The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
O comportamento assintótico da potência luminosa a grandes distâncias em um sistema de guia de ondas aleatório com comprimento de correlação curto e um mecanismo matemático do comportamento assintótico são esclarecidos. A discussão é baseada na teoria do modo acoplado. Primeiro, para a propagação da luz em um sistema ordenado de guias de ondas, é apresentada uma nova descrição em termos de potência luminosa. Uma solução da equação integro-diferencial que descreve a potência luminosa é expressa como uma integral de contorno no domínio da transformada de Laplace. As singularidades do integrando são pontos de ramificação e a integral de corte de ramificação determina o comportamento assintótico da solução. A potência da luz diminui na proporção inversa à distância. Em segundo lugar, a descrição é estendida ao caso de um sistema de guia de ondas aleatório. A equação diferencial do tipo recorrência que descreve a potência incoerente é reduzida à equação integro-diferencial e é mostrado que o kernel é o produto do kernel para um sistema ordenado e o termo de amortecimento. A equação é resolvida usando o mesmo procedimento para um sistema ordenado e uma representação integral do contorno da solução é obtida. As singularidades do integrando são pólos e pontos de ramificação. Os pólos surgem do termo de amortecimento do kernel e os resíduos dos pólos determinam o comportamento assintótico da solução. A potência incoerente diminui na proporção inversa à raiz quadrada da distância.
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Akira KOMIYAMA, "Asymptotic Analysis of the Light Propagation in a Random Waveguide System" in IEICE TRANSACTIONS on Electronics,
vol. E92-C, no. 1, pp. 85-91, January 2009, doi: 10.1587/transele.E92.C.85.
Abstract: The asymptotic behaviour of the light power at large distance in a random waveguide system with a short correlation length and a mathematical mechanism of the asymptotic behaviour are clarified. The discussion is based on the coupled mode theory. First, for the light propagation in an ordered waveguide system a new description in terms of the light power is presented. A solution of the integro-differential equation describing the light power is expressed as a contour integral in the Laplace transform domain. Singularities of the integrand are branch points and the branch cut integral determines the asymptotic behaviour of the solution. The light power decreases in inverse proportion to the distance. Secondly the description is extended to the case of a random waveguide system. The differential equation of the recurrence type describing the incoherent power is reduced to the integro-differential equation and it is shown that the kernel is the product of the kernel for an ordered system and the damping term. The equation is solved by using the same procedure as that for an ordered system and a contour integral representation of the solution is obtained. Singularities of the integrand are poles and branch points. The poles arise from the damping term of the kernel and the residues of the poles determine the asymptotic behaviour of the solution. The incoherent power decreases in inverse proportion to the square root of the distance.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/transele.E92.C.85/_p
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@ARTICLE{e92-c_1_85,
author={Akira KOMIYAMA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Asymptotic Analysis of the Light Propagation in a Random Waveguide System},
year={2009},
volume={E92-C},
number={1},
pages={85-91},
abstract={The asymptotic behaviour of the light power at large distance in a random waveguide system with a short correlation length and a mathematical mechanism of the asymptotic behaviour are clarified. The discussion is based on the coupled mode theory. First, for the light propagation in an ordered waveguide system a new description in terms of the light power is presented. A solution of the integro-differential equation describing the light power is expressed as a contour integral in the Laplace transform domain. Singularities of the integrand are branch points and the branch cut integral determines the asymptotic behaviour of the solution. The light power decreases in inverse proportion to the distance. Secondly the description is extended to the case of a random waveguide system. The differential equation of the recurrence type describing the incoherent power is reduced to the integro-differential equation and it is shown that the kernel is the product of the kernel for an ordered system and the damping term. The equation is solved by using the same procedure as that for an ordered system and a contour integral representation of the solution is obtained. Singularities of the integrand are poles and branch points. The poles arise from the damping term of the kernel and the residues of the poles determine the asymptotic behaviour of the solution. The incoherent power decreases in inverse proportion to the square root of the distance.},
keywords={},
doi={10.1587/transele.E92.C.85},
ISSN={1745-1353},
month={January},}
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TY - JOUR
TI - Asymptotic Analysis of the Light Propagation in a Random Waveguide System
T2 - IEICE TRANSACTIONS on Electronics
SP - 85
EP - 91
AU - Akira KOMIYAMA
PY - 2009
DO - 10.1587/transele.E92.C.85
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E92-C
IS - 1
JA - IEICE TRANSACTIONS on Electronics
Y1 - January 2009
AB - The asymptotic behaviour of the light power at large distance in a random waveguide system with a short correlation length and a mathematical mechanism of the asymptotic behaviour are clarified. The discussion is based on the coupled mode theory. First, for the light propagation in an ordered waveguide system a new description in terms of the light power is presented. A solution of the integro-differential equation describing the light power is expressed as a contour integral in the Laplace transform domain. Singularities of the integrand are branch points and the branch cut integral determines the asymptotic behaviour of the solution. The light power decreases in inverse proportion to the distance. Secondly the description is extended to the case of a random waveguide system. The differential equation of the recurrence type describing the incoherent power is reduced to the integro-differential equation and it is shown that the kernel is the product of the kernel for an ordered system and the damping term. The equation is solved by using the same procedure as that for an ordered system and a contour integral representation of the solution is obtained. Singularities of the integrand are poles and branch points. The poles arise from the damping term of the kernel and the residues of the poles determine the asymptotic behaviour of the solution. The incoherent power decreases in inverse proportion to the square root of the distance.
ER -