We analytically calculate the optical emission spectrum of nanolasers and nano-LEDs based on a model of many incoherently pumped two-level emitters in a cavity. At low pump rates, we find two peaks in the spectrum for large coupling strengths and numbers of emitters. We interpret the double-peaked spectrum as a signature of collective Rabi splitting, and discuss the difference between the splitting of the spectrum and the existence of two eigenmodes. We show that an LED will never exhibit a split spectrum, even though it can have distinct eigenmodes. For systems where the splitting is possible, we show that the two peaks merge into a single one when the pump rate is increased. Finally, we compute the linewidth of the systems, and discuss the influence of inter-emitter correlations on the lineshape.

Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier expansion for the laser in the light-emitting diode (LED) regime. Fluctuations of populations of lasing levels are taken into account as perturbations. The spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons, and broaden the spectrum of a bad cavity threshold-less and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.

Internal quantum efficiencies of the surface photoemission (SPE) and the volume photoemission (VPE) from metal nanoparticles into a semiconductor environment are found and compared with each other, taking into account the discontinuity in the electron effective mass on the metal-semiconductor interface. It is found that SPE is less sensitive to the discontinuity of the electron effective mass than VPE. This advantage, along with other advantages, makes SPE more efficient than VPE for generation of hot electrons from small metal nanoparticles. General formulas for quantum efficiencies and analytical expressions for quantum efficiency on the red photoeffect limit are presented. High efficiency of SPE from spherical gold nanoparticles with the step potential barrier on the metal-semiconductor interface is demonstrated.

Landau damping in the metal nanosphere is considered beyond the quasistatic approximation with the use of the exact Mie theory when an incident plane wave can excite not only the dipole mode but also higher-order modes. In resonance approximation, when one considers excitation of a single mode, the analytical formula for the Landau damping coefficient for various modes has been derived. It was demonstrated that the simultaneous excitation of several eigenmodes, which are overlapped in the frequency domain, can lead to substantial correction of the Landau damping coefficients for the modes.

We theoretically investigated the bistability in a small Fabry-Perot interferometer (FPI) with the optical wavelength size cavity, the nonlinear Kerr medium, and only a few photons, on average, excited by the external quantum field. Analytical expressions for the stationary mean photon number, the bistability domain, the field, and the photon number fluctuation spectra are obtained. Multiple stationary states of the FPI cavity field with different spectra are possible at realistic conditions, for example, in the FPI with the photonic crystal cavity and the semiconductor-doped glass nonlinear medium.