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IEVref:705-01-28ID:
Language:enStatus: Standard
Term: wave vector
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Definition: 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.


Publication date:1995-09
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