We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increas
ing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well distinguished statistical properties of the emitted radiation. For small cavity decay rate, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared to the emitter-cavity coupling) and for few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-art techniques of Q-switch of resonant cavities, allied with the recent capability to tune single emitters in and out of resonance, suggest this system as a versatile source of different quantum states of light.
A theoretical description of radiation-matter coupling for semiconductor-based photonic crystal slabs is presented, in which quantum wells are embedded within the waveguide core layer. A full quantum theory is developed, by quantizing both the electr
omagnetic field with a spatial modulation of the refractive index and the exciton center of mass field in a periodic piecewise constant potential. The second-quantized hamiltonian of the interacting system is diagonalized with a generalized Hopfield method, thus yielding the complex dispersion of mixed exciton-photon modes including losses. The occurrence of both weak and strong coupling regimes is studied, and it is concluded that the new eigenstates of the system are described by quasi-particles called photonic crystal polaritons, which can occur in two situations: (i) below the light line, when a resonance between exciton and non-radiative photon levels occurs (guided polaritons), (ii) above the light line, provided the exciton-photon coupling is larger than the intrinsic radiative damping of the resonant photonic mode (radiative polaritons). For a square lattice of air holes, it is found that the energy minimum of the lower polariton branch can occur around normal incidence. The latter result has potential implications for the realization of polariton parametric interactions in photonic crystal slabs.
According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87, 061107 (2005)], the triangular lattice of triangular air holes may allow to achieve a complete photonic band gap in two-dimensional photonic crystal slabs. In this work we pres
ent a systematic theoretical study of this photonic lattice in a high-index membrane, and a comparison with the conventional triangular lattice of circular holes, by means of the guided-mode expansion method whose detailed formulation is described here. Photonic mode dispersion below and above the light line, gap maps, and intrinsic diffraction losses of quasi-guided modes are calculated for the periodic lattice as well as for line- and point-defects defined therein. The main results are summarized as follows: (i) the triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode, but the useful region is generally limited by the presence of second-order waveguide modes; (ii) the lattice may support the usual photonic band gap for even modes (quasi-TE polarization) and several band gaps for odd modes (quasi-TM polarization), which could be tuned in order to achieve doubly-resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second-harmonic frequency; (iii) diffraction losses of quasi-guided modes in the triangular lattices with circular and triangular holes, and in line-defect waveguides or point-defect cavities based on these geometries, are comparable. The results point to the interest of the triangular lattice of triangular holes for nonlinear optics, and show the usefulness of the guided-mode expansion method for calculating photonic band dispersion and diffraction losses, especially for higher-lying photonic modes.
