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On the core of the fractional Fourier transform and its role in composing complex fractional Fourier transformations and Fresnel transformations
  • ISSN号：2095-0462
  • 期刊名称：《物理学前沿：英文版》
  • 时间：0
  • 分类：O438[机械工程—光学工程;理学—光学;理学—物理] O174.22[理学—数学;理学—基础数学]
  • 作者机构：[1]Department of Physics, Ningbo University, Ningbo 315211, China, [2]Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 相关基金：The work was supported by the National Natural Science Foundation of China （Grant Nos. 11105133 and 11175113） and the National Basic Research Program of China （973 Program） （Grant No. 2012CB922001）.
作者： Hong-Yi Fan[1,2], Jun-Hua Chen[2]
关键词： 分数傅里叶变换, 分数傅立叶变换, 菲涅耳, 合成, 力学分析, 变换特性, 添加剂, 操作者, fractional Fourier transform, core operator, IWOP technique, entangled state of con-tinuum variables, Fresnel operator
中文摘要：

由量添加剂规则 F 的机械分析<潜水艇class=“ a-plus-plus ”> [F <潜水艇class=“ a-plus-plus ”> [f]]=F <潜水艇class=“ a-plus-plus ”>哪个的+[f],部分 Fourier 转变( FrFT ) F <潜水艇class=“ a-plus-plus ”>[f]应该满足，我们表明相互转变的操作员是的位置动量为构造 FrFT 的集成内核的核心元素。基于这观察并且二互相结合纠缠状态的代表，我们然后为启用复杂部分 Fourier 转变(CFrFT ) 导出一个核心操作员，它也服从添加剂规则。以一种类似的方式，我们也为夫累Ｘ尔操作员的一种类型揭示部分转变性质。

英文摘要：

By a quantum mechanical analysis of the additive rule Fa [Fβ[f]] = Fα＋β[f], which the fractional Fourier transformation （FrFT） Fα [f] should satisfy, we reveal that the position-momentum mutual- transformation operator is the core element for constructing the integration kernel of FrFT. Based on this observation and the two mutually conjugate entangled-state representations, we then derive a core operator for enabling a complex fractional Fourier transformation （CFrFT）, which also obeys the additive rule. In a similar manner, we also reveal the fractional transformation property for a type of Fresnel operator.

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期刊信息
  • 《物理学前沿：英文版》
  • 主管单位:中华人民共和国教育部
  • 主办单位:高等教育出版社
  • 主编：赵光达
  • 地址：北京市朝阳区惠新东街4号富盛大厦15层
  • 邮编：100029
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：2095-0462
  • 国内统一刊号：ISSN：11-5994/O4
  • 邮发代号:80-965
  • 获奖情况:
  • 国内外数据库收录:
  • 荷兰文摘与引文数据库,美国科学引文索引（扩展库）,英国科学文摘数据库
  • 被引量:3