Acoustic vs Optical Phonons

Introduction

In crystalline solids, lattice vibrations (phonons) fall into two broad classes: acoustic and optical modes. These names are not arbitrary: they reflect how the vibrations manifest physically, and whether they can couple to light.

Acoustic Phonons

In acoustic modes, atoms in the unit cell move in phase (together in the same direction) when the wavevector ().

  • Dispersion: Their frequency vanishes at \(\mathbf{k}=0\), with a linear slope: \[ \omega \approx v_s k, \] where \(v_s\) is the speed of sound.
  • Physical meaning: These vibrations correspond to sound waves propagating through the crystal. Density oscillations travel as in a continuous elastic medium.
  • Coupling to light: No net dipole is created because all charge centers shift together. Therefore, acoustic modes do not interact with light directly (except weakly via higher-order effects such as Brillouin scattering).

Optical Phonons

In optical modes, atoms in the unit cell move out of phase (positive and negative ions oscillate in opposite directions).

  • Dispersion: At (=0), the frequency remains finite. These modes occupy the optical branch of the phonon dispersion.
  • Physical meaning: Out-of-phase motion produces a time-varying macroscopic polarization

\[ \mathbf{P}(t) = \frac{Z^*}{V}\,\mathbf{u}(t), \]

where \(Z^*\) is the effective charge and () is the displacement. This oscillating dipole can radiate or absorb light. - Coupling to light: Because the polarization oscillates at the phonon frequency, optical phonons are infrared-active and can also appear in Raman spectra. This is why they are called “optical.”

Why the Names?

  • Acoustic: These modes behave like sound waves in the lattice, carrying vibrations through elastic deformations.

  • Optical: These modes couple strongly to electromagnetic radiation, especially in the infrared and visible range. Early infrared absorption experiments on ionic crystals revealed them, leading to the term “optical phonons.”

  • Acoustic phonons: Atoms move in phase, no dipole change, interact with sound but not light.

  • Optical phonons: Atoms move out of phase, create oscillating dipoles, interact strongly with light.

Thus the terminology reflects both the physical behavior and the experimental signatures of these fundamental lattice vibrations.

Phonon–Light Interaction

Light is an electromagnetic wave. For lattice vibrations to interact with it, two conditions must be satisfied:

  • Dipole moment oscillation
    The vibration must create a time-varying macroscopic polarization \(P(t)\).
    • This occurs if positive and negative ions move out of phase (opposite directions).
    • Such displacements shift charge centers, producing a dipole that oscillates at the phonon frequency.
    • The oscillating dipole couples to the electric field \(E(t)\) of light.
  • Momentum matching
    Photons in the optical/IR range carry very small wavevectors:
    \[|\mathbf{k}_{\text{ph}}| \approx 10^{-3} \,\text{Å}^{-1}.\]
    Only phonons near the Brillouin zone center (\(\mathbf{q}\approx 0\)) can couple directly.
    This is why IR absorption probes only the zone-center optical phonons.

Why do Optical Phonons Couple

In an optical mode, sublattices move against each other:

\[ +Z^* \;\;\longleftrightarrow\;\; -Z^*. \]

This produces a nonzero polarization:

\[ P(t) = \frac{Z^*}{V} \, u(t), \]

where \(Z^*\) is the effective charge, \(V\) the unit cell volume, and \(u(t)\) the displacement.

The polarization oscillates at the phonon frequency, which means it can radiate or absorb light.
Therefore, optical phonons appear in infrared absorption (IR-active modes) and Raman scattering (if they modulate polarizability).

… But Acoustic Phonons Don’t

In an acoustic mode, all atoms in the unit cell move in phase.

  • The positive and negative charge centers shift together, so no macroscopic dipole is created: \[ P(t) \approx 0 \quad \text{for } \mathbf{q} \to 0. \]

  • Since there is no oscillating dipole, the electric field of light has nothing to couple to.

Acoustic phonons still play a role in electron scattering and heat transport, but they do not directly interact with light (except weakly through higher-order processes such as Brillouin scattering).