  Semiconductor microcavities can exhibit various macroscopic quantum
phenomena, including Bose-Einstein condensation of polaritons,
Bardeen-Cooper-Schrieffer (BCS) states of polaritons, and photon lasing (lasing
with negligible Coulombic exciton effects). An important aspect of possible
experimental identification of these states is a gap in the excitation spectrum
(the BCS gap in the case of a polaritonic BCS state). Similar to the
polaritonic BCS gap, a light-induced gap can exist in photon lasers. Although
polaritonic BCS states have been observed on the basis of spectroscopy in the
vicinity of the laser frequency, the direct observation of polaritonic BCS gaps
using light spectrally centered at or around the emission frequency has not
been achieved. It has been conjectured that low-frequency (terahertz)
spectroscopy should be able to identify such gaps. In this first of two
studies, a theory aimed at identifying features of light-induced gaps in the
linear terahertz spectroscopy of photon lasers is developed and numerically
evaluated. It is shown that spectral features in the intraband conductivity,
and therefore in the system's transmissivity and absorptivity can be related to
the light-induced gap. For sufficiently small Drude damping this includes
spectral regions of THz gain. A future study will generalize the present
formalism to include Coulomb effects.
