We present results from a study of the coherence properties of a system inv
olving 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 stat
es and two lasers. We show that in the tripod scheme, there exist two popul
ation napping conditions; in some case. these conditions are easier to sati
sfy than the single trapping condition in a two-state LICS. Depending on th
e pulse timing, various effects can be observed. We derive some basic prope
rties of the tripod scheme, such as the solution for coincident pulses, the
behavior of the system in the adiabatic limit for delayed pulses, the cond
itions for no ionization and for maximal ionization, and the optimal condit
ions for population transfer between the discrete states via the continuum.
In the case when one of the discrete states is strongly coupled to the con
tinuum, the population dynamics reduces to a standard two-state LICS proble
m (involving the other two states) with modified parameters; this provides
the opportunity to customize the parameters of a given two-state LICS syste
m.