  We calculated the infrared conductivity spectrum of orbitally ordered
LaMnO$_3$ in phonon frequency and overtone frequency ranges. We considered
orbital exchange, Jahn-Teller electron-phonon coupling, and phonon--phonon
coupling. The fundamental excitation of the phonon-coupled orbiton was only
Raman active, not infrared active, while its overtone modes were both Raman and
infrared active. Our calculations reproduced the small peaks near 1300
cm$^{-1}$ observed both in Raman scattering and infrared conductivity spectra,
as consistent with previous experimental results.
