Spontaneous parametric downconversion in waveguides: What's loss got to do with it?

TL;DR

This paper develops a theoretical framework to analyze how linear scattering loss in nonlinear waveguides affects the spectral properties and generation efficiency of photon pairs produced via spontaneous parametric downconversion (SPDC).

Contribution

It introduces a Hamiltonian formalism incorporating loss into SPDC analysis, revealing how loss influences the joint spectral intensity and photon correlations in waveguides.

Findings

Loss modifies the biphoton spectral distribution and correlations.

Balanced loss conditions can replicate lossless SPDC spectral properties.

Frequency-dependent loss can reduce photon pair generation efficiency.

Abstract

We derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss. Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients. In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator, and we find that this density operator is naturally composed of two photon, one photon, and zero photon contributions. The biphoton probability density, or joint spectral intensity (JSI), associated with the two-photon contribution is determined not only by a phase matching term, but also by a loss matching term. The relative size of the loss coefficients within this term lead to three qualitatively different regimes of SPDC JSIs. If either the pump or generated photon loss is much higher than the other, the side lobes of the phase matching squared sinc function are washed out. On the other hand, if pump and generated photon loss are appropriately balanced, the lossy JSI is identical to the lossless JSI. Finally, if the generated photon loss is frequency dependent, the shape of the JSI can be altered more severely, potentially leading to generated photons that are less frequency correlated though also produced less efficiently when compared to photons generated in low-loss waveguides.