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The Z-scan Technique Using the Laguerre-Gaussian Beam: Variational Analysis
R-P. Chen, J-L. Chen and C-Q. Dai

We have studied the propagation of Laguerre-Gaussian (LG) beams in a Kerr medium by using the variational method. The characteristics of the LG beams in the Kerr medium and the field distribution in the far field after propagating through the Kerr medium are demonstrated. The expression for the on-axis normalized transmittance in the far field as a function of the beam parameters and position is derived. The characteristics of the Z-scan technique using the LG beams was analysed and the peak and valley of the on-axis normalized transmittance was seen to decrease with increasing radial modes, p, for angular mode m = 0, but increase with increasing radial modes for other angular modes. When the medium thickness increased the peak and the valley of the normalized transmittance initially increased linearly and then began to saturate when the thickness exceeded the threshold.

Keywords: Laguerre-Gaussian (LG) beams, Kerr effect, nonlinear optics, variational method, nonlinear refraction, Z-scan

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