Optimization of gain in intersubband quantum well lasers by supersymmetry

Abstract

A systematic method is described for the optimized design of quantum-well structures, in respect to maximizing the stimulated gain in optically pumped intersubband lasers. It relies on applying supersymmetric quantum mechanics to an initial Hamiltonian, in order to ͑i͒ add one bound state below the spectral range of the initial Hamiltonian, and ͑ii͒ to generate a parameter-controlled family of isospectral Hamiltonians with the desired energy spectrum. By changing the value of 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 an appropriate smooth or stepwise-constant graded Al x Ga 1Ϫx As ternary alloy quantum well. PRB 62 TOMIĆ , MILANOVIĆ , AND IKONIĆ

Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm

“…In addition, the inverse scattering technique has considerable difficulty incorporating the bound states of a quantum structure. A supersymmetric quantum mechanics (SUSYQM) optimization technique has been recently reported by Tomic et al [16] for the design of optically-pumped intersubband lasers. The SUSYQM method is limited by the constraints on the relative placement of energy eigen-states.…”

“…The dipole matrix elements Z 31 for the pump transition and Z 32 for the lasing transition must also be maximized. Tomic et al [16] reported an optimization technique for the design of optically-pumped lasers, with respect to maximizing the parameter . The method starts with an initial Poschl-Teller potential, which is a smoothly varying potential well, and for which the eigen-energy solutions are known.…”

“…The two lasing states are chosen from the onset with E 31 = 80 meV, so that In addition, the SUSYQM method produces a truly smooth optimized potential profile that must be realized via discretization. The optimized design of the QC laser, as proposed by Tomic et al [16], is taken as the initial design and the structure is analyzed using the present method to yield three bound states: E 1 = 76 meV, E 2 = 110 meV, and E 3 = 189 meV. The two lower states are separated by 36 meV, the LO phonon resonance energy in GaAs.…”

“…For intersubband lasers, the levels' relaxation rates via LO phonon emission play a very important role and must be taken into account. The gain of optically-pumped three level intersubband lasers is proportional to a merit parameter [16] …”

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

“…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.…”