Vector analysis of the coherent anti-Stokes Raman scattering signals generated under the tightly focused condition

In a coherent anti-Stokes Raman scattering (CARS) microscope, when samples with different shapes and dimensions are excitated by collinearly introduced and tightly focused Gaussian beams, the microscopic structure will be determined by the spatial distributions of generated CARS signals. Therefore, we build a theoretical model for CARS signals from spherical sample under the tightly focused condition. The intensity and phase distributions of tightly focused linear polarization Gaussian beams are analyzed with vector wave equations. The vector wave equation of CARS signals is derived from Green's function. The far-field CARS radiation patterns of spherical scatters with different diameters are simulatively calculated. Theoretical analysis and simulative calculation results show that the intensities of forward and backward CARS signals from the small spherical sampler are similar. The images with high contrast can be obtained by backward detection method from an objective with a high numerical aperture. For big spherical samplers, intensities of CARS signals are greatly increased. The emission direction is mainly concentrated in a spatial angle. The forward CARS signals can be effectively collected by an objective with low numerical aperture.