Abstract

The effect of transmitter and receiver array configurations on the performance of free-space optical interconnects (FSOIs) was investigated. Experimentally measured, spectrally resolved, near-field images of vertical-cavity surface-emitting laser (VCSEL) transverse modes were used as extended sources in our simulation model and combined with laser relative intensity noise and the receiver noise to determine the optimal array geometry. Our results demonstrate the importance of stray-light cross talk in both square and hexagonal configurations. By changing the array lattice geometry from square to hexagonal, we obtained an overall optical signal-to-noise ratio improvement of 3  dB. We demonstrated that the optical signal-to-noise ratio is optimal for the hexagonal channel arrangement regardless of the transverse mode structure of the VCSEL beam. We also determined the VCSEL drive current required for the best performance of the FSOI system.

© 2007 Optical Society of America

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References

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  1. D. A. B. Miller, "Invited paper: Physical reasons for optical interconnection," Int. J. Optoelectron. 11, 155-168 (1997).
  2. D. A. B. Miller, "Rationale and challenges for optical interconnects to electronic chips," Proc. IEEE 88, 728-749 (2000).
    [CrossRef]
  3. D. V. Plant and A. G. Kirk, "Optical interconnects at the chip and board level: challenges and solutions," Proc. IEEE 88, 806-818 (2000).
    [CrossRef]
  4. D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
    [CrossRef]
  5. N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
    [CrossRef]
  6. K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
    [CrossRef]
  7. R. H. Havemann and J. A. Hutchby, "High-performance interconnects: An integration overview," Proc. IEEE 89, 586-601 (2001).
    [CrossRef]
  8. 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).
  9. M. W. Haney, M. P. Christensen, P. Milojkovic, J. Ekman, P. Chandramani, R. Rozier, F. Kiamilev, Y. Liu, and M. Hibbs-Brenner, "Multichip free-space global optical interconnection demonstration with integrated arrays of vertical-cavity surface-emitting lasers and photodetectors," Appl. Opt. 38, 6190-6200 (1999).
  10. E. M. Strzelecka, D. A. Louderback, B. J. Thibeault, G. B. Thompson, K. Bertilsson, and L. A. Coldren, "Parallel free-space optical interconect based on arrays of vertical-cavity lasers and detectors with monolithic microlenses," Appl. Opt. 37, 2811-2821 (1998).
  11. 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).
  12. R. Wong, A. D. Rakic, and M. L. Majewski, "Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers," Opt. Commun. 167, 261-271 (1999).
    [CrossRef]
  13. X. Zheng, P. J. Marchand, D. Huang, and S. C. Esener, "Free-space parallel multichip interconnection system," Appl. Opt. 39, 3516-3524 (2000).
  14. N. S. Petrovic and A. D. Rakic, "Modeling diffraction in free-space optical interconnects by the mode expansion method," Appl. Opt. 42, 5308-5318 (2003).
  15. X. Zheng, P. J. Marchand, D. Huang, O. Kibar, and S. C. Esener, "Cross talk and ghost talk in a microbeam free-space optical interconnect system with vertical-cavity surface-emitting lasers, microlens, and metal-semiconductor-metal detectors," Appl. Opt. 39, 4834-4841 (2000).
  16. 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).
  17. F.-C. F. Tsai, C. J. O'Brien, and A. D. Rakic, "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]
  18. N. S. Petrović, A. D. Rakić, and M. L. Majewski, "Free-space optical interconnect with improved signal-to-noise ratio," in Proceedings of the 27th European Conference on Optical Communication (ECOC, 2001), Vol. 13, pp. 292-293.
  19. G. Keiser, Optical Fiber Communications (McGraw-Hill, 2000).
  20. D. Derickson,Fiber Optic Test and Measurement (Prentice Hall PTR, 1998).
  21. A. E. Siegman, Lasers (University Science Books, 1986).
  22. K. Petermann, Laser Diode Modulation and Noise (KTK Scientific Publishers, 1991).

2005

2003

2002

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).

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).

K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
[CrossRef]

2001

R. H. Havemann and J. A. Hutchby, "High-performance interconnects: An integration overview," Proc. IEEE 89, 586-601 (2001).
[CrossRef]

2000

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).

