Vectorial approach to studying second harmonic generation in collagen using linearly and radially polarized beams

The study of second harmonic generation (SHG) has been examined using a vectorial approach for both linearly and radially polarized beams. This approach is necessary for situations when the beam is tightly focused such as in a microscope. Using the vectorial approach, the result of including the y and z components of the electric field is that previously ignored 'cross-component' terms are now found to have an influence on the SHG polarization and the radiation patterns obtained. Since SHG is dependent on the susceptibility tensor, the inclusion of these 'cross-component' terms can help to identify structural changes in biological materials simply by studying the changes in the tensor via the SHG polarization. In particular, we calculate the second harmonic polarization induced in collagen for both linearly and radially polarized beams.