Photons and excitons in a semiconductor microcavity interact to form exciton-polariton condensates. These are governed by a nonlinear quantum-mechanical system involving exciton and photon wavefunctions. We calculate all non-traveling harmonic solito
n solutions for the one-dimensional lossless system. There are two frequency bands of bright solitons when the inter-exciton interactions produce an attractive nonlinearity and two frequency bands of dark solitons when the nonlinearity is repulsive. In addition, there are two frequency bands for which the exciton wavefunction is discontinuous at its symmetry point, where it undergoes a phase jump of pi. A band of continuous dark solitons merges with a band of discontinuous dark solitons, forming a larger band over which the soliton far-field amplitude varies from zero to infinity; the discontinuity is initiated when the operating frequency exceeds the free exciton frequency. The far fields of the solitons in the lowest and highest frequency bands (one discontinuous and one continuous dark) are linearly unstable, whereas the other four bands have linearly stable far fields, including the merged band of dark solitons.
Bose-Einstein condensates of exciton-polaritons are described by a Schrodinger system of two equations. Nonlinearity due to exciton interactions gives rise to a frequency band of dark soliton solutions, which are found analytically for the lossless z
ero-velocity case. The solitons far-field value varies from zero to infinity as the operating frequency varies across the band. For positive detuning (photon frequency higher than exciton frequency), the exciton wavefunction becomes discontinuous when the operating frequency exceeds the exciton frequency. This phenomenon lies outside the parameter regime of validity of the Gross-Pitaevskii (GP) model. Within its regime of validity, we give a derivation of a single-mode GP model from the initial Schrodinger system and compare the continuous polariton solitons and GP solitons using the healing length notion.
This work analyzes the effects of cubic nonlinearities on certain resonant scattering anomalies associated with the dissolution of an embedded eigenvalue of a linear scattering system. These sharp peak-dip anomalies in the frequency domain are often
called Fano resonances. We study a simple model that incorporates the essential features of this kind of resonance. It features a linear scatterer attached to a transmission line with a point-mass defect and coupled to a nonlinear oscillator. We prove two power laws in the small coupling <gamma> to 0 and small nonlinearity <mu> to 0 regime. The asymptotic relation <mu> ~ C<gamma>^4 characterizes the emergence of a small frequency interval of triple harmonic solutions near the resonant frequency of the oscillator. As the nonlinearity grows or the coupling diminishes, this interval widens and, at the relation <mu> ~ C<gamma>^2, merges with another evolving frequency interval of triple harmonic solutions that extends to infinity. Our model allows rigorous computation of stability in the small <mu> and <gamma> limit. In the regime of triple harmonic solutions, those with largest and smallest response of the oscillator are linearly stable and the solution with intermediate response is unstable.
We investigate Fano-type anomalous transmission of energy of plane waves across lossless slab scatterers with periodic structure in the presence of non-robust guided modes. Our approach is based on rigorous analytic perturbation of the scattering pro
blem near a guided mode and applies to very general structures, continuous and discrete.
