  We demonstrate control over optical coupling between air-suspended carbon
nanotubes and air-mode nanobeam cavities by spectral tuning. Taking advantage
of the large dielectric screening effects caused by adsorbed molecules, laser
heating is used to blueshift the nanotube photoluminescence. Significant
increase of the cavity peak is observed when the nanotube emission is brought
into resonance, and the spontaneous emission enhancement is estimated from the
photoluminescence spectra. We find that the enhancement shows good correlation
to the spectral overlap of the nanotube emission and the cavity peak. Our
technique offers a convenient method for controlling the optical coupling of
air-suspended nanotubes to photonic structures.
