In this letter, we propose ultra-compact TE-polarized even-to-odd mode converter designs by introducing Ge/Si patterns into silicon waveguide-integrated functional region. The Ge areas with continuous boundaries are determined by topology optimization that combines finite element method, geometric projection method, and method of moving asymptotes. Both two-dimensional (2D) and quasi-3D designs are presented. Simultaneous beam splitting and phase shifting are achieved in the functional region with only 1.0 × 1.55 μm 2 area. Based on the 3D finite-difference time-domain simulations, the quasi-3D designs possess satisfactory mode purity (>0.99) at center wavelength 1550 nm, and the mode purity keeps higher than 0.92 within the wavelength range from 1500 to 1600 nm. Meanwhile, the forward transmission efficiency is shown higher than 0.89 within the operational bandwidth. Moreover, the robustness is demonstrated by considering the loss of Ge material and the geometric deviations. The proposed mode-order converters bring together advantages including wavelength footprint, high mode purity, low insertion loss, and large operational bandwidth.
Continuous variable (CV) quantum squeezed state and entangled state are important quantum resources, which have been widely used in quantum communication, quantum metrology and quantum computation. In recent years, people have paid much attention to the multi-mode optical parametric amplifier (OPO) process because the multi-mode non-classical light field is able to construct the multiplexing quantum information system for improving the working efficiency and channel capacity. As a special multi-mode optical field, optical frequency comb has been used in optical frequency measurement, atomic spectroscopy and frequency-division multiplex-based communication. Especially, there are a number of notable researches where quantum frequency combs are used, which exhibit multimode-entangled photon states. The quantum frequency combs provide a promising platform for quantum information technology based on time-bin-encoded qubits. In this paper, the entanglement characteristics of frequency comb in type II nondegenerate optical parametric amplifier (NOPA) below threshold are investigated experimentally. The bipartite entanglement with frequency comb structure between idle light (<inline-formula><tex-math id="M1">\begin{document}$\hat a_{{\rm{i}}, + n\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M1.png"/></alternatives></inline-formula>) and signal light(<inline-formula><tex-math id="M2">\begin{document}$\hat a_{{\rm{s}}, + n\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M2.png"/></alternatives></inline-formula>) is generated by the NOPA whose free spectral range (<i>Ω</i>) is 1.99 GHz operated in the de-amplification state and then analyzed by dual balanced homodyne detection system (BHD) with different values of frequency <inline-formula><tex-math id="M3">\begin{document}$\omega \pm n\varOmega $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M3.png"/></alternatives></inline-formula> (<i>n </i>= 0, 1, 2). The local light of BHD with frequency <inline-formula><tex-math id="M4">\begin{document}$\omega \pm n\varOmega $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M4.png"/></alternatives></inline-formula> is generated by the fiber intensity modulator and tailored by the mode cleaner. Here, we measure the correlation noise of side and frequency combs normalized to the shot noise limit relating to the phase of local oscillator beam, and we show the correlation noise of <inline-formula><tex-math id="M5">\begin{document}$\hat a_{\rm{i}}^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$\hat a_{\rm{s}}^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M6.png"/></alternatives></inline-formula>, the correlation noise of <inline-formula><tex-math id="M7">\begin{document}$\hat a_{{\rm{i}}, + \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M7.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M8.png"/></alternatives></inline-formula>, the correlation noise of <inline-formula><tex-math id="M9">\begin{document}$\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M9.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M10">\begin{document}$\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M10.png"/></alternatives></inline-formula>, the correlation noise of <inline-formula><tex-math id="M11">\begin{document}$\hat a_{{\rm{i}}, + 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M11.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M12">\begin{document}$\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M12.png"/></alternatives></inline-formula> and the correlation noise of <inline-formula><tex-math id="M13">\begin{document}$\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M13.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M14">\begin{document}$\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M14.png"/></alternatives></inline-formula>. The experimental results show that the five pairs of entangled states with 4.5 dB entanglement are simultaneously produced by a type II OPO. Next, we can redesign NOPA to reduce its free spectral range and intracavity loss, and prepare local light with a high-order sideband frequency by fiber modulators with high bandwidth, it promises to obtain huge multiple bipartite entangled states. As a kind of extensible quantum information system, the frequency comb CV entanglement can be used to provide a necessary light source for realizing the experiment of frequency division multiplexing multi-channel teleportation, which lays a foundation for the future large-capacity quantum communication and network.
There always are some breakpoints and bifurcation points in measured data of target radiation and scattering characteristics, which have a great impact on the data effectiveness. While among the existed pre-processing methods, the original bifurcation point becomes more prominent or makes a part of a signal. These pre-processing methods will have an effect on subsequent extraction and recognition for features. A data pre-processing method based on multithreshold which effectively removes the numerical singularity and enhances the signal to noise ratio without changing the original signal is given in this paper.
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