Abstract

A new sensing scheme, capable of measuring various quantities using the Goos–Hänchen shift in the polarization phase domain, is proposed. The phase retardation between s and p polarizations on total reflection is enhanced by using multiple reflections in a plane-parallel transparent plate. This phase shift can be sensitively and stably detected using an in-line heterodyne method. As an application of this method, a displacement sensor utilizing the deflection of a light beam by a lens is developed. This displacement sensor has a resolution of 60 nm over a dynamic range of 120 μm. Good agreement between theoretical and experimental results is shown.

© 1989 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, Oxford, UK, 1964), p. 50.
  2. T. Yoshino, in Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, D.C., 1988), p. 40.

Born, M.

M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, Oxford, UK, 1964), p. 50.

Wolf, E.

M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, Oxford, UK, 1964), p. 50.

Yoshino, T.

T. Yoshino, in Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, D.C., 1988), p. 40.

Other (2)

M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, Oxford, UK, 1964), p. 50.

T. Yoshino, in Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, D.C., 1988), p. 40.

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Figures (7)

Fig. 1
Fig. 1

Calculated dependence of the total-reflection retardation δ on the angle of incidence θi for different specific indices n. The dotted curve represents the case for the BK7 glass–air interface (n = 0.66); the slope is 9 at θi = 42°.

Fig. 2
Fig. 2

Scheme for retardation enhancement through multiple total reflections and heterodyne detection.

Fig. 3
Fig. 3

Calculated dependence of the total-reflection retardation δ on the specific refractive index n for different angles of incidence θi. The dotted curve represents the case of θi = 42°; the slope is 857 at n = 0.66.

Fig. 4
Fig. 4

Displacement sensor head.

Fig. 5
Fig. 5

Experimental setup of the heterodyne displacement sensor using the Goos–Hänchen shift. CRT, cathode-ray tube.

Fig. 6
Fig. 6

Measurement characteristics of the displacement sensor with θi = 42°, D = 3.5 mm, n = 0.66, and m = 12.

Fig. 7
Fig. 7

Stability characteristics of the displacement sensor for different PZT voltages.

Equations (6)

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tan δ 2 = cos θ i sin 2 θ i n 2 sin 2 θ i ,
I i = a 2 + b 2 + 2 ab cos ( Δ ωt + Δ i ) ,
I o = a 2 + b 2 + 2 ab cos ( Δ ωt + + Δ o ) ,
Δ o = Δ i + , Δ ω = 2 π ( f 1 f 2 ) ,
1 f + 2 Δ x + Δ θ D = 1 f ,
Δ θ = 2 D f 2 Δ x ,

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