Second-harmonic generation in InAs/GaAs self-assembled quantum dots

We have observed third-harmonic generation associated with intraband transitions in semiconductor quantum dots. The frequency tripling (12 mm!4 mm) occurs in the valence band of InAs/GaAs self-assembled quantum dots. We show that the third-harmonic generation is enhanced due to the achievement of the double resonance condition between intraband transitions. A third-order nonlinear susceptibility ux 3v (3) u as large as 1.5310 214 (m/V) 2 is measured for one dot plane. @S0163-1829~99!08211-9# In two-dimensional ~2D! semiconductor heterostructures, optical nonlinearities associated with intersubband transitions are known to be greatly enhanced as compared to nonlinearities in bulk semiconductors. Midinfrared second- 1 and third-harmonic 2,3 generation ~THG! have been demonstrated in quantum wells along with other types of second- and third-order nonlinear processes. 4 Record third-order nonlinear susceptibilities, as large as five orders of magnitude greater than in bulk GaAs, 2 have been measured in coupled quantum wells. The enhancement of the nonlinearities in the quantum wells stems from the large oscillator strength of the intersubband transitions 5 and from the band-structure engineering, which enables us to satisfy the resonance conditions. Large optical nonlinearities are also expected to occur in semiconductor quantum dots. The 3D confinement potential leads to a d-like density of states. The transitions between the confined levels in the conduction or in the valence band, referred to as intraband transitions in the following, have been observed using different techniques. 6,7 The optical nonlinearities associated with these intraband transitions are anticipated to be large for the following reasons. Like intersubband transitions in quantum wells, the intraband dipole lengths extend over the quantum dot size and are about a fraction of nm. The two- or three-photon resonance between excited states involved in the intraband transitions can also be achieved by choosing the dot size and geometry. In addition, the narrow homogeneous linewidth of the intraband transitions of individual quantum dots should contribute to enhance the nonlinear susceptibility. Indeed, the intraband transitions are foreseen to be lifetime broadened as a direct consequence of the d-like density of states: any inelastic dephasing process corresponds to the scattering of the carriers from one level to another and is, therefore, associated with the lifetime of the carriers. Thus, by analogy with atomic physics, one expects for the quantum dots a direct correlation between the relaxation lifetime T1 and the coherence lifetime T2 , i.e., T252T1 . This feature is of importance since the quantum dot relaxation time is predicted to be slowed down due to the so-called ‘‘phonon bottleneck.’’ 8 Based on these ideas, we have investigated the intraband optical nonlinearities in quantum dots. The standard selfassembled InAs/GaAs quantum-dot system grown by molecular beam epitaxy has been chosen and we have investigated the harmonic conversion in the midinfrared. We show in this paper that frequency tripling can be achieved in the valence band of the quantum dots. The resonant enhancement of the nonlinearity is demonstrated and a large thirdorder nonlinear susceptibility is deduced from our measurements, as a consequence of the large coherence lifetime, which is inherent to the quantum dots. Beyond this particular measurement, our results are of wide interest since they demonstrate that large intraband optical nonlinearities can be observed in three-dimensionally confined semiconductor heterostructures.