Spontaneous Emission of Vector Vortex Beams

Harnessing the spontaneous emission of incoherent quantum emitters is one of the hallmarks of nano-optics. Yet, an enduring challenge remains—making them emit vector beams, which are complex forms of light associated with fruitful developments in fluorescence imaging, optical trapping, and high-speed telecommunications. Vector beams are characterized by spatially varying polarization states whose construction requires coherence properties that are typically possessed by lasers—but not by photons produced by spontaneous emission. Here, we show a route to weave the spontaneous emission of an ensemble of colloidal quantum dots into vector beams. To this end, we use holographic nanostructures that impart the necessary spatial coherence, polarization, and topological properties to the light originating from the emitters. We focus our demonstration on vector vortex beams, which are chiral vector beams carrying nonzero orbital angular momentum, and argue that our approach can be extended to other forms of vectorial light.

Figure 1

(a) Scanning electron microscope (SEM) micrograph of an m = 3 sample (dimensions given in the text). The light (respectively, dark) gray areas are the top (respectively, bottom) of the grooves. The vector vortex beam is emitted perpendicularly to this image. Scale bar: 1 µm. Inset: schematic cross section of the sample consisting of $\mathrm{Pb}\mathrm{S}$ CQDs (white dots) coated on an $\mathrm{Au}$ nanostructured surface. (b) Photoluminescence spectrum of the $\mathrm{Pb}\mathrm{S}$ CQDs. (c) Images in false colors of the back focal plane when the CQDs are pumped with a 633-nm $\mathrm{He}\text{−}\mathrm{Ne}$ laser focused at the center of the three-arm spiral. Each panel corresponds to an observation of the beam profile at a different wavelength, as indicated above the images. The beam propagation is perpendicular to the images. (d) Theoretical predictions of the beam profile at the same wavelengths. (e) Theoretical predictions of the phase. The white circle of all these plots has a radius k/k₀= 0.65, which corresponds to the numerical aperture of our objective.

Figure 2

(a) SEM micrograph of a structure generating two interfering vortices with opposite topological charges m = 3 and n = −3 (dimensions given in the text). Scale bar: 1 µm. (b) Experimental image of the back focal plane. (c) Theoretical predictions assuming a point-source emitter. (d) Theory when the finite size of the photoluminescence spot is taken into account. (e)–(h) Results for two interfering beams with m = 4 and n = −4. The geometry consists of two four-arm spirals with radial pitch 1.095 µm and opposite windings. (i)–(l) Results for two interfering beams with m = 5 and n = −5. The radial pitch of the structure (two five-arm spirals with opposite windings) is 1 µm. (m)–(p) Results for two interfering beams with m = 5 and n = 0. Here, the geometry is obtained by superimposing a bull’s eye structure with a five-arm spiral, both structures having a radial pitch of 1.045 µm. The white circle of all these plots has a radius k/k₀= 0.65. The wavelength is 1100 nm for all panels. The color map is the same as in Figs. 1–1, except that the colors for the point-source calculations are saturated by a few percent for a better comparison with the experiments.

Figure 3

Images of the back focal plane at 1050 nm for the m = 3 structure already studied in Fig. 1 (the same color code is used). Here, a linear polarizer is inserted in front of the $\mathrm{In}\mathrm{Ga}\mathrm{As}$ camera. The orientation of the polarization axis is indicated with the double arrows on each panel.

Figure 4

(a) Experimental (negative k_x) and theoretical (positive k_x) dispersion relation for the m = 3 spiral discussed throughout the text. (b) Normalized back focal plane (BFP) profile of the m = 3 beam. The gray curve is the profile of the full polychromatic beam while the black curve is a cross section of Fig. 1 showing the result at the wavelength λ = 1200 nm. The blue curve is a cross section of Fig. 4 revealing the profile of the beam at λ = 1200 nm produced by an m = 3 spiral fabricated on glass (i.e., only the corrugations are made in $\mathrm{Au}$). (c) Same experiment as in the rightmost panel of Fig. 1 (λ = 1200 nm) for a spiral fabricated on glass. The same color map is used.