Abstract

It has been shown previously that the spatial coherence of a source can be modulated and demodulated; hence it can be used as the basis for a new dimension of multiplexing in high-speed optical communication links. We address the sensitivity of such a system to misalignments of the receiver with respect to the beam and examine how changing transverse modes affect the spatial coherence in the lateral direction. Specifically, we show that such a system is surprisingly robust for both lateral offsets, in which the receiver is not properly aligned on the beam center, and rotational offsets, in which the receiver is tilted with respect to the plane of the spatial coherence modulation. The presence of higher-order transverse modes or changes in the transverse-mode structure are also shown to have little effect on the system operation.

© 1998 Optical Society of America

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References

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  1. J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
    [CrossRef]
  2. K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. 30, 337–344 (1991).
    [CrossRef]
  3. J.-P. Goedgebuer, A. Hamel, “Coherence multiplexing using a parallel array of electrooptic modulators and multimode semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 2224–2236 (1987).
    [CrossRef]
  4. J.-P. Goedgebuer, A. Hamel, H. Porte, N. Butterlin, “Analysis of optical crosstalk in coherence multiplexed systems employing a short coherence laser diode with arbitrary power spectrum,” IEEE J. Quantum Electron. 26, 1217–1226 (1990).
    [CrossRef]
  5. B. L. Anderson, L. J. Pelz, “Spatial coherence modulation for free-space communication,” Appl. Opt. 34, 7443–7450 (1995).
    [CrossRef] [PubMed]
  6. P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
    [CrossRef]
  7. L. J. Pelz, B. L. Anderson, “Practical use of the spatial coherence function for determining laser transverse mode structure,” Opt. Eng. 34, 3323–3328 (1995).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10, pp. 505–507.
  9. B. L. Anderson, P. L. Fuhr, “Twin-fiber interferometric method for measuring spatial coherence,” Opt. Eng. 32, 926–932 (1993).
    [CrossRef]

1995 (2)

B. L. Anderson, L. J. Pelz, “Spatial coherence modulation for free-space communication,” Appl. Opt. 34, 7443–7450 (1995).
[CrossRef] [PubMed]

L. J. Pelz, B. L. Anderson, “Practical use of the spatial coherence function for determining laser transverse mode structure,” Opt. Eng. 34, 3323–3328 (1995).
[CrossRef]

1993 (1)

B. L. Anderson, P. L. Fuhr, “Twin-fiber interferometric method for measuring spatial coherence,” Opt. Eng. 32, 926–932 (1993).
[CrossRef]

1991 (1)

K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. 30, 337–344 (1991).
[CrossRef]

1990 (1)

J.-P. Goedgebuer, A. Hamel, H. Porte, N. Butterlin, “Analysis of optical crosstalk in coherence multiplexed systems employing a short coherence laser diode with arbitrary power spectrum,” IEEE J. Quantum Electron. 26, 1217–1226 (1990).
[CrossRef]

1987 (1)

J.-P. Goedgebuer, A. Hamel, “Coherence multiplexing using a parallel array of electrooptic modulators and multimode semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 2224–2236 (1987).
[CrossRef]

1985 (1)

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

1980 (1)

P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
[CrossRef]

Anderson, B. L.

B. L. Anderson, L. J. Pelz, “Spatial coherence modulation for free-space communication,” Appl. Opt. 34, 7443–7450 (1995).
[CrossRef] [PubMed]

L. J. Pelz, B. L. Anderson, “Practical use of the spatial coherence function for determining laser transverse mode structure,” Opt. Eng. 34, 3323–3328 (1995).
[CrossRef]

B. L. Anderson, P. L. Fuhr, “Twin-fiber interferometric method for measuring spatial coherence,” Opt. Eng. 32, 926–932 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10, pp. 505–507.

Brooks, J. L.

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

Butterlin, N.

J.-P. Goedgebuer, A. Hamel, H. Porte, N. Butterlin, “Analysis of optical crosstalk in coherence multiplexed systems employing a short coherence laser diode with arbitrary power spectrum,” IEEE J. Quantum Electron. 26, 1217–1226 (1990).
[CrossRef]

Chu, K. W.

