## Modeling Diffraction in Free-Space Optical Interconnects by the Mode Expansion Method

Applied Optics, Vol. 42, Issue 26, pp. 5308-5318 (2003)

http://dx.doi.org/10.1364/AO.42.005308

Acrobat PDF (231 KB)

### Abstract

Free-space optical interconnects (FSOIs), made up of dense arrays of vertical-cavity surface-emitting lasers, photodetectors and microlenses can be used for implementing high-speed and high-density communication links, and hence replace the inferior electrical interconnects. A major concern in the design of FSOIs is minimization of the optical channel cross talk arising from laser beam diffraction. In this article we introduce modifications to the mode expansion method of Tanaka *et al*. [IEEE Trans. Microwave Theory Tech. **MTT-20,** 749 (1972)] to make it an efficient tool for modelling and design of FSOIs in the presence of diffraction. We demonstrate that our modified mode expansion method has accuracy similar to the exact solution of the Huygens-Kirchhoff diffraction integral in cases of both weak and strong beam clipping, and that it is much more accurate than the existing approximations. The strength of the method is twofold: first, it is applicable in the region of pronounced diffraction (strong beam clipping) where all other approximations fail and, second, unlike the exact-solution method, it can be efficiently used for modelling diffraction on multiple apertures. These features make the mode expansion method useful for design and optimization of free-space architectures containing multiple optical elements inclusive of optical interconnects and optical clock distribution systems.

© 2003 Optical Society of America

**OCIS Codes**

(200.2610) Optics in computing : Free-space digital optics

(200.4650) Optics in computing : Optical interconnects

(260.1960) Physical optics : Diffraction theory

**Citation**

Novak S. Petrović and Aleksandar D. Rakić, "Modeling Diffraction in Free-Space Optical Interconnects by the Mode Expansion Method," Appl. Opt. **42**, 5308-5318 (2003)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-42-26-5308

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### References

- D. A. B. Miller, “Invited paper: Physical reasons for optical interconnection,” Int. J. Optoelectron. 11, 155–168 (1997).
- D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–749 (2000).
- D. V. Plant and A. G. Kirk, “Optical interconnects at the chip and board level: Challenges and solutions,” Proc. IEEE 88, 806–818 (2000).
- D. Fey, W. Erhard, M. Gruber, J. Jahns, H. Bartelt, G. Grimm, L. Hoppe, and S. Sinzinger, “Optical interconnects for neural and reconfigurable VLSI architectures,” Proc. IEEE 88, 838–848 (2000).
- N. McArdle, M. Naruse, H. Toyoda, Y. Kobayashi, and M. Ishikawa, “Reconfigurable optical interconnections for parallel computing,” Proc. IEEE 88, 829–837 (2000).
- 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).
- Y. Liu, B. Robertson, G. C. Boisset, M. H. Ayliffe, R. Iyer, and D. V. Plant, “Design, implementation, and characterization of a hybrid optical interconnect for a four-stage free-space optical backplane demonstrator,” Appl. Opt. 37, 2895–2914 (1998).
- D. F.- Brosseau, F. Lacroix, M. H. Ayliffe, E. Bernier, B. Robertson, F. A. P. Tooley, D. V. Plant, and A. G. Kirk, “Design, implementation, and characterization of a kinematically aligned, cascaded spot-array generator for a modulator-based free-space optical interconnect,” Appl. Opt. 39, 733–745 (2000).
- G. Li, D. Huang, E. Yuceturk, P. J. Marchand, S. C. Esener, V. H. Ozguz, and Y. Liu, “Three-dimensional optoelectronic stacked processor by use of free-space optical interconnection and three-dimensional VLSI chip stacks,” Appl. Opt. 41, 348–360 (2002).
- F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, and A. Y. Feldblum, “Optical interconnections using microlens arrays,” Opt. Quantum Electron. 24, S465–S477 (1992).
- F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. M. Sasian, H. S. Hinton, K. O. Mersereau, and A. Y. Feldblum, “Corrigendum: ‘Optical interconnections using microlens arrays’,” Opt. Quantum Electron. 24, 1209–1212 (1992).
- S. Tang, R. T. Chen, L. Garrett, D. Gerold, and M. M. Li, “Design limitations of highly parallel free-space optical interconnects based on arrays of vertical cavity surface-emitting laser diodes, microlenses, and photodetectors,” J. Lightwave Technol. 12, 1971–1975 (1994).
- C. J. Kuo, Y. S. Su, and H. T. Chang, “Wavelength-division microlens interconnection using weakly diffracted Gaussian beam,” Opt. Quantum Electron. 28, 381–394 (1996).
- H. J. Zhou, V. Morozov, J. Neff, and A. Fedor, “Analysis of a vertical-cavity surface-emitting laser-based bidirectional free-space optical interconnect,” Appl. Opt. 36, 3835–3853 (1997).
- 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, microlenses, and metal-semiconductor-metal detectors,” Appl. Opt. 39, 4834–4841 (2000).
- R. Wang, A. D. Rakić, 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).
- R. Wang, A. D. Rakić, 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).
- J. P. Campbell and L. G. DeShazer, “Near fields of truncated-Gaussian apertures,” J. Opt. Soc. Am. 59, 1427–1429 (1969).
- G. O. Olaofe, “Diffraction by Gaussian apertures,” J. Opt. Soc. Am. 60, 1654–1657 (1970).
- R. G. Schell and G. Tyras, “Irradiance from an aperture with a truncated-Gaussian field distribution,” J. Opt. Soc. Am. 61, 31–35 (1971).
- C. Campbell, “Fresnel diffraction of Gaussian laser beams by circular apertures,” Opt. Eng. 26, 270–275 (1987).
- K. Tanaka, M. Shibukawa, and O. Fukumitsu, “Diffraction of a wave beam by an aperture,” IEEE Trans. Microwave Theory Tech. MTT-20, 749–755 (1972).
- P. Belland and J. P. Crenn, “Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture,” Appl. Opt. 21, 522–527 (1982).
- S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1941).
- H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).
- D. H. Martin and J. W. Bowen, “Long-wave optics,” IEEE Trans. Microwave Theory Tech. 41, 1676–1690 (1993).
- O. O. Andrade, “Mode coupling by circular apertures,” Appl. Opt. 15, 2800–2803 (1976).
- J. A. Murphy, S. Withington, and A. Egan, “Mode conversion at diffracting apertures in millimeter and submillimeter wave optical systems,” IEEE Trans. Microwave Theory Tech. 41, 1700–1702 (1993).
- J. A. Murphy, A. Egan, and S. Withington, “Truncation in millimeter and submillimeter-wave optical systems,” IEEE Trans. Antennas Propag. 41, 1408–1413 (1993).
- S. Withington and J. A. Murphy, “Analysis of diagonal horns through Gaussian-Hermite modes,” IEEE Trans. Antennas Propag. 40, 198–206 (1992).
- J. A. Murphy and A. Egan, “Examples of Fresnel diffraction using Gaussian modes,” Eur. J. Phys. 14, 121–127 (1993).
- F. M. Dickey and S. C. Holswade, eds., Laser Beam Shaping Theory and Techniques (Marcel Dekker Inc., New York, 2000).
- E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, New York, 1989).
- I. S. Gradshteyn and I. M. Ryzhik, Table 1 of Integrals, Series, and Products (Academic, San Diego, Calif., 2000).

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