What is a Light Line and Its Significance in Photonics - Explained

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A "light line" in photonics represents the boundary between propagating and non-propagating modes of light in a medium. It is derived from the relationship between frequency and wavevector, indicating whether a given mode can exist above or below this line. The significance of the light line lies in its ability to determine the conditions under which light can be guided or confined in photonic structures. Understanding this concept is essential for applications in photonics, such as waveguides and photonic crystals. Further exploration of the topic can enhance comprehension of its implications in the field.
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What is a "light line"?

The graph pictured below contains a "light line." What does it signify? What equation did it come from? All I know is it's important if something is above or below the light line, but other than that I don't have a clue. I would appreciate any explanation. A web link would be great too.
The graph is on the 2nd page of this paper: http://www.stanford.edu/group/fan/publication/Fink-Science-282-1679-1998.pdf
The paper is just an example, the light line is not specific to this paper. It seems to be a standard tool in the photonics field.

http://snag.gy/hdeb3.jpg
 
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The definition is given in the paper you linked.

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But I confess. That is pretty dense and I don't understand it myself.
 
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