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We analyze the spectrum of spatially uniform, single-particle fluctuationmodes in the linear electromagnetic response of a semiconductor laser. We showthat if the decay rate of the interband polarization, $\gamma_p$, and therelaxation rate of the occupation distribution, $\gamma_f$, are different, agapless regime exists in which the order parameter $\Delta^{(0)} (k)$ (linearin the coherent photon field amplitude and the interband polarization) isfinite but there is no gap in the real part of the single-particle fluctuationspectrum. The laser being a pumped-dissipative system, this regime may beconsidered a non-equilibrium analog of gapless superconductivity. We analyzethe fluctuation spectrum in both the photon laser limit, where the interactionsamong the charged particles are ignored, and the more general model withinteracting particles. In the photon laser model, the order parameter isreduced to a momentum-independent quantity, which we denote by $\Delta$. Wefind that, immediately above the lasing threshold, the real part of thefluctuation spectrum remains gapless when $0 < | \Delta | < \sqrt{2 / 27} \, |\gamma_f - \gamma_p |$ and becomes gapped when $| \Delta |$ exceeds the upperbound of this range. Viewed as a complex function of $|\Delta|$ and theelectron-hole energy, the eigenvalue set displays some interesting exceptionalpoint (EP) structure around the gapless-gapped transition. The transition pointis a third-order EP, where three eigenvalues (and eigenvectors) coincide.Switching on the particle interactions in the full model modifies the spectrumof the photon laser model and, in particular, leads to a more elaborate EPstructure. However, the overall spectral behavior of the continuous(non-collective) modes of the full model can be understood on the basis of therelevant results of the photon laser model.

Gapless fluctuations and exceptional points in semiconductor lasers