Abstract

Dynamic measurements of optical phase modulation in a single-mode fiber subjected to controlled mechanical vibrations are reported. An accurate analysis of the fiber strain state explains the observed phase vs frequency characteristic behavior. The integration properties of the single-mode fiber are evaluated quantitatively for the vibrations applied. The experimental results emphasize the excellent capabilities of optical fibers to sense mechanical vibrations.

© 1981 Optical Society of America

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References

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  1. G. B. Hocker, Appl. Opt. 18, 1445 (1979).
    [CrossRef] [PubMed]
  2. S. A. Kingsley, Microwave Opt. Acoust. 2, 204 (1978).
    [CrossRef]
  3. C. D. Butter, G. B. Hocker, Appl. Opt. 17, 2867 (1978).
    [CrossRef] [PubMed]
  4. M. Martinelli, C. Liguori, Prac. SPIE 236, 486 (1980).
    [CrossRef]
  5. A. M. Smith, Appl. Opt. 19, 2606 (1978).
    [CrossRef]
  6. R. Ulrich, S. C. Rashleigh, W. Eickhoff, Opt. Lett. 5, 273 (1980).
    [CrossRef] [PubMed]
  7. H. Harms, A. Papp, K. Kempter, Appl. Opt. 15, 799 (1976).
    [CrossRef] [PubMed]
  8. S. C. Lin, T. G. Giallorenzi, Appl. Opt. 18, 915 (1979).
    [CrossRef] [PubMed]
  9. J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1967).
  10. S. Timoshenko, D. H. Young, Vibration Problems in Engineering (D. Van Nostrand, Princeton, 1955).
  11. S. Timoshenko, S. H. Goodier, Theory of Elasticity (McGraw–Hill, New York, 1951).
  12. W. T. Thomson, M. V. Barton, J. Appl. Mech. 6, 248 (1957).

1980 (2)

1979 (2)

1978 (3)

1976 (1)

1957 (1)

W. T. Thomson, M. V. Barton, J. Appl. Mech. 6, 248 (1957).

Barton, M. V.

W. T. Thomson, M. V. Barton, J. Appl. Mech. 6, 248 (1957).

Butter, C. D.

Eickhoff, W.

Giallorenzi, T. G.

Goodier, S. H.

S. Timoshenko, S. H. Goodier, Theory of Elasticity (McGraw–Hill, New York, 1951).

Harms, H.

Hocker, G. B.

Kempter, K.

Kingsley, S. A.

S. A. Kingsley, Microwave Opt. Acoust. 2, 204 (1978).
[CrossRef]

Liguori, C.

M. Martinelli, C. Liguori, Prac. SPIE 236, 486 (1980).
[CrossRef]

Lin, S. C.

Martinelli, M.

M. Martinelli, C. Liguori, Prac. SPIE 236, 486 (1980).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1967).

Papp, A.

Rashleigh, S. C.

Smith, A. M.

Thomson, W. T.

W. T. Thomson, M. V. Barton, J. Appl. Mech. 6, 248 (1957).

Timoshenko, S.

S. Timoshenko, D. H. Young, Vibration Problems in Engineering (D. Van Nostrand, Princeton, 1955).

S. Timoshenko, S. H. Goodier, Theory of Elasticity (McGraw–Hill, New York, 1951).

Ulrich, R.

Young, D. H.

S. Timoshenko, D. H. Young, Vibration Problems in Engineering (D. Van Nostrand, Princeton, 1955).

Appl. Opt. (5)

J. Appl. Mech. (1)

W. T. Thomson, M. V. Barton, J. Appl. Mech. 6, 248 (1957).

Microwave Opt. Acoust. (1)

S. A. Kingsley, Microwave Opt. Acoust. 2, 204 (1978).
[CrossRef]

Opt. Lett. (1)

Prac. SPIE (1)

M. Martinelli, C. Liguori, Prac. SPIE 236, 486 (1980).
[CrossRef]

Other (3)

J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1967).

S. Timoshenko, D. H. Young, Vibration Problems in Engineering (D. Van Nostrand, Princeton, 1955).

S. Timoshenko, S. H. Goodier, Theory of Elasticity (McGraw–Hill, New York, 1951).

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Figures (3)

Fig. 1
Fig. 1

Sketch of the adopted mechanical mounting. It is possible to see how the bar supporting the optical fiber has been constrained realizing a double hinge.

