Phase matching considerations in second harmonic generation from tissues: Effects on emission directionality, conversion efficiency and observed morphology

We present a heuristic treatment which relates SHG image intensities, signal directionality, and observed morphology to the physical structure of collagen and cellulose fibrillar tissues. The SHG creation model is based upon relaxed phase matching conditions which account for dispersion, randomness, and axial momentum contributions from the media, and includes a mathematical treatment which relates SHG conversion efficiency to fibril diameter and packing through the inclusion of potential intensity amplification resultant from quasi-phase matching (QPM). A direct consequence of this theory is that SHG in biological tissues is not strictly a coherent process, and that the forward directed SHG has a longer coherence length than the backward component, Through this treatment, we show that the emission directionality and also conversion efficiency do not arise solely from the fibril size but also depend on packing density and order of the inter-fibril structure. We demonstrate these principles in comparing the SHG response in normal and Osteogenesis Imperfecta (OI) skin. We show that the observed directionality and decreased relative intensity in the diseased state is consistent with phase matching conditions arising from the decreased fibril size and more random assembly. We further use this theory to explain the differences in morphology seen in forward and backward collected SHG in fibrillar tissues (e.g., collagenous and cellulosic). Specifically, we attribute segmented appearance to destructive interference between small fibrils separated by less than the coherence length. We suggest the approach based on relaxed phasematching conditions is general in predicting the SHG response in tissues and may be broadly applicable in interpreting the SHG contrast for diagnostic applications.