## Relevance of the light line in planar photonic crystal waveguides with weak vertical confinement |

Optics Express, Vol. 19, Issue 24, pp. 24344-24353 (2011)

http://dx.doi.org/10.1364/OE.19.024344

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### Abstract

The concept of the so-called light line is a useful tool to distinguish between guided and non-guided modes in dielectric slab waveguides. Also for more complicated structures with 2D mode confinement, the light lines can often be used to divide a dispersion diagram into a region of a non-guided continuum of modes, a region of discrete guided modes and a forbidden region, where no propagating modes can exist. However, whether or not the light line is a concept of practical relevance depends on the geometry of the structure. This fact is sometimes ignored. For instance, in the literature on photonic crystal waveguides, it is often argued that substrate-type photonic crystal waveguides with a weak vertical confinement are inherently lossy, since the entire bandgap including the line defect modes is typically located above the light line of the substrate. The purpose of this article is to illustrate that this argument is inaccurate and to provide guidelines on how an improved light line concept can be constructed.

© 2011 OSA

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(230.7370) Optical devices : Waveguides

(130.5296) Integrated optics : Photonic crystal waveguides

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: August 18, 2011

Revised Manuscript: November 4, 2011

Manuscript Accepted: November 4, 2011

Published: November 14, 2011

**Citation**

P. Kaspar, R. Kappeler, D. Erni, and H. Jäckel, "Relevance of the light line in planar photonic crystal waveguides with weak vertical confinement," Opt. Express **19**, 24344-24353 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24344

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