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arXiv 1111.3448quant-ph
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PT对称复杂晶体中的不可见性

Invisibility in PT-symmetric complex crystals

Stefano Longhi

摘要:

本文从理论上研究了有限厚度正弦PT对称复杂晶体中的布拉格散射,导出了用修正的第一类贝塞尔函数表示的反射系数和透射系数的精确解析表达式。分析结果表明,最近用耦合模理论预言的这种晶体的单向不可见性[Z。Lin等人,物理修订版信函106,213901(2011)],分解为含有大量晶胞的晶体。特别是,对于给定的调制深度在浅正弦电位,三个制度遇到的晶体厚度增加。在短长度的晶体是无反射和不可见的,当从一侧探测(单向不可见),而在中间长度的晶体保持无反射,但不是不可见的;对于较长的晶体单向无反射和不可见的属性都被打破。

英文摘要:

Bragg scattering in sinusoidal PT-symmetric complex crystals of finite thickness is theoretically investigated by the derivation of exact analytical expressions for reflection and transmission coefficients in terms of modified Bessel functions of first kind. The analytical results indicate that unidirectional invisibility, recently predicted for such crystals by coupled-mode theory [Z. Lin et al., Phys. Rev. Lett. 106, 213901 (2011)], breaks down for crystals containing a large number of unit cells. In particular, for a given modulation depth in a shallow sinusoidal potential, three regimes are encountered as the crystal thickness is increased. At short lengths the crystal is reflectionless and invisible when probed from one side (unidirectional invisibility), whereas at intermediate lengths the crystal remains reflectionless but not invisible; for longer crystals both unidirectional reflectionless and invisibility properties are broken.

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