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arXiv:quant-ph/0110058 · Physical Review A

Biphoton focusing for two-photon excitation

Magued B. Nasr, Ayman F. Abouraddy, Mark C. Booth, Bahaa E. A. Saleh, Alexander V. Sergienko, Malvin Carl Teich, Michael Kempe, Ralf Wolleschensky

Published Jan 17, 2002• 29 citations
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Abstract

We study two-photon excitation using biphotons generated via the process of spontaneous parametric down conversion in a nonlinear crystal. We show that the focusing of these biphotons yields an excitation distribution that is the same as the distribution of one-photon excitation at the pump wavelength. We also demonstrate that biphoton excitation in the image region yields a distribution whose axial width is approximately that of the crystal thickness and whose transverse width is that of the pump at the input to the crystal.

DOI
10.1103/physreva.65.023816

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We study two-photon excitation using biphotons generated via the process of spontaneous parametric down conversion in a nonlinear crystal. We show that the focusing of these biphotons yields an excitation distribution that is the same as the distribution of one-photon excitation at the pump wavelength. We also demonstrate that biphoton excitation in the image region yields a distribution whose axial width is approximately that of the crystal thickness and whose transverse width is that of the pump at the input to the crystal.
A method for generating two-photon wave packets (biphotons) with a small width of the spatial intensity correlation function (correlation radius) has been considered. We propose to prepare a two-photon wave packet inhomogeneously broadened in the angle by means of spontaneous parametric down-conversion in an inhomogeneous crystal. Such biphotons are not diffraction limited; i.e., their correlation radius is much larger than the inverse width of the spatial spectrum. However, the correlation radius of such a biphoton decreases as the biphoton propagates in free space, and transverse compression occurs at a certain distance from the crystal; i.e., the biphoton becomes diffraction limited.
We investigate theoretically the strong anisotropy in the wave packet distribution of biphoton pairs generated via spontaneous parametric down-conversion (SPDC) process with biaxial crystals. From the angle relationship in biaxial crystals, we deduce the wave function of type I SPDC by considering the longitudinal detuning under paraxial approximation. Taking BiB3O6 (BIBO) as an example, we numerically simulate the single-particle and coincidence distributions in two observation planes under the optimum phase-matching scheme. In contrast to uniaxial crystals, a stronger anisotropy effect and a higher entanglement of the photon pair states are obtained, which are attributed to the complex structure of biaxial crystals. These results are important for the generation of highly entangled biphoton pairs, especially for multi-photon pairs generation.
An analysis is made of ω 1 +ω 2 =ω 3 sum-frequency generation in a nonlinear crystal and also of twophoton absorption under the action of "biphotons," i.e., correlated two-photon fields formed as a result of spontaneous parametric scattering of the initial pump field in another crystal. It is shown that at low pump powers, the biphoton efficiency in two-photon processes is considerably higher than the efficiency of classically correlated fields of the same intensity. It is found that in the case of coherent pumping, the regenerated sum-frequency field is also coherent.
We propose and realize a method of high intensity generation of broadband biphotons and achieve its value up to 150 THz. The source is based on a thin BBO crystal with a thickness of 100 microns, in which spontaneous parametric down-conversion takes place. To compensate for the intensity decrease of the down-conversion caused by the small thickness of the crystal, it is placed inside the cavity of an Ar+ laser. In general, this experiment relates to the widely discussed problem of two-photon shaping in the frequency and/or angular domain.
We experimentally study the spatial properties of the field generated by spontaneous parametric down-conversion (SPDC) when the pump laser beam is strongly focused in the nonlinear crystal. Special attention is paid to classical intensity measurements with a CCD camera. We introduce the concept of a classical equivalent source that replicates all the coherence properties of SPDC light and explains all our experimental results. We show that, in contrast with experiments with a well-collimated pump, here both the phase-matching conditions and the position of the focusing plane determine the measured intensity profiles in the image plane of the crystal. The transition from the near-field regime to the far field is investigated. Measurements of two-photon correlations under strong focusing are also presented and the special features thereof are discussed.
We report two-photon correlation experiments using spontaneous parametric down-conversion under a severe manipulation of the input pump field. Considering the case of passing the laser beam through a focusing lens before the down-conversion crystal, theoretical calculations and a series of imaging experiments demonstrate two-photon geometric optics effects. In particular, the imaging in coincidence counts of an aperture placed in one of the down-conversion beams is found to be the analog of a simple spherical mirror system, which displays a ``vacuum dispersion'' effect in that the object and image distances are wavelength weighted. \textcopyright{} 1996 The American Physical Society.