Saturation and self-lensing in self-assembled quantum dots with constant-wave driving

The nonlinear optical response of self-assembled quantum dots to cw driving is analyzed via numerical simulations of a spatially resolved rate equation model. The saturation is shown to follow a behavior in between the one for a dominantly, homogeneously, and inhomogeneously broadened medium. Self-lensing is suggested to probe the refractive-index nonlinearities and to open a complementary way of characterizing phase-amplitude coupling ($\alpha$ factor) in quantum-dots samples. For conservative assumptions on current samples the minimum focal length is predicted to be $\pm 1.7\text{mm}$ for an input beam with $15\mu \text{m}$ radius at a detuning of 1.1 inhomogeneous linewidths from gain center.

Figure 1

(Color online) Modal-gain coefficient as a function of the normalized intensity in the center of the Gaussian input beam for different values of the detuning in the absorption (circles) and gain regimes (squares). Detuning increases from bottom to top curve for absorption case (lower part of the figure) and from top to bottom for gain case (upper part of the figure). The inset shows the saturation power as function of the detuning in both cases.

Figure 2

(Color online) Spatial profile of the real part of the susceptibility for low (upper, blue line, amplitude enhanced by a factor of 10), intermediate (central, black line) and high excitation (lower, red line). $\Lambda =0$, ${\Delta }_i=1.1$. The total excursion is $\Delta n=1.6\times {10}^{-4}$.

Figure 3

(Color online) Focal power as function of normalized peak intensity for different detunings in (a) the absorption case and (b) the gain case. ($\Lambda =1.8$ was chosen because it reproduced the experimental finding that maximal gain is about half the absorption coefficient.)

Figure 4

(Color online) Real and Imaginary part of the linear susceptibility as function of detuning for different ratios between inhomogeneous and homogeneous broadening. The $\Gamma ∕{\gamma }_p$ ratio decreases from bottom to the top.