Abstract

A method for detecting sound using a single step-index multimode fiber is presented. The detected signal results from differences in acoustically induced phase shifts between two different waveguide modes propagating in the fiber. The relative sensitivity of this technique compared with a two-path interferometer was experimentally determined and agreed with that calculated using the fiber parameters. Because the sensitivity of this approach is proportional to the difference in propagation constants for modes in the fiber, it is approximately 10−3 less sensitive than the single-mode interferometer arrangement.

© 1979 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Bucaro, H. D. Dardy, E. F. Carome, Appl. Opt. 16, 1761 (1977).
    [Crossref] [PubMed]
  2. J. H. Cole, R. L. Johnson, P. G. Bhuta, J. Acoust. Soc. Am. 62, 1136 (1977).
    [Crossref]
  3. J. A. Bucaro, H. D. Dardy, E. F. Carome, J. Acoust. Soc. Am. 62, 1302 (1977).
    [Crossref]
  4. E. Snitzer, J. Opt. Soc. Am. 51, 494 (1961).
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 33.
  6. N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972), pp. 164–179, 205–222.
  7. D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), p. 11.
  8. E. Snitzer, H. Osterberg, J. Opt. Soc. Am. 51, 500 (1961).
  9. J. A. Bucaro, E. F. Carome, Appl. Opt. 17, 330 (1978).
    [Crossref] [PubMed]

1978 (1)

1977 (3)

J. A. Bucaro, H. D. Dardy, E. F. Carome, Appl. Opt. 16, 1761 (1977).
[Crossref] [PubMed]

J. H. Cole, R. L. Johnson, P. G. Bhuta, J. Acoust. Soc. Am. 62, 1136 (1977).
[Crossref]

J. A. Bucaro, H. D. Dardy, E. F. Carome, J. Acoust. Soc. Am. 62, 1302 (1977).
[Crossref]

1961 (2)

E. Snitzer, J. Opt. Soc. Am. 51, 494 (1961).

E. Snitzer, H. Osterberg, J. Opt. Soc. Am. 51, 500 (1961).

Bhuta, P. G.

J. H. Cole, R. L. Johnson, P. G. Bhuta, J. Acoust. Soc. Am. 62, 1136 (1977).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 33.

Bucaro, J. A.

Burke, J. J.

N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972), pp. 164–179, 205–222.

Carome, E. F.

Cole, J. H.

J. H. Cole, R. L. Johnson, P. G. Bhuta, J. Acoust. Soc. Am. 62, 1136 (1977).
[Crossref]

Dardy, H. D.

J. A. Bucaro, H. D. Dardy, E. F. Carome, Appl. Opt. 16, 1761 (1977).
[Crossref] [PubMed]

J. A. Bucaro, H. D. Dardy, E. F. Carome, J. Acoust. Soc. Am. 62, 1302 (1977).
[Crossref]

Johnson, R. L.

J. H. Cole, R. L. Johnson, P. G. Bhuta, J. Acoust. Soc. Am. 62, 1136 (1977).
[Crossref]

Kapany, N. S.

N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972), pp. 164–179, 205–222.

Keck, D. B.

D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), p. 11.

Osterberg, H.

E. Snitzer, H. Osterberg, J. Opt. Soc. Am. 51, 500 (1961).

Snitzer, E.

E. Snitzer, H. Osterberg, J. Opt. Soc. Am. 51, 500 (1961).

E. Snitzer, J. Opt. Soc. Am. 51, 494 (1961).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 33.

Appl. Opt. (2)

J. Acoust. Soc. Am. (2)

J. H. Cole, R. L. Johnson, P. G. Bhuta, J. Acoust. Soc. Am. 62, 1136 (1977).
[Crossref]

J. A. Bucaro, H. D. Dardy, E. F. Carome, J. Acoust. Soc. Am. 62, 1302 (1977).
[Crossref]

J. Opt. Soc. Am. (2)

E. Snitzer, J. Opt. Soc. Am. 51, 494 (1961).

E. Snitzer, H. Osterberg, J. Opt. Soc. Am. 51, 500 (1961).

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 33.

N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972), pp. 164–179, 205–222.

D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), p. 11.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

The relationship between the propagation constant β and the mode type, as a function of the V-value of the fiber.7

Fig. 2
Fig. 2

Schematic drawing showing the direction of the transverse electric field for four of the lowest waveguide modes.

