Multiphoton propagation eigenmodes for sum-frequency generation

In linear optics, modes correspond to a set of fields that are mutually orthogonal, however, in the nonlinear regime the principle of linear superposition is no longer valid and consequently, the method of mode decomposition breaks down. This is the case when considering sum-frequency generation in a nonlinear crystal. Here, we use the non-depleting pump approximation to describe the nonlinear interaction with low-intensity multiphoton fields. We show that the description of multiphoton fields using the propagation eigenmodes simplifies the Fock state quantum behaviour of the system while remaining equivalent to the standard approach.