Quantum Theory of Polarized Superlattice Optical Response: Faithful Reproduction of Nakamura’s Blue Laser Spectra

Earlier quantum calculations of the optical response of Nakamura’s blue laser diode, assuming Kronig–Penney-like band-edge profiles, omitted the effects of charge polarization, cladding-layer asymmetry, and recombination delay times, while such simplified model reproduces the overall emission structure, underestimates the spectral width and fails to capture the decrease in peak intensities at higher energies. Here, we present a detailed quantum theory of polarized-asymmetric superlattices that explicitly incorporates spontaneous and piezoelectric polarization, confining-layer asymmetry, and recombination lifetimes. Local Stark fields are modeled by linear band-edge potentials, and the corresponding Schrödinger equation is solved using Airy functions within the Theory of Finite Periodic Systems. This approach enables the exact calculation of subband eigenvalues, eigenfunctions, transition probabilities and optical spectra. We show that to faithfully reproduce Nakamura’s blue laser spectra, smaller effective masses must be considered, unless unrealistically small barrier heights and widths are assumed. Furthermore, by employing the time distribution of transition probabilities, we capture the energy dependence of recombination lifetimes and their influence on peak intensities. The resulting analysis reproduces the observed spectral broadening and peak-height evolution, while also providing estimates of the magnitude of the Stark effect and mean recombination lifetimes.