Spatially inhomogeneous optical gain in semiconductor photonic-crystal structures

The optical and electronic properties of semiconductor heterostructures in the vicinity of photonic crystals are discussed. The theoretical approach provides a self-consistent solution of the dynamics of the electromagnetic field and the material excitations. Due to the influence of the structured dielectric environment on the Coulomb interaction, the exciton resonances and the quasiequilibrium carrier densities in the spatially homogeneous semiconductor become space dependent. It is demonstrated that these inhomogeneities lead to distinct modifications of the optical absorption and gain spectra. As an application, numerically calculated density-dependent optical spectra are analyzed for an array of semiconductor quantum wires which are close to a two-dimensional photonic crystal. The spatial inhomogeneities result in novel excitonic absorption features and modification of the optical gain in these structures.

Figure 1

(a) Schematical drawing of the considered structure which defines the parameters $D$, $d$, $R$, and $r$. (b) The calculated linear optical absorption spectra are displayed for different radii $R$ of the air cylinders of the photonic crystals as indicated. $R=0$ corresponds to an array of wires which is homogeneously surrounded by dielectric material. $R\to \infty$ denotes a structure where the dielectric material of the photonic crystal has been completely replaced by air and therefore in this case the array of wires is separated by $D$ from a planar interface between dielectric material and air. The energetically lowest and highest $1s$-excitonic resonances are denoted by $H$ and $I$, respectively. The band gap of the homogeneous situation $(R=0)$ corresponds to $1.5\mathrm{eV}$. In the calculations a decay rate for the polarization has been used which results in a homogeneous broadening of $1.3\mathrm{meV}$ (full width at half maximum).

Figure 2

(a) The space-dependent single-particle potential (self energies), i.e., $(e^2∕2)\delta V(x,x)$, is shown for $R=2.65a_B$. (b) The corresponding space-dependent electron (solid) and hole (dotted) quasiequilibrium populations at $T=50\mathrm{K}$ are shown for four total carrier densities of $n=0.1∕a_B$, $n=0.2∕a_B$, $n=0.3∕a_B$, and $n=0.4∕a_B$. The zero of the $x$ axis coincides with a position underneath the center of an air cylinder.

Figure 3

(Color online) Density-dependent absorption/gain spectra are displayed for two structures. (a) An array of wires that is separated by $D=0.2a_B$ from the photonic crystal with air cylinder radius $R=2.65a_B$. (b) An array of wires that is homogeneously surrounded by dielectric material $(R=0)$. The presence of negative absorption, i.e., optical gain, is highlighted by changing the lines from black to green (gray in the printed version). In the calculations a decay rate for the polarization has been used which results in a homogeneous broadening of $1.7\mathrm{meV}$ (full width at half maximum).