  The amplified spontaneous emission spectrum of the light field in the
non-lasing supermode of two coupled semiconductor lasers is analyzed using
linearized Langevin equations. It is shown that the interference betweeen the
laser mode and the fluctuating light field in the non-lasing mode causes
spatial holeburning. This effect introduces a phase sensitive coupling between
the laser field and the fluctuations in the non-lasing mode. For high laser
fields, this coupling splits the spectrum of the non-lasing mode into a triplet
consisting of two relaxation oscillation sidebands which are in phase with the
laser light and a center line at the lasing frequency with a phase shift of pi
half relative to the laser light. As the laser intensity is increased close to
threshold, the spectrum shows a continuous transition from the single amplified
spontaneous emission line at the frequency of the laser mode to the triplet
structure. An analytical expression for this transition is derived and typical
features are discussed.
