Abstract
We use a vector field model to analyze third-harmonic generation (THG) from model geometries (interfaces, slabs, periodic structures) illuminated by Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams focused by a high NA lens. Calculations show that phase matching conditions are significantly affected by the tailoring of the field distribution near focus. In the case of an interface parallel to the optical axis illuminated by an odd HG mode, the emission patterns and signal level reflect the relative orientation of the interface and the focal field structure. In the case of slabs and periodic structures, the emission patterns reflect the interplay between focal field distribution (amplitude and phase) and sample structure. Forward-to-backward emission ratios using different beam shapes provide sub-wavelength information about sample spatial frequencies.
Highlights
Coherent nonlinear microscopies based on parametric processes such as coherent anti-Stokes Raman scattering (CARS), second-harmonic generation (SHG) or third-harmonic generation (THG) are receiving considerable attention
The general idea is that measurable emission patterns reflect the interplay between the sample structure and a known field distribution
Studying focus-engineered THG is informative because third-harmonic generation can be obtained from simple sample geometries and is highly sensitive to the focal phase distribution
Summary
Coherent nonlinear microscopies based on parametric processes such as coherent anti-Stokes Raman scattering (CARS), second-harmonic generation (SHG) or third-harmonic generation (THG) are receiving considerable attention. Phase and polarization may be modified by controlling the wavefront at the pupil of the objective, resulting in a modulation of phase-matching conditions and far-field emission patterns This concept has been explored recently for SHG microscopy, where focused beams with strong axial components were used to enhance signal from fibers parallel to the optical axis [1, 2], and in CARS microscopy where focus engineering was used to highlight interfaces [3, 4]. We here present a numerical study of vectorial and phase-matching aspects of THG by tightly focused Gaussian, Hermite-Gaussian (HG), and Laguerre-Gaussian (LG) beams incident on slabs, interfaces, and axially periodic samples These calculations provide insight on the interplay between field and sample structure in THG microscopy with focused complex beams, and should more generally prove useful for designing coherent nonlinear microscopy (SHG, THG, CARS) experiments with engineered beams. Our strategy for simulations follows the framework described in [15], but integrates a complete vector field model to account for vectorial effects with arbitrary excitation beam profiles
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