  We present results from a study of the coherence properties of a system
involving three discrete states coupled to each other by two-photon processes
via a common continuum. This tripod linkage is an extension of the standard
laser-induced continuum structure (LICS) which involves two discrete states and
two lasers. We show that in the tripod scheme, there exist two population
trapping conditions; in some cases these conditions are easier to satisfy than
the single trapping condition in two-state LICS. Depending on the pulse timing,
various effects can be observed. We derive some basic properties of the tripod
scheme, such as the solution for coincident pulses, the behaviour of the system
in the adiabatic limit for delayed pulses, the conditions for no ionization and
for maximal ionization, and the optimal conditions for population transfer
between the discrete states via the continuum. In the case when one of the
discrete states is strongly coupled to the continuum, the population dynamics
reduces to a standard two-state LICS problem (involving the other two states)
with modified parameters; this provides the opportunity to customize the
parameters of a given two-state LICS system.
