  We study the third order spontaneous parametric down conversion (TOSPDC)
process, as a means to generate entangled photon triplets. Specifically, we
consider thin optical fibers as the nonlinear medium to be used as the basis
for TOSPDC in configurations where phase matching is attained through the use
of more than one fiber transverse modes. Our analysis in this paper, which
follows from our earlier paper Optics Letters 36, 190 (2011), aims to supply
experimentalists with the details required in order to design a TOSPDC
photon-triplet source. Specifically, our analysis focuses on the photon triplet
state, on the rate of emission, and on the TOSPDC phasematching characteristics
for the cases of frequency degenerate and frequency nondegenerate TOSPDC.
