- #1
thomas430
- 17
- 0
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.
Thomas.
I've just read the following:
Each bound mode of a fibre is orthogonal to all other bound modes. Physically this means that if a particular mode is propagating along a fibre, it cannot excite any other mode.
Mathematically, orthogonality between the j'th and k'th bound modes is expressible in terms of the vanishing of the integral off a triple scalar product of electric field of the j'th mode and the magnetic field of the k'th mode over the infinite cross-section of the fibre.
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,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.
Thomas.