Deep learning has become an extremely effective tool for image classification and image restoration problems. Here, we apply deep learning to microscopy and demonstrate how neural networks can exploit the chromatic dependence of the point-spread function to classify the colors of single emitters imaged on a grayscale camera. While existing localization microscopy methods for spectral classification require additional optical elements in the emission path, e.g., spectral filters, prisms, or phase masks, our neural net correctly identifies static and mobile emitters with high efficiency using a standard, unmodified singlechannel configuration. Furthermore, we show how deep learning can be used to design new phase-modulating elements that, when implemented into the imaging path, result in further improved color differentiation between species, including simultaneously differentiating four species in a single image.

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Simulation of photonic structures is a necessary step in the design of devices with tailored optical properties. As 3D simulations are time-intensive, the effective index method (EIM) is widely used to reduce systems to 2D models, including in the design of photonic crystal devices. We show that the EIM is poorly suited to model photonic crystal waveguides, giving inaccurate approximations of group velocity and propagation loss. The proposed effective period method provides significantly more accurate estimations of device behaviour without any increase of computation time.

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Coupled cavities have been used previously to realize on-chip low-dispersion slow-light waveguides, but the bandwidth was usually narrower than 10 nm and the total length was much shorter than 1 mm. Here we report long (0.05-2.5 mm) slow-light coupled cavity waveguides formed by using 50, 200, and 1,000 L3 photonic crystal nanocavities with an optical volume smaller than (λ/n), slanted from Γ-K orientation. We demonstrate experimentally the formation of a single-mode wideband coupled cavity mode with a bandwidth of up to 32nm (4THz) in telecom C-band, generated from the ultra-narrow-band (~300 MHz) fundamental mode of each L3 nanocavity, by controlling the cavity array orientation. Thanks to the ultrahigh-Q nanocavity design, coupled cavity waveguides longer than 1 mm exhibited low loss and allowed time-of-flight dispersion measurement over a bandwidth up to 22 nm by propagating a short pulse over 1,000 coupled L3 nanocavities. The highly-dense slanted array of L3 nanocavity demonstrated unprecedentedly high cavity coupling among the nanocavities. The scheme we describe provides controllable planar dispersion-managed waveguides as an alternative to W1-based waveguides on a photonic crystal chip.