Complex Coupling Coefficient - what is the length dimension and difference from a coupling constant?

iqnloiqnlo Member Posts: 7

Dear forum and fellow Lumerical users,

We are trying to simulate the coupling coefficient between two neighbouring waveguides to predict the behaviour in a waveguide arrray and follow the usual commands from Lumerical that give either the 'complex coupling coefficient' or the 'power coupling' as below:

out = overlap("test_mode1","test_mode2");

?out(1);  # overlap
?out(2);  # power coupling
?coupling("test_mode1","test_mode2"); # the complex coupling coefficient
?abs(coupling("test_mode1","test_mode2"))^2; # same as out(2), the power coupling


However, there has been ample confusion about its similarity to the coupling constant kappa, the ordinary 'coupling coefficient' and especially the dimensions.

My questions are therefore :

1. Are the coupling coefficients formulated as per /um or /mm ?

2. Does the complex part refer to losses?

3. Is this the same as the 'coupling constant' or 'coupling coefficient' that waveguide papers commonly refer to?

I would be sincerely grateful for a clarification and thank you very much in advance!

Answers

  • gsungsun Posts: 1,376Ansys Employee

    Frankly speaking, coupling coefficients loosely used in literature are not unanimously well defined.

    Since script "coupling" only involves two mode profiles, it is dimensionless. Otherwise we cannot get the power coupling from it.

    the complex property of this coefficient simply means there is a phase change.

    "coupling constant" might means the complex coupling constant kappa but in different literature it can mean others. But Kappa may have a well defined meaning in Yariv's book.

    Since this script refers Snyder's book, you may check that book for details.

  • iqnloiqnlo Posts: 15Member

    Thank you for your helpful response!

    I have checked the book, but am still unclear on the following point: as coupling is dependent on the propagation distance along z, I am not clear on how to apply the coefficient to a system with a certain propagation distance without knowing if it expresses coupling between two modes per um or mm for example. In other words, I don't know in which units (um or mm or cm) to express the propagation distance in connection with the coefficient.

    (Snyder, page 615, Modal methods for Maxwell's Equations)


    Thank you very much in advance for your help.

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