O'Reilly logo

Applied Optics Fundamentals and Device Applications by Mark A. Mentzer

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

5Integrated Optics

5.1 Planar Optical Waveguide Theory

We first discuss the case of the planar waveguide in terms of the carrier compensation process. If the waveguide core layer is assumed homogeneous, then the amount of free-carrier compensation necessary for waveguiding, that is, at least for the fundamental transverse electric mode (TE0) to propagate, can be calculated. This cutoff condition for TE0 to propagate is [1]

2πdλ0n12-n22arctann22-n32n12-n32(5.1)

Since n2n3 and n1n2, the argument of the inverse tangent is much greater than unity but is not always large enough in the cases considered for arctan(x) to be approximated by π/2. Therefore, the simple mathematical identify arctan(x) = π/2—arctan(1/x) allows an accurate Taylor ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required