Gratings 1 and holograms 2 are patterned surfaces that tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be discovered 3 , 4 . Further advances could exploit Fourier optics 5 , which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. To shape the optical wavefront, the ideal surface profile should contain a precise sum of sinusoidal waves, each with a well-defined amplitude, spatial frequency, and phase. However, because fabrication techniques typically yield profiles with at most a few depth levels, complex ‘wavy’ surfaces cannot be obtained, limiting the straightforward mathematical design and implementation of sophisticated diffractive optics. Here we present a simple yet powerful approach to eliminate this design–fabrication mismatch by demonstrating optical surfaces that contain an arbitrary number of specified sinusoids. We combine thermal scanning-probe lithography 6 – 8 and templating 9 to create periodic and aperiodic surface patterns with continuous depth control and subwavelength spatial resolution. Multicomponent linear gratings allow precise manipulation of electromagnetic signals through Fourier-spectrum engineering 10 . Consequently, we overcome a previous limitation in photonics by creating an ultrathin grating that simultaneously couples red, green, and blue light at the same angle of incidence. More broadly, we analytically design and accurately replicate intricate twodimensional moiré patterns 11 , 12 , quasicrystals 13 , 14 , and holograms 15 , 16 , demonstrating a variety of previously impossible diffractive surfaces. Therefore, this approach can provide benefit for optical devices (biosensors 17 , lasers 18 , 19 , metasurfaces 4 , and modulators 20 ) and emerging topics in photonics (topological structures 21 , transformation optics 22 , and valleytronics 23 ).

No abstract

Nearly all colloidal quantum dots, when measured at the single-emitter level, exhibit fluorescence “blinking”. However, despite over 20 years of research on this phenomenon, its microscopic origins are still debated. One reason is a gap in available experimental information, specifically for dynamics at short (submillisecond) time scales. Here, we use photon-correlation analysis to investigate microsecond blinking events in individual quantum dots. While the strongly distributed kinetics of blinking normally makes such events difficult to study, we show that they can be analyzed by excluding photons emitted during long bright or dark periods. Moreover, we find that submillisecond blinking events are more common than one might expect from extrapolating the power-law blinking statistics observed on longer (millisecond) time scales. This result provides important experimental data for developing a microscopic understanding of blinking. More generally, our method offers a simple strategy for analyzing microsecond switching dynamics in the fluorescence of quantum emitters.

Fifty years ago, Drexhage et al. showed how photon emission from an electric dipole can be modified by a nearby mirror. Here, we study the two-dimensional analog for surface plasmon polaritons (SPPs). We print Eu^{3+}-doped nanoparticles, which act as both electric- and magnetic-dipole sources of SPPs, near plasmonic reflectors on flat Ag films. We measure modified SPP radiation patterns and emission rates as a function of reflector distance and source symmetry. The results, which agree with an analytical self-interference model, provide simple strategies to control SPP radiation in plasmonic devices.

Plasmonic lasers generate strongly confined electromagnetic fields over a narrow range of wavelengths. This is potentially useful for enhancing nonlinear effects, sensing chemical species, and providing on-chip sources of plasmons. By placing a semiconductor gain layer near a metallic interface with a gap layer in between, plasmonic lasers have been demonstrated. However, the role of gain in this common design has been understudied, leading to suboptimal choices. Here, we examine planar metallic lasers and explore the effect of gain on the lasing behavior. We print semiconductor nanoplatelets as a gain layer of controllable thickness onto alumina-coated silver films with integrated planar Fabry−Peŕot cavities. Lasing behavior is then monitored with spectrally and polarization-resolved far-field imaging. The results are compared with a theoretical waveguide model and a rate-equation model, which consider both plasmonic and photonic modes and explicitly include losses and gain. We find that the nature of the lasing mode is dictated by the gain-layer thickness and, contrary to conventional wisdom, a gap layer with a high refractive index can be advantageous for plasmonic lasing in planar Fabry−Peŕot cavities. Our rate-equation model also reveals a regime where plasmonic and photonic modes compete in an unintuitive way, potentially useful for facile, active mode switching. These results can guide future design of metallic lasers and could lead to on-chip lasers with controlled photonic and plasmonic output.