Previous works verified experimentally that interactions between vortex-induced vibration (VIV) and galloping may greatly improve the performance of piezoelectric wind energy harvesters (PWEHs) at low wind speeds. However, no mathematical model has been available to date to predict the responses or optimize the structures of PWEHs. In this paper, a distributed-parameter electromechanical coupling model of a VIV-galloping interactive PWEH was derived and was then experimentally validated using two harvester prototypes. For the first prototype, while the theoretical critical galloping speed is approximately 2.1 times the theoretical critical VIV speed, the experiments verified the proposed model's prediction that this harvester involves full interaction between VIV and galloping because there is only one wind speed region (in the wind speed range of interest) that offers high electrical output. For the second prototype, whose theoretical galloping speed is about 2.3 times the critical VIV speed, the model indicates that there are two completely separate wind speed regions that have relatively high electrical outputs, implying that this is a harvester without the interaction between VIV and galloping, coinciding with the experimental results. For both prototypes, the model is accurate enough to predict the onset reduced speeds for the wind speed regions with high electrical outputs, and can be used to obtain the output voltage in the wind speed range of interest. The proposed model can thus be used to design VIV-galloping interactive PWEHs with enhanced performance in the collection of low speed airflows.
Most wind energy harvesters (WEHs) that have been reported in the literature collect wind energy using only one type of wind-induced vibration, such as vortex-induced vibration (VIV), galloping, and flutter or wake galloping. In this letter, the interaction between VIV and galloping is used to improve the performance of WEHs. For a WEH constructed by attaching a bluff body with a rectangular cross-section to the free end of a piezoelectric cantilever, the measures to realize the interaction are theoretically discussed. Experiments verified the theoretical prediction that the WEHs with the same piezoelectric beam may demonstrate either separate or interactive VIV and galloping, depending on the geometries of the bluff bodies. For the WEHs with the interaction, the wind speed region of the VIV merges with that of the galloping to form a single region with high electrical outputs, which greatly increases the electrical outputs at low wind speeds. The interaction can be realized even when the predicted galloping critical speed is much higher than the predicted VIV critical speed. The proposed interaction is thus an effective approach to improve the scavenging efficiencies of WEHs operating at low wind speeds.
The generation of a sub-diffraction optical hollow ring is of great interest in various applications, such as optical microscopy, optical tweezers, and nanolithography. Azimuthally polarized light is a good candidate for creating an optical hollow ring structure. Various of methods have been proposed theoretically for generation of sub-wavelength hollow ring by focusing azimuthally polarized light, but without experimental demonstrations, especially for sub-diffraction focusing. Super-oscillation is a promising approach for shaping sub-diffraction optical focusing. In this paper, a planar sub-diffraction diffractive lens is proposed, which has an ultra-long focal length of 600 λ and small numerical aperture of 0.64. A sub-diffraction hollow ring is experimentally created by shaping an azimuthally polarized wave. The full-width-at-half-maximum of the hollow ring is 0.61 λ, which is smaller than the lens diffraction limit 0.78 λ, and the observed largest sidelobe intensity is only 10% of the peak intensity.
The generation of a sub-diffraction longitudinally polarized spot is of great interest in various applications, such as optical tweezers, super-resolution microscopy, high-resolution Raman spectroscopy, and high-density optical data storage. Many theoretical investigations have been conducted into the tight focusing of a longitudinally polarized spot with high-numerical-aperture aplanatic lenses in combination with optical filters. Optical super-oscillation provides a new approach to focusing light beyond the diffraction limit. Here, we propose a planar binary phase lens and experimentally demonstrate the generation of a longitudinally polarized sub-diffraction focal spot by focusing radially polarized light. The lens has a numerical aperture of 0.93 and a long focal length of 200λ for wavelength λ = 632.8 nm, and the generated focal spot has a full-width-at-half-maximum of about 0.456λ, which is smaller than the diffraction limit, 0.54λ. A 5λ-long longitudinally polarized optical needle with sub-diffraction size is also observed near the designed focal point.
In traditional optics, the focal spot size of a conventional lens is restricted to the diffraction limit 0.5λ/NA, where λ is the wavelength in vacuum and NA is the numerical aperture of the lens. Recently, various sub-diffraction focusing optical devices have been demonstrated, but they usually have short focal length and high numerical aperture. Moreover, they always suffer the problem of huge sidelobes near the focal spot and small field of view, especially when the focal spot size is less than the super-oscillation criteria 0.38λ/NA. To address the problem, here, we reported a far-field sub-diffraction point-focusing lens based on binary phase and amplitude modulation with ultra-long focal length 252.8 μm (399.5λ) and small numerical aperture 0.78, and experimentally demonstrated a super-oscillatory focusing of circularly polarized light with spot size 287 nm (0.454λ), smaller than the diffraction limit 0.64λ and the super-oscillation criterion 0.487λ. What’s more, on the focal plane, in the measured area within the radius of 142λ, the largest sidelobe intensity is less than 26% of the central lobe intensity. Such ultra-long distance super-oscillatory focusing with small sidelobes and large field of view has great potential applications in far-field super-resolution microscopy, ultra-high-density optical storage and nano-fabrication.
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