Second-order perturbation theory for optical resonators (A)

Gilad Almogy, Amnon Yariv

The solution of the coupled-wave equations for second-harmonic generation in a near-resonant three-level system is extended to include absorption. It is shown, within second-order perturbation theory, that double resonance is the optimal conversion condition, despite absorption enhancement. We extend the solution numerically, using nonperturbative susceptibilities derived within the rotating-wave approximation, to saturating intensities and discuss the modifications to the perturbative conclusions as well as the regimes of validity for the various approximations.

V. K. Ablekov, Vadim S. Belyaev, V. P. Vasil'ev +3 more

Baozhen Chen, 北京师范大学低能核物理研究所

In this article, the second order perturbation theory is used to obtain the expression of T-matrix for the Simultaneous photon-electron excitations of hydrogen. The convergence and resonance of the T-matrix are discussed in brief.

Baida Lü, Wenyu Chen

Anja Grage, Florian Gebhard, Jörg Rissler

For the one-dimensional, extended Peierls–Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the density-matrix renormalization group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the bandwidth. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approaches. In Wannier theory, we perturb the Wannier exciton states to second order. In two-step perturbation theory, similar in spirit to the GW -BSE approach (where the Bethe–Salpeter equation is solved for quasi-particles which are calculated in the GW -approximation), we form excitons from dressed electron–hole excitations. We find the Wannier approach to be superior to the two-step perturbation theory. For singlet excitons, Wannier theory is applicable up to Coulomb parameters as large as half the bandwidth. For triplet excitons, second-order perturbation theory quickly fails completely.

V. K. Ablekov, Vadim S. Belyaev