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Flat optical devices thinner than a wavelength promise to replace conventional free-space components for wavefront and polarization control. Transmissive flat lenses are particularly interesting for applications in imaging and on-chip optoelectronic integration. Several designs based on plasmonic metasurfaces, high-contrast transmitarrays and gratings have been recently implemented but have not provided a performance comparable to conventional curved lenses. Here we report polarization-insensitive, micron-thick, high-contrast transmitarray micro-lenses with focal spots as small as 0.57 l. The measured focusing efficiency is up to 82%. A rigorous method for ultrathin lens design, and the trade-off between high efficiency and small spot size (or large numerical aperture) are discussed. The micro-lenses, composed of silicon nano-posts on glass, are fabricated in one lithographic step that could be performed with high-throughput photo or nanoimprint lithography, thus enabling widespread adoption.

Classical and quantum dynamics of nanomechanical systems promise new applications in nanotechnology 18,19 and fundamental tests of quantum mechanics in mesoscopic objects 2,9 . Recent development of nanoscale electromechanical (NEMS) and optomechanical systems has enabled cooling of mechanical systems to their quantum ground state 7,8 , which brings the possibility of quantum information processing with mechanical devices 20,21 . On the other hand, for practical application at room temperature -such as signal processing 22 A rendering of the optomechanical system used in this study is shown in Fig. 1a. ) and yet to allow large oscillation amplitudes. Due to the residual compressive stress introduced by the SOI wafer bonding process, the freestanding doubly clamped beams are slightly buckled and have two stable configurations at rest 37 : buckled up and buckled down (see Fig. 1b). Therefore, the out-of-plane motion of the buckled beam can be described by a double-well potential, where both the 'up'and 'down' states correspond to the minima in the potential. The thermomechanical displacement noise spectra in Fig. 1e show that the two states have slightly different mechanical resonance frequencies, which indicates that the double-well potential is not completely symmetric.The two mechanical states are discriminated in optical transmission measurements because the optical mode has a different effective refractive index in the two states:when the waveguide is closer to the substrate (buckled-down state) the effective refractive index is larger than in the buckled-up state as the optical mode interacts stronger with the substrate. Therefore the optical cavity resonance shifts towards longer wavelengths when the resonator flips from the buckled-up state to the buckled-down state. Consequently, the optical cavity has distinct optical resonances in the two stable configurations as shown in low power optical transmission spectra in Fig. 1c. The low 4 power spectrum probes the static optomechanical resonances, but at high power the mechanical resonator starts to oscillate when the pump wavelength is scanned close to the optical resonance. Fig. 1d shows the optical transmission spectrum measured when the input optical power is well above the threshold for self-sustained oscillations (SSO) of ~600 μW. When the wavelength is scanned across the optical resonance, the transmission no longer shows the low-power Lorentzian shape, rather the resonance is dragged from the "up" to the "down" state: as soon the laser is blue detuned w.r.t. the "up" state, the self-sustained oscillations start and the cavity frequency oscillates back and forth with an amplitude A p-p ·g, where A p-p is the mechanical resonator oscillation amplitude. The SSO in turn modulate the optical transmission at the mechanical oscillation frequency, indicated by the high-frequency components of the optical transmission ( Fig. 1d). The SSO appear in the entire wavelength range between the "up"and "down" state optical modes, which indicates that the energy of th...

Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent oscillation and mutual locking of resonators with dynamics beyond the widely accepted phase oscillator (Kuramoto) model. In addition to the phase difference between the oscillators, also their amplitudes are coupled, resulting in the emergence of sidebands around the synchronized carrier signal.

Light emitted from single-mode semiconductor lasers generally has large divergence angles, and high numerical aperture lenses are required for beam collimation. Visible and near infrared lasers are collimated using aspheric glass or plastic lenses, yet collimation of mid-infrared quantum cascade lasers typically requires more costly aspheric lenses made of germanium, chalcogenide compounds, or other infrared-transparent materials. Here we report mid-infrared dielectric metasurface flat lenses that efficiently collimate the output beam of single-mode quantum cascade lasers. The metasurface lenses are composed of amorphous silicon posts on a flat sapphire substrate and can be fabricated at low cost using a single step conventional UV binary lithography. Mid-infrared radiation from a 4.8 µm distributed-feedback quantum cascade laser is collimated using a polarization insensitive metasurface lens with 0.86 numerical aperture and 79% transmission efficiency. The collimated beam has a half divergence angle of 0.36 • and beam quality factor of M 2 =1.02. 132, 498-507 (2008).