Abstract

We present an analysis of crosstalk in aligned and misaligned free-space optical interconnect (FSOI) systems. On the basis of a generalized diffraction integral formula, an analytical expression of irradiation distribution for FSOI systems and a convenient approach to calculate crosstalk noise signal ratios (CNSR) are proposed. Simulations are performed to analyze the factors affecting the CNSR. The analyses indicate that small beam quality factor and wide channel pitch will significantly improve performance of the FSOIs. Furthermore, the displacement of the transmitter microlens array will affect the interconnection distance much more significantly than that of the receiver microlens array.

© 2010 Optical Society of America

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References

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  1. E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, and L. A. Coldren, “Parallel free-space optical interconnect based on arrays of vertical-cavity lasers and detectors with monolithic microlenses,” Appl. Opt. 37, 2811-2821 (1998).
    [CrossRef]
  2. Y. Liu, B. Robertson, D. V. Plant, H. S. Hinton, and W. M. Robertson, “Design and characterization of a microchannel optical interconnect for optical backplanes,” Appl. Opt. 36, 3127-3141 (1997).
    [CrossRef] [PubMed]
  3. M. Châteauneuf, A. G. Kirk, D. V. Plant, T. Yamamoto, and J. D. Ahearn, “512-channel vertical-cavity surface-emitting laser-based free-space optical link,” Appl. Opt. 41, 5552-5561 (2002).
    [CrossRef] [PubMed]
  4. F. F. Tsai, C. J. O'Brien, N. S. Petrović, and A. D. Rakić, “Analysis of optical channel cross talk for free-space optical interconnects in the presence of higher-order transverse modes,” Appl. Opt. 44, 6380-6387 (2005).
    [CrossRef] [PubMed]
  5. R. Wong, A. D. Rakic, and M. L. Majewski, “Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays,” Appl. Opt. 41, 3469-3478 (2002).
    [CrossRef]
  6. N. S. Petrović and A. D. Rakić, “Modeling diffraction and imaging of laser beams by the mode-expansion method,” J. Opt. Soc. Am. B 22, 556-566 (2005).
    [CrossRef]
  7. N. S. F. Ozkan, W. L. Hendrick, P. J. Marchand, and S. C. Esener, “Misalignment tolerance analysis of free-space optical interconnects via statistical methods,” Appl. Opt. 41, 2686-2694 (2002).
    [CrossRef] [PubMed]
  8. F. Lacroix, M. Châteauneuf, X. Xue, and A. G. Kirk, “Experimental and numerical analyses of misalignment tolerances in free-space optical interconnects,” Appl. Opt. 39, 704-713 (2000).
    [CrossRef]
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    [CrossRef]
  10. X. Du and D. Zhao, “Propagation of elliptical Gaussian beams in apertured and misaligned optical systems,” J. Opt. Soc. Am. A 23, 1946-1950 (2006).
    [CrossRef]
  11. X. Lu and Y. Cai, “Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system,” Opt. Commun. 269, 39-46 (2007).
    [CrossRef]
  12. J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752-1756 (1988).
    [CrossRef]
  13. D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401-1405 (2004).
    [CrossRef]
  14. F. F. Tsai, C. J. O'Brien, N. S. Petrović, and A. D. Rakić, “Analysis of hexagonal array geometry for free-space optical interconnects with improved signal-to-noise ratio,” Appl. Opt. 46, 2434-2442 (2007).
    [CrossRef] [PubMed]
  15. N. S. Petrović and A. D. Rakić, “Channel density in free-space optical interconnects,” in Proceedings of IEEE Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2002), p. 133.

2007 (2)

X. Lu and Y. Cai, “Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system,” Opt. Commun. 269, 39-46 (2007).
[CrossRef]

F. F. Tsai, C. J. O'Brien, N. S. Petrović, and A. D. Rakić, “Analysis of hexagonal array geometry for free-space optical interconnects with improved signal-to-noise ratio,” Appl. Opt. 46, 2434-2442 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (2)

2004 (1)

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401-1405 (2004).
[CrossRef]

2002 (3)

2000 (1)

1998 (1)

1997 (1)

1988 (1)

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752-1756 (1988).
[CrossRef]

1970 (1)

Ahearn, J. D.

Bertilsson, K.