K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. 30, 337–344 (1991).
[CrossRef]

Dickey, F. M.

K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. 30, 337–344 (1991).
[CrossRef]

Fuhr, P. L.

B. L. Anderson, P. L. Fuhr, “Twin-fiber interferometric method for measuring spatial coherence,” Opt. Eng. 32, 926–932 (1993).
[CrossRef]

Goedgebuer, J.-P.

J.-P. Goedgebuer, A. Hamel, H. Porte, N. Butterlin, “Analysis of optical crosstalk in coherence multiplexed systems employing a short coherence laser diode with arbitrary power spectrum,” IEEE J. Quantum Electron. 26, 1217–1226 (1990).
[CrossRef]

J.-P. Goedgebuer, A. Hamel, “Coherence multiplexing using a parallel array of electrooptic modulators and multimode semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 2224–2236 (1987).
[CrossRef]

Hamel, A.

J.-P. Goedgebuer, A. Hamel, H. Porte, N. Butterlin, “Analysis of optical crosstalk in coherence multiplexed systems employing a short coherence laser diode with arbitrary power spectrum,” IEEE J. Quantum Electron. 26, 1217–1226 (1990).
[CrossRef]

J.-P. Goedgebuer, A. Hamel, “Coherence multiplexing using a parallel array of electrooptic modulators and multimode semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 2224–2236 (1987).
[CrossRef]

Kim, B. Y.

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

Pelz, L. J.

B. L. Anderson, L. J. Pelz, “Spatial coherence modulation for free-space communication,” Appl. Opt. 34, 7443–7450 (1995).
[CrossRef] [PubMed]

L. J. Pelz, B. L. Anderson, “Practical use of the spatial coherence function for determining laser transverse mode structure,” Opt. Eng. 34, 3323–3328 (1995).
[CrossRef]

Porte, H.

J.-P. Goedgebuer, A. Hamel, H. Porte, N. Butterlin, “Analysis of optical crosstalk in coherence multiplexed systems employing a short coherence laser diode with arbitrary power spectrum,” IEEE J. Quantum Electron. 26, 1217–1226 (1990).
[CrossRef]

Shaw, H. J.

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

Spano, P.

P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
[CrossRef]

Tur, M.

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

Wentworth, R. H.

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10, pp. 505–507.

Youngquist, R. C.

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

J.-P. Goedgebuer, A. Hamel, “Coherence multiplexing using a parallel array of electrooptic modulators and multimode semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 2224–2236 (1987).
[CrossRef]

J.-P. Goedgebuer, A. Hamel, H. Porte, N. Butterlin, “Analysis of optical crosstalk in coherence multiplexed systems employing a short coherence laser diode with arbitrary power spectrum,” IEEE J. Quantum Electron. 26, 1217–1226 (1990).
[CrossRef]

J. Lightwave Technol. (1)

J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, H. J. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. LT-3, 1062–1071 (1985).
[CrossRef]

Opt. Commun. (1)

P. Spano, “Connection between spatial coherence and modal structure in optical fibers and semiconductor lasers,” Opt. Commun. 33, 265–270 (1980).
[CrossRef]

Opt. Eng. (3)

L. J. Pelz, B. L. Anderson, “Practical use of the spatial coherence function for determining laser transverse mode structure,” Opt. Eng. 34, 3323–3328 (1995).
[CrossRef]

K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. 30, 337–344 (1991).
[CrossRef]

B. L. Anderson, P. L. Fuhr, “Twin-fiber interferometric method for measuring spatial coherence,” Opt. Eng. 32, 926–932 (1993).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10, pp. 505–507.

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Figures (9)

Fig. 1
Fig. 1

Electro-optic modulator used to change the number of spatial modes of a beam.

Fig. 2
Fig. 2

SCF |μ(x, -x)| as a function of x, the distance from the beam center. Solid line: Only one spatial mode is present. Dashed curve: Two modes are present in equal weights. The spot size σ is measured at the 1/e 2 intensity point of the fundamental mode.

Fig. 3
Fig. 3

Electro-optic demodulator device as an interferometer that measures the visibility corresponding to the SCF |μ(x, -x)|.

