Gain optimization in optically pumped AlGaAs unipolar quantum-well lasers

Abstract

Abstract-A method is described for the optimized design of quantum-well (QW) structures, in respect to maximizing the stimulated gain in optically pumped intersubband lasers. It relies on applying supersymmetric quantum mechanics (SUSYQM) to an initial Hamiltonian, in order to both map one bound state below the spectral range of the initial Hamiltonian, and to generate a parameter-controlled family of isospectral Hamiltonians with the desired energy spectrum. By varying the control parameter, one changes the potential shape and, thus, the values of dipole matrix elements and electron-phonon scattering matrix elements. The use of this procedure is demonstrated by designing smoothly graded and stepwise-constant Al Ga 1 As ternary alloy QWs, with the self-consistent potential taken into account. Finally, the possibility of employing layer interdiffusion to get optimal smooth potentials is discussed.Index Terms-Layer interdiffusion, quantum-well lasers, supersymmetric quantum mechanics.

Digitally graded active region for optically pumped intersubband lasers and nonlinear wavelength convertors

“…24 It has been shown 25 that this technique may provide a very good reproduction of the transition energies or the density of states, as compared to the corresponding values in the potential that was approximated by digital grading. It is therefore plausible to expect that the optimal smooth profiles we have derived for the optically pumped intersubband laser 10,22 or the SHG 20 may be effectively realized by digital grading. In particular, we consider the digitally graded approximants of the optimal smooth profile for the optically pumped laser with ⌬E 32 Ϸ80 meV ͑corresponding to the laser wavelength of Ϸ15.5 m͒, pumped by ⌬E 32 ϩប LO ϭ116 meV ͑CO 2 laser͒ radiation, derived using the IST, 10 and of the optimal smooth QW optimized for the SHG of បϭ116 meV pump, derived using SUSYQM.…”

“…It is therefore plausible to expect that the optimal smooth profiles we have derived for the optically pumped intersubband laser 10,22 or the SHG 20 may be effectively realized by digital grading. In particular, we consider the digitally graded approximants of the optimal smooth profile for the optically pumped laser with ⌬E 32 Ϸ80 meV ͑corresponding to the laser wavelength of Ϸ15.5 m͒, pumped by ⌬E 32 ϩប LO ϭ116 meV ͑CO 2 laser͒ radiation, derived using the IST, 10 and of the optimal smooth QW optimized for the SHG of បϭ116 meV pump, derived using SUSYQM. 20 The derivation of these smooth profiles has been described in detail previously 10,19-22 and will not be repeated here.…”

“…18 We have previously used this approach to tailor the QW profile so that the SHG 19,20 or gain in optically pumped intersubband lasers are maximized. 10,21,22 While the figures of merit for the corresponding effects, achieved this way, significantly exceed the values available in conventional coupled or step graded QWs, the designed optimal profiles required smooth grading of the alloy composition. The task of realizing a smoothly graded composition with good precision is clearly much more difficult than realizing a step-modulated structure with just a few layers.…”

Gain-maximized GaAs/AlGaAs quantum-cascade laser with digitally graded active region

“…It relies on recently established techniques for generating an optimal smooth quantum well profile by inverse spectral theory. 22,23 In the three-level QCL model with assumed unity-injection efficiency, 24 we define the figure of merit: ⌶ϭ(1Ϫ 64 / 96 ) 9 z 96 2 , which depends directly on the active region profile, and is proportional to the modal gain. In our full 15-level model, the subscripts 9, 6, and 4 denote the upper, lower, and ground laser levels in the active region, respectively ͑Fig.…”

“…1͒, z 96 is the optical dipole matrix element, i j are the scattering times, and 9 the upper laser level lifetime. The maximization of gain, i.e., of the factor ⌶, may be accomplished by varying the profile of the active region in an isospectral manner, 22,23 which affects only the wave functions and not the state spacing. The procedure starts with an arbitrary initial potential and generates a family of potentials, which all have the required state spacings, their shape being controlled by a few parameters.…”