John F. Dreyer

Apparatus and method for converting mechanical wave energy to optical energy

A piezo-optic cell having a nematic liquid crystal film and first and second wedge-shaped plates on opposite surfaces of the film which serve to vary its frequency response along the length of the cell. The cell is illuminated with polarized light and is insonified by an acoustic wave pattern to produce a real-time visual image of the acoustic wave. By exposing the cell to the applied acoustic energy, one or more resonance conditions are created to produce an extremely strong and well defined image.

Introduction to a Nematic Liquid Crystal Acousto‐Optic Conversion Cell

Real‐time acoustic images have been shown capable of visualization by means of a nematic liquid crystal cell. [P. Greguss, J. Acoust. Soc. Am. 53, 306(A) (1973)]. The cell is composed of a thin film of a nematic liquid crystal in the homeotropic state between polarizers. Irradiation with ultrasonic waves produces birefringence re suiting in a visible pattern. The cell is a combination of a 1‐mil‐thick layer of a room‐temperature liquid crystal between glass which contains a light polarizer and a light diffuser. The most sensitive viewing condition is at 25° from the normal on a diagonal with the polarizers. Two effects are observed. Low‐intensity ultrasonic produces a proportionate transparent birefringence with higher energy at a threshold giving light diffusion. It is theorized that the acoustic pressure produces an electric potential due to the piezoelectric property of the liquid crystal and that this potential alters the direction of the molecules. Wavefront patterns obtained are shown.

The transmission of ultrasonic waves at oblique incidence through a thin layer

An investigation of the production of birefringence in a layer showed sharp frequency peaks that were highly responsive. These peaks were also sensitive to incident angle. The variation of the frequency versus thickness of the layer identified these sharp peaks as being shear waves. A study of oblique incidence transmission was made since shear waves, at mainly perpendicular incidence, produce birefringence. The harmonic resonance equation was found to apply to the longitudinal wave transmission and indicates that the longitudinal waves in the layer are perpendicular to the interface regardless of the incident angle. The relationship of the incident angle to frequency is a modified form of Snell’s law for the longitudinal waves, and a complex modified form for the shear waves. Conversion of longitudinal waves to shear waves and shear waves to longitudinal was found to occur at low harmonics and at incident angle smaller than the first critical angle.

The acoustic resonance modes of two and three layers

Comprehensive equations for the acoustic wave pressure propagation through two and three layers are derived using the exponential method. The two resonant modes for two layers and four for three layers are described. They are expressed relative to φ which = fd 2π/c. The three layer equation consists of eight sinusoidal permutations related with impedances. Their plus or minus combinations control the modes. This equation is verified by test using two layers in water. Under this condition the maximum transmission is obtained when tan φ2 × tan φ3 = 2(Z1)(Z2)/[(Z1)2 + (Z2)2]. The comprehensive three‐layer equation is: For three layers A5A1 = 2[[−+++[1+z1z5]cosφ2 cosφ3 cosφ4++−+[z1z4z3z5+z3z4]cosφ2 sinφ3 sinφ4+−++[z1z4z2z5+z2z4]sinφ2 cosφ3 sinφ4+++−[z2z3+z1z3z2z5]sinφ2 sinφ3 cosφ4]2+[+−+−[z4z5+z1z4] cosφ2 cosφ3 sinφ4++++[z1z3+z3z5] cosφ2 sinφ3 cosφ4+−−+[z1z2+z2z5] sinφ2 cosφ3 cosφ4−−++[z2z4z3z5+z1z3z2z4]sinφ2 sinφ3 sinφ4]2]12

Acoustic wave propagation through a plate

By using variations in the complex exponential approach a new equation for transmission through a plate is developed. Energy and single interface transmission relationships are met. The supporting equations give the amplitude of the forward and reflected pressure and velocity components at the two interfaces. The pressure amplitude of the reflection at the first interface of an immersed plate is found to vary through zero from positive to negative as the thickness wave number is decreased.