Electro-refraction in quantum dots: dependence on lateral size and shape

Photonic switches require low-loss polarization-independent phase-shifting elements. In a composite quantum well, a 0.46-mm phase shifter provides a π/4 phase shift by combining the quantum confined Stark effect (QCSE) and the carrier depletion effect. We investigate whether the discrete energy levels and the high peak absorption in quantum dots (QDs) provide an opportunity for increasing the electro-refraction. The electro-refraction in strained cylindrical InAs-GaAs QDs is explored using a numerical model based on the 4 × 4 Luttinger-Kohn Hamiltonian. The excitonic states are calculated by matrix diagonalization with plane-wave basis states. We observe that the QCSE sharply increases with the height of the QD and is also optimized for small-radius QDs. The QCSE in pyramidal QDs is considerably larger than in a box or cylinders. We find a peak electro-refraction of Δn=0.35 in cone-shaped pyramidal QDs, which is a factor of 35 larger than in the quantum-well case. Finally, in the waveguide geometry, we find an electro-refraction of 1.3×10^-2 at a residual QD absorption of 0.15 dB/cm.