Fig. 2
Fig. 2

Scheme of the realized Mach-Zender interferometer, including the optical fiber and the ADP phase compensator.

Fig. 3
Fig. 3

Spectrum of the phase-change signal vs frequency obtained from the FFT processing of the photodiode signal. Sections (a), (b), and (c) refer, respectively, to relative excitation powers 1, 10, and 100 supplied to the bar as described in the text.

Tables (2)

Tables Icon

Table I Fiber and Steel Bar Characteristic Parameters

Tables Icon

Table II Summary of the Computed and Experimental Results

Equations (34)

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d ϕ = β · d + · d β ,
d ϕ β · d + · β 0 · d n ,
d ϕ β d - 1 2 β 0 n 3 d ( 1 n 2 ) .
Δ ϕ ( ν ) = 0 d ϕ ( x , ν ) d x d x ,
S j = [ x x - μ x x - μ x x 0 x z 0 ] ,
d = x x d x .
p i j = [ p 11 p 12 p 12 0 0 0 p 12 p 11 p 12 0 0 0 p 12 p 12 p 11 0 0 0 0 0 0 p 44 0 0 0 0 0 0 p 44 0 0 0 0 0 0 p 44 ] .
d ( 1 / n 2 ) i = d x L j 6 1 p i j S j ,
d ( 1 / n 2 ) z = 1 L [ p 12 - μ ( p 11 + p 12 ) ] x x d x
Δ ϕ ( ν ) = n β 0 { 1 - n 2 2 [ p 12 - μ ( p 11 + p 12 ) ] } 0 L x x ( x , ν ) d x .
0 L x x ( x , ν ) d x
x x ( x , ν ) = a ( r π L ) 2 u r sin r π L x             for ν = ν r ,
Δ ϕ ( ν ) = n β 0 { 1 - n 2 2 [ p 12 - μ ( p 11 + p 12 ) ] } 2 a r π L u r for ν = ν r 0. for ν ν r
E I 2 u ( x , t ) x 2 = - M ,
Q = d M d x = - d d x ( E I 2 u ( x , t ) x 2 ) .
[ σ x 0 τ x z 0 0 0 τ x z 0 0 ] .
σ x = M a I             τ x z = Q 2 a b .
[ x x 0 x z 0 - μ x x 0 x z 0 - μ x x ]
S j = [ x x - μ x x - μ x x 0 x z 0 ] ,
x x = M a E I             x z = Q 2 a b 2 G ,
u ( x , t ) = r q r ( t ) ψ r ( x ) ,
q ¨ r + ( 1 + i g ) ω r 2 q r = Q r ( w ) m r ,
u ( x , t ) = r Q r ( t ) exp ( i θ r ) m r ω r 2 [ ( 1 - ω 2 ω r 2 ) 2 + g 2 ] 1 / 2 ψ r ( x ) .
Q r ( t ) = sin ω t 0 L F 0 δ ( L / 2 ) ψ r ( x ) d x = F 0 ψ r ( L / 2 ) sin ω τ m r = 0 L ψ r 2 ( x ) d m = m
u ( x , t ) = F 0 sin ω t m r ψ r ( L / 2 ) ψ r ( x ) exp ( i θ r ) ω r 2 [ ( 1 - ω 2 ω r 2 ) 2 + g 2 ] 1 / 2 .
u r ( x , t ) = F 0 sin ω r t m g ω r 2 ψ r ( L / 2 ) ψ r ( x ) .
ψ r ( x ) = 2 sin K r x ,
sin K r L = 0
K r L = π , 2 π , r π
ν r = 1 2 π ( K r L ) 2 ( E I m L 3 ) 1 / 2 .
u r ( x , t ) = 2 F 0 m g ω r 2 sin r π 2 sin r π L x sin ω r t .
u r ( L / 2 ) = 2 F 0 m g ω r 2
u r ( x , t ) = u r sin r π L x sin ω r t .
x x ( x , t ) = a ( r π L ) 2 u r sin r π L x sin ω r t .

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