## Theory of Modulation Response of Semiconductor Quantum Dot Lasers

##### Abstract

In this dissertation, a theory of modulation response of a semiconductor quantum dot (QD) laser is developed. The effect of the following factors on the modulation bandwidth of a QD laser is studied and the following results are obtained:

1) Carrier capture delay from the optical confinement layer into QDs

Closed-form analytical expressions are obtained for the modulation bandwidth omega_{-3 dB} of a QD laser in the limiting cases of fast and slow capture into QDs. omega_{-3 dB} is highest in the case of instantaneous capture into QDs, when the cross-section of carrier capture into a QD sigma_n = infinity. With reducing sigma_n, omega_{-3 dB} decreases and becomes zero at a certain non-vanishing sigma_n^{min}. This sigma_n^{min} presents the minimum tolerable capture cross-section for the lasing to occur at a given dc component j_0 of the injection current density. The higher is j_0, the smaller is sigma_n^{min} and hence the direct modulation of the output power is possible at a slower capture. The use of multiple layers with QDs is shown to considerably improve the modulation response of the laser -- the same omega_{-3 dB} is obtained in a multi-layer structure at a much lower j_0 than in a single-layer structure.

2) Internal optical loss in the optical confinement layer

The internal optical loss, which increases with free-carrier density in the waveguide region, considerably reduces the modulation bandwidth omega_{-3 dB} of a QD laser. With internal loss cross-section sigma_int increasing and approaching its maximum tolerable value, the modulation bandwidth decreases and becomes zero. There exists the optimum cavity length, at which omega_{-3 dB} is highest; the larger is sigma_int, the longer is the optimum cavity.

3) Excited states in QDs

Direct and indirect (excited-state-mediated) mechanisms of capture of carriers from the waveguide region into the lasing ground state in QDs are considered, and the modulation response of a laser is calculated. It is shown that, when only indirect capture is involved, the excited-to-ground-state relaxation delay strongly limits the ground-state modulation bandwidth of the laser -- at the longest tolerable relaxation time, the bandwidth becomes zero. When direct capture is also involved, the effect of excited-to-ground-state relaxation is less significant and the modulation bandwidth is considerably higher.

1) Carrier capture delay from the optical confinement layer into QDs

Closed-form analytical expressions are obtained for the modulation bandwidth omega_{-3 dB} of a QD laser in the limiting cases of fast and slow capture into QDs. omega_{-3 dB} is highest in the case of instantaneous capture into QDs, when the cross-section of carrier capture into a QD sigma_n = infinity. With reducing sigma_n, omega_{-3 dB} decreases and becomes zero at a certain non-vanishing sigma_n^{min}. This sigma_n^{min} presents the minimum tolerable capture cross-section for the lasing to occur at a given dc component j_0 of the injection current density. The higher is j_0, the smaller is sigma_n^{min} and hence the direct modulation of the output power is possible at a slower capture. The use of multiple layers with QDs is shown to considerably improve the modulation response of the laser -- the same omega_{-3 dB} is obtained in a multi-layer structure at a much lower j_0 than in a single-layer structure.

2) Internal optical loss in the optical confinement layer

The internal optical loss, which increases with free-carrier density in the waveguide region, considerably reduces the modulation bandwidth omega_{-3 dB} of a QD laser. With internal loss cross-section sigma_int increasing and approaching its maximum tolerable value, the modulation bandwidth decreases and becomes zero. There exists the optimum cavity length, at which omega_{-3 dB} is highest; the larger is sigma_int, the longer is the optimum cavity.

3) Excited states in QDs

Direct and indirect (excited-state-mediated) mechanisms of capture of carriers from the waveguide region into the lasing ground state in QDs are considered, and the modulation response of a laser is calculated. It is shown that, when only indirect capture is involved, the excited-to-ground-state relaxation delay strongly limits the ground-state modulation bandwidth of the laser -- at the longest tolerable relaxation time, the bandwidth becomes zero. When direct capture is also involved, the effect of excited-to-ground-state relaxation is less significant and the modulation bandwidth is considerably higher.

##### Collections

- Doctoral Dissertations [11232]