Strong Light-Field Driven Nanolasers

Einstein established the quantum theory of radiation and paved the way for modern laser physics including single-photon absorption by charge carriers and finally pumping an active gain medium into population inversion. This can be easily understood in the particle picture of light. Using intense, ultrashort pulse lasers, multiphoton pumping of an active medium has been realized. In this nonlinear interaction regime, excitation and population inversion depend not only on the photon energy but also on the intensity of the incident pumping light, which can be still described solely by the particle picture of light. We demonstrate here that lowering significantly the pump photon energy further still enables population inversion and lasing in semiconductor nanowires. The extremely high electric field of the pump bends the bands and enables tunneling of electrons from the valence to the conduction band. In this regime, the light acts by the classical Coulomb force and population inversion is entirely due to the wave nature of electrons, thus the excitation becomes independent of the frequency but solely depends on the incident intensity of the pumping light.


Nanowire growth and sample preparation
A scanning electron microscope (SEM) image of the disordered NW array used in the experiments is shown in Fig. S1. The diameter and the length of the nanowires are 200-250 nm and 5-10 m, respectively. The batches of single crystalline, wurtzite ZnO nanowires were synthesized using a simple vapor-phase-transport (VPT) technique in a horizontal tube furnace 1 .
For the synthesis of the disordered batches, the vapor-liquid-solid (VLS) mechanism was enabled 2 . Briefly, approximately 1g of ZnO powder was used as a source material. Silicon chips with a 10 nm thin Au layer on the top were used as growth substrates. The ZnO powder was heated to 1350 C and the pressure was kept constant at 100 mbar. A flow of 50 sccm Ar gas carried the ZnO vapor towards the growth substrates for a growth time of 1 hour. During the growth process the Au layer melts and forms catalyst droplets acting as nucleation sites. Therefore, the nanowires grow without preferential alignment. The dimensions and morphology of the nanowire arrays were determined with a FEI Helios 600 SEM/FIB system with a lateral resolution of about 1 nm.
Single nanowires were transferred to clean SiO 2 /Si (1.5 µm of SiO 2 on top) substrates using a dry imprint method: pressing the sample face-to-face. The substrates had a lithographically imprinted coordinate system. Thus, using an optical imaging system (see below), it was possible to locate the transferred well-separated individual nanowires laying at the surface of the substrate and address them in different optical systems. Figure S1. SEM-image of a randomly oriented ZnO nanowire array grown by a simple vapor transport method via the VLS mechanism.

Laser systems
The experiments at 0.8 µm were carried out by using 35 fs laser pulses from a Ti:Saphire amplifier system operating at 1 kHz repetition rate and generating pulses with energies up to 0.8 mJ. For calibration of the intensity on the target, the pulse duration was measured using an interferometric autocorrelator (Femtolasers Femtometer) as the spatial distribution of the intensity in the focus was recorded with a CCD-camera (ThorLabs BC106N-VIS).
Mid-IR 0.1 mJ, 100 fs laser pulses at a repetition rate of 500 Hz were generated in a 3-stage In all experiments the intensity on the target was calculated from the measured pulse energy, temporal pulse profile and spatial intensity distribution on the sample.   Figure S5. The almost constant threshold as a function of spot size indicates that lasing observed in our experiments is unlikely due to random lasing, as the threshold should decrease with increasing spot size for such a scenario. hot enough that their kinetic energy is above a certain threshold value , they can excite further electrons from the VB to the CB via electron by impact ionization/excitation. Therefore, we describe the population in the CB by two fraction of electrons, the hot fraction and the cold ℎ fraction , related by the following rate equations:

µ-Photoluminescence setup for single wire experiments
Here the strong field excitation rate is calculated using the Keldysh expression 4 , and are complete elliptic integrals, ∑ ℰ and , is the Keldysh parameter, is the = Dawson integral, is the intrinsic band gap, is the effective electron mass, is the laser ∆ * frequency, e is the elementary charge and F is the amplitude of the electric field in the laser pulse shift.
The second term in Eq. (1) describes the thermalization of the hot excited electrons with a single exponential decay rate 1/τ c due to electron-phonon scattering. The third term describes the growth in the hot electron population due to free-carrier absorption (FCA) and electron impact excitation from the VB. This is, in fact, the term which is responsible for the avalanche ionization in the material. The conductivity was describes the dynamics of the population of the hot electron fraction on a fs-time scale of the pump pulse, which is much shorter than the intra-band relaxation time scale τ C . Thus, the cold electron fraction remains negligible on the time scale of the material interaction with the pump pulse. Then the hot electron fraction relaxes to the cold one on a picosecond time scale, which is much shorter than the radiative spontaneous decay time τ e . Therefore, the pump threshold intensity is determined by the condition that the maximal excited carrier density reaches a number of 2•10 19 cm -3 , the value derived in Ref. 16 and enabling a negative absorption (gain).