  Stimulated emission tomography (SET) is an excellent tool for characterizing
the process of spontaneous parametric down-conversion (SPDC), which is commonly
used to create pairs of entangled photons for use in quantum information
protocols. The use of stimulated emission increases the average number of
detected photons by several orders of magnitude compared to the spontaneous
process. In a SET measurement, the parametric down-conversion is seeded by an
intense signal field prepared with specified mode properties rather than by
broadband multi-modal vacuum fluctuations, as is the case for the spontaneous
process. The SET process generates an intense idler field in a mode that is the
complex conjugate to the signal mode. In this work we use SET to estimate the
joint spatial mode distribution (JSMD) in the Laguerre-Gaussian (LG) basis of
the two photons of an entangled photon pair. The pair is produced by parametric
down-conversion in a beta barium borate (BBO) crystal with type-II phase
matching pumped at a wavelength of 405 nm along with a 780-nm seed signal beam
prepared in a variety of LG modes to generate an 842-nm idler beam of which the
spatial mode distribution is measured. We observe strong idler production and
good agreement with the theoretical prediction of its spatial mode
distribution. Our experimental procedure should enable the efficient
determination of the photon-pair wavefunctions produced by low-brightness SPDC
sources and the characterization of high-dimensional entangled-photon pairs.
