Wave mixing and the intricate optical interactions therein have traditionally been regarded as hallmarks of nonlinear optics.A quintessential example of wave mixing lies in the nonlocal triple correlation between the ...Wave mixing and the intricate optical interactions therein have traditionally been regarded as hallmarks of nonlinear optics.A quintessential example of wave mixing lies in the nonlocal triple correlation between the pump beam and the generated twin photons via spontaneous parametric down-conversion(SPDC).However,the SPDC process typically requires intense laser pumping and suffers from inherently low conversion efficiencies,necessitating single-photon detection.In this work,we establish that analogous triple correlations can be effectively produced using low-power continuous-wave illumination,achieved through a commercially available spatial light modulator(SLM)in a linear optical configuration.Specifically,we show how to spatially manipulate and customize this triple correlation and further investigate the applicability across diverse domains,including pattern recognition,intelligent nonlocal image processing,and sensitivity-enhanced optical metrology.Our findings establish,to our knowledge,a novel framework for classical,linear emulation of quantum and nonlinear optical information processing paradigms rooted in multi-wave mixing.展开更多
Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized...Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized Fourier coefficients,respectively.In this paper,we investigate the correlations of triple sums associated to these Fourier coefficientsλ_(f)(n),λ_(g)(n),λ_(h)(n)over certain polynomials,and obtain some power-saving asymptotic estimates which beat the trivial bounds.展开更多
Autocorrelations, crosscorrelations and triple correlations are three important concepts for signal design and analysis, although the triple ones are not so popular as auto-and cross-ones. This poper concentrates on d...Autocorrelations, crosscorrelations and triple correlations are three important concepts for signal design and analysis, although the triple ones are not so popular as auto-and cross-ones. This poper concentrates on designing new polyphase sequences with good correlations and on recovering signals from their triple correlations. The close relationship between Costas armys and the triple correlations Of m-sequences are initially recognized.展开更多
基金National Natural Science Foundation of China(12274037,11735005,11654003,61675028)Science and Technology Development Fund from Macao SAR(FDCT)(0105/2023/RIA2)Interdiscipline Research Funds of Beijing Normal University。
文摘Wave mixing and the intricate optical interactions therein have traditionally been regarded as hallmarks of nonlinear optics.A quintessential example of wave mixing lies in the nonlocal triple correlation between the pump beam and the generated twin photons via spontaneous parametric down-conversion(SPDC).However,the SPDC process typically requires intense laser pumping and suffers from inherently low conversion efficiencies,necessitating single-photon detection.In this work,we establish that analogous triple correlations can be effectively produced using low-power continuous-wave illumination,achieved through a commercially available spatial light modulator(SLM)in a linear optical configuration.Specifically,we show how to spatially manipulate and customize this triple correlation and further investigate the applicability across diverse domains,including pattern recognition,intelligent nonlocal image processing,and sensitivity-enhanced optical metrology.Our findings establish,to our knowledge,a novel framework for classical,linear emulation of quantum and nonlinear optical information processing paradigms rooted in multi-wave mixing.
基金Supported in part by NSFC(Nos.12401011,12201214)National Key Research and Development Program of China(No.2021YFA1000700)+3 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics(No.23JSQ053)Science and Technology Program for Youth New Star of Shaanxi Province(No.2025ZC-KJXX-29)Natural Science Basic Research Program of Shaanxi Province(No.2025JC-YBQN-091)Scientific Research Foundation for Young Talents of WNU(No.2024XJ-QNRC-01)。
文摘Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized Fourier coefficients,respectively.In this paper,we investigate the correlations of triple sums associated to these Fourier coefficientsλ_(f)(n),λ_(g)(n),λ_(h)(n)over certain polynomials,and obtain some power-saving asymptotic estimates which beat the trivial bounds.
文摘Autocorrelations, crosscorrelations and triple correlations are three important concepts for signal design and analysis, although the triple ones are not so popular as auto-and cross-ones. This poper concentrates on designing new polyphase sequences with good correlations and on recovering signals from their triple correlations. The close relationship between Costas armys and the triple correlations Of m-sequences are initially recognized.
