Semiconductor laser theory

They consist of complex multi-layer structures requiring nanometer scale accuracy and an elaborate design.

Their theoretical description is important not only from a fundamental point of view, but also in order to generate new and improved designs.

The carrier inversion results in an electromagnetic polarization which drives an electric field

In most cases, the electric field is confined in a resonator, the properties of which are also important factors for laser performance.

The choice of material depends on the desired wavelength and properties such as modulation speed.

All these structures can be described in a common framework and in differing levels of complexity and accuracy.

[1] Light is generated in a semiconductor laser by radiative recombination of electrons and holes.

In order to generate more light by stimulated emission than is lost by absorption, the system's population density has to be inverted, see the article on lasers.

A laser is, thus, always a high carrier density system that entails many-body interactions.

Various approximations can be made: The above-mentioned models yield the polarization of the gain medium.

The differences in lineshape for the two theoretical approaches are obvious especially for the high carrier density case which applies to a laser system.

For the low density case, the T2-time approximation also overestimates the strength of the tails.

Therefore, the eigenmode expansion of the electric field is done not in plane waves but in the eigenmodes of the resonator which may be calculated, e.g., via the transfer-matrix method in planar geometries; more complicated geometries often require the use of full Maxwell-equations solvers (finite-difference time-domain method).

In the laser diode rate equations, the photon life time

Fully microscopic modeling of laser emission can be performed with the semiconductor luminescence equations[7] where the light modes enter as an input.

This approach includes many-body interactions and correlation effects systematically, including correlations between quantized light and the excitations of the semiconductor.

Such investigations can be extended to studying new intriguing effects emerging in semiconductor quantum optics.

Semiconductor lasers (520nm, 445nm, 635nm)
Semiconductor lasers (660nm, 532nm, 405nm)
Comparison of gain and absorption calculated in Hartree–Fock approximation (dotted line) and fully taking into account collision terms (solid line). The sample is a Ga(AsSb) quantum well surrounded by GaAs spacers. For the top figure, a density of 1.3 x 10 12 cm −2 was used which is well above lasing threshold. For the bottom figure, the carrier density is negligible. The differences in lineshape are obvious especially for the lasing structure. The Hartree–Fock approximation leads to absorption below the bandgap (below about 0.94 eV), which is a natural consequence of the relaxation time approximation, but is completely unphysical. For the low density case, the T 2 -time approximation also leads to extended tails.