Single Quantum Dot Spontaneous Emission in a Finite-Size Photonic Crystal Waveguide: Proposal for an Efficient “On Chip” Single Photon Gun

Spontaneous emission rate enhancements from a single quantum dot embedded in a finite-size, planar photonic-crystal waveguide are investigated. Short waveguide lengths of only 10 to 20 unit cells are found to produce very large Purcell factors associated with a waveguidelike sharp resonance feature in the local density of photon states. Aided by theoretical insight and rigorous computational calculations, we explain the physics behind these remarkable emission enhancements and subsequently propose a “single-photon gun” with on-chip unidirectional collection efficiencies greater than 60% into an output wire waveguide. The advantages over recent proposals for infinitely long photonic-crystal waveguides are highlighted.

Figure 1

(a) Schematic of a 10 unit-cell planar-PC waveguide (W1) along the $x$ axis and a single quantum dot (QD: filled red circle) embedded at the center of the slab. The structure parameters used in the simulations are as follows: hole radius $r=0.275a$, slab thickness $0.5a$, refractive index $n=\sqrt{12}$ and lattice constant $a=420\mathrm{nm}$. (b) The band structure of modes (solid and dashed curves) corresponding to an infinite-length planar-PC waveguide [parameters as in (a)] shown within the TE-like band gap. The gray shaded region above the lightline represents the continuum of radiation modes.

Figure 2

(a) Spontaneous emission factors ($F$) versus frequency for a QD embedded in a 10 unit-cell finite-size waveguide surrounded by PML. Dashed (solid) line is for the case when the dipole orientation of the QD is along the $x(y)$ axis, and the dotted vertical line shows the band edge of the fundamental waveguide mode of an infinite structure. (b) Same as in (a) but with the waveguide ends surrounded by air. (c) Center of the slab contour of the $|E_y{|}^2$ field distribution corresponding to the peak Purcell factor shown in (b). (d) As in (c) but for the $|E_x{|}^2$ component of the $E$ field.

Figure 3

(a) A comparison of the SE factor ($F$) versus frequency for a QD embedded in a 10 unit-cell sized planar-PC waveguide with both ends surrounded by air (chain curve), and with one end of the waveguide surrounded a regular PC (solid curve); the dotted vertical line shows the band edge of the fundamental waveguide mode of an infinitely long structure; the inset shows the QD permittivity for two different dipole moments (see text). (b) Center of the slab contour of the $|E_y{|}^2$ field distribution corresponding to the peak SE factor shown in (a) with a circle. (c),(d) Same as in case (a),(b) but with 20 unit-cell waveguide. (e) A comparison of SE factors in the case of 10 unit-cell sized PC mirror waveguide with different boundaries. PML surroundings (dashed line) and a wire-waveguide coupler (solid line). (f) Same as (b) but with a wire-waveguide output coupler.