  Suppression of wave scattering and the realization of transparency effects in
engineered optical media and surfaces have attracted great attention in the
past recent years. In this work the problem of transparency is considered for
optical wave propagation in a nonlinear dielectric medium with second-order
$\chi^{(2)}$ susceptibility. Because of nonlinear interaction, a reference
signal wave at carrier frequency $\omega_1$ can exchange power, thus being
amplified or attenuated,when phase matching conditions are satisfied and
frequency conversion takes place. Therefore, rather generally the medium is not
transparent to the signal wave because of 'scattering' in the frequency domain.
Here we show that broadband transparency, corresponding to the full absence of
frequency conversion in spite of phase matching, can be observed for the signal
wave in the process of sum frequency generation whenever the effective
susceptibility $\chi^{(2)}$ along the nonlinear medium is tailored following a
suitable spatial apodization profile and the power level of the pump wave is
properly tuned. While broadband transparency is observed under such conditions,
the nonlinear medium is not invisible owing to an additional effective
dispersion for the signal wave introduced by the nonlinear interaction.
