Light-matter interaction and lasing in semiconductor nanowires: A combined finite-difference time-domain and semiconductor Bloch equation approach

Robert Buschlinger, Michael Lorke, and Ulf Peschel

Phys. Rev. B 91, 045203 – Published 20 January 2015; Erratum Phys. Rev. B 91, 159903 (2015)

Abstract

We present a time-domain model for the simulation of light-matter interaction in semiconductors in arbitrary geometries and across a wide range of excitation conditions. The electromagnetic field is treated classically using the finite-difference time-domain method. The polarization and occupation numbers of the semiconductor material are described using the semiconductor Bloch equations including many-body effects in the screened Hartree-Fock approximation. Spontaneous emission noise is introduced using stochastic driving terms. As an application, we present simulations of the dynamics of a nanowire laser including optical pumping, seeding by spontaneous emission, and the selection of lasing modes.

Received 28 October 2014

DOI:https://doi.org/10.1103/PhysRevB.91.045203

Erratum

Erratum: Light-matter interaction and lasing in semiconductor nanowires: A combined finite-difference time-domain and semiconductor Bloch equation approach [Phys. Rev. B 91, 045203 (2015)]

Robert Buschlinger, Michael Lorke, and Ulf Peschel

Phys. Rev. B 91, 159903 (2015)

Authors & Affiliations

Robert Buschlinger¹, Michael Lorke², and Ulf Peschel¹

¹Institute of Optics, Information and Photonics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
²Bremen Center for Computational Materials Science BCCMS, University of Bremen, 28359 Bremen, Germany

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Issue

Vol. 91, Iss. 4 — 15 January 2015

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Images

Figure 1
Bands and transitions with their relative dipole matrix elements for the case of a 2-6 semiconductor with wurtzite structure and a crystal axis pointing into the $z$ direction. Grayed-out items are not included in the calculations.
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Figure 2
Absorption spectra of CdS calculated with the multiband semiconductor Bloch equation model for different excitation densities $N$ . (a) Excitation polarized perpendicular to the crystal $c$ axis. (b) Excitation polarized along the crystal $c$ axis. The peaks labeled A and B correspond to the exciton $1 s$ resonances of the transitions respectively involving valence band $a$ and valence band $b$ .
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Figure 3
Sketch of the simulated nanowire geometry including polarization and propagation direction of the exciting pulse. The wire is centered on $z = 0$ .
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Figure 4
Temporal field dynamics inside a nanowire laser ( $l = 7.5 μ m, d = 250$ nm) excited with a pump pulse (central wavelength $λ_{0} = 500$ nm, temporal width $w_{t} = 100$ fs) polarized perpendicularly to the wire axis. (a) Dynamics of electron volume density and electric field intensity inside the wire. The inset shows a zoom into the temporal region of the initial laser pulse. (b) Temporal dynamics of the individual longitudinal modes obtained from a windowed Fourier transform of the temporal fields (normalization per time slice). (c) Population dynamics in $k$ space. (d) Spectrum showing the emission lines (black). For better orientation, the absorption coefficients for a low excitation density (blue) and a high excitation density (red), similar to the densities present after the absorption of the pump pulse, are included.
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Figure 5
Spatiotemporal field dynamics inside a nanowire laser ( $l = 7.5 μ m, d = 250$ nm). (a),(d) Electric field intensity in an $x z$ and an $x y$ slice of the simulation volume during pumping. (b) ${| E |}^{2}$ averaged across transverse slices and plotted along $z$ and $t$ . (e)–(g) Transverse intensity profiles inside the wire during lasing emission. (c) Intensity profile in an $x z$ slice after the maximum of the lasing emission.
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Figure 6
Dynamics inside a nanowire laser ( $l = 7.5 μ m, d = 250$ nm) consisting of a two-level material with a gain profile fitted to that of highly excited CdS [see panel (c)]. (a) Temporal dynamics of field strength ${| E |}^{2}$ and excitation density $n_{e}$ . (b) Mode dynamics obtained from windowed Fourier transform (normalized per time slice). (c) Absorption spectrum of the two-level system (red). The absorption spectrum for the full model is plotted in blue for comparison.
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