Optically reconfigurable polarized emission in Germanium

Light polarization can conveniently encode information. Yet, the ability to tailor polarized optical fields is notably demanding but crucial to develop practical methods for data encryption and to gather fundamental insights into light-matter interactions. Here we demonstrate the dynamic manipulation of the chirality of light at telecom wavelengths. This unique possibility is enrooted in the multivalley nature of the conduction band of a conventional semiconductor, namely Ge. In particular, we demonstrate that optical pumping suffices to govern the kinetics of spin-polarized carriers and eventually the chirality of the radiative recombination. We found that the polarized component of the emission can be remarkably swept through orthogonal eigenstates without magnetic field control or phase shifter coupling. Our results provide insights into spin-dependent phenomena and offer guiding information for the future selection and design of spin-enhanced photonic functionalities of group IV semiconductors.

Measurements are relative to a p-type Ge:Ga wafer, with an acceptor concentration of 3.6 × 10 18 cm −3 (panel a) and an intrinsic Ge sample, with a resistivity of 47  cm, named i-Ge (panel b). The former demonstrates a |R⟩ while the latter a |L⟩ polarization eigenstates. Remarkably, none of the samples demonstrates a change in helicity upon varying the pump power. The circular polarization degree (PC) lies between -0.23 and -0.3 for the i-Ge, while for p-Ge +0.10 ≤ ≤ +0.11. Supplementary Note 1. Kinetic model. A three-state system is taken into account. It is based on a state at the bottom of the Γ valley, Γ < , from which carriers recombine radiatively. A second higher energy level, Γ > , hosts electrons photo-excited from the top of the valence band. A third additional state is assumed to exist in the X valleys. Owning to the indirect band gap of Ge, the majority of electrons accumulates at the L valleys and thereby do not contribute to the zone-centre radiative recombination.
All the relevant processes between these states result in the following rate equations: where refers to the excess electron density induced by the optical excitation with respect to the intrinsic level and is the net scattering rate from state i to j. Scattering rates are set as in Supplementary Table 1. As the X→Γ transition is believed to be significantly affected by the Coulomb scattering between the photo-generated electrons and the background carriers, by a first order approximation, the transition rate XΓ is modelled as linearly increasing with the population of electrons in the X state, i.e. XΓ = XΓ 0 + XΓ 1 ⋅ X . The two unknown parameters, namely XΓ 0 and XΓ 1 , are derived from the experimental data (see below).
The first three equations in (1) trace the relaxation path of the spin-down high-energy electrons promoted in the Γ > state by photo-generation with rate ↓ . The latter approximately corresponds to the 95% of the overall generation rate = (ℎ ) −1 П (with = 16321 −1 being the absorption coefficient of Ge at ℎ = 1.16 meV as the laser excitation energy). The cooling to the Γ < state occurs via the X state, with the yield reduced by the scattering towards the L valleys. The last equation in (1) sets the population of the Γ < states by spin-up polarized electrons generated from the SO band, with rate ↑ ≈0.05 . Electrons in the Γ < band bottom can recombine radiatively with rate R or be Literature Ref. [1] Γ > X 28 −1 Fit from exp.  (1).
scattered toward the L valleys. The relative < > ⁄ population upon light absorption has been derived from a recent literature work dealing with Ge [2].
Due to the final spin polarization of the electron population at the Γ < level, determined by the relative efficiency of the relaxation channels, the emitted light has a net circular polarization degree . As shown in Ref. [2], photo-generated electrons are partially polarized: ~30% for the spin-down electrons and ~90% for the spin-up population. We can therefore conclude that where the 1/2 factor accounts for the spin depolarization resulting from the radiative recombination with the unpolarized holes at the top of the VB. In order to provide a simple estimate for the total concentration of the excess carriers, n, corresponding to the various excitation power densities, , exploited in this work, we utilize the following simplified one-dimensional continuity equation: where the overall generation rate, G, has been determined according to the infrared excitation condition as described in the Supplementary Note 1. As shown in Supplementary Figure 3, the effective carrier lifetime, e, in the Ge:As samples having an impurity concentration of 8.3×10 16 cm -3