Measurement of internal stress and electric field in a resonant piezoelectric transformer using the electro-optic and photoelastic effects

Full characterization of a piezoelectric transformer (PT) requires knowledge of internal operating parameters such as electric field, stress, and strain. Finite-element numerical models can determine these parameters with respect to the geometry of the PT and input conditions. However, experimental verification of these parameters for a resonating PT are challenging due to the mechanical vibration and electrical loading effects. An optical measurement has been designed to measure internal electric field by taking advantage of the electro-optic and photoelastic effects that also occur in lithium niobate (LiNbO
₃
). The optical measurement can probe the PT without influencing its operation. A linearly polarized helium-neon laser beam was used to transversely probe a PT with respect to the input and output electric fields. As the piezoelectric effect caused variations in the internal electric field and strain, the superposition of the photoelastic and electro-optic effects resulted in a relative phase shift in the linearly polarized beam. The resultant phase shift was measured via intensity variations at a photodiode following a second linear polarizer. Internal parameters such as stress, strain, and electric field were calculated based on the coupled piezoelectric, photoelastic, and electro-optic equations. These results are presented for varying positions along the output section of a resonating LiNbO
₃
length-extensional PT.