Physics – Optics
Scientific paper
2007-10-08
Physics
Optics
49 pages, 7 figures. V2: A few typos corrected, some new material added
Scientific paper
The reflection of a three-dimensional vectorial Maxwell-Gaussian beam by a planar surface is studied. The surface is characterized by its complex reflection coefficients $r_s(\bk)$ and $r_p(\bk)$ for TE and TM electromagnetic plane waves of wavevector $\bk$, respectively. The field impinging upon the reflecting surface is modeled as a quasi-monochromatic fundamental Gaussian beam suitably modified in order to satisfy Maxwell equations (Maxwell-Gaussian beam). Analytical expressions, correct up to the second order in a perturbation expansion, are given for the reflected electric and magnetic field, respectively. We found that first order terms in the perturbation expansion account for a longitudinal shift (Goos-H\"{a}nchen effect) of the whole reflected beam, while second order terms modifies the transverse shape of the beam which is, at this order, no longer cylindrically symmetric.
Aiello Andrea
Woerdman Han
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