Second-harmonic generation spectroscopy of excitons in ZnO

Abstract

Nonlinear optics of semiconductors is an important field of fundamental and applied research, but surprisingly the role of excitons in the coherent processes leading to harmonics generation has remained essentially unexplored. Here we report results of a comprehensive experimental and theoretical study of the three-photon process of optical second harmonic generation (SHG) involving the exciton resonances of the noncentrosymmetric hexagonal wide-band-gap semiconductor ZnO in the photon energy range of 3.2 − 3.5 eV. Resonant crystallographic SHG is observed for the 1s(A, B), 2s(A, B), 2p(A, B), and 1s(C) excitons. We show that strong SHG signals at these exciton resonances are induced by the application of a magnetic field when the incident and the SHG light wave vectors are along the crystal z-axis where the crystallographic SHG response vanishes. A microscopic theory of SHG generation through excitons is developed, which shows that the nonlinear interaction of coherent light with excitons has to be considered beyond the electric-dipole approximation. Depending on the particular symmetry of the exciton states SHG can originate from the electric-and magnetic-field-induced perturbations of the excitons due to the Stark effect, the spin as well as orbital Zeeman effects, or the magneto-Stark effect. The importance of each mechanism is analyzed and discussed by confronting experimental data and theoretical results for the dependencies of the SHG signals on photon energy, magnetic field, electric field, crystal temperature, and light polarization. Good agreement is obtained between experiment and theory proving the validity of our approach to the complex problem of nonlinear interaction of light with ZnO excitons. This general approach can be applied also to other semiconductors.

Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals

“…The latter 2Ω response corresponds to the SHG. It is experimentally shown that the excitons can contribute to the optical rectification [19,20] and the SHG [21][22][23]. While the optical rectification and the SHG are well-known nonlinear optical effects, their enhancement due to the exciton resonance has not been fully explored from the viewpoint of topology and geometry of the Bloch electrons.…”

Study of the Transition to Instability in Second-Harmonic Generation with Scale Index Method

“…Today, the nonlinear optical phenomena are widely used for applied researches [6]. Meanwhile, frequency conversion processes play an important role in nonlinear optical phenomena such as second or higher order harmonics generations [7]. Owing to rich classical nonlinear dynamics of frequency doubling processes, the second harmonic generation (SHG) is analyzed in this study [8].…”

Quadrupole second harmonic generation and sum-frequency generation in ZnO quantum dots

“…For the optical transitions associated with the second order nonlinear processes, the parity selection rules are different for contributing electronic states from those in linear phenomena. 20 Therefore, when the electric quadrupole allowed transition processes are taken into account, then an n th order electric-dipole-forbidden process can be stronger than an (n + 1) th order electric dipole allowed process. In the present investigation we realize it for observing second order nonlinear susceptibilities for the ZnO QD structure.…”

“…4,20 The nonlinear optical properties are reported for different forms of ZnO such as single crystals, thin films, nanowires and nano-ribbons. 14 The enhancement of the nonlinear optical properties as compared to bulk counterpart is observed for thin films.…”

“…8,[10][11][12][13][14][15][16][17][18][19] The second order nonlinear optical properties in semiconductor nanostructures associated with the interband transitions (between the levels of different bands) and the intraband transitions (between levels of the same band) have been studied by several authors. 8,20,21 The second order nonlinearity has potential applications such as in harmonic generation, biological imaging, and nonlinear optical microscopy. Most of the studies on the second order nonlinear processes are reported using quantum wells 16,[22][23][24] and only fewer reports have used quantum wires 25 and quantum dots (QDs).…”