Fig. 3
Fig. 3

Calculated spatial variation of the magnitude of the interference term on the fiber endface for a combination of HE11 and HE12 modes in a V = 4 fiber. The intensity in the image is proportional to the magnitude. The dashed line indicates the core radius.

Fig. 4
Fig. 4

Calculated variation of the HE11 mode and HE12 mode intensity, as well as the magnitude of the interference term across one diameter: (a) magnitude of the interference term; (b) HE11 mode intensity; (c) HE12 mode intensity. The power carried in the HE11 and HE12 modes is equal.

Fig. 5
Fig. 5

Spatial variation of the magnitude of the interference term on the fiber endface for a combination of HE11 and TM01 modes in a V = 4 fiber. The intensity is proportional to the magnitude, and the dashed line indicates the core radius.

Fig. 6
Fig. 6

Calculated variation of the HE11 and TM01 mode intensity, as well as the magnitude of the interference terms, across one diameter: (a) magnitude of the interference term; (b) HE11 mode intensity; (c) TM01 mode intensity. The power carried in the HE11 and TM01 modes is equal.

Fig. 7
Fig. 7

Experimental frequency spectrum of the mode-mode beat signal. The sound frequency fs is 23.3 kHz. The signals near zero frequency are due to electronic and mechanical noise.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

ϕ i = β i l + ψ i ,
ϕ i ( t ) = [ ( β i P ) l + β i ( l P ) ] P sin ω s t ϕ i sin ω s t .
E 1 ( ρ , θ , t ) = E 1 ( ρ , θ ) exp [ i ( β 1 l - ω t ) + i ψ 1 ] H 1 ( ρ , θ , t ) = H 1 ( ρ , θ ) exp [ i ( β 1 l - ω t ) + i ψ 1 ] E 2 ( ρ , θ , t ) = E 2 ( ρ , θ ) exp [ i ( β 2 l - ω t ) + i ψ 2 ] H 2 ( ρ , θ , t ) = H 2 ( ρ , θ ) exp [ i ( β 2 l - ω t ) + i ψ 2 ] } .
A m ( ρ , θ , t ) = A m ( ρ , θ ) exp i ( β m l - ω t + ψ m + ϕ m sin ω s t ) .
I ( ρ , θ , t ) = I 1 ( ρ , θ ) + I 2 ( ρ , θ ) + ½ { [ E 1 ( ρ , θ ) × H 2 * ( ρ , θ ) ] exp i ( Δ β l + Δ ψ ) + [ E 2 ( ρ , θ ) × H 1 * ( ρ , θ ) ] exp - i ( Δ β l + Δ ψ ) } · ( cos Δ ψ + l Δ β ) [ J 0 ( Δ ϕ ) + 2 k = 1 J 2 k ( Δ ϕ ) cos ( 2 k ω s t ) ] - sin ( Δ ψ + l Δ β ) { 2 k = 0 J 2 k + 1 ( Δ ϕ ) sin [ ( 2 k + 1 ) ω s t ] } ) ,
I 1 = ½ ( E 1 × H 1 * ) ,             I 2 = ½ ( E 2 × H 2 * ) , Δ ψ = ψ 1 - ψ 2 ,             Δ ϕ = ϕ 1 - ϕ 2 ,             Δ β = β 1 - β 2 ,
I ( ρ , θ , t ) = I 1 ( ρ , θ ) + I 2 ( ρ , θ ) + ½ { [ E 1 ( ρ , θ ) × H 2 * ( ρ , θ ) ] exp i Δ β l + [ E 2 ( ρ , θ ) × H 1 * ( ρ , θ ) ] exp - i Δ β l } · [ cos ( Δ ψ + l Δ β ) - Δ ϕ sin ( Δ ψ + l Δ β ) sin ω s t ] .
Δ ϕ = Δ β ( 1 l l P ) l P ,
Δ ϕ max = k ( n c o - n c l ) ( 1 l l P ) l P .
Δ ϕ ϕ = Δ β β 1 l l P ( 1 l l P + 1 β β P ) .
I ( t ) = 2 cos ( Δ ψ + Δ β ) [ k = 1 J 2 k ( Δ ϕ ) cos 2 k ω s t ] - 2 sin ( Δ ψ + Δ β ) [ k = 0 J 2 k + 1 ( Δ ϕ ) sin ( 2 k + 1 ) ω s t ] .

Metrics