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)
An
´
alisis de la reflexi
´
on de ondas
electromagn
´
eticas a trav
´
es de placas paralelas
is
´
otropas
Analysis of Electromagnetic Wave Reflection through Isotropic Parallel Plates
German Caro
∗†1
, Eduardo Acosta
†
Liliana Perez
†
Francisco Veiras
†
†
Universidad de Buenos Aires. Facultad de Ingenier
´
ıa.
Grupo de L
´
aser,
´
Optica de Materiales y Aplicaciones Electromagn
´
eticas. Buenos Aires, Argentina.
∗
Consejo Nacional de Investigaciones Cient
´
ıficas y T
´
ecnicas, (CONICET)
Godoy Cruz 2290, C1425FQB, Buenos Aires, Argentina
1
gcaro@fi.uba.ar
Resumen—Este estudio se enfoca en la reflexi
´
on de ondas
electromagn
´
eticas a trav
´
es de placas paralelas isotr
´
opicas
utilizando el m
´
etodo interferom
´
etrico, en lugar de tratar el
sistema como un todo y resolverlo con las condiciones de
contorno. Esto consiste en considerar cada una de las m
´
ultiples
reflexiones que se dan en este tipo de sistemas, de forma de
obtener un desarrollo con distintos t
´
erminos que convergan
a la soluci
´
on exacta. As
´
ı buscamos examinar si las primeras
reflexiones son suficientes para una buena aproximaci
´
on.
Se derivaron expresiones para los coeficientes de reflexi
´
on
para polarizaciones paralelas (p) y perpendiculares (s). Los
resultados muestran que considerar solo la primera reflexi
´
on
no es una buena aproximaci
´
on, pero si lo es considerar los
primeros dos t
´
erminos.
Palabras clave: is
´
otropos; reflexi
´
on de ondas; placas
plano-paralelas.
Abstract—This study focuses on the reflection of
electromagnetic waves through isotropic parallel plates
using the interferometric method, instead of treating the
system as a whole and solving it with boundary conditions.
This involves considering each of the multiple reflections
that occur in these types of systems to obtain a development
with different terms that converge to the exact solution.
Thus, we aim to examine whether the initial reflections alone
are sufficient for a good approximation. Expressions for
the reflection coefficients for parallel (p) and perpendicular
(s) polarizations were derived. The results demonstrate
that relying solely on the first reflection is not a suitable
approximation, whereas considering the first two terms proves
to be accurate.
Keywords: isotropic; wave reflection; plane-parallel plate.
I. INTRODUCCI
´
ON
Las ondas planas que inciden en una interfaz que separa
dos medios diel
´
ectricos generan campos reflejados y trans-
mitidos que pueden calcularse a partir de la ecuaci
´
on de
Snell y las condiciones de contorno [1]. Esta premisa se
mantiene en el caso de sistemas multicapas y en particular
en el caso de una placa diel
´
ectrica inmersa entre dos medios
diel
´
ectricos. Sin embargo, se nos presenta otra opci
´
on para
este
´
ultimo escenario: podemos considerar que la onda plana
se refleja y transmite infinitas veces y sumar cada una de
estas contribuciones [2] [3]. El m
´
etodo interferom
´
etrico nos
permite visualizar la relevancia de cada t
´
ermino en la serie
de reflexiones y transmisiones [4]. De esta manera se puede
emplear los cambios en la intensidad de la luz reflejada y/o
transmitida para obtener las caracter
´
ısticas de los materiales
involucrados [5]. En este trabajo se analiza cu
´
antos t
´
erminos
son necesarios para obtener una buena aproximaci
´
on en el
m
´
odulo del coeficiente de reflexi
´
on.
Este estudio tiene inter
´
es tecnol
´
ogico para el dise
˜
no de
sensores [6] y la selecci
´
on de los par
´
ametros constructivos
[7] [8], como son las caracter
´
ısticas de los medios, espesor
de la placa o
´
angulo de incidencia. Si alguno de los
par
´
ametros no es conocido resulta dif
´
ıcil a partir de medi-
ciones experimentales calcularlo. Con estas aproximaciones
intentamos disminuir la dificultad de resolver el problema
inverso [9] y poder as
´
ı hallar configuraciones que permitan
tener una mayor sensibilidad a peque
˜
nos cambios en uno de
los medios.
II. REFLEXI
´
ON Y REFRACCI
´
ON EN INTERFACES
IS
´
OTROPAS
En una interfaz entre dos medios distintos, las compo-
nentes tangenciales de los campos
E y
H en la interfaz son
continuas, as
´
ı como las componentes normales de
D y
B. Si
la normal a la interfaz es ˆn, estas condiciones de continuidad
pueden escribirse de la siguiente manera:
(
D
2
−
D
1
).ˆn = 0 (1)
(
B
2
−
B
1
).ˆn = 0 (2)
ˆn × (
E
2
−
E
1
) = 0 (3)
ˆn × (
H
2
−
H
1
) = 0 (4)
donde el supra
´
ındice 1 indica a los campos en el medio
desde el que incide la onda y el supra
´
ındice 2 a los campos
transmitidos. A partir de ellas se obtiene que en general
al incidir una onda desde un medio is
´
otropo con
´
ındice
de refracci
´
on n
1
y velocidad de fase u
1
a uno de
´
ındice
de refracci
´
on n
2
y velocidad de fase u
2
habr
´
a una onda
reflejada y una transmitida. A partir de ellas se obtiene
Revista elektron, Vol. 7, No. 2, pp. 71-76 (2023)
Recibido: 18/11/23; Aceptado: 14/12/23
Creative Commons License - Attribution-NonCommercial-
NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
https://doi.org/10.37537/rev.elektron.7.2.187.2023
Original Article