Microcavity polaritonlike dispersion doublet in resonant Bragg gratings

Periodic structures resonantly coupled to excitonic media allow the existence of extra intragap modes (“Braggoritons”) due to the coupling between Bragg photon modes and bulk excitons. This induces unique dispersive features, which can be tailored by properly designing the photonic band gap around the exciton resonance. We report that Braggoritons realized with semiconductor gratings have the ability to mimic the dispersion of quantum-well microcavity polaritons. This gives rise to peculiar nonlinear phenomena, such as slow-light-enhanced nonlinear propagation and an efficient parametric scattering at two “magic frequencies.”

Figure 1

(Color online) (a)–(c) Polariton dispersion on the $\left(\delta ,q\right)$ plane for three different values of $d$. Dashed lines are the bare Bragg photon and exciton dispersions. Blue solid (dark gray) lines indicate upper-photon (UP) and lower-photon (LP) branches; red solid (light gray) lines are upper-Braggoriton (UB) and lower-Braggoriton (LB) branches. (d) Reflectivity $R_j$ in blue solid (dark gray) line and absorbance $A_j$ in black dotted line as functions of $\delta$ for a finite grating ($L\simeq 14\mu \text{m}$ for our proposed ZnO design). The dispersion is shown with red dashed (light gray) lines.

Figure 2

(Color online) (a) Physical parts of the dispersion branches [for which $R\left(\delta \right)\le 1$] are indicated with blue solid (dark gray) lines, for $d=-0.04$. Red (light gray) dots indicate the position of the two inflection points on the UB and LB branches, which are located at $q$’s that have the same magnitude but opposite signs, see also [Fig. 3b]. (b) GVD $\left({\partial }^2{q}_j/\partial {\delta }^2\right)$ as a function of $\delta$. Red (light gray) dots indicate zero-GVD points. (c) and (d) Solid blue (dark gray) lines are the group velocities $v_{g,j}/c={\left(\partial q_j/\partial \delta \right)}^{-1}$ as functions of $q$, for $d=0$ and $d=-0.04$, respectively. Red dashed (light gray) lines indicate the dispersion.

Figure 3

(Color online) (a) Effective polariton mass parameter ${\mathcal{M}}_j$ for all branches (indicated) as a function of $d$. (b) Schematics of the parametric amplification process occurring in the proximity of the inflection points of both Braggoriton branches, for $d=-0.04$. Gray areas indicate the photonic subgaps. (c) Matrix element for the intraband parametric scatterings shown in (b), for the LB branch in blue (dark gray) line and for the UB branch in red (light gray) line. (d) Same as (c) but for the LP branch in blue (dark gray) line and for the UP branch in red (light gray) line. (e) Sketch of our proposed design for a polaritonic Bragg stack. The excitonic material is ZnO (shown in red/gray, ${\lambda }_{\text{x}}=367.4\text{nm}$), while the second material is ${\text{ZrO}}_2$ (shown in blue/light gray).