Optical characterization and selective addressing of the resonant modes of a micropillar cavity with a white light beam

We have performed white light reflectivity measurements on GaAs/AlAs micropillar cavities with diameters ranging from $1\mu \text{m}$ up to $20\mu \text{m}$. We are able to resolve the spatial field distribution of each cavity mode in real space by scanning a small-sized beam across the top facet of each micropillar. We spectrally resolve distinct transverse-optical cavity modes in reflectivity. Using this procedure we can selectively address a single mode in the multimode micropillar cavity. Calculations for the coupling efficiency of a small-diameter beam to each mode are in very good agreement with our reflectivity measurements.

Figure 1

(Color online) (a) Top view optical microscopy image of a micropillar field with pillar diameters ranging from $6\mu \text{m}$ (upper left corner) to $1\mu \text{m}$ diameter (lower right). (b) Scanning electron micrograph cross section of a cleaved micropillar. The alternating shadings denote the alternating GaAs/AlAs $\lambda /4$ layers in the Bragg stacks. The arrow indicates the position of the GaAs $\lambda$ layer, having a thickness of $d=261.7\text{nm}$. (c) White light reflectivity measurement on a $20\mu \text{m}$ diameter micropillar cavity (squares) and a transfer-matrix calculation model (curve). The calculation fits the experimental spectrum well and thus explains all observed features. The stopband, ranging from $10100{\text{cm}}^{-1}$ to $11400{\text{cm}}^{-1}$ has a relative bandwidth of 12.8% and the resonance of the cavity is at ${\omega }_{cav}=10755{\text{cm}}^{-1}$.

Figure 2

(Color online) Schematic of the reflectivity setup. The beam from a broadband white light laser source is focused onto the sample using a gold-coated dispersionless reflecting microscope objective with NA 0.65. The reflected signal is then analyzed using a FTIR spectrometer and a Si detector. Separately, light from a halogen lamp illuminates the sample and is then focused onto a CCD camera to monitor the positioning of the sample with respect to the laser beam.

Figure 3

(Color online) (a) Detailed reflectivity spectra of the cavity resonance for three different micropillar diameters: $20\mu \text{m}$ (triangles), $6\mu \text{m}$ (squares), and $3\mu \text{m}$ (circles), respectively. The number of observed modes increases with pillar diameter. The bars denote the frequency of each measured mode. The spectra of the 6 and $3\mu \text{m}$ pillar are shifted down for clarity. (b) Comparison between the reflectivity (squares) and photoluminescence (circles) spectra of a $3\mu \text{m}$ diameter pillar. The spacings between the observed modes are $55{\text{cm}}^{-1}$ (reflectivity) and $56{\text{cm}}^{-1}$ (photoluminescence), respectively.

Figure 4

(Color online) Measured (symbols) and calculated (curves) mode frequency shift versus pillar diameter. The reference frequency is the cavity resonance of a planar cavity. The agreement between experiment and calculation is very good and shows the mode shift due to the lateral confinement in the micropillar. The modes are labeled using the standard notation for cylindrical dielectric waveguides (Refs. 27, 28).

Figure 5

(Color online) Reflectivity spectra of the cavity resonance for a $6\mu \text{m}$ diameter micropillar at different lateral positions of the beam. The spectra are offset with respect to each other for a better comparison. The position of the illumination spot is shown exemplarily for three spectra on the microscopy images on the right (the micropillar boundaries denoted by the white circle). The spectrum in the center is measured at the center of the micropillar’s top facet.

Figure 6

(Color online) Color-scale representation of the relative reflectivity at the different transverse positions of the beam vs the frequency of a $6\mu \text{m}$ diameter micropillar.

Figure 7

(Color online) Cross sections of the measured spatial transverse mode profiles for the first four modes of a $6\mu \text{m}$ diameter micropillar (filled symbols), taken from Fig. 6. The dashed lines are a guide to the eyes and typical error bars are included for the measurements. The calculated coupling efficiencies are plotted as solid lines. The calculated line shapes agree very well with the experiments.

Figure 8

(Color online) Calculated coupling efficiencies for different diameter of the incoming beam for the ${\text{HE}}_{12}$ mode of the $6\mu \text{m}$ diameter micropillar. With increasing beam diameter the spatial profile of the mode is not visible any more. Additionally, the experiment is shown (filled symbols).