Finite thickness lens model for self-focusing (defocusing) in Kerr medium

Abstract

A “finite thickness lens” model for self-focusing (defocusing) in Kerr medium is presented. An onaxis normalization transmittance formula is presented for arbitrary nonlinear phase shift for the finite thickness Kerr medium by introducing a nonlinear ABCD-matrix for the transition of a Gaussian beam from linear to nonlinear medium, without complex calculation for the beam radius at the far field aperture. The variation of the peak and valley transmittance difference is found to enhance linearly as the phase shift at the focus increases by increasing the thickness of the medium. If the ratio of the Rayleigh distance divided by the thickness of the medium (d/z0) is constant and small enough, the peak and valley transmittance difference stays constant. Finally, a qualitative formula is presented to express the relationship between the system parameters and the on-axis phase shift at the focus.

Keywords

finite thickness lens model / ABCD matrix / transmittance

References

[1] R. E. Lara, N. Z. Meza, D. M. Iturbe Castillo, and G. C. Trecino Palacios, Opt. Exp., 2007, 15: 2517

[2] T. Geethakrishnan and P. K. Palanisamy, Opt. Commun., 2007, 270: 424

[3] I. R. Aleksandr and P. Bruno, Appl. Opt., 2006, 45: 2773

[4] A. I. Amiel, T. V. Luat, D. G. Taylor, and L. G. Alexander, Opt. Lett., 2008, 33: 13

[5] M. Sheik-bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett., 1989, 14: 955

[6] M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, Quantum Electron, 1990, 26: 760

[7] M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, Opt. Lett., 1992, 17: 258

[8] T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, Opt. Lett., 1994, 19: 317

[9] J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, Opt. Soc. Am. B,1994, 11: 1009

[10] H. C. Kwak, L. Y. Lee, and S. G. Kim, Opt. Soc. Am. B, 1999, 16: 600

[11] B. P. Chapple, J. Staromlynska, A. J. Hermann, J. T. Mckay, and G. R. MeDuff, Non. Opt. Phys. Mat., 1997, 6: 251

[12] H. Tomoharu, N. Tatsuo, and S. Naoki, Opt. Commun., 2005, 250: 411

[13] X. D. Liu, S. L. Guo, H. T. Wang, and L. T. Hou, Opt. Commun., 2001, 197: 431

[14] V. Magni, G. Cerullo, and D. S. Silvestri, Opt. Commun., 1993, 96: 348

[15] I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, Optical & Technology, 1997, 29: 355

[16] G. Yang, W. T. Wang, L. Yan, H. B. Lu, G. Z. Yang, and Z. H. Chen, Opt. Commun., 2002, 209: 445

[17] M. D. Dvorak, B. L. Justus, and A. D. Berry, Opt. Commun., 1995, 116: 149

[18] X. Chen, B. Lavorel, T. Dreier, N. Genetier, H. Misserey, and X. Michaut, Opt. Commun., 1998, 153: 301

[19] J. Zhou, Y. B. Pun Edwin, S. Chung Po, and X. H. Zhang, Opt. Commun., 2001, 191: 427

[20] H. Kogelnik and T. Li, Appl. Opt., 1966, 5: 1550

[21] D. Kliger, Ultrasensitive Laser Spectroscopy, New York: Academic, 1983: 175

[22] M. Sheik-Bahae, A. A. Said, J. D. Hagan, J. M. Soileau, and W. E. Van Stryland, Opt. Eng., 1990, 30: 1228

[23] C. M. D. Iturbe, J. J. Sánchez-Mondragón, and S. I. Stepanov, Optik, 1995, 100: 49

[24] D. Weaire, B. S. Wherrett, D. A. B. Miller, and S. D. Smith, Opt. Lett., 1974, 4: 331

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg