Photon Bloch Oscillations in Porous Silicon Optical Superlattices

We report the first observation of oscillations of the electromagnetic field in an optical superlattice based on porous silicon. These oscillations are an optical equivalent of well-known electronic Bloch oscillations in crystals. Elementary cells of our structure are composed by microcavities whose coupling gives rise to the extended collective modes forming optical minigaps and minibands. By varying thicknesses of the cavities along the structure axis, we have created an effective electric field for photons. A very high quality factor of the confined optical state of the Wannier-Stark ladder may allow lasing in porous silicon-based superlattices.

Figure 1

Cross-sectional SEM image of the 20-cavity sample. The inset shows the amplified view of the structure.

Figure 2

(a) Solid line: Reflectivity of the 20-cavity sample measured at the incidence angle of $6°$. The spectra above and below 1100 meV have been recorded with two different detectors. The dashed line shows the calculated reflectivity of this sample. (b) Band structure of the 20-cavity sample calculated by Eq. (5). White areas represent the allowed minibands and black areas represent the minigaps.

Figure 3

(a) Propagation of a 50 fs long light pulse within the 20-cavity sample: Light intensity is shown versus time and space. Bloch oscillations in time domain are clearly seen. (b) Scattering states of the 20-cavity sample. A change from blue to red color (or from dark to bright if the figure appears black and white) corresponds to the increase of the intensity of light. White lines are guides for the eyes. One can observe the formation of the PWSL confined between two minigaps. The states observable in reflection are the broad ones around 1400 meV which are weakly coupled to the outside. Completely confined modes, at lower energy, have very high quality factors. They might allow the occurrence of lasing effect. (c) Solid line: time-resolved reflection of the 20-cavity sample obtained from the measured reflection spectra by formula (7). The dashed line shows the theoretical time-resolved reflection. The dotted line shows the incident light pulse we assumed. (d) Spacing between the states of the PWSL versus excitation angle for the 20-cavity sample (circles) and the 30-cavity sample (squares). The solid line is calculated from Eq. (9) for the 20-cavity sample.