D. A. B. Miller, "Rationale and challenges for optical interconnects to electronic chips," Proc. IEEE 88, 728-749 (2000).
[CrossRef]

D. V. Plant and A. G. Kirk, "Optical interconnects at the chip and board level: challenges and solutions," Proc. IEEE 88, 806-818 (2000).
[CrossRef]

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
[CrossRef]

X. Zheng, P. J. Marchand, D. Huang, and S. C. Esener, "Free-space parallel multichip interconnection system," Appl. Opt. 39, 3516-3524 (2000).

X. Zheng, P. J. Marchand, D. Huang, O. Kibar, and S. C. Esener, "Cross talk and ghost talk in a microbeam free-space optical interconnect system with vertical-cavity surface-emitting lasers, microlens, and metal-semiconductor-metal detectors," Appl. Opt. 39, 4834-4841 (2000).

1999

1998

1997

D. A. B. Miller, "Invited paper: Physical reasons for optical interconnection," Int. J. Optoelectron. 11, 155-168 (1997).

Ahearn, J. D.

Allerman, A. A.

K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
[CrossRef]

Bartelt, H.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Bertilsson, K.

Chandramani, P.

Châteauneuf, M.

Choquette, K. D.

K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
[CrossRef]

Christensen, M. P.

Coldren, L. A.

Derickson, D.

D. Derickson,Fiber Optic Test and Measurement (Prentice Hall PTR, 1998).

Ekman, J.

Erhard, W.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Esener, S. C.

Fey, D.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Geib, K. M.

K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
[CrossRef]

Grimm, G.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Gruber, M.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Haney, M. W.

Hargett, T. W.

K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
[CrossRef]

Havemann, R. H.

R. H. Havemann and J. A. Hutchby, "High-performance interconnects: An integration overview," Proc. IEEE 89, 586-601 (2001).
[CrossRef]

Hibbs-Brenner, M.

Hoppe, L.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Huang, D.

Hutchby, J. A.

R. H. Havemann and J. A. Hutchby, "High-performance interconnects: An integration overview," Proc. IEEE 89, 586-601 (2001).
[CrossRef]

Ishikawa, M.

N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
[CrossRef]

Jahns, J.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Keiser, G.

G. Keiser, Optical Fiber Communications (McGraw-Hill, 2000).

Kiamilev, F.

Kibar, O.

Kirk, A. G.

Kobayashi, Y.

N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
[CrossRef]

Lacroix, F.

Liu, Y.

Louderback, D. A.

Majewski, M. L.

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).

R. Wong, A. D. Rakic, and M. L. Majewski, "Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers," Opt. Commun. 167, 261-271 (1999).
[CrossRef]

N. S. Petrović, A. D. Rakić, and M. L. Majewski, "Free-space optical interconnect with improved signal-to-noise ratio," in Proceedings of the 27th European Conference on Optical Communication (ECOC, 2001), Vol. 13, pp. 292-293.

Marchand, P. J.

McArdle, N.

N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, "Rationale and challenges for optical interconnects to electronic chips," Proc. IEEE 88, 728-749 (2000).
[CrossRef]

D. A. B. Miller, "Invited paper: Physical reasons for optical interconnection," Int. J. Optoelectron. 11, 155-168 (1997).

Milojkovic, P.

Naruse, M.

N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
[CrossRef]

O'Brien, C. J.

Petermann, K.

K. Petermann, Laser Diode Modulation and Noise (KTK Scientific Publishers, 1991).

Petrovic, N. S.

N. S. Petrovic and A. D. Rakic, "Modeling diffraction in free-space optical interconnects by the mode expansion method," Appl. Opt. 42, 5308-5318 (2003).

N. S. Petrović, A. D. Rakić, and M. L. Majewski, "Free-space optical interconnect with improved signal-to-noise ratio," in Proceedings of the 27th European Conference on Optical Communication (ECOC, 2001), Vol. 13, pp. 292-293.

Plant, D. V.

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).

D. V. Plant and A. G. Kirk, "Optical interconnects at the chip and board level: challenges and solutions," Proc. IEEE 88, 806-818 (2000).
[CrossRef]

Rakic, A. D.

