Microscopic second-order susceptibility tensor analysis

Summary form only given. Recent advances in nonlinear microscopy show great potential to study organization and morphology of biological structures [1]. This is especially important for biomedical applications where structural changes can lead to, or be utilized as diagnostic tools of severe diseases [1]. Nonlinear microscopies are in general minimally invasive facilitating in vivo imaging, and can provide deeper penetration than traditional linear microscopy techniques. In addition, coherent nonlinear modalities, such as second-harmonic generation (SHG) microscopy, can provide more quantitative morphological information of the protein conformational order than traditional linear techniques [2,3]. This is due to the intrinsic sensitivity of SHG to symmetry properties of the excited matter, which in conjunction with polarization measurements can be utilized to extract microscopic morphological information [3]. But all the developed quantitative approaches require a varying degree of a priori information, such as knowledge of the overall symmetry or orientation of the material. Neither are they applicable for extracting the complex susceptibility tensor limiting the potential applicability of the techniques [4].Here, we demonstrate a tensor analysis technique which can retrieve information of the complex secondorder susceptibility and can be performed in situ using a polarized SHG microscope. The potential solutions for the nonlinear inverse scattering problem imposed by the focusing scheme are searched using a genetic algorithm, which iteratively searches for fitting complex susceptibility solutions and compares them with the measured polarization-sensitive SHG responses. In order to demonstrate the technique, we characterize the second-order nonlinear responses of cell membranes of Halobacterium salinarium bacteria in a polarized SHG microscope (NA=0.8, =1060 nm). The excitation polarization is modulated by rotating a quarter-wave plate. These cell membranes, commonly known as purple membranes, consist of crystalline bacteriorhodopsin (bR) trimers, which contain three photoactive retinal molecules in a known geometry possessing C3 symmetry [5]. The threedimensional trimer structures are schematically shown in Fig.1(a). In order to reach good convergence, we assume that the total SHG response is dominantly due the zzz, zxx and xxz=xzx components of the retinal hyperpolarizability. Few example solutions for the complex susceptibility are shown in Fig.1(b), demonstrating good convergence of the algorithm. We believe, that our technique could be developed into a highly useful noninvasive and in-situ analysis tool to study protein conformation and tissue morphology.