A full numerical description of second- and third-harmonic generation (SHG and THG) at the focus of a nonlinear microscope is presented. The numerical implementation takes into account reflections and refraction by an arbitrary number of interfaces perpendicular to the optical axis in the focal region. The calculation of the second- and third-harmonic far-field radiation pattern is based on a Green function approach and is presented for any collection direction. The calculations are sped up by using the chirp- transform for the focusing fields as well as for the far-field radiation calculation. Numerical evidence is presented for deviations in the measurement of the second-order nonlinear susceptibility ratio of collagen fibers in SHG microscopy at high excitation numerical aperture. When interface reflections are taken into account, significant direct backward THG is demonstrated from interfaces and multilayer structures.
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