Abstract

Parallel high-density free-space optical interconnects typically relay multiple channels in an array configuration; thus, they require good uniformity across their aperture for optimum performance. Rigorous coupled wave analysis is used to determine the throughput off-axis diffraction efficiency for Fresnel lenses within a diffractive imaging relay. The rigorous results are compared with scalar theory and show a significant nonuniformity not predicted by scalar theory. However, the polarization sensitivity is found to be negligible for the f-numbers considered (f/2.9 to f/10.2). These results are supported by experiment.

© 2005 Optical Society of America

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References

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2002

G. Li, E. Yuceturk, D. Huang, S. C. Esener, “Analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked processor,” Opt. Commun. 202, 319–329 (2002).
[CrossRef]

M. Chateauneuf, A. Kirk, D. Plant, T. Yamamoto, J. Ahearn, “512 Vertical-cavity surface-emitting laser based free-space optical link,” Appl. Opt. 41, 5552–5561 (2002).
[CrossRef]

2001

1999

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

1998

1997

1996

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Sub-wavelength structures and their use in diffractive optics,” Opt. Eng. 35, 726–731 (1996).
[CrossRef]

1995

1993

1976

P. Facq, “Diffraction by periodically limited cylindrical structures,” Ann. Telecommun. 31, 99–107 (1976).

Ahearn, J.

Banerjee, P. P.

J. M. Jarem, P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems (Marcel Dekker, New York, 2000).

Buchholz, D. B.

Chateauneuf, M.

Châteauneuf, M.

M. Châteauneuf, A. G. Kirk, “Determination of the optimum cluster parameters for a free-space optical interconnect,” in 2002 IEEE/LEOS Annual Meeting Conference Proceedings (IEEE, Piscataway, N.J., 2002), Vol. 2, pp. 899–900.

Collischon, M.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Sub-wavelength structures and their use in diffractive optics,” Opt. Eng. 35, 726–731 (1996).
[CrossRef]

Esener, S. C.

G. Li, E. Yuceturk, D. Huang, S. C. Esener, “Analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked processor,” Opt. Commun. 202, 319–329 (2002).
[CrossRef]

Facq, P.

P. Facq, “Diffraction by periodically limited cylindrical structures,” Ann. Telecommun. 31, 99–107 (1976).

Feldman, M. R.

W. H. Welch, M. R. Feldman, R. D. Te Kolste, “Diffractive optics for head mounted displays,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 209–210 (1995).
[CrossRef]

Feng, D.

Friberg, A. T.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Gaylord, T. K.

Goodman, J. G.

J. G. Goodman, Introduction to Fourier Optics (McGraw-Hill, Toronto, 1996).

Grann, E. B.

Gupta, M. C.

Haidner, H.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Sub-wavelength structures and their use in diffractive optics,” Opt. Eng. 35, 726–731 (1996).
[CrossRef]

Huang, D.

G. Li, E. Yuceturk, D. Huang, S. C. Esener, “Analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked processor,” Opt. Commun. 202, 319–329 (2002).
[CrossRef]

Jarem, J. M.

J. M. Jarem, P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems (Marcel Dekker, New York, 2000).

Johnson, E. G.

E. G. Johnson, A. D. Kathman, “Rigorous electromagnetic modeling of diffractive optical elements,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 209–216 (1991).
[CrossRef]

Kathman, A. D.

E. G. Johnson, A. D. Kathman, “Rigorous electromagnetic modeling of diffractive optical elements,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 209–216 (1991).
[CrossRef]

Katsikadelis, J. T.

J. T. Katsikadelis, Boundary Elements: Theory and Applications (Elsevier, New York, 2002).

Kettunen, V.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Kipfer, P.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Sub-wavelength structures and their use in diffractive optics,” Opt. Eng. 35, 726–731 (1996).
[CrossRef]

Kirk, A.

Kirk, A. G.

M. Châteauneuf, A. G. Kirk, “Determination of the optimum cluster parameters for a free-space optical interconnect,” in 2002 IEEE/LEOS Annual Meeting Conference Proceedings (IEEE, Piscataway, N.J., 2002), Vol. 2, pp. 899–900.

Kuittinen, M.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Kunz, K. S.

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

Larochelle, S.

Li, G.

G. Li, E. Yuceturk, D. Huang, S. C. Esener, “Analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked processor,” Opt. Commun. 202, 319–329 (2002).
[CrossRef]

Luebbers, R. J.

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

Magnusson, R.

R. Magnusson, D. Shin, “Diffractive optical components,” in Encyclopedia of Physical Science and Technology, 3rd ed., R. A. Meyers, ed. (Academic, New York, 2001), Vol. 4, pp. 421–440.

Moharam, M. G.

Morrison, R. L.

Noponen, E.

Plant, D.

Pommet, D. A.

Prather, D.

Pustai, D.

Schwider, J.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Sub-wavelength structures and their use in diffractive optics,” Opt. Eng. 35, 726–731 (1996).
[CrossRef]

Sergienko, N.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Sheng, Y.

Shi, S.

Shin, D.