Fig. 4
Fig. 4

Signals of a spatial-coherence-multiplexed link. The voltage applied to the receiver increases linearly, so that fringes (top signal) appear at the receiver output when there is coherence (first half of SCF signal). The intensity varies from high to low (not zero), as shown in the second line of the figure. The resulting detected signal shows bright and dim fringes when the SCF equals 1, and it shows bright and dim light with no fringes when the SCF equals zero.

Fig. 5
Fig. 5

Geometry for lateral misalignment of the receiver.

Fig. 6
Fig. 6

Effect of lateral offsets on the spatial coherence and visibility (a) when one lateral mode is present and (b) when two lateral modes are present in equal weights. (c) The resulting extinction ratio. The extinction ratio exceeds 1 for some misalignments because the visibility for logic 0 can exceed the visibility for logic 1 for some misalignments.

Fig. 7
Fig. 7

Rotational misalignment geometry. Open circles indicate the locations of intended measurements; filled circles indicate the actual measurement locations.

Fig. 8
Fig. 8

Effect of tilt misalignment on the extinction ratio.

Fig. 9
Fig. 9

Close-up of the effect of higher-order transverse (y-dependent) modes on one of the SCF zeros. The tilt angle is 10°; the strengths of the TEM00 and TEM10 modes are equal in all cases. The left-most curve is for the case in which none of the energy is in the TEM01 mode.

Equations (9)

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E ( x ,   y ,   t ) = n m   a n a m f n ( x ) f m ( y ) × exp { i [ ω t + ϕ n t + ϕ m t ] } ,
I ( r 1 ,   r 2 ) = [ E ( x 1 ,   y 1 ,   t ) + E ( x 2 ,   y 2 ,   t + τ ) ]   *   [ E ( x 1 ,   y 1 ,   t ) + E ( x 2 ,   y 2 ,   t + τ ) ] = ( n m   a n a m f n ( x 1 ) f m ( y 1 ) exp { i [ ω t + ϕ n ( t ) + ϕ m ( t ) ] } n m   a n a m f n ( x 2 ) f m ( y 2 ) exp { i [ ω ( t + τ ) + ϕ n ( t + τ ) + ϕ m ( t + τ ) ] } ) c . c . = n m   a n 2 a m 2 f n 2 ( x 1 ) f m 2 ( y 1 ) + n m   a n 2 a m 2 f n 2 ( x 2 ) f m 2 ( y 2 ) + 2   Re n m   a n 2 a m 2 f n ( x 1 ) f n ( x 2 ) f m ( y 1 ) f m ( y 2 ) exp ( i ω τ ) ,
2 I 1 I 2   | μ r 1 ,   r 2 | cos ω τ ,
| μ ( r 1 ,   r 2 ) | = n m   a n 2 a m 2 f n ( x 1 ) f n ( x 2 ) f m ( y 1 ) f m ( y 2 ) [ n m   a n 2 a m 2 f n 2 ( x 1 ) f m 2 ( y 1 ) n m   a n 2 a m 2 f n 2 ( x 2 ) f m 2 ( y 2 ) ] 1 / 2 .
V = I max - I min I max + I min = 2 I 1 r 1 I 2 r 2 I 1 r 1 + I 2 r 2   | μ r 1 ,   r 2 | .
| μ ( x 1 ,   y 1 ;   - x 1 ,   y 1 ) | = n   a n 2 f n ( x 1 ) f n ( - x 1 ) m   a m 2 f m 2 ( y 1 ) [ n   a n 2 f n 2 ( x 1 ) ] 1 / 2 [ n   a n 2 f n 2 ( - x 1 ) ] 1 / 2 m   a m 2 f m 2 ( y 1 ) = n   a n 2 f n ( x 1 ) f n ( - x 1 ) [ n   a n 2 f n 2 ( x 1 ) ] 1 / 2 [ n   a n 2 f n 2 ( - x 1 ) ] 1 / 2 .
= V 0 V 1 ,
x 2 = x 1 cos   θ ,
y 2 = x 1 sin   θ .

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