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Area Radio wave propagation / Essential characteristics of electromagnetic fields and waves

IEV ref705-01-28

en
wave vector
a complex vector K _ = K +j K MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaamaamaaabaGaam4saaaaaiaawEniaiabg2da9maaFiaabaGabm4sayaafaaacaGLxdcacqGHRaWkciGGQbWaa8HaaeaaceWGlbGbayaaaiaawEniaaaa@441A@ which characterizes a sinusoidal electromagnetic wave relative to a point in space when each of the electromagnetic field vectors can be represented, in a domain of space in the neighbourhood of this point, by an expression such as:

V _ i = V _ oi e j( ωt K _ r ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaamaamaaabaGaamOvaaaadaWgaaWcbaGaaiyAaaqabaaa kiaawEniaiabg2da9maaFiaabaGabmOvayaaDaWaaSbaaSqaaiaac+ gacaGGPbaabeaaaOGaay51GaGaaGPaVJqaaiaa=vgadaahaaWcbeqa aiaacQgadaqadaqaaGWaaiab+L8a3jaadshacqGHsisldaWhcaqaai aadUeaaiaawEniaiabgwSixpaaFiaabaGaamOCaaGaay51GaaacaGL OaGaayzkaaaaaaaa@5370@

in which:

- vectors V _ oi MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmaadaWaaiWabaabaiaafaaake aadaWhcaqaaiqadAfagaqhamaaBaaaleaacaGGVbGaaiyAaaqabaaa kiaawEniaiaaykW7aaa@3FE0@ , generally complex, are independent of time and practically constant in the domain considered,
- K _ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaamaamaaabaGaam4saaaaaiaawEniaaaa@3C23@ vector is practically constant in the domain considered,
- ω is the angular frequency,
- t is time,
- r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aaceWGYbGbaSaaaaa@3A98@ is the vector joining the origin of coordinates to the point of interest in the domain

Note 1 – If the wave can be characterized by a wave vector at every point in a domain, there exists a wavefront containing the point and orthogonal to the real part K MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaaiqadUeagaqbaaGaay51Gaaaaa@3C1F@ of the wave vector. The magnitude of K _ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaamaamaaabaGaam4saaaaaiaawEniaaaa@3C23@ is 2π divided by the wavelength.

Note 2 – The wave has an elliptical polarization if the imaginary part of each vector V _ oi MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmaadaWaaiWabaabaiaafaaake aadaWhcaqaaiqadAfagaqhamaaBaaaleaacaGGVbGaaiyAaaqabaaa kiaawEniaiaaykW7aaa@3FE0@ is neither zero nor collinear with its real part; the wave has a linear polarization in the other cases.


fr
vecteur d'onde, m
vecteur complexe K _ = K +j K MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaamaamaaabaGaam4saaaaaiaawEniaiabg2da9maaFiaabaGabm4sayaafaaacaGLxdcacqGHRaWkciGGQbWaa8HaaeaaceWGlbGbayaaaiaawEniaaaa@441A@ caractérisant une onde électromagnétique sinusoïdale en un point lorsque chacun des vecteurs du champ électromagnétique peut être représenté, dans un domaine au voisinage de ce point, par une expression de la forme:

V _ i = V _ oi e j( ωt K _ r ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaamaamaaabaGaamOvaaaadaWgaaWcbaGaaiyAaaqabaaa kiaawEniaiabg2da9maaFiaabaGabmOvayaaDaWaaSbaaSqaaiaac+ gacaGGPbaabeaaaOGaay51GaGaaGPaVJqaaiaa=vgadaahaaWcbeqa aiaacQgadaqadaqaaGWaaiab+L8a3jaadshacqGHsisldaWhcaqaai aadUeaaiaawEniaiabgwSixpaaFiaabaGaamOCaaGaay51GaaacaGL OaGaayzkaaaaaaaa@5370@

dans laquelle:

- les vecteurs V _ oi MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmaadaWaaiWabaabaiaafaaake aadaWhcaqaaiqadAfagaqhamaaBaaaleaacaGGVbGaaiyAaaqabaaa kiaawEniaiaaykW7aaa@3FE0@ , généralement complexes, sont indépendants du temps et pratiquement constants dans le domaine considéré,
- le vecteur K _ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaamaamaaabaGaam4saaaaaiaawEniaaaa@3C23@ est pratiquement constant dans le domaine considéré,
- ω est la pulsation,
- t est le temps,
- r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aaceWGYbGbaSaaaaa@3A98@ est le vecteur joignant l'origine des coordonnées au point considéré du domaine

Note 1 – Si l'onde peut être caractérisée en chaque point d'un domaine par un vecteur d'onde, il existe une surface d'onde passant par ce point et normale à la partie réelle K MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaaiqadUeagaqbaaGaay51Gaaaaa@3C1F@ du vecteur d'onde. La norme de K _ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaake aadaWhcaqaamaamaaabaGaam4saaaaaiaawEniaaaa@3C23@ est le quotient de 2π par la longueur d'onde

Note 2 – L'onde est à polarisation elliptique si la partie imaginaire de chaque vecteur V _ oi MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meWabaGacmaadaWaaiWabaabaiaafaaake aadaWhcaqaaiqadAfagaqhamaaBaaaleaacaGGVbGaaiyAaaqabaaa kiaawEniaiaaykW7aaa@3FE0@ n'est ni nulle ni colinéaire à sa partie réelle, elle est à polarisation rectiligne dans les autres cas.


ar
متجه موجة

de
Wellenvektor, m

es
vector de onda

it
vettore d'onda

ko
파 벡터
파수 벡터

ja
波動ベクトル

pl
wektor fali

pt
vector de onda

sv
vågvektor

Publication date: 1995-09
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