DOI: 10.1007/s00340-006-2302-2 Appl. Phys. B 85, 231–234 (2006) Lasers and Optics Applied Physics B c. pfl ¨ ugl ∗ m. austerer ✉ s. golka w. schrenk a.m. andrews t. roch g. strasser Second-harmonic generation in three-well and bound-to-continuum GaAs-based quantum-cascade lasers Zentrum für Mikro- und Nanostrukturen, Technische Universität Wien, Floragasse 7, 1040 Vienna, Austria Received: 24 March 2006/Revised version: 2 May 2006 Published online: 24 June 2006 • © Springer-Verlag 2006 ABSTRACT We present efficient second-harmonic generation in state of the art GaAs-based quantum-cascade lasers with nonlinear output powers up to 100 μ W. The nonlinear output was significantly improved by applying an AlGaAs waveguide structure, which guides both, the fundamental and nonlinear light. We further show the influence of the doping in the ac- tive region on the nonlinear light generation by comparing two similar structures with different doping levels. PACS 42.55.Px; 42.65.Ky; 81.05.Ea 1 Introduction The beginning of the field of nonlinear optics, in general, is often taken to be the discovery of second-harmonic generation by Franken et al. [1] in 1961. The same effect started the investigation of intracavity nonlinear optics in quantum-cascade lasers (QCLs) [2] in 2003. Since that time much progress in this field has been reported. This includes the optimization of second-harmonic generation (SHG) based on resonant intersubband transitions in the InP material sys- tem [3] as well as the achievement of phase matching for the fundamental and nonlinear light in the laser cavities [4, 5]. SHG was also reported in GaAs-based QCLs based on inter- subband transitions [6, 7] and by using the bulk nonlinearities of the hosting materials, which was achieved by the growth on 〈111〉 substrates [8]. However, SHG is only the tip of the iceberg of possible nonlinear effects having the potential to extend the working range of QCLs beyond the limits imposed on the straightforward laser action. Recently, stokes Raman lasing [9] as well as anti-stokes Raman emission [10] have been experimentally demonstrated, and several other nonlin- ear effects in multi-quantum well systems like inversionless lasing have been proposed [11]. We investigated SHG observed in typical three-well- and bound-to-continuum design GaAs-based QCLs. The pre- sented structures are regrowths of structures discussed in [12, ✉ Fax: +43 1 58801 36299, E-mail: maximilian.austerer@tuwien.ac.at ∗ Current adress: LabSem, Centro de Estudos em Telecomuniçacões, Pontif´ ıcia Universidade Cat´ olica do Rio de Janeiro, Rua Marquês de São Vicente 225, Rio de Janeiro, RJ 22453-900, Brazil 13], respectively. The origins of the observed nonlinear light generation are resonant intersubband transitions included in the active region of our devices. While designing QCL struc- tures that show SHG, one has to make a trade-off between high power fundamental laser action and high second-order non- linear susceptibility χ 2 . In the case of nonlinear effects based on intersubband transitions this is a difficult task as linear ab- sorption, decreasing fundamental laser action, increases with the optimization of χ 2 . Nevertheless, three-well and bound- to-continuum QCLs always intrinsically have higher lying levels, where the transition between these states and the upper laser level is in near resonance to the lasing transition. 2 Bandstructure engineering The bandstructure and the moduli squared of the most important wavefunctions of both structures (three- well S1, bound-to-continuum S2) are shown in Fig. 1. The lasing transitions take place between the states 3 and 2. We calculated the transition energies for structures S1/S2 to be 143 meV/124 meV and the matrix elements to be 20.9Å/20.7Å. The lower laser level is depleted by LO- phonon emission. Detailed descriptions about the lasing prop- erties are given in [12, 13], respectively. For structure S1, SHG is based on the intersubband tran- sitions between states 2–3–4. State 2 and the intermediate state 3 are bound states in the quantum wells, whereas the fi- nal one, 4, is a resonance in the continuum, slightly above the barrier conduction band. The calculated energy difference be- tween states 3 and 4 is 148 meV, the respective matrix element is calculated to be 2.2Å. The matrix element between states 2 and 4 is 0.6Å. Although this structure was not designed for SHG the values are in the range of the values given in [3] and give rise to efficient SHG. As nonlinear effects based on resonant intersubband tran- sitions strongly depend on the doping level and the carrier distribution in the active region, we grew the nominally identi- cal active region with two different doping levels in the active region in order to investigate this influence. The nonlinear po- larization for structure S1 in the χ 2 approximation reads P (2ω) ≈ e 3 N e E 2 z (ω) h 2  z 23 z 34 z 24 Γ 42  n 3 − n 4 Γ 43 + n 3 − n 2 Γ 32  , (1)