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Question on Brillouin diagram

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thefly0

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Hi all,
I'm studying periodic loaded waveguides from "Foundation for microwave engineering" (Collin) and I've obtained a Brillouin diagram (or ω-β diagram). Since for each value of k*d on the vertical axis (associated to one frequency value) are associated multiple values of β*d on the horizontal axis, how to choose which of such values is to be used.
thanks in advance for any help
 

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