  We study selective upconversion of optical signals according to their
detailed transverse electromagnetic modes, and demonstrate its proof of
operations in a nonlinear crystal. The mode selectivity is achieved by
preparing the pump wave in an optimized spatial profile to drive the
upconversion. For signals in the Laguerre-Gaussian modes, we show that a mode
can be converted with up to 60 times higher efficiency than an overlapping but
orthogonal mode. This nonlinear-optical approach may find applications in
compressive imaging, pattern recognition, quantum communications, and others
where the existing linear-optical methods are limited.
