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We develop a non-perturbative formulation based on the Green-functionquantization method, that can describe spontaneous parametric down-conversionin the high-gain regime in nonlinear optical structures with arbitrary amountof loss and dispersion. This formalism opens the way for description and designof arbitrary complex and/or open nanostructured nonlinear optical systems inquantum technology applications, such as squeezed-light generation,nonlinearity-based quantum sensing, and hybrid quantum systems mediated bynonlinear interactions. As an example case, we numerically investigate thescenario of integrated quantum spectroscopy with undetected photons, in thehigh-gain regime, and uncover novel gain-dependent effects in the performanceof the system.

Non-perturbative theory of spontaneous parametric down-conversion in open and dispersive optical systems