Abstract

The understanding of the spatiotemporal structure of the spectrum is of importance for all applications where entanglement in energy is the relevant degree of freedom and allows optimizing the spectrum for specific applications. Here, we consider spontaneous parametric down-conversion (SPDC) induced by an undepleted monochromatic pump beam of angular frequency 𝜔_𝑝 with a transverse field distribution ${ℰ}_p^{+}(q_p)$, which propagates along the 𝑧-axis of a periodically poled potassium titanyl phosphate (PPKTP) crystal. The pump photon (p) is down-converted into the idler (i) and signal (s) photon with frequency 𝜔_i = 𝜔_p − 𝜔_s and 𝜔_s respectively. All involved photons are identically polarized, i.e. in type-0 configuration. Adapting the derivation of the entangled two-photon state in [1] for quasi-phase-matched type-0 configuration with finite crystal length yields to

© 2013 IEEE