# Why are lattice vibrations called optical and acoustic?

## Answer #1

The dispersion relation \( \omega(k) \) of a one-dimensional crystal lattice with a diatomic basis has two branches. These branches result from the solution of two differential equations for this problem of diatomic chains.

The one branch (one solution) \(\omega_-(k) \) is called **acoustic** because in this case the lattice planes oscillate *in phase*, as is the case of acoustic waves.

The other branch (the other solution) \(\omega_+(k) \) is called **optical** because this solution of the respective differential equation gives an *opposite-phase* oscillation of the lattice planes (with \(m_1\) and \(m_2\)). For example, if the atoms are ions, then they are electrically charged. An antiphase oscillation creates electric dipole moments in the crystal, which affects the optical properties of the crystal.