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Homework Help: Orthogonality between optical fibre modes

  1. Apr 19, 2010 #1
    Hi there,

    I've just read the following:

    The expression that is given is:
    [tex]\int_{A \infty} e_j \times h_k* \cdot \widehat{z} dA = 0 [/tex]

    where * denotes the complex conjugate, and z^ is the unit vector in the direction of propagation (along the axis of the fibre).


    Can anyone explain why this mathematical expression indicates orthogonality? I am trying to interpret the mathematics rather than just accept it.

    What I've done:
    I tried to explain it by saying that the dot product between two perpendicular vectors will be 0. But in this sense, I only see the indication that a component perpendicular to both e and h (cross product) is perpendicular to the direction of propagation.
    Thanks for any help,

    Thomas.
     
  2. jcsd
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