At low temperatures, microwave cavities are often preferred for the readout and control of a variety of systems. In this paper, we present design and measurements on an optomechanical device based on a 3-dimensional rectangular waveguide cavity. We show that by suitably modifying the electromagnetic field corresponding to the fundamental mode of the cavity, the equivalent circuit capacitance can be reduced to 29 fF. By coupling a mechanical resonator to the modified electromagnetic mode of the cavity, we achieved a capacitance participation ratio of 43 $%$. We demonstrate an optomechanical cooperativity, $C$$sim$40, characterized by performing measurements in the optomechanically-induced absorption (OMIA) limit. In addition, due to a low-impedance environment between the two-halves of the cavity, our design has the flexibility of incorporating a DC bias across the mechanical resonator, often a desired feature in tunable optomechanical devices.
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