Nonlinear Optical Response Of Semiconductors Research Articles

Scissors implementation within length-gauge formulations of the frequency-dependent nonlinear optical response of semiconductors

We show that previous calculations of the nonlinear optical response of semiconductors using the ``length-gauge'' approach of Aversa and Sipe[Phys. Rev. B 52, 14636 (1995)] have incorrectly implemented the scissors correction. Previous calculations have first modified the expressions such that the crystal momentum position operator interband matrix elements ${r}_{nm}^{a}(\mathbf{k})$ and their generalized $k$-derivatives ${r}_{nm;b}^{a}(\mathbf{k})$ are written in terms of the local density approximation (LDA) momentum matrix elements and energy eigenvalues, which are then adjusted to account for the scissors correction. This method is incorrect as it violates specific sum rules. We give a consistent implementation that respects the sum rules: ${r}_{nm}^{a}(\mathbf{k})$ and ${r}_{nm;b}^{a}(\mathbf{k})$, when written in terms of momentum matrix elements and energy eigenvalues, should be evaluated within Kohn--Sham LDA and not with the scissored one. Calculated spectra via full potential augmented plane wave plus local orbital band structures for the second-harmonic generation tensor ${\ensuremath{\chi}}_{2}^{xyz}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ show that the errors in previous calculations are approximately 39% and 28% for GaAs and GaP, respectively.

Coherent manipulation of biexcitonic transitions and other two-pair correlations

Two-pair correlations are shown to induce dependences of the nonlinear optical response of semiconductors that can be used for a coherent manipulation of the resulting emission. Influences of biexcitonic transitions as well as transitions to two-pair scattering states are discussed within a microscopic density matrix approach. It is shown that the coherent control of biexciton beats is selective with respect to the propagation direction of the emitted signal, in contrast to the control of beats where all beat partners are generated by single photon processes. Furthermore, it is demonstrated that memory structures induced by exciton–exciton scattering states enable coherent manipulations of the excitonic line shape that allow us to estimate lower bounds for the corresponding memory time from experimentally accessible data.

Many-body and correlation effects in semiconductors.

Solids consist of 1022-1023 particles per cubic centimetre, interacting through infinite-range Coulomb interactions. The linear response of a solid to a weak external perturbation is well described by the concept of non-interacting 'quasiparticles' first introduced by Landau. But interactions between quasiparticles can be substantial in dense systems. For example, studies over the past decade have shown that Coulomb correlations between quasiparticles dominate the nonlinear optical response of semiconductors, in marked contrast to the behaviour of atomic systems. These Coulomb correlations and other many-body interactions are important not only for semiconductors, but also for all condensed-matter systems.

CANONICAL TRANSFORMATION APPROACH TO THE ULTRAFAST NONLINEAR OPTICAL DYNAMICS OF SEMICONDUCTORS

We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the "bare" system onto the linear response of a "dressed" system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.

Nonlinear optical response of semiconductors in the independent-particle approximation.

We present a formalism for the calculation of the optical response of semiconductors in the independent-particle approximation. The unphysical divergences at zero frequency that plagued earlier approaches are eliminated by a careful treatment of interband and intraband motion, yet the calculations can be made in a way very analogous to usual perturbation theory. The general formalism is illustrated by deriving an expression for the response coefficient for second-harmonic generation.