  Higgs mediated flavor violating electromagnetic interactions, induced at the
one--loop level by a nondiagonal $Hf_if_j$ vertex, with $f_i$ and $f_j$ charged
leptons or quarks, are studied within the context of a completely general
effective Yukawa sector that comprises $SU_L(2)\times U_Y(1)$--invariant
operators of up to dimension--six. Exact formulae for the one--loop $\gamma
f_if_j$ and $\gamma \gamma f_if_j$ couplings are presented and their related
processes used to study the phenomena of Higgs mediated lepton flavor
violation. The experimental limit on the $\mu \to e\gamma$ decay is used to
derive a bound on the branching ratio of the $\mu \to e\gamma \gamma$
transition, which is 6 orders of magnitude stronger than the current
experimental limit. Previous results on the $\tau \to \mu \gamma$ and $\tau \to
\mu \gamma \gamma$ decays are reproduced. The possibility of detecting signals
of lepton flavor violation at $\gamma \gamma$ colliders is explored through the
$\gamma \gamma \to l_il_j$ reaction, putting special emphasis on the $\tau \mu$
final state. Using the bound imposed on the $H\tau \mu$ vertex by the current
experimental data on the muon anomalous magnetic moment, it is found that about
half a hundred events may be produced in the International Linear Collider.