F.-C. F. Tsai, C. J. O'Brien, and A. D. Rakic, "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]

N. S. Petrovic and A. D. Rakic, "Modeling diffraction in free-space optical interconnects by the mode expansion method," Appl. Opt. 42, 5308-5318 (2003).

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).

R. Wong, A. D. Rakic, and M. L. Majewski, "Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers," Opt. Commun. 167, 261-271 (1999).
[CrossRef]

N. S. Petrović, A. D. Rakić, and M. L. Majewski, "Free-space optical interconnect with improved signal-to-noise ratio," in Proceedings of the 27th European Conference on Optical Communication (ECOC, 2001), Vol. 13, pp. 292-293.

Rozier, R.

Serkland, D. K.

K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Sinzinger, S.

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

Strzelecka, E. M.

Thibeault, B. J.

Thompson, G. B.

Toyoda, H.

N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
[CrossRef]

Tsai, F.-C. F.

Wong, R.

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).

R. Wong, A. D. Rakic, and M. L. Majewski, "Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers," Opt. Commun. 167, 261-271 (1999).
[CrossRef]

Xue, X.

Yamamoto, T.

Zheng, X.

Appl. Opt.

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).

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

M. W. Haney, M. P. Christensen, P. Milojkovic, J. Ekman, P. Chandramani, R. Rozier, F. Kiamilev, Y. Liu, and M. Hibbs-Brenner, "Multichip free-space global optical interconnection demonstration with integrated arrays of vertical-cavity surface-emitting lasers and photodetectors," Appl. Opt. 38, 6190-6200 (1999).

X. Zheng, P. J. Marchand, D. Huang, and S. C. Esener, "Free-space parallel multichip interconnection system," Appl. Opt. 39, 3516-3524 (2000).

X. Zheng, P. J. Marchand, D. Huang, O. Kibar, and S. C. Esener, "Cross talk and ghost talk in a microbeam free-space optical interconnect system with vertical-cavity surface-emitting lasers, microlens, and metal-semiconductor-metal detectors," Appl. Opt. 39, 4834-4841 (2000).

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).

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).

N. S. Petrovic and A. D. Rakic, "Modeling diffraction in free-space optical interconnects by the mode expansion method," Appl. Opt. 42, 5308-5318 (2003).

F.-C. F. Tsai, C. J. O'Brien, and A. D. Rakic, "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]

IEEE J. Sel. Top. Quantum Electron.

K. M. Geib, K. D. Choquette, D. K. Serkland, A. A. Allerman, and T. W. Hargett, "Fabrication and performance of two-dimensional matrix addressable arrays of integrated vertical-cavity lasers and resonants cavity photodetectors," IEEE J. Sel. Top. Quantum Electron. 8, 943-947 (2002).
[CrossRef]

Int. J. Optoelectron.

D. A. B. Miller, "Invited paper: Physical reasons for optical interconnection," Int. J. Optoelectron. 11, 155-168 (1997).

Opt. Commun.

R. Wong, A. D. Rakic, and M. L. Majewski, "Analysis of lensless free-space optical interconnects based on multi-transverse mode vertical-cavity-surface-emitting lasers," Opt. Commun. 167, 261-271 (1999).
[CrossRef]

Proc. IEEE

D. A. B. Miller, "Rationale and challenges for optical interconnects to electronic chips," Proc. IEEE 88, 728-749 (2000).
[CrossRef]

D. V. Plant and A. G. Kirk, "Optical interconnects at the chip and board level: challenges and solutions," Proc. IEEE 88, 806-818 (2000).
[CrossRef]

D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, "Optical interconnects for neural and reconfigurable VLSI architecture," Proc. IEEE 88, 838-847 (2000).
[CrossRef]

N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, "Reconfigurable optical interconnections for parallel computing," Proc. IEEE 88, 829-837 (2000).
[CrossRef]

R. H. Havemann and J. A. Hutchby, "High-performance interconnects: An integration overview," Proc. IEEE 89, 586-601 (2001).
[CrossRef]

Other

N. S. Petrović, A. D. Rakić, and M. L. Majewski, "Free-space optical interconnect with improved signal-to-noise ratio," in Proceedings of the 27th European Conference on Optical Communication (ECOC, 2001), Vol. 13, pp. 292-293.

