Abstract

An analytical expression capable of calculating the on-axis far-field electric field of a Gaussian beam carrying a phase with a Gaussian profile is obtained. This result is based on the Huygens–Fresnel principle and is not limited to small Gaussian phases. The analytical results are particularized to the z-scan case, agreeing with the Gaussian-decomposition results for small phases. For Gaussian phases with amplitude up to π, a small deviation of the constant peak-to-valley distance is found, but a significant displacement of the axis crossing point is predicted. The theoretical expression of the two-color z-scan is also obtained, and it agrees exactly with the expression obtained by the Gaussian-decomposition method, to first-order approximation. Also we apply our result to the case of a thick sample, verifying the range of coincidence between two different formalisms.

© 1998 Optical Society of America

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