Calculation of Δn2 and κ for an acoustically induced distributed Bragg reflector (ADBR)

The preliminary feasibility analysis and theoretical design of an acoustically induced distributed Bragg reflector (ADBR) suitable for possible integration with a III-V semiconductor laser is presented. The proposed ADBR structure consists of a simple unapodized interdigitated transducer (IDT) patterned by e-beam lithography atop a III-V compound semiconductor optical waveguide structure. It is proposed that a gigahertz-range surface acoustic wave (SAW) could present a tunable distributed Bragg reflector (DBR) index grating to a colinearly propagating guided optical wave. Both the change in the impermeabiility tensor, Δn², and the resulting distributed feedback (DFB) coupling coefficient, κ, in the ADBR section are calculated due to only the classic photoelastic effect by employing a Laguerre polynomial SAW analysis technique. The SAW fields are normalized using the normal mode IDT equivalent circuit model and a power balance technique to provide realistic κ values in order to assess the feasibility of this device while driven at its center frequency. The analysis of the ADBR κ is limited to the coupling between counterpropagating TE optical modes and is calculated using general overlap integral expression. For an example λ₀=1.55 μm In_1-xGa_xAs_yP_1-y-InP multiple-quantum-well (MQW) laser structure coated with a 0.1-μm ZnO piezoelectric layer, the maximum ADBR κ was calculated to be 4.9 cm^-1 when using a series-inductor-tuned submicron electrode IDT-SAW reflector configuration driven by a RF source operating at approximately 2.9 GHz. It is shown that exceeding the maximum strain on the substrate or the occurrence of dielectric breakdown fan put an upper limit on the realizable value of κ. The potential optical tunability of an ADBR section is estimated for the case when an unapodized LDT is used for SAW generation. Finally, various fabrication and design techniques are listed which may enhance the ADBR κ value, along with a list of other physical effects which may need to be considered in future analyses