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Anderson localization in a partially random Bragg grating and a conserved area theorem

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Arash Mafi

Optics · Submitted 15 Jul 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Second, for any amount of disorder, the average transmittance decays exponentially with the number of grating layers in the simple form of $\exp(-\eta N)$ for sufficiently large $N$, where $\eta$ is a constant and $N$ is the number of layers.

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arXiv ID1507.04284 (version 1)
Pith IDEZBY3BWD, Pith's permanent record of this paper and its review
CitationArash Mafi. "Anderson localization in a partially random Bragg grating and a conserved area theorem." arXiv:1507.04284 (2015). https://pith.science/paper/EZBY3BWD
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,924 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.17 · randomized assignment 0.02 · states quantitative result 0.69 · compares with prior results 0.20 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We investigate the gradual emergence of the disorder-related phenomena in intermediate regimes between a deterministic periodic Bragg grating and a fully random grating and highlight two critical properties of partially disordered Bragg gratings. First, the integral of the logarithm of the transmittance over the reciprocal wavevector space is a conserved quantity. Therefore, adding disorder merely redistributes the transmittance over the reciprocal space. Second, for any amount of disorder, the average transmittance decays exponentially with the number of grating layers in the simple form of $\exp(-\eta N)$ for sufficiently large $N$, where $\eta$ is a constant and $N$ is the number of layers. Conversely, the simple exponential decay form does not hold for small $N$ except for a highly disordered system. Implications of these findings are demonstrated.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We investigate the gradual emergence of the disorder-related phenomena in intermediate regimes between a deterministic periodic Bragg grating and a fully random grating and highlight two critical properties of partially disordered Bragg gratings. contribution 0.99 0.92 0.11 asserted 0.98
s1 First, the integral of the logarithm of the transmittance over the reciprocal wavevector space is a conserved quantity. result 0.99 0.76 0.35 asserted 1.00
s2 Therefore, adding disorder merely redistributes the transmittance over the reciprocal space. interpretation 0.97 0.71 0.16 asserted 1.00
s3 Second, for any amount of disorder, the average transmittance decays exponentially with the number of grating layers in the simple form of $\exp(-\eta N)$ for sufficiently large $N$, where $\eta$ is a constant and $N$ is the number of layers. result 1.00 0.87 0.37 asserted 1.00
s4 Conversely, the simple exponential decay form does not hold for small $N$ except for a highly disordered system. result 0.91 0.81 0.08 asserted 1.00
s5 Implications of these findings are demonstrated. interpretation 0.87 0.54 0.04 asserted 0.87

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.74.

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  • references and citing sentences
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  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We investigate the gradual emergence of the disorder-related phenomena in intermediate regimes between a deterministic periodic Bragg grating and a fully random grating and highlight two critical properties of partially disordered Bragg gratings. First, the integral of the logarithm of the transmittance over the reciprocal wavevector space is a conserved quantity. Therefore, adding disorder merely redistributes the transmittance over the reciprocal space. Second, for any amount of disorder, the average transmittance decays exponentially with the number of grating layers in the simple form of $\exp(-\eta N)$ for sufficiently large $N$, where $\eta$ is a constant and $N$ is the number of layers. Conversely, the simple exponential decay form does not hold for small $N$ except for a highly disordered system. Implications of these findings are demonstrated.

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