The effect of scattering loss on connections between classical and quantum processes in second-order nonlinear waveguides

We show that a useful connection exists between spontaneous parametric downconversion (SPDC) and sum frequency generation in nonlinear optical waveguides with arbitrary scattering loss, while the same does not hold true for SPDC and difference frequency generation. This result deepens the relationship between quantum and classical second-order nonlinear optical processes in waveguides, and identifies the most accurate characterization of their quantum performance in the presence of loss based solely on classical measurements.

Spontaneous parametric downconversion in waveguides: Whats loss got to do with it?

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.

Parasitic nonlinearities in photon pair generation via integrated spontaneous four-wave mixing: critical problem or distraction?

We consider integrated photon pair sources based on spontaneous four-wave mixing and derive expressions for the pump powers at which various nonlinear processes become relevant for a variety of source materials and structures. These expressions serve as rules of thumb in identifying reasonable parameter regimes for the design of such sources. We demonstrate that if pump powers are kept low enough to suppress cross-phase modulation, multi-pair events as well as many other nonlinear effects are often also constrained to negligible levels.

Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magneto-electric medium

We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through its ability to accommodate strong dispersion and loss, our theory provides a rigorous foundation for the study of quantum optical processes in structures incorporating metamaterials, provided these may be modeled as magneto-electric media. Previous canonical treatments of dielectric and magneto-dielectric media have expressed the electromagnetic field operators in either a Green function or mode expansion representation. Here we present our results in the mode expansion picture with a view to applications in guided wave and cavity quantum optics.