Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average

McGurn, Arthur R.; Christensen, Kenneth T.; Mueller, F. M.; Maradudin, A. A.

doi:10.1103/physrevb.47.13120

Cited by 134 publications

(72 citation statements)

References 3 publications

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“…At frequencies inside the gaps, the ͗ln(T)͘ and the localization length increases by increasing the disorder as a result of the fact that the density of states ͑DOS͒ become higher due to the creation of localized states inside the gap. [27][28][29][30] In order to find how the different types of disorder affect the gaps we plot ͑Fig. 5͒ the localization length of s-polarized waves at 6.5 GHz ͓this is in the middle of the first gap; see Fig.…”

Section: Disordermentioning

confidence: 99%

Localization of electromagnetic waves in two-dimensional disordered systems

et al. 1996

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We calculate the average transmission for s-and p-polarized electromagnetic ͑EM͒ waves and consequently the localization length of two-dimensional ͑2D͒ disordered systems which are periodic on the average; the periodic systems form a square lattice consisting of infinitely long cylinders parallel to each other and embedded in a different dielectric medium. In particular, we study the dependence of the localization length on the frequency, the dielectric function ratio between the scatterer and the background, and the filling ratio of the scatterer. We find that the gaps of the s-polarized waves can sustain a higher amount of disorder than those of the p-polarized waves, due to the fact that the gaps of the s-polarized waves are wider than those of the p-polarized waves. For high frequencies, the gaps of both types of waves easily disappear, the localization length is constant and it can take very small values. The optimum conditions for obtaining localization of EM waves in 2D systems will be discussed.

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Section: Disordermentioning

confidence: 99%

Localization of electromagnetic waves in two-dimensional disordered systems

et al. 1996

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“…It has been shown that for homogeneously random systems there exists a universal distribution for the reflection coefficient. Moreover, the localization length in the presence of absorption follows the same relation obtained for the case of amplification, except replacing the gain length by the attenuation length [7,9,14]. It should be mentioned that, physically, the reduction of the localization length in a gain medium is due to the enhancement of the coherent backscattering effect.…”

Section: Discussionmentioning

confidence: 71%

“…We consider a periodic medium consisting of two types of layers with dielectric constants A and B and layer thicknesses a and b. To introduce randomness, instead of making thickness random, without losing generality, we have chosen A to be random [14]. Thus, for a disordered sample of 2L + 1 layers, the thickness a n and the dielectric constant n of the nth layer can be written as…”

Section: Model System and Mismatched Boundary Conditionmentioning

confidence: 99%

“…Most of the systems in this class possess only two medium parameters. In 1D, the localization length behaviour of such random systems that are periodic on average has been studied both theoretically [14] and experimentally [11,15]. In the presence of gain, the statistical distribution of the reflection (R) and transmission (T ) coefficients and the localization length behaviour of such systems have not been investigated.…”

Section: Introductionmentioning

confidence: 99%

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Statistics of amplified light in periodically correlated layered systems with randomness

Chiu

Zhang

1997

Waves in Random Media

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Abstract. We study the statistics of reflection and transmission coefficients of light in randomly layered amplifying media that are periodic on average. We are interested in one-dimensional universal scaling behaviours in such systems. Our study shows that while a homogeneous medium boundary condition is capable of reproducing universal scaling at low frequencies, a periodic medium boundary condition is necessary for high frequencies. Although the statistics depends on the boundary condition, the saturation length, where the reflection coefficient reaches a stationary distribution, and the localization length do not. Implications of these results are discussed.

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“…The effort in searching for localization of classical waves such as acoustic and electro-magnetic waves is tremendous. It has drawn intensive attentions from both theorists [2][3][4][5][6][7][8] and experimentalists [9,10]. Snice the pioneering work of Anderson et.al.…”

Section: Introductionmentioning

confidence: 99%

Statistics of the Lyapunov exponent in one-dimensional layered systems

Luan

2001

Phys. Rev. E

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Localization of acoustic waves in a one dimensional water duct containing many randomly distributed air filled blocks is studied. Both the Lyapunov exponent and its variance are computed. Their statistical properties are also explored extensively. The results reveal that in this system the single parameter scaling is generally inadequate no matter whether the frequency we consider is located in a pass band or in a band gap. This contradicts the earlier observations in an optical case. We compare the results with two optical cases and give a possible explanation of the origin of the different behaviors.

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Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average

Cited by 134 publications

References 3 publications

Localization of electromagnetic waves in two-dimensional disordered systems

Localization of electromagnetic waves in two-dimensional disordered systems

Statistics of amplified light in periodically correlated layered systems with randomness

Statistics of the Lyapunov exponent in one-dimensional layered systems

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