Theoretical-experimental method of nonlinear optics: the Z-scan technique


  • Antonio-Alfonso Rodriguez-Rosales
  • Omar Guillermo Morales Saavedra
  • Fabiola Cristina Rodríguez Estrada
  • Juan Antonio Murillo Vargas
  • Carlos Jesús Román Moreno



nonlinear optics, Z-scan, thermal lens, liquid crystals


We did this work to help professors and students of physics and engineering in Optics and Lasers courses who require a theoretical-experimental introductory framework to nonlinear optics. We showed in this article the basic principles of the theory, focusing on third-order nonlinear optical phenomena, using the well-known Z-scan technique for its demonstration. For this, we propose the design of a simple experiment that the interested party can do in an optics laboratory. Once the data has been obtained and processed, we implemented a practical method of interpretation of the typical graphs obtained by this technique to carry out the calculations that allow the measurement of the refractive index and the nonlinear absorption coefficient in materials that present these optical properties, as the case exemplified here of nematic liquid crystals doped with an organic dye.


Boyd, R. W. (2020). Nonlinear Optics. Elsevier Gezondheidszorg.

Christian, G. D. (1977). Analytical Chemistry. Wiley.

Gómez, S., Cuppo, F., & Figueiredo Neto, A. (2003). Nonlinear optical properties of liquid crystals probed by Z-scan technique. Brazilian Journal of Physics, 33(4), 813–820.

Hecht, E. (1987). Optics (2nd ed.). Addison-Wesley.

Idrobo, L. M. F., Velasco, M. P., & Niebles, F. R. (2005). Observación de la autofocalización en azul de metileno utilizando “Z SCAN.” Revista De La Sociedad Colombiana De Física, 38(1), 205–208.

Madhana Sundari, R., & Palanisamy, P. (2006). Self-diffraction and Z-scan studies in organic dye doped thin films. Applied Surface Science, 252(6), 2281–2287.

Marrucci, L. (2002). Mechanisms of giant optical nonlinearity in light-absorbing liquid crystals: a brief primer. Liquid Crystals Today, 11(3), 6–33.

Rodríguez, L., & Ramirez, J. (2004). Lente térmica inducida por diodo láser como experiencia didáctica de laboratorio de física. Revista Mexicana De Física E, 51(1), 1–4.

Rodríguez Rosales, A. A. (2001). Estudio de propiedades ópticas no lineales en nuevos materiales orgánicos monomericos [Tesis de maestría]. Universidad Nacional Autónoma de México.

Rodríguez-Rosales, A. A., Morales-Saavedra, O. G., Román-Moreno, C. J., & Ortega-Martínez, R. (2008). Variation of nonlinear refractive index in dye-doped liquid crystals by local and nonlocal mechanisms. Optical Materials, 31(2), 350–360.

Rodríguez-Rosales, A. A., Ortega-Martínez, R., Arroyo Carrasco, M. L., Reynoso Lara, E., Treviño Palacios, C. G., Baldovino-Pantaleón, O., Ramos García, R., & Iturbe-Castillo, M. D. (2008). Neither Kerr Nor Thermal Nonlinear Response of Dye Doped Liquid Crystal Characterized by the Z-Scan Technique. Molecular Crystals and Liquid Crystals, 489(1), 9/[335]-21/[347].

Sheik-Bahae, M., Said, A. A., & Van Stryland, E. W. (1989). High-sensitivity, single-beam n2 measurements. Optics Letters, 14(17), 955.

Sheik-Bahae, M., Said, A., Wei, T. H., Hagan, D., & Van Stryland, E. (1990). Sensitive measurement of optical nonlinearities using a single beam. IEEE Journal of Quantum Electronics, 26(4), 760–769.

Sheik-Bahae, M. (1991). Nonlinear refraction and optical limiting in media. Optical Engineering, 30(8), 1228.

Van Stryland, E. W., & Sheik-Bahae, M. (1997). Z-scan technique for nonlinear materials characterization. SPIE Proceedings.




How to Cite

Rodriguez-Rosales, A.-A., Saavedra, O. G. M., Estrada, F. C. R., Vargas, J. A. M., & Moreno, C. J. R. (2023). Theoretical-experimental method of nonlinear optics: the Z-scan technique. South Florida Journal of Development, 4(4), 1807–1827.