  A model is presented to explain the normal mode features of dust particles in
a planar zigzag crystal chain for the first and second neighbors. The degrees
of freedom of particles are the longitudinal and transverse displacements in
plane coupled by the first and second neighbor harmonic forces in
two-dimensions (2D). The constant electric force duded to the electrodes to
keep the zigzag structure is calculated. The coupling between transverse and
longitudinal dust-lattice (DL) modes is derived. The latter is considered due
to the energy of the electrostatic (Yukawa) potential. Moreover coupled
(acoustic and optical) and decoupled (longitudinal and transverse) branches of
dust lattice modes for different lattice parameters and structures are studied.
Propagation of the longitudinal and acoustic modes is found to be strictly
dependent on the value of the distance between the two chains; below that value
mode may not propagate Finally it is shown that the frequencies of the acoustic
(optical) branches increase (decrease) with increasing the distance between the
two chains.
