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Abbe's resolution limit, one of the best-known physical limitations, poses a great challenge for any wave systems in imaging, wave transport, and dynamics. Originally formulated in linear optics, this Abbe's limit can be broken using nonlinear optical interactions. Here we extend the Abbe theory into a nonlinear regime and experimentally demonstrate a far-field, label-free, and scan-free super-resolution imaging technique based on nonlinear four-wave mixing to retrieve near-field scattered evanescent waves, achieving sub-wavelength resolution of $\lambda/15.6$. This method paves the way for application in biomedical imaging, semiconductor metrology, and photolithography.

Multi-modal data is becoming more common in big data background. Finding the semantically similar objects from different modality is one of the heart problems of multi-modal learning. Most of the current methods try to learn the inter-modal correlation with extrinsic supervised information, while intrinsic structural information of each modality is neglected. The performance of these methods heavily depends on the richness of training samples. However, obtaining the multi-modal training samples is still a labor and cost intensive work. In this paper, we bring a extrinsic correlation between the space structures of each modalities in coreference resolution. With this correlation, a semi-supervised learning model for multi-modal coreference resolution is proposed. We firstly extract high-level features of images and text, then compute the distances of each object from some reference points to build the space structure of each modality. With a shared reference point set, the space structures of each modality are correlated. We employ the correlation to build a commonly shared space that the semantic distance between multi-modal objects can be computed directly. The experiments on two multi-modal datasets show that our model performs better than the existing methods with insufficient training data., Comment: 9 pages, 6 figures

Negative refraction has attracted much interest for its promising capability in imaging applications. Such an effect can be implemented by negative index meta-materials, however, which are usually accompanied by high loss and demanding fabrication processes. Recently, alternative nonlinear approaches like phase conjugation and four wave mixing have shown advantages of low-loss and easy-to-implement, but associated problems like narrow accepting angles can still halt their practical applications. Here we demonstrate theoretically and experimentally a new scheme to realize negative refraction by nonlinear difference frequency generation with wide tunability, where a thin BBO slice serves as a negative refraction layer bending the input signal beam to the idler beam at a negative angle. Furthermore, we realize optical focusing effect using such nonlinear negative refraction, which may enable many potential applications in imaging science.

Electromagnetically induced transparency has the unique ability to optically control transparency windows with low light in atomic systems. However, its practical applications in quantum physics and information science are limited due to rigid experimental requirements. Here, we demonstrate a new mechanism of optically induced transparency in a micro-cavity by introducing a four-wave mixing gain to nonlinearly couple two separated resonances of the micro-cavity in an ambient environment. A signature Fano-like resonance was observed owing to the nonlinear interference of the two coupled resonances. Moreover, we show that the unidirectional gain of the four-wave mixing can lead to the remarkable effect of non-reciprocal transmission at the transparency windows. Optically induced transparency may offer a unique platform for a compact, integrated solution to all-optical and quantum information., Comment: Revised version. 12 pages, 3 figures