By employing the dielectric continuum model and Loudon's
uniaxial crystal model, the interface optical (IO) phonon modes
in a freestanding quasi-one-dimensional (Q1D) wurtzite rectangular
quantum wire are derived and analyzed. Numerical calculation on a
freestanding wurtzite GaN quantum wire is performed. The results
reveal that the dispersion frequencies of IO modes sensitively
depend on the geometric structures of the Q1D wurtzite rectangular
quantum wires, the free wave-number kz in z-direction and the
dielectric constant of the nonpolar matrix. The degenerating
behavior of the IO modes in Q1D wurtzite rectangular quantum wire
has been clearly observed in the case of small wave-number kz and
large ratio of length to width of the rectangular crossing profile.
The limited frequency behaviors of IO modes have been analyzed deeply,
and detailed comparisons with those in wurtzite planar quantum wells
and cylindrical quantum wires are also done. The present theories can
be looked on as a generalization of that in isotropic rectangular
quantum wires, and it can naturally reduce to the case of Q1D isotropic
quantum wires once the anisotropy of the wurtzite material is ignored.