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Applied Optics

Applied Optics


  • Vol. 42, Iss. 15 — May. 20, 2003
  • pp: 2730–2738

Synthesis of Hadamard transformers by use of multimode interference optical waveguides

Atma Ram Gupta, Kiyoshi Tsutsumi, and Junichi Nakayama  »View Author Affiliations

Applied Optics, Vol. 42, Issue 15, pp. 2730-2738 (2003)

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We propose a synthesis method of optical Hadamard transformers using multimode interference (MMI) couplers. By using the signal transfer matrix of 2 × 2, 4 × 4, and 8 × 8 MMI couplers, we show that sum and difference units of input signals can be synthesized. An interchange unit of two signals can also be synthesized. One synthesis method of Hadamard transformers is a combination of only 2 × 2 units, and the other is a combination of N × N(N ≥ 4) units as well as 2 × 2 units. The design examples of operation units are shown, and the size and the output power of Hadamard transformers are estimated.

© 2003 Optical Society of America

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(130.3120) Integrated optics : Integrated optics devices
(230.3120) Optical devices : Integrated optics devices
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits

Original Manuscript: April 19, 2002
Revised Manuscript: November 26, 2002
Published: May 20, 2003

Atma Ram Gupta, Kiyoshi Tsutsumi, and Junichi Nakayama, "Synthesis of Hadamard transformers by use of multimode interference optical waveguides," Appl. Opt. 42, 2730-2738 (2003)

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  1. L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995). [CrossRef]
  2. O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am. 63, 416–419 (1973). [CrossRef]
  3. R. Ulrich, T. Kamiya, “Resolution of self-images in planar optical waveguides,” J. Opt. Soc. Am. 68, 583–592 (1978). [CrossRef]
  4. M. Bachmann, P. A. Besse, H. Melchior, “General self-imaging properties in N × M multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994). [CrossRef] [PubMed]
  5. M. Bachmann, P. A. Besse, H. Melchior, “Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting,” Appl. Opt. 34, 6898–6910 (1995). [CrossRef] [PubMed]
  6. P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004–1009 (1994). [CrossRef]
  7. E. R. Thoen, L. A. Molter, J. P. Donnelly, “Analysis of N × M waveguide splitters and couplers with multimode guiding sections,” in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, G. Griffel, H. L. Bertoni, eds. (Plenum, New York, 1995), pp. 143–153.
  8. M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, “Accurate numerical analysis of multimode-interference-based 3-dB couplers,” Appl. Opt. 37, 5672–5678 (1998). [CrossRef]
  9. M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, “A rigorous comparison of the performance of directional couplers with multimode interference devices,” J. Lightwave Technol. 17, 243–248 (1999). [CrossRef]
  10. J. M. Heaton, R. M. Jenkins, “General matrix theory of self-imaging in multimode interference (MMI) couplers,” IEEE Photon. Technol. Lett. 11, 212–214 (1999). [CrossRef]
  11. E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, R. J. Hawkins, “Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference,” Appl. Phys. Lett. 59, 1926–1928 (1991). [CrossRef]
  12. L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol. 10, 1843–1850 (1992). [CrossRef]
  13. T. Saida, A. Himeno, M. Okuno, A. Sugita, K. Okamoto, “Silica-based 2 × 2 multimode interference coupler with arbitrary power splitting ratio,” Electron. Lett. 35, 2031–2033 (1999). [CrossRef]
  14. J. E. Zucker, K. L. Jones, T. H. Chiu, K. Brown-Goebeler, “Strained quantum wells for polarization-independent electrooptic waveguide switches,” J. Lightwave Technol. 10, 1926–1930 (1992). [CrossRef]
  15. R. M. Jenkins, J. M. Heaton, D. R. Wight, J. T. Parker, J. C. H. Birbeck, G. W. Smith, K. P. Hilton, “Novel 1 × N and N × N integrated optical switches using self-imaging multimode GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 64, 684–686 (1994). [CrossRef]
  16. M. P. Earnshaw, J. B. D. Soole, M. Cappuzzo, L. Gomez, E. Laskowski, A. Paunescu, “Compact, low-loss 4 × 4 optical switch matrix using multimode interferometers,” Electron. Lett. 37, 115–116 (2001). [CrossRef]
  17. R. J. Deri, E. C. M. Pennings, A. Scherer, A. S. Gozdz, C. Caneau, N. C. Andreadakis, V. Shah, L. Curtis, R. J. Hawkins, J. B. D. Soole, J. I. Song, “Ultracompact monolithic integration of balanced, polarization diversity photodetectors for coherent lightwave receivers,” IEEE Photon. Technol. Lett. 4, 1238–1240 (1992). [CrossRef]
  18. R. van Roijen, E. C. M. Pennings, M. J. N. van Stralen, T. van Dongen, B. H. Verbeek, J. M. M. van der Heijden, “Compact InP-based ring lasers employing multimode interference couplers and combiners,” Appl. Phys. Lett. 64, 1753–1755 (1994). [CrossRef]
  19. T. Saida, Y. Orihara, H. Yamada, K. Takiguchi, T. Goh, K. Okamoto, “Integrated optical polarisation analyser on planar lightwave circuit,” Electron. Lett. 35, 1948–1949 (1999). [CrossRef]
  20. T. Saida, K. Okamoto, K. Uchiyama, K. Takiguchi, T. Shibata, A. Sugita, “Integrated optical digital-to-analogue converter and its application to pulse pattern recognition,” Electron. Lett. 37, 1237–1238 (2001). [CrossRef]
  21. F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992).
  22. K. G. Beauchamp, Applications of Walsh and Related Functions with an Introduction to Sequency Theory (Academic, London, 1984), Chap. 2.
  23. E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice-Hall, Upper Saddle River, N.J., 1988), Chap. 8.
  24. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Sec. 5.2.
  25. B. E. Krivenkov, P. E. Tverdokhleb, Yu. V. Chugui, “Analysis of images by Hadamard optical transform,” Appl. Opt. 14, 1829–1834 (1975). [CrossRef] [PubMed]
  26. R. G. Hunsperger, Integrated Optics: Theory and Technology, 3rd ed. (Springer-Verlag, New York, 1991), Sec. 17.1.1. [CrossRef]
  27. M. N. Armenise, V. M. N. Passaro, “Optical signal processors and applications,” in Advances in Integrated Optics, S. Martellucci, A. N. Chester, M. Bertolotti, eds. (Plenum, New York, 1994), pp. 303–312. [CrossRef]
  28. D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An integrated-optical approach to the Fourier transform,” IEEE J. Quantum Electron. QE-13, 268–275 (1977). [CrossRef]
  29. D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of optical-waveguide lens technologies,” IEEE J. Quantum Electron. QE-13, 275–282 (1977). [CrossRef]
  30. K. Tsutsumi, T. Sueta, “A proposed integrated-optical device for Hadamard transformation,” Trans. IECE Jpn. J60-C, 500–502 (1977).
  31. K. Tsutsumi, T. Sueta, “A synthesis of optical guided-wave signal transformers,” Trans. IECE Jpn. J62-C, 381–388 (1979).
  32. K. Tsutsumi, “Studies on synthesis of guided-wave optical signal transformers,” Ph.D. dissertation (Graduate School of Engineering Science, Osaka University, Osaka, Japan, 1980).
  33. M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. 12, 63–65 (1987). [CrossRef] [PubMed]

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