Improved acoustic attenuation materials and applications are provided. An improved acoustic attenuation material may include a woven layer of fibers made of porous polymers, such as porous polytetrafluoroethylene (PTFE), that include interstitial space. An improved acoustic attenuation material may include sheets of porous polymers interleaved with layers of epoxy. The sheets of porous polymers may include through holes. An embodiment of an ultrasonic transducer that includes a backing with woven layers of porous PTFE fibers is provided. The ultrasonic transducer that includes a backing with woven layers of porous PTFE fibers may be used in a three-dimensional ultrasound imaging apparatus. An embodiment of an ultrasonic transducer that includes a plurality of sheets of porous PTFE interleaved with layers of epoxy is provided. The ultrasonic transducer that includes a plurality of sheets of porous PTFE may be used in an ultrasonic imaging catheter.