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arXiv 1707.06181physics.opticscond-mat.other
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任意长程耦合光波导阵列中的精确布洛赫振荡

Exact Bloch oscillations in optical waveguide arrays with arbitrary long-range coupling

R. Arjona, E. Diaz, F. Dominguez-Adame

摘要:

我们发现在任意长程耦合的影响下,弯曲光波导之字形阵列中存在精确的布洛赫振荡。曲率在光演化方程中引起线性横向电势梯度。在具有二阶耦合的阵列的情况下,稳态可以作为整数指数的贝塞尔函数的线性组合来获得。相应的本征值是等距的,并形成众所周知的Wannier-Stark阶梯,间隔是独立的二阶耦合。我们还精确地求解了波包动力学,并与实验结果进行了比较。因此,我们发现,一个宽的光脉冲进行布洛赫振荡。基本布洛赫频率的倍频在二阶耦合的有限值处成立。相反,当单个波导最初被激发时,呼吸模式被激活而没有布洛赫振荡的特征。我们提出了一个概括我们的结果受到远程耦合的波导阵列。在一般情况下,波包的质心显示了布洛赫频率的倍数的出现,直到相互作用的阶数。

英文摘要:

We find the exact Bloch oscillations in zigzag arrays of curved optical waveguides under the influence of arbitrary long-range coupling. The curvature induces a linear transverse potential gradient in the equations of the light evolution. In the case of arrays with second-order coupling, steady states can be obtained as linear combinations of Bessel functions of integer index. The corresponding eigenvalues are equally spaced and form the well-known Wannier-Stark ladder, the spacing being independent of the second-order coupling. We also solve exactly the wave packet dynamics and compare it with experimental results. Accordingly we find that a broad optical pulse performs Bloch oscillations. Frequency doubling of the fundamental Bloch frequency sets up at finite values of the second-order coupling. On the contrary when a single waveguide is initially excited, a breathing mode is activated with no signature of Bloch oscillations. We present a generalization of our results to waveguide arrays subject to long-range coupling. In the general case the centroid of the wave packet shows the occurrence of multiples of the Bloch frequency up to the order of the interaction.

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