Analytic solution for the peak reflectivity of an asymmetric mirror.

Asymmetric Bragg reflectors have been shown to optimize mirror performance in strained-layer material systems. Although the theory behind the reflectivity of symmetric mirrors has been well studied, little is known about asymmetric mirror designs. We present a closed-form solution for the peak reflectivity of an asymmetric mirror that results from applying a tanh substitution. This elegant technique has been shown to yield a markedly simplified calculation of the peak reflectivity of a symmetric mirror. These analytic expressions will be useful in mirror design by providing a straightforward way to compare the trade-offs between asymmetric and symmetric mirror designs.

Theory of reflectivity of an asymmetric mirror.

By using the concept of transfer matrices and Bloch waves, we have derived a set of equations that provide insight into the operation of asymmetric Bragg reflectors that have been demonstrated to be useful in achieving high reflectivities in strained-material systems. These equations will be useful in the design of asymmetric mirrors and can be used to compare the trade-offs between the conventional, symmetric (quarter-wavelength), and asymmetric mirrors.

Four-wavelength Bragg mirror using GaAs/AlAs.

We report on the design and growth by molecular beam epitaxy of a GaAs/AlAs Bragg mirror with four reflectivity bands. High reflectivity is achieved in all the bands, and there is good agreement between measured and simulated results.