Presented is a method of operating a capacitive microfabricated ultrasonic transducer (cMUT) array with multiple firings of varying bias voltage polarity patterns to improve its performance in imaging non-linear media, such as in contrast agent imaging or tissue harmonic imaging. Additionally, transducers incorporating the method are provided. The method of cMUT operation and the corresponding cMUT does not require pre-distortion or phase inversion of the transmit signal and can achieve an improvement in the elevation focus of the cMUT, as compared to the elevation focus that a single firing can achieve. Further, the method of operating the cMUT minimizes the deleterious effects that result from insulators being subjected to high electric fields.