Harmonic entanglement with second-order nonlinearity

We investigate the second-order nonlinear interaction as a means to generate entanglement between fields of differing wavelengths and show that perfect entanglement can, in principle, be produced between the fundamental and second-harmonic fields in these processes. Neither pure second-harmonic generation nor parametric oscillation optimally produce entanglement; such optimal entanglement is rather produced by an intermediate process.