Tilmann Kuhn
Optical excitations in semiconductor structures are governed by selection rules. Examples are the (almost) vertical transitions in k-space when exciting the system with plane waves or the spin selection rules related to the circular polarization of the exciting light, also referred to as its spin angular momentum (SAM). Optical vortex beams with their rich variety of spatial profiles and vectorial character of electric and magnetic fields provide a plethora of new excitation channels, which can be used to address specific transitions and suppress others [1]. The most obvious new degree of freedom is the orbital angular momentum (OAM) that couples directly to the orbital (envelope) angular momentum of the excitonic excitations in nanostructures. Even more degrees of freedom appear when going beyond the paraxial limit, i.e., when using tightly focused beams or beams with a very small beam waist. These beams may exhibit strong field components in the propagation direction or prominent magnetic field components at the beam center, which again can be used to address specific transitions in the nanostructures. In the first part of my talk, I will review characteristic features of optical vortex beams in the nonparaxial regime and discuss how they can be derived from potentials either in the Lorenz or in the Coulomb gauge [2]. I will address both Bessel beams, which have the advantage of being exact solutions of the wave equation, and Laguerre-Gauss beams, which satisfy the paraxial wave equation and where nonparaxial corrections will appear. It turns out that different assumptions on the structure of vector and scalar potentials may lead to quite different nonparaxial corrections in the region close to the beam center. In the second part of the talk, I will discuss how these properties of vortex beams can be used to control the excitation of semiconductor nanostructures, in particular quantum dot structures. Interesting candidates for such control schemes are light hole excitons, where already the Bloch part of the wave function exhibits a mixing of spin and orbital angular momentum of the valence band, which is extended by an orbital angular momentum of the envelope function [3]. Specifically shaped vortex beams could be used to reveal the spatial shape of higher excited exciton wave functions [4]. Furthermore, vortex beams with a pronounced longitudinal component could be used to either excite directly excitons with zero angular momentum [3] or, by exciting higher excited exciton states, to populate the dark exciton ground state after a relaxation process of the excited exciton [5]. These examples show that the enhanced control schemes introduced by the excitation with vortex beams can thus provide new pathways for applications of quantum dots in quantum technologies.
References
[1] G. F. Quinteiro Rosen, P. I. Tamborenea and T. Kuhn, Rev. Mod. Phys. 94,035003 (2022).
[2] G. F. Quinteiro, C. T. Schmiegelow, D. E. Reiter and T. Kuhn, Phys. Rev. A 99, 023845 (2019).
[3] G. F. Quinteiro and T. Kuhn, Phys. Rev. B 90, 115401 (2014).
[4] M. Holtkemper, G. F. Quinteiro, D. E. Reiter and T. Kuhn, Phys. Rev. B 102, 165315 (2020).
[5] M. Holtkemper, G. F. Quinteiro, D. E. Reiter and T. Kuhn, Phys. Rev. Res. 3, 013024 (2021).