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Exact Bloch oscillations in optical waveguide arrays with arbitrary long-range coupling | | R. Arjona
; E. Diaz
; F. Dominguez-Adame
; | | Date: |
19 Jul 2017 | | Abstract: | 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. | | Source: | arXiv, 1707.6181 | | Services: | Forum | Review | PDF | Favorites | |
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