Attenuation in waveguides on FR-4 boards due to periodic substrate undulations

The guided-mode attenuation associated with optical-interconnect-polymer waveguides fabricated on FR-4 printed-circuit boards is quantified. The rigorous transmission-line network approach is used and the FR-4 substrate is treated as a long-period substrate grating. A quantitative metric for an appropriate matrix truncation is presented. The peaks of attenuation are shown to occur near the Bragg conditions that characterize the leaky-wave stop bands. For a typical 400 microm period FR-4 substrate with an 8 microm corrugation depth, a buffer layer thickness of about 40 microm is found to be needed to make the attenuation negligibly small.