  The three-dimensional instability of two coupled electromagnetic waves in an
unmagnetized plasma is investigated theoretically and numerically. In the
regime of two-plasmon decay, where one pump wave frequency is approximately
twice the electron plasma frequency, we find that the coupled pump waves give
rise to enhanced instability with wave vectors between those of the two beams.
In the case of ion parametric decay instability, where the pump wave decays
into one Langmuir wave and one ion acoustic wave, the instability regions are
added with no distinct amplification. Our investigation can be useful in
interpreting laser-plasma as well as ionospheric heating experiments.