G. Keiser, Optical Fiber Communications (McGraw-Hill, 2000).

D. Derickson,Fiber Optic Test and Measurement (Prentice Hall PTR, 1998).

A. E. Siegman, Lasers (University Science Books, 1986).

K. Petermann, Laser Diode Modulation and Noise (KTK Scientific Publishers, 1991).

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Figures (10)

Fig. 1
Fig. 1

(Color online) Schematic of a microchannel free-space optical interconnect.

Fig. 2
Fig. 2

Structure of the transmitter and the receiver microlens arrays in (a) square configuration and (b) hexagonal configuration.

Fig. 3
Fig. 3

(Color online) Schematic of a free-space optical interconnect showing (a) diffraction-caused cross talk and (b) stray-light cross talk.

Fig. 4
Fig. 4

Experimental setup used to measure the VCSEL optical spectrum and the spectrally resolved and polarization-resolved beam profiles. Spatial scanning of the beam profile in the XY plane was implemented using a single-mode fiber and an actuator.

Fig. 5
Fig. 5

Experimental setup for RIN measurement.

Fig. 6
Fig. 6

Measured RIN spectra for VCSEL drive currents between 4 and 12   mA .

Fig. 7
Fig. 7

Comparison of the optical SNR including DCCN only and a combined noise of DCCN and SLCN with increasing array geometry offset value. Different transverse modes are shown: (a) LG 00 , (b) LG 01 , (c) LG 10 , (d) LG 02 .

Fig. 8
Fig. 8

Optical SNR ratio with increasing interconnect density ( c h a n n e l s / m m 2 ) for different transverse modes.

Fig. 9
Fig. 9

Optical SNR with increasing interconnection distance for different transverse modes.

Fig. 10
Fig. 10

SNR with increasing VCSEL drive current for different interconnect pitch values and receiver bandwidths.

Tables (1)

Tables Icon

Table 1 Parameter Values Used in the Simulation

Equations (75)

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

3   dB
3   dB
z = 0
z = d 1
d 2 + d 3
d 4 = d 1
d 2
d 3
β = D / Δ
1 / Δ 2
L = d 1 + d 2 + d 3 + d 4
OSNR = 10 log 10 S N = 10 log 10 S SLCN + DCCN ,
SNR 10 log 10 X 2 ( R S ) 2 RIN ( R S + R N ) 2 B + 2 q ( R S + R N + I d ) B + ( 4 k B T / R e q ) B F t + X 2 ( R N ) 2 .
I d
F t
k B
R e q
X = ( ER 1 ) / ( ER + 1 )
( Δ / 2 )
ω 0
d 2
{ LG n m ( r , θ , z ) LG n m * ( r , θ , z ) } = K n m ( r 2 w ( z ) ) m L n ( m ) ( 2 r 2 w ( z ) 2 ) × exp ( r 2 w ( z ) 2 j k r 2 2 R ( z ) ) { cos ( m θ ) sin ( m θ ) } ,
K n m = A n m N n m ,
A n m = exp { j [ ( 2 n + m + 1 ) arctan λ ( z z s ) π w s 2 k ( z z s ) ] } ,
N n m = 2 w ( z ) π ( 1 + δ o m ) [ n ! ( n + m ) ! ] 1 / 2 .
k = 2 π / λ
z R = 1 2 k w s 2
w s
z = z s = 0
w ( z ) = w s 1 + ( z z R ) 2 ,
R ( z ) = z [ 1 + ( z R z ) 2 ] .
( 2 n + m )
( n , m > 0 )
7 × I t h
I t h
( 7 × I t h )
I t h
7 × I t h
15 × 15
LG 00
LG 01
LG 02
LG 10 + LG 02
δ P ( t )
R I N = δ P 2 P 2 .
114
126
130
136 dB / Hz
12   mA
64 × 64
LG 00
LG 01
LG 10
LG 02
101 × 101
12   mm
250   μm
LG 01
( LG 01 )
LG 00
8   mm
LG 01
LG 00
200   μm
3   dB
LG 00
LG 01
LG 10 + LG 02
12   mA
LG 00
LG 01
LG 10
LG 02
( c h a n n e l s / m m 2 )

Metrics