It has been shown that high reflectivity mirrors can be formed by deeply etched semiconductor/air distributed Bragg reflectors (DBRs). The DBR structures are almost identical to multilayers of semiconductor and air. Current etching technologies can produce deep uniform etches in semiconductors. The finite dif-ference time domain (FDTD) method directly solves Maxwell’s equation in time. It is remarkably robust

providing accurate modeling for various electromagnetic wave interaction and field problem. Rapid advances in computer technology make the FDTD method more and more attractive every day. In this work we use the FDTD method in two dimensions to study a GaN-based semiconductor/air DBR structure. We take account of the TE mode and considering the geometry to be invariant in the lateral direction perpendicular to the light propagation. The spectral reflectivity is calculated by comparing the spectral content of the incident and reflected pulse. FDTD simulations show that vertical sidewall tilt is a crucial concern for obtaining a high-reflectivity DBR in a conventional design. The middle widths of semiconductor should increase to obtain the high reflec-tivity with the sidewall angle decreasing. To obtain high reflectivity at designed wavelength

the difference of optical path for one DBR pitch should keep constant. When the sidewall tilted

the difference of optical paths decrease. This phenomena can be explained using the knowledge of interference. To increase the optical paths difference

the air space and/or semiconductor width should be increased. The increase of air space will also increase the diffractive spreading loss

which arises because modal confinement is limited to the semiconductor region. In the air gaps

light is not confined and the refractive index of the air is much lower than that of the semiconductor

the optical field diverges quickly upon reaching the semiconductor-air interface. So

the semiconductor width should be increased to increase the optical width. Thus

high reflectivity can be reached with the proper design even with a large vertical sidewall tilt. Experimentally

it is difficult to etch vertical sidewalls of GaN-based materials

so the new design to overcome this difficulty is very meaningful.