Numerical simulation of polarization-resolved second-harmonic microscopy in birefringent media

Polarization-resolved second-harmonic microscopy has recently emerged as a valuable technique for in situ imaging of collagen structure in tissues. Nevertheless, collagen-rich tissues such as tendon, ligament, skin dermis, bone, cornea, or artery exhibit a heterogeneous and anisotropic architecture that results in complex optical properties. While experimental evidence of polarization distortions has been reported in various tissues, the physics of second-harmonic imaging within such tissues is not fully understood yet. In this work, we performed numerical simulations of polarization-resolved second-harmonic generation in a strongly focused regime within a birefringent tissue. We show that vectorial components due to strong focusing have a rather small effect on the measurement of the second-harmonic tensorial response, while birefringence and optical dispersion may affect these measurements dramatically. We show indeed that a difference in the focal field distribution for ordinary and extraordinary waves results in different phase-matching conditions, which strongly affects the relative efficacy of second-harmonic generation for different polarizations. These results are of great interest for extracting reliable quantitative parameters from second-harmonic images.