R. Magnusson, D. Shin, “Diffractive optical components,” in Encyclopedia of Physical Science and Technology, 3rd ed., R. A. Meyers, ed. (Academic, New York, 2001), Vol. 4, pp. 421–440.

Stamnes, J. J.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Strasser, T. A.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” (Lincoln Laboratory MIT, Lexington, Mass., 1991).

Te Kolste, R. D.

W. H. Welch, M. R. Feldman, R. D. Te Kolste, “Diffractive optics for head mounted displays,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 209–210 (1995).
[CrossRef]

Turunen, J.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[CrossRef]

Vahimaa, P.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Vasara, A.

Welch, W. H.

W. H. Welch, M. R. Feldman, R. D. Te Kolste, “Diffractive optics for head mounted displays,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 209–210 (1995).
[CrossRef]

Yamamoto, T.

Yuceturk, E.

G. Li, E. Yuceturk, D. Huang, S. C. Esener, “Analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked processor,” Opt. Commun. 202, 319–329 (2002).
[CrossRef]

Ann. Telecommun.

P. Facq, “Diffraction by periodically limited cylindrical structures,” Ann. Telecommun. 31, 99–107 (1976).

Appl. Opt.

J. Mod. Opt.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

G. Li, E. Yuceturk, D. Huang, S. C. Esener, “Analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked processor,” Opt. Commun. 202, 319–329 (2002).
[CrossRef]

Opt. Eng.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Sub-wavelength structures and their use in diffractive optics,” Opt. Eng. 35, 726–731 (1996).
[CrossRef]

Other

J. M. Jarem, P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems (Marcel Dekker, New York, 2000).

J. T. Katsikadelis, Boundary Elements: Theory and Applications (Elsevier, New York, 2002).

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” (Lincoln Laboratory MIT, Lexington, Mass., 1991).

M. Châteauneuf, A. G. Kirk, “Determination of the optimum cluster parameters for a free-space optical interconnect,” in 2002 IEEE/LEOS Annual Meeting Conference Proceedings (IEEE, Piscataway, N.J., 2002), Vol. 2, pp. 899–900.

E. G. Johnson, A. D. Kathman, “Rigorous electromagnetic modeling of diffractive optical elements,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 209–216 (1991).
[CrossRef]

R. Magnusson, D. Shin, “Diffractive optical components,” in Encyclopedia of Physical Science and Technology, 3rd ed., R. A. Meyers, ed. (Academic, New York, 2001), Vol. 4, pp. 421–440.

W. H. Welch, M. R. Feldman, R. D. Te Kolste, “Diffractive optics for head mounted displays,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 209–210 (1995).
[CrossRef]

J. G. Goodman, Introduction to Fourier Optics (McGraw-Hill, Toronto, 1996).

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Figures (9)

Fig. 1
Fig. 1

Diagram of optical interconnect that joins two integrated circuit boards (IC1 and IC2)6.

Fig. 2
Fig. 2

Section of Fresnel lens with equivalent local linear grating. Note that the equivalent grating is linear and has a constant period.

Fig. 3
Fig. 3

Polarization relative to the front of the Fresnel lens. The corner and edge beams are also labeled.

Fig. 4
Fig. 4

Diffraction efficiency as a function of radius for Fresnel lens with f = 8.5 mm.

Fig. 5
Fig. 5

Edge and corner element transmission efficiency versus array size for two consecutive relays.

Fig. 6
Fig. 6

Corner transmission efficiency for a system containing either one or two relays.

Fig. 7
Fig. 7

Schematic of experimental setup. P, polarizer, L, lens, S, beam splitter, FS, free space.

Fig. 8
Fig. 8

Comparison of experimental and theoretical diffraction efficiencies as a function of beam position.

Fig. 9
Fig. 9

Schematic showing the source of the zero-order bump in the data. Upper diagram, measurement near the axis where all the orders are detected. Lower diagram, off-axis measurement where only the first order is detected.

Equations (9)

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

r m = [ 2 m λ f + ( λ f ) 2 ] 1 / 2 .
d ( r ) = 2 π | d Φ ( r ) d r | - 1 = λ [ 1 + ( f r ) 2 ] 1 / 2 .
Φ ( r ) = ( 2 π / λ ) [ f - ( f 2 + r 2 ) 1 / 2 ] .
E ( x ,     y ,     z ) = E 0 exp [ - ( x ω 0 ) 2 ] exp [ - ( y ω 0 ) 2 ] × exp [ i ( k z - ω t ) ] = E 0 exp [ - ( r ω 0 ) 2 ] exp [ i ( k z - ω t ) ] .
A ( k x ,     k y ,     0 ) = FT [ E ( x ,     y ,     z ) ] = E 0 π ω 0 2 exp ( - k t 2 ω 0 2 4 ) ,
η Total = i = 1 N η Local ( i ) U G ( i ) N ,
η = sinc 2 ( 1 / N ) ,
E ¯ = E x exp ( i ϕ x ) i ^ + E y exp ( i ϕ y ) j ^ + E z exp ( i ϕ z ) k ^ .
ϕ k = arctan ( E k - im E k - real ) ,

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