Imaging Single Quantum Dots in Three-Dimensional Photonic Crystals

Performing fluorescence wide-field microscopy we have imaged single semiconductor quantum dots deep inside a 3-dimensional photonic crystal prepared from colloidal polymer beads. Exploring the emission diffraction patterns in defocused images of quantum dots we demonstrate that the direction-dependent photonic stop band imprints an anisotropy to the angular emission of a single quantum dot. Hence a single, quasi-point-like emitter is manipulated to radiate its photons only to certain well-defined directions by means of the anisotropic light propagation in photonic crystals. The experiments thus provide new routes to evaluate local, frequency selective optical properties in 3-dimensional photonic crystals employing single emitters.

Figure 1

Fluorescence images of single CdSe/ZnS quantum dots embedded in a colloidal photonic crystal detected at different focus positions $d$ relative to the photonic-crystal–quartz interface: (a) $d=2.5\mu \mathrm{m}$, (b) $d=4.98\mu \mathrm{m}$, (c) $d=6.8\mu \mathrm{m}$ inside the opal. (d) Experimental reflection spectrum along the [111] direction of the prepared photonic crystal showing a photonic stop band in the range of 570 to 610 nm. The horizontal dashed lines denote the range of the photonic stop band. (e) Shift of the photonic stop band with increasing angle to the [111] direction together with emission spectra of three different single CdSe/ZnS quantum dots [light gray curves (red online)]. The solid horizontal lines mark the center emission wavelength of the quantum dots. The vertical dashed lines show the corresponding aperture angles of the Bragg cones expected for the emission wavelength. (f) Fluorescence image of two selected quantum dots located at the photonic-crystal–quartz interface [top, $d=0\mu \mathrm{m}$ marked QDA in (a)] and $d=3.7\mu \mathrm{m}$ [bottom, marked QDB in (c)] inside the photonic crystal. Both quantum dots are by $f=3.5\mu \mathrm{m}$ out of focus.

Figure 2

Top row: Fluorescence images of a single CdSe/ZnS quantum dot (QDA) located at the photonic-crystal–quartz interface. The images are taken at different focus positions relative to the location of the quantum dot ($d=0\mu \mathrm{m}$, $f=1.6\mu \mathrm{m}$ and $f=4.4\mu \mathrm{m}$ defocusing). Middle row: Calculated defocused wide-field images of a single quantum dot at the experimentally adjusted focus positions. Bottom row: Comparison of the radial intensity distribution of the experimental [light curve (red online)] and theoretical image [dark curve (blue online)].

Figure 3

(a) Sketch of the experimental idea. If the quantum dot emission is within the photonic stop band of the opal, light propagation is prohibited within a certain cone (Bragg cone) with an aperture angle $\alpha$. Light which would propagate within this cone is not able to contribute to the image formation by the microscope objective (with a collecting numerical aperture NA) and therefore distorts the image especially at slight defocusing $f$. (b) Calculated defocusing series for a single quantum dot in a photonic crystal at various aperture angles $\alpha$ of the Bragg cone. The numbers above the top row denote the position of the focus $f$ relative to the quantum dot location. The corresponding aperture angle and the emission wavelength of the quantum dot are denoted on the side of each row.

Figure 4

a) Experimental defocusing series for a single CdSe/ZnS quantum dot embedded in a colloidal photonic crystal. The quantum dot is $d=3.7\mu \mathrm{m}$ away from the photonic-crystal–quartz interface and obeys a Bragg cone aperture angle of 19° at an emission wavelength of 588 nm. b) Experimental defocusing series for a single CdSe/ZnS quantum dot embedded in a colloidal photonic crystal. The quantum dot is $d=4.0\mu \mathrm{m}$ away from the photonic-crystal–quartz interface and obeys a Bragg cone aperture angle of 15° at an emission wavelength of 595 nm. The graphs below the images in (a) and (b) show the radial intensity distributions of the experimental images [light curve (red online)] compared to the calculated ones [dark curve (blue online)].