Mid-IR upconversion imaging: theory and applications

Upconversion imaging using a χ(2) material can conveniently be viewed as an optical filter known from Fourier optics. First part discusses the solution to Helmholtz Equation with a nonlinear source term representing the χ(2) interaction process. Assuming non-depleted interaction, an explicit solution can be found using Greens Function. In the far-field the solution is found in terms of a simple 3D Fourier integral. We will analyze a 4f-setup, with the nonlinear crystal situated in the Fourier plane, for upconversion imaging. While the results resembles the linear case known from standard imaging systems, χ(2) imaging has an additional phase match term, dictated by the dispersion and birefringence amongst the three interacting fields. Birefringent crystals can be implemented as the nonlinear medium to ensure phase matching, i.e. efficient conversion of the mid-IR signal to the visible. When interaction takes place in the fs regime, group velocity mismatch will be included. The main features of the theory is presented, including applications.