Phase matching of backward second harmonic generation assisted by lattice structure in collagen tissues

Phase matching of backward second harmonic generation (SHG) in a periodic structure of collagen fibrils is investigated through theoretical modeling, simulation, and experiments. The lattice structure of collagen fibrils is considered to provide a virtual momentum for assisting the phase matching of backward SHG. Phase matching over a relatively wide excitation wavelength range is achieved by tilting the angle of the fundamental excitation and SHG wave vectors. The SHG intensity in the periodic structure is simulated to quantify the phase matching effect. The effect of the fundamental excitation and the SHG emission angles on the peak excitation wavelength of the SHG excitation spectrum is further validated in experiments, where the excitation and emission angles are controlled by spatial filtering. It is found that an optimized excitation wavelength exists for a certain collagen fibril structure, which shifts toward a shorter wavelength when the excitation and emission angles are increased. Our results show that the lattice structure of collagen fibrils can assist the phase matching, providing a mechanism for generating backward SHG in multiphoton microscopy.