Model for a Torsional-Mode Ultrasonic Transducer for an Acousto-Optic In-Fiber Isolator

Figure 4

Displacement 𝑢(𝑟) (a) and (d), strain 𝜀_𝑟𝜃(𝑟) (b) and (e), and strain 𝜀_𝑧𝜃(𝑟) (c) and (f) are shown at the two ends of the transducer. Transverse coordinate 𝑟 is relative to the fiber radius 𝑎. Scaling is arbitrary. The normalized frequency is 𝛾=5.13767. Red (𝑧=0) and green (𝑧=−𝐿) curves are for unit reflectivity of the 𝑠=1 mode back towards 𝑧=−𝐿 with phase Θ=0. Blue curve is for zero reflectivity and the same transducer amplitude 𝑈. (a), (b), (c), and (d) show the real parts, corresponding to times when 𝑢(1)=𝑈. (d), (e), and (f) show the imaginary parts, corresponding to times when 𝑢(1)=0. High-frequency oscillations in some of the curves are a numerical artifact. Since 𝜀_𝑧𝜃(𝑟) in the absence of reflection has opposite signs at 𝑧=0 and 𝑧=−𝐿, the right-hand green plots have been multiplied by minus 1 for better comparison with the blue plots.

(a)

(b)

(c)

(d)

(e)

(f)