We have analyzed the collinear phase matching (PM) conditions for thir
d-harmonic generation (THG) in biaxial crystals and derived the expres
sions of the effective nonlinear optical susceptibility when PM direct
ions are in the three principal planes using the matrices in contracte
d subscript form. Phase matched THG in lithium formate monohydrate (LF
HM) crystals are observed, which agree well with the calculated phase
matching directions..