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Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki

Parametric production of coherent emission in a spatially incoherent pump field

A. A. Babin, N. N. Belyaeva, Iu. N. Beliaev, Gennadii I Freidman

Published Jul 1, 1976• 0 citations
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We investigate the emergence of spatial and temporal coherence for the fields in the noncritical nondegenerate parametric second-order down-conversion process pumped with low spatial and temporal coherence beams. It is shown that in this scenario, which is of considerable practical importance, the parametric gain in the near field breaks down into an ensemble of mutually incoherent beamlets containing parametric waves. The field generated in a single beamlet is fully spatially coherent. The size of such coherent parametric gain regions is governed by the near-field spatial coherence radius of the pump, which also acts as a parameter, restraining the linear diffraction of the parametric waves generated in the nonlinear interaction. Furthermore, we experimentally demonstrate how the spatial and temporal coherence can be substantially enhanced by manipulating the spatial field correlation of the multilongitudinal and multi-transversal mode pump.
Entangled-photon pairs (biphotons) generated by spontaneous optical parametric down-conversion exhibit a number of properties that are analogous to those of ordinary photons generated by incoherent sources. The spatial pump-field distribution and the two-particle wave function in the biphoton case play the respective roles of the source intensity distribution and the second-order coherence function in the incoherent case. The van Cittert--Zernike theorem, which is applicable for incoherent optical sources emitting independent photons, has a counterpart for biphotons. Likewise, the partial-coherence theory of image formation has an analogous counterpart for biphoton beams transporting spatial information. However, an underlying duality, rather than analogy, accompanies the mathematical similarity between incoherent and biphoton emissions if the comparison is made between the photon count rate in the incoherent case and the biphoton count rate in the entangled-photon case. The smaller the size of an incoherent source, the more separable is the coherence function and the more coherent is the field, and therefore the higher the visibility of ordinary interference fringes. In contrast, the narrower the size of a biphoton pump source, the more separable is the wave function and the less entangled is the field, and therefore the lower the visibility of biphoton interference fringes. This duality is similar to the complementarity between single and two-photon interference exhibited for biphotons.
Spontaneous parametric down conversion (SPDC)-based sources of photonic entangled states are usually generated using coherent pump fields. For temporal, spatial, and polarization degree of freedom, the down-converted light entanglement is limited by the coherence of the pump in the same degree of freedom. However, the effect of pump coherence on the entanglement in a different degree of freedom remains largely unexplored. Here we experimentally demonstrate the generation of polarization entanglement from SPDC pumped by a light emitting diode (LED), a spatiotemporally incoherent pump. The two-photon state is found to have a concurrence of 0.562 and purity of 0.647.