ABSTRACT
Most of us have an intuitive understanding of light as a geometric ray: something that travels in straight lines in a uniform medium. Interfaces between different materials (e.g., glass and air) can alter the direction of these rays. In this section, we will focus on light propagation in waveguides: special material structures that confine and direct the propagation of light with near perfect efficiency. Waveguides can be thought of as wires for light; they allow us to send optical signals over long distances in fiber optics and allow the construction of larger photonic circuits and systems on integrated chips. Waveguides are poorly explained by the intuitive ray description, so a more appropriate description of light as a wave is introduced. Figure 3.1 summarizes some of the main results associated with waveguides. (a) A slab waveguide (WG) in 2D with a dielectric cladding and core where <italic>n<sub>core</sub> </italic> > <italic>n</italic> <sub>clad</sub>. <italic>x</italic> is the propagation direction. Three transverse electric (TE) modes are plotted in red. TE means the electric field vector is in the <italic>z</italic> direction. At a given frequency, there are a discrete number of field profiles that satisfy boundary conditions, (b) The dispersion diagram for the slab WG, plotting frequency (<italic>ω</italic>) vs. propagation wavenumber (<italic>k<sub>x</sub> </italic>). Blue curves correspond to different modes. At a given <italic>ω</italic>, there are a finite number of supported modes, which have symmetric forward and backward propagating versions. Guided modes cannot exist within the so-called light cone (yellow region) because they would leak out into the cladding. The fundamental mode TE<sub>0</sub> is always present in dielectric WGs, but higher order modes TE<sub>1</sub>, TE<sub>2</sub>, etc. have minimum cutoff frequencies, which depend on the relationship between frequncy and WG dimensions. This means single-mode waveguides can be designed below the cutoff of the second mode. https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315370590/694adb39-a3ab-4859-b5dd-cd1ca150afbf/content/fig3_1.tif"/>
