tmy+1/2ezi+1,j,tmy+1/2ezi1,j,tmy+1/2=Bezi,j,tm+C1(ezi,j,t+1m+ezi,j,t1m)=hi,j,tmCezi,j,tmz+1/2ezi,j+1,tmz+1/2ezi,j1,tmz+1/2=Dezi,j,tmy+1/2+C2(ezi+1,j,tmy+1/2+ezi1,j,tmy+1/2)=gi,j,tmy+1/2Eezi,j,tm+1ezi,j,t+1m+1ezi,j,t1m+1=Fezi,j,tmz+1/2+C3(ezi,j+1,tmz+1/2+ezi,j1,tmz+1/2)=di,j,tmz+1/2.
A=2i(Δy)2k0ek0oΔx+2,B=2(Δy)2k0ek0oδe(Δt)2+iγe(1+iω0τc)ρ(Δy)2k0ek0o2i(Δy)2k0ek0oΔxC=2i(Δz)2k0ek0oΔx+2,D=2i(Δz)2k0ek0oΔx2(Δz)2(Δy)2,E=2i(Δt)2δeΔx+2+iγe(1+iω0τc)ρ(Δt)2/δeF=+2k0ok0e(Δt)2δe(Δz)2+2i(Δt)2δeΔx,C1=(Δy)2k0ek0oδe(Δt)2,C2=((Δz)2(Δy)2),C3=k0ok0e(Δt)2δe(Δz)2.

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