Abstract
The transmissivity of a one-dimensional random system that is periodic on average is studied. It is shown that the transmission coefficient for frequencies corresponding to a gap in the band structure of the average periodic system increases with increasing disorder while the disorder is weak enough. This property is shown to be universal, independent of the type of fluctuations causing the randomness. In the case of strong disorder the transmission coefficient for frequencies in allowed bands is found to be a non monotonic function of the strength of the disorder. An explanation for the latter behavior is provided.
Highlights
It is well known today [1] that in the propagation of a classical wave through a onedimensional periodic structure of finite length the amplitude of the transmitted wave decreases exponentially with increasing length of the system when the frequency of the wave is in a gap in the photonic band structure of the infinite lattice of the same period
The width of the ith slab is given by ai = a(1 + ∆i), where the ∆i are independent random variables that are uniformly distributed in the interval (−∆, ∆), where clearly 0 ≤ ∆ < 1
The initial increase of l−1(ω) with increasing ∆ is readily understood as the suppression of the transmission in this frequency range due to the multiple scattering of the incident wave caused by the disorder
Summary
It is well known today [1] that in the propagation of a classical wave through a onedimensional periodic structure of finite length the amplitude of the transmitted wave decreases exponentially with increasing length of the system when the frequency of the wave is in a gap in the photonic band structure of the infinite lattice of the same period.
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