Vibrations of a Lithium Niobate Fiber

Vibrations of a Lithium Niobate Fiber By LYNN O. WILSON (Manuscript received March 8, 1977) We discuss wave propagation along a crystalline piezoelectric fiber composed of lithium niobate or some other material in the trigonal 3m crystal class. The crystalline c axis is aligned with the fiber axis. We obtain an analytical description of all the vibrational modes. The method used is to make perturbation expansions about the modes of a hexagonal 6mm piezoelectric fiber, for which exact solutions are known. I. INTRODUCTION A single crystal of lithium niobate, grown in the form of a long fiber, has been considered for use as a low-loss acoustic delay line. Lithium niobate is of special interest because it is piezoelectric: it becomes electrically polarized when strained and, conversely, becomes strained when placed in an electric field. This piezoelectricity provides a means for electrically generating and detecting acoustic signals. In this paper we study mathematically the vibrational properties of a LiNbC>3 crystal fiber, with the crystalline c axis aligned along the fiber axis. T h e problem is by no means simple. We illustrate this by giving a brief history of related problems for which exact solutions have been obtained. The elastic, or acoustic, wave equations for an infinitely long circularly cylindrical isotropic rod were solved exactly by Pochhammer 1 in 1876 and independently by Chree 2 in 1889. Even for an isotropic medium, exact solutions for a rod of finite length have not been obtained.