Breazeale, M. A.

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752-1756 (1988).
[CrossRef]

Cai, Y.

X. Lu and Y. Cai, “Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system,” Opt. Commun. 269, 39-46 (2007).
[CrossRef]

Châteauneuf, M.

Coldren, L. A.

Collins, S. A.

Ding, D.

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401-1405 (2004).
[CrossRef]

Du, X.

Esener, S. C.

Hendrick, W. L.

Hinton, H. S.

Kirk, A. G.

Lacroix, F.

Liu, Y.

Louderback, D. A.

Lu, X.

X. Lu and Y. Cai, “Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system,” Opt. Commun. 269, 39-46 (2007).
[CrossRef]

Majewski, M. L.

Marchand, P. J.

O'Brien, C. J.

Ozkan, N. S. F.

Petrovic, N. S.

Plant, D. V.

Rakic, A. D.

Robertson, B.

Robertson, W. M.

Strzelecka, E. M.

Thibeault, B. J.

Thompson, G. B.

Tsai, F. F.

Wen, J. J.

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752-1756 (1988).
[CrossRef]

Wong, R.

Xue, X.

Yamamoto, T.

Zhang, Y.

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401-1405 (2004).
[CrossRef]

Zhao, D.

Appl. Opt. (8)

F. Lacroix, M. Châteauneuf, X. Xue, and A. G. Kirk, “Experimental and numerical analyses of misalignment tolerances in free-space optical interconnects,” Appl. Opt. 39, 704-713 (2000).
[CrossRef]

Y. Liu, B. Robertson, D. V. Plant, H. S. Hinton, and W. M. Robertson, “Design and characterization of a microchannel optical interconnect for optical backplanes,” Appl. Opt. 36, 3127-3141 (1997).
[CrossRef] [PubMed]

E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, and L. A. Coldren, “Parallel free-space optical interconnect based on arrays of vertical-cavity lasers and detectors with monolithic microlenses,” Appl. Opt. 37, 2811-2821 (1998).
[CrossRef]

N. S. F. Ozkan, W. L. Hendrick, P. J. Marchand, and S. C. Esener, “Misalignment tolerance analysis of free-space optical interconnects via statistical methods,” Appl. Opt. 41, 2686-2694 (2002).
[CrossRef] [PubMed]

R. Wong, A. D. Rakic, and M. L. Majewski, “Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays,” Appl. Opt. 41, 3469-3478 (2002).
[CrossRef]

M. Châteauneuf, A. G. Kirk, D. V. Plant, T. Yamamoto, and J. D. Ahearn, “512-channel vertical-cavity surface-emitting laser-based free-space optical link,” Appl. Opt. 41, 5552-5561 (2002).
[CrossRef] [PubMed]

F. F. Tsai, C. J. O'Brien, N. S. Petrović, and A. D. Rakić, “Analysis of optical channel cross talk for free-space optical interconnects in the presence of higher-order transverse modes,” Appl. Opt. 44, 6380-6387 (2005).
[CrossRef] [PubMed]

F. F. Tsai, C. J. O'Brien, N. S. Petrović, and A. D. Rakić, “Analysis of hexagonal array geometry for free-space optical interconnects with improved signal-to-noise ratio,” Appl. Opt. 46, 2434-2442 (2007).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (2)

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752-1756 (1988).
[CrossRef]

D. Ding and Y. Zhang, “Notes on the Gaussian beam expansion,” J. Acoust. Soc. Am. 116, 1401-1405 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

X. Lu and Y. Cai, “Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system,” Opt. Commun. 269, 39-46 (2007).
[CrossRef]

Other (1)

N. S. Petrović and A. D. Rakić, “Channel density in free-space optical interconnects,” in Proceedings of IEEE Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2002), p. 133.

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Figures (8)

Fig. 1
Fig. 1

Schematic of misaligned optical system.

Fig. 2
Fig. 2

Schematic of single channel of misaligned FSOI system.

Fig. 3
Fig. 3

Schematic of FSOI system.

Fig. 4
Fig. 4

Normalized irradiance distributions in the front surface of receiver microlens when (a) M 2 = 1 , ϵ x = ϵ y = 0 and (b) M 2 = 2 , ϵ x = ϵ y = 10 μ m .

