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I am an EE undergrad currently studying group velocity dispersion (GVD) for coupled waveguides, and am quite confused on the following question: how do you characterize group velocity dispersion for a coupled waveguide system, like a conventional symmetric directional coupler? I can certainly get the dispersion relation (\$\beta-\omega\$ relation) for the individual waveguides, be them planar, rectangular and so on as they are almost always treated in an integrated optics or photonics textbook, but how do you characterize GVD for the coupled system (come up with a "coupled propagation constant"?), and is there a general treatment for it? Any help or even suggestion on references is appreciated!

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You generally wouldn't try to specify group velocity dispersion for such a system. Instead, you'd simply measure (or estimate from simulation) S-parameters for the 4-port network formed by a certain length of coupled waveguides.

From there you could determine a group delay for signals propagating from one port to any of the other 3 (or reflecting back to the input port for that mater). But you shouldn't expect this delay to grow linearly as the length of the coupled section is increased, so it probably doesn't make sense to talk about group velocity of the structure.

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  • \$\begingroup\$ Ok I see. However, I am doing some research on this topic and would like to characterize GVD for coupled waveguides and was hoping that someone could hint on how this can be done. \$\endgroup\$
    – Nen
    Sep 15, 2016 at 14:38
  • \$\begingroup\$ @Eddy, if it's research, then the idea is you should come up with some new ideas of how to do things that other people haven't done before. \$\endgroup\$
    – The Photon
    Sep 15, 2016 at 15:21
  • \$\begingroup\$ Thank you very much for the advice. I think I know how to deal with this problem now. \$\endgroup\$
    – Nen
    Sep 15, 2016 at 15:23

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