You are trying to see reverse SHG effect, for this you need to first model the crystal by defining it as an anisotropic medium with necessary dispersion parameters (μ,σ,ε).
For simplicity, you can model OPO as a blackbox with one input and two outputs. If you don't want to go into trouble to model the crystal, you can model it as a beam splitter with different wavelength outputs.
Modelling the cavity is not that simple unfortunately. You need to model both mirrors and the crystal for complete behavior of cavity. But this might only be necessary to a precision point, it ends up in your error tolerance.
TEM mode beam will not have any electric field component along the propagation path. You can plot Gaussian pattern of your beam but that will not include electric field.