  Standard radiation zeros arise from the factorization properties of
tree-level amplitudes involving a massless photon and can occur when all
charged particles in the initial and final state have the same sign. We
investigate how several different processes involving new scalar particles
beyond the standard model may exhibit radiation zeros and how this structure
might be exploited to probe their electromagnetic structure. We focus on (i)
unnoticed aspects of angular zeros in the process e- + e- --> Delta-- + gamma
for doubly charged Higgs boson (or any bilepton) production and (ii) the
process gamma + e- --> q + S/V for scalar (S) or vector (V) leptoquarks (LQs).
We also discuss how factorized amplitudes and radiation zeros may appear in the
gauge boson fusion production of non-conjugate leptoquark pairs via gamma + W
--> S_i + S_j* in high energy ee reactions and how the zeros affect the
production cross-sections for various types of scalar leptoquarks.
