By variational approach, we analyze the characteristics of beam propagation through a cubic optical nonlinear medium using a laser beam that has a transverse elliptic Gaussian profile. The analytic solution to the normalized transmittance at the center of the far field as a function of medium position and the beam characteristics is obtained and compared with the numerical simulation, which is realized by a combination of algorithms. We also analyze the peak-valley transmittance difference as a function of medium length, ellipticity, and astigmatism. The relationship between peak-valley normalized transmittance difference of the <i>z</i>-scan trace and aperture size or the slit width are obtained. Meanwhile, the comparison of <i>z</i>-scan characteristics with an elliptic Gaussian beam with those using a circular symmetric Gaussian beam is made.
© 2003 Optical Society of America
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(190.3270) Nonlinear optics : Kerr effect
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.5940) Nonlinear optics : Self-action effects
Wei-Ping Zang, Jian-Guo Tian, Zhi-Bo Liu, Wen-Yuan Zhou, Chun-Ping Zhang, and Guang-Yin Zhang, "Variational Analysis of z Scan of Thick Medium with an Elliptic Gaussian Beam," Appl. Opt. 42, 2219-2225 (2003)