Abstract

A specklegram in a multimode fiber (MMF) has successfully been used as a sensor for detecting external disturbance. Our experiments showed that the sensitivity in the sensor with a multiple longitudinal-mode laser as its source was much higher than that with a single longitudinal-mode laser. In addition, the near-field pattern observations indicated that the coupling between different transverse modes in the MMF is quite weak. Based on the experimental results, a theoretical model for the speckle formation is proposed, taking a bend-caused phase factor into consideration. It is shown in the theoretical analysis that the interferences between different longitudinal modes make a larger contribution to the specklegram signals.

© 2007 Optical Society of America

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References

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1997

1996

1995

1994

1993

1991

1989

Anderson, D. Z.

Bolshtyansky, M. A.

Cheng, F.

Erdogan, T.

Fuhr, P. L.

Gafsi, R.

Kline, B. R.

Labarre, M.

Lecoy, P.

Malki, A.

Maurice, L. B.

Michel, L.

Pan, K.

Ruffin, P. B.

Spillman, W. B.

Uang, C.-M.

Wen, M.

Wu, S.

Yin, S.

Yu, F. T. S.

Zel'dovich, B. Ya.

Zhang, J.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Lett.

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Figures (9)

Fig. 1
Fig. 1

Experimental setup of a SMF-MMF-SMF sensing configuration.

Fig. 2
Fig. 2

Spectrum of (a) a 1310 nm fewer-mode laser and (b) a 1550   nm single-mode laser.

Fig. 3
Fig. 3

(Color online) Output voltage versus vibration amplitude of 1310 and 1550   nm laser diodes.

Fig. 4
Fig. 4

(Color online) Measured signal varied with vibration amplitude.

Fig. 5
Fig. 5

(Color online) Near-field patterns observed in two different connection ways: (a) tight connection; (b) loose connection with a small gap of 1 m m .

Fig. 6
Fig. 6

Schematic denoting optical fields at different locations.

Fig. 7
Fig. 7

Additive phase caused by fiber bending.

Fig. 8
Fig. 8

(Color online) Normalized field distributions for the SMF L P 0 l mode (curve a), and the five coupled modes in MMFs (curves b–f).

Fig. 9
Fig. 9

(Color online) Calculated relative output versus disturbance amplitude, taking into account (a) a single longitudinal mode with transverse modes, and (b–d) 2, 3, and 4 longitudinal modes with the same transverse mode.

Equations (85)

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62.5   μm
9   μm
50   Hz
1310   nm
1550   nm
D = 100   mm
6   mm
6   μm
50   μm
650   nm
200   m
150   mm
220   mm
1   mm
9   μm
10   mm
1   mm
200   m
1 .5   m
I i = A i { 1 + B i [ cos δ i F ( t ) ϕ i sin δ i ] } ,
F ( t )
δ ( Δ β m l z ) F ( t )
I i
Δ I m , n sin [ ϕ 0 m ϕ 0 n + Δ ϕ 0 m Δ ϕ 0 n ] × sin [ Δ ϕ 0 m Δ ϕ 0 n ] ,
ϕ 0 i
Δ ϕ 0 i
( x , y )
E 1
E 2
E 3
E 4
E 1
E 4
L P 01
f ( r , θ )
E 2
g m n
E 2 ( r , θ ) = m , n a m n g m n ( r , θ ) ,
a m n = f ( r , θ ) g m n ( r , θ ) r d r d θ
L P 01
L P 0 l
E 2 ( r , θ ) = l a l g 0 l ( r , θ ) .
E 3 ( r , θ ) = l b l g 0 l ( r , θ ) exp ( i β 0 l L ) .
b l = ( a l + Δ a l ) exp i δ l ,
Δ a l
δ l
| E 3 | 2 ( r , θ ) = l ( a l + Δ a l ) 2 | g 0 l | 2 + l m ( a l + Δ a l ) × ( a m * + Δ a m * ) g 0 l g 0 m * exp [ i ( β l L β m L + δ l δ m ) ] l a l 2 | g 0 l | 2 + l m a l a m * g 0 l g 0 m * × exp [ i ( β l L β m L + δ l δ m ) ] .
I 4 = η { l a l 2 S M F | g 0 l | 2 d A + l m a l a m * × exp [ i ( β l L β m L + δ l δ m ) ] S M F g 0 l g 0 m * d A } .
Δ ϕ ( x )
Δ ϕ ( x , y ) = 2 π n λ D R ( x cos φ + y sin φ ) 2 π n λ 8 h D ( x cos φ + y sin φ ) ,
Δ ϕ ( x , y ) = 16 π n λ i h i D i ( x cos φ i + y sin φ i ) .
10   μm
φ = 0
E 3 ( r , θ ) = l b l g 0 l ( r , θ ) exp i [ β 0 l L + Δ ϕ 0 l ( x ) ] ,
| E 3 | 2 = l , m b l b m * g 0 l g 0 m * exp i [ ( β 0 l β 0 m ) × L + ( Δ ϕ 0 l Δ ϕ 0 m ) ] = l , m b l b m * g 0 l g 0 m * exp i [ ( β 0 l β 0 m ) × ( L + 8 x h / D ) ] ,
I 4 = η { l , m b l b m * exp [ i ( β 0 l β 0 m ) L ] S M F g 0 l g 0 m * × exp [ i 8 ( β 0 l β 0 m ) x h / D ] d A } l , m b l b m * S M F g 0 l g 0 m * cos ( 8 Δ β l m x h / D ) d A .
g ( r , θ )
L P 0 l
L P 0 l
Δ ϕ 0 l ( λ p ) Δ ϕ 0 l ( λ q ) = 16 π n 0 l ( 1 λ p 1 λ q ) x h D 16 π n 0 l x h Δ λ λ p λ q D ,
Δ λ
Δ λ
n 0 l
| E 3 | 2 l , p , q b l ( λ p ) b l * ( λ q ) | g 0 l ( r , θ ) | 2 cos 16 π n 0 l x h Δ λ λ p λ q D ,
I 4 l , p , q b l ( λ p ) b l * ( λ q ) S M F | g 0 l | 2 cos 16 π n 0 l x h Δ λ λ p λ q D  d A .
g 0 l
g 0 m
16 π n 0 l x h Δ λ / ( λ 2 D )
16 π ( n 0 l n 0 m ) x h / ( λ D )
n 0 l Δ λ / ( n 0 l n 0 m ) λ
L P 0 l
62.5   μm
L P 01
a 01 = 0.486
a 02 = 0.564
a 03 = 0.474
a 04 = 0.348
a 05 = 0.228
E H 1 l ( L P 2 l )
H E 1 l ( L P 0 l )
Δ I 4 / I 4
1550   nm
1550   nm
1 m m
L P 0 l

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