Modal, spectral, and polarization entanglement in guided-wave parametric down-conversion

We examine the modal, spectral, and polarization entanglement properties of photon pairs generated in a nonlinear periodically poled two-mode waveguide (one-dimensional planar or two-dimensional circular) via nondegenerate spontaneous parametric down-conversion. Any of the possible degrees of freedom---mode number, frequency, or polarization---can be used to distinguish the down-converted photons while the others serve as attributes of entanglement. Distinguishing the down-converted photons based on their mode numbers enables us to efficiently generate spectral or polarization entanglement that is either narrowband or broadband. On the other hand, when the generated photons are distinguished by their frequencies in a type-0 process, modal entanglement turns out to be an efficient alternative to polarization entanglement. Moreover, modal entanglement in type-II down-conversion may be used to generate a doubly entangled state in frequency and polarization.