Fig. 5
Fig. 5

CNSR versus interconnection distance for aligned FSOI system with several different incident lasers.

Fig. 6
Fig. 6

CNSR versus interconnection distance for aligned FSOI system with several different channel pitches.

Fig. 7
Fig. 7

CNSR versus x direction displacement of transmitter microlens array and receiver microlens array.

Fig. 8
Fig. 8

CNSR growth rate versus x-direction displacement of transmitter microlens array for (a) several different interconnection distances, δ = 1 mm ; (b) several different channel pitches, l 0 = 1 cm .

Equations (27)

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E ( r 2 ) = i λ det ( B ) D E ( r 1 ) exp ( i k 2 r 1 T B 1 A r 1 ) exp [ i k 2 ( r 2 T B 1 D r 2 2 r 1 T B 1 r 2 ) ] exp [ i k 2 ( r 1 T B 1 e f + r 2 T B 1 g h ) ] d r 1 ,
A = [ a 0 0 a ] , B = [ b 0 0 b ] ,
C = [ c 0 0 c ] , D = [ d 0 0 d ] .
e = 2 ( α T ϵ x + β T θ x ) , f = 2 ( α T ϵ y + β T θ y ) ,
g = 2 ( b γ T d α T ) ϵ x + 2 ( b δ T d β T ) θ x ,
h = 2 ( b γ T d α T ) ϵ y + 2 ( b δ T d β T ) θ y .
w = w 0 1 + M 4 λ 2 f 2 π 2 w 0 4 .
E ( r 2 ) = i λ det ( B ) D E ( r 1 ) H ( r 1 ) × exp [ i k 2 ( r 1 T B 1 A r 1 + r 2 T B 1 D r 2 ) ] × exp [ i k 2 ( r 1 T B 1 e f 2 r 1 T B 1 r 2 ) ] d r 1 ,
A = [ 1 l f 0 0 1 l f ] , B = [ l 0 0 l ] .
C = [ 1 f 0 0 1 f ] , D = [ 1 0 0 1 ] .
E ( r 1 ) = exp ( i k 2 r 1 Q 1 r 1 ) ,
Q 1 = [ 2 i k w 2 0 0 2 i k w 2 ] .
H ( r 1 ) = { 1 , if r 1 is located inside the aperture 0 , if r 1 is located outside the aperture } .
H ( r 1 ) = n = 1 N A n × exp [ ( r 1 T ϵ ) T n ( r 1 ϵ ) ] ,
T n = [ B n ρ 0 2 0 0 B n ρ 0 2 ] ,
E ( r 2 ) = n = 1 10 A n det ( Q n ) exp [ i k 2 ( r 2 T B 1 Q n 1 r 2 ) ] exp [ i k 2 ( ϵ T R n ϵ + r 2 T D B 1 r 2 ) ] exp [ i k 2 ( r 2 T B 1 Q n 1 e f n ) ] exp [ i k 8 ( e f n T B 1 Q n 1 e f n ) ] .
R n = 2 i k T n ,
e f n = e f 2 B R n ϵ ,
Q n = A + B Q 1 + B R n .
1 f n = 1 f 1 i k ρ 0 2 2 B n 1 i k w 2 , 1 l = 1 i k w 2 ,
P = S E ( r 2 ) E * ( r 2 ) d r 2 = n = 0 10 m = 0 10 S E n ( r 2 ) E m * ( r 2 ) d r 2 = n = 0 10 m = 0 10 A n A m * det ( Q n ) det ( Q m * ) × S exp { i k 2 [ 1 f m l 1 f n l ] × [ r 2 ( 1 + l l ) ϵ ] T [ r 2 ( 1 + l l ) ϵ ] } d r 2 .
( x 2 ϵ x ) 2 + ( y 2 ϵ y ) 2 ρ 0 2 .
( x 2 ± δ ϵ x ) 2 + ( y 2 ϵ y ) 2 ρ 0 2 ,
( x 2 ϵ x ) 2 + ( y 2 ± δ ϵ y ) 2 ρ 0 2 .
P s = S 0 E ( r 2 ) E * ( r 2 ) d r 2
P n = S E ( r 2 ) E * ( r 2 ) d r 2 .
CNSR = P n P s .

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