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Journal of the Optical Society of America B

Photodetection tails in parametric downconversion

Roger Andrews, Edward R. Pike, Sarben Sarkar

Published May 1, 1995• 0 citations
Publisher

Abstract

A new theory for multimode parametric downconversion is given that yields differen, t predictions from existing treatments for photodetection tails. The theory is rigorous and is derived from first principles. The cases of both a single-atom and a nonlinear-crystal source are treated. The detection is taken to be far from the source. For a single atom the photodetection amplitude has a tail in the reduced time that falls off asymptotically as the inverse second power. The corresponding tail for the case of a crystal has an inverse quartic falloff.

DOI
10.1364/josab.12.000853

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A new theory for multimode parametric downconversion is given that yields differen, t predictions from existing treatments for photodetection tails. The theory is rigorous and is derived from first principles. The cases of both a single-atom and a nonlinear-crystal source are treated. The detection is taken to be far from the source. For a single atom the photodetection amplitude has a tail in the reduced time that falls off asymptotically as the inverse second power. The corresponding tail for the case of a crystal has an inverse quartic falloff.
When a laser beam interacts with a nonlinear crystal, some of the incident photons fission into two lower frequency signal and idler photons through the process of spontaneous parametric downconversion. It is shown that, as a result of the strong positive correlation between signal and idler photons, the normalized intensity cross-correlation function λ12(τ) should be inversely proportional to the downconverted light intensity and ideally should be given by the inverse of the mean number of photons counted in the resolving time. This unusual relationship, which is a reflection of the quantum mechanical character of the downconverted optical field, has been confirmed in photoelectric counting measurements. The experiment makes use of the light from an argon-ion laser oscillating at 351.1 nm interacting with an 8-cm long crystal of KDP. The downconverted light is extracted at 633.5 and 788.0 nm in two directions that satisfy the phase-matching condition and is allowed to fall on two counting photomultipliers. The output pulses are fed to a time-to-digital converter that yields the cross-correlation function.
In this paper we study photon pairs generated in a nonlinear cavity composed of a nonlinear crystal surrounded by mirrors, by the process of spotaneous parametric downconversion. We analyze two different regimes: singly-resonant cavities where the signal and idler modes are resonant and doubly-resonant cavities where the pump mode is also resonant. We present analytic expressions for the joint spectral amplitude in these two cases and study the reduction in emission bandwidth as the cavity coefficient finesse is increased. We also study the enhancement of the source brightness from the presence of the cavity.
A multimode photodetection theory is developed that includes both the presence of radiation sources and the damping of the field due to the measurement. Making use of Green's-function techniques and the rotating-wave approximation, the counting statistics is calculated in terms of input field quantities. The treatment of the detector-field interaction yields expressions that essentially differ from the results of nonperturbative single-mode theories but are very similar to those of the well-known perturbative photodetection theories. The field damping due to the detection of photons is found to lead to a renormalized detector response function that approaches a maximum value if the number of detector atoms tends to infinity. It is worth noting that our result may be closely related to those of Mandel's heuristic description of photodetection based on the concept of configuration-space photon number operators.
We investigate the coupling efficiency of parametric downconversion light (PDC) into single and multimode optical fibers as a function of the pump beam diameter, crystal length, and walk-off. We outline two different theoretical models for the preparation and collection of either single-mode or multimode PDC light (defined by, for instance, multimode fibers or apertures). Moreover, we define the mode-matching collection efficiency, important for realizing a single-photon source based on PDC output into a well-defined single mode. We also define a multimode collection efficiency that is useful for single-photon detector calibration applications.