OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 11 — Nov. 1, 2006
  • pp: 2919–2931

Composition methods for four-port couplers in photonic integrated circuitry

Tiberiu Constantinescu, Viswanath Ramakrishna, Nicholas Spears, L. Roberts Hunt, Jian Tong, Issa Panahi, Govind Kannan, Duncan L. MacFarlane, Gary Evans, and Marc P. Christensen  »View Author Affiliations

JOSA A, Vol. 23, Issue 11, pp. 2919-2931 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (354 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Planar photonic integrated circuits based on four-port couplers offer enhanced sophistication and functionality. Each four-port coupler is characterized by sixteen signal coupling coefficients governed by ten energy constraints. The ability to generate the constrained sixteen coupling coefficients is needed in the analysis of the four-port coupler. However, the energy constraint equations are nonlinear and cumbersome to solve directly. We introduce two techniques to reduce these signal coupling coefficients to a set of six free parameters. Hence we can characterize all possible couplers in terms of their sixteen constrained coupling coefficients, or either of two sets of six free parameters. This reduction in parameters has significant ramifications for the design, specification, and empirical characterization of these useful building blocks.

© 2006 Optical Society of America

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(130.1750) Integrated optics : Components
(130.6750) Integrated optics : Systems
(230.1360) Optical devices : Beam splitters
(230.3120) Optical devices : Integrated optics devices
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Integrated Optics

Original Manuscript: February 9, 2006
Revised Manuscript: May 19, 2006
Manuscript Accepted: May 23, 2006

Tiberiu Constantinescu, Viswanath Ramakrishna, Nicholas Spears, L. Roberts Hunt, Jian Tong, Issa Panahi, Govind Kannan, Duncan L. MacFarlane, Gary Evans, and Marc P. Christensen, "Composition methods for four-port couplers in photonic integrated circuitry," J. Opt. Soc. Am. A 23, 2919-2931 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, "Fiber optic lattice signal processing," Proc. IEEE 72, 909-930 (1984). [CrossRef]
  2. F. J. Fraile-Peláez, J. Capmany, and M. A. Muriel, "Transmission bistability in a double-coupler fiber ring resonator," Opt. Lett. 16, 907-909 (1991). [CrossRef] [PubMed]
  3. K. Sasayama, M. Okuno, and K. Habara, "Coherent optical transversal filter using silica-based waveguides for high-speed signal processing," J. Lightwave Technol. 9, 1225-1230 (1991). [CrossRef]
  4. D. L. MacFarlane and E. M. Dowling, "Z-domain techniques in the analysis of Fabry-Perot etalons and multilayer structures," J. Opt. Soc. Am. A 11, 236-245 (1994). [CrossRef]
  5. E. M. Dowling and D. L. MacFarlane, "Lightwave lattice filters for optically multiplexed communication systems," J. Lightwave Technol. 12, 471-486 (1994). [CrossRef]
  6. Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, "Waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1995). [CrossRef]
  7. D. L. MacFarlane, E. M. Dowling, and V. Narayan, "Ring resonators with N×M couplers," Fiber Integr. Opt. 14, 195-210 (1995). [CrossRef]
  8. C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).
  9. L. R. Hunt, V. Govindan, I. Panahi, J. Tong, G. Kannan, D. L. MacFarlane, and G. Evans, "Active optical lattice filters," EURASIP J. Appl. Signal Process. 10, 1-11 (2005).
  10. I. M. S. Panahi, G. Kannan, L. R. Hunt, D. L. MacFarlane, and J. Tong, "Lattice filter with adjustable gains and its application in optical signal processing," in 2005 IEEE/SP 13th Workshop on Statistical Signal Processing (IEEE Press, 2005), pp. 321-326. [CrossRef]
  11. D. L. MacFarlane, J. Tong, C. Fafadia, V. Govindan, L. R. Hunt, and I. Panahi, "Extended lattice filters enabled by four directoinal couplers," Appl. Opt. 43, 6124-6133 (2004). [CrossRef] [PubMed]
  12. G. Griffel, "Synthesis of optical filters using ring resonator arrays," IEEE Photon. Technol. Lett. 12, 810-812 (2000). [CrossRef]
  13. D. Hoffmann, H. Heidrich, G. Wenke, R. Langenhorst, and E. Dietrich, "Integrated optics eight-port 90° hybrid on LiNbO3," J. Lightwave Technol. 7, 794-798 (1989). [CrossRef]
  14. D. Roh, T. Masood, S. Patterson, N. V. Amarasinghe, S. McWilliams, G. A. Evans, and J. Butler, "Dual-wavelength AllnGaAS-InP grating-outcoupled surface-emitting laser with an integrated two dimensional photonic lattice outcoupler," IEEE Photon. Technol. Lett. 17, 270-273 (2005). [CrossRef]
  15. H. J. Carlin, "The scattering matrix in network theory," IRE Trans. Circuit Theory CT-3, 88-97 (1956).
  16. D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, 1998).
  17. J. Reed and G. J. Wheeler, "A method of analysis of symmetrical four port networks," IRE Trans. Microwave Theory Tech. MTT-4, 246-252 (1956). [CrossRef]
  18. C. R. Boyd, Jr., "On a class of multiple line directional couplers," IRE Trans. Microwave Theory Tech. MTT-10, 287-294 (1962). [CrossRef]
  19. K. Kurokawa, "Power waves and the scattering matrix," IEEE Trans. Microwave Theory Tech. MTT-13, 194-202 (1965). [CrossRef]
  20. S. Hagelin, "A flow graph analysis of 3- and 4-port junction circulators," IEEE Trans. Microwave Theory Tech. MTT-14, 243-249 (1966). [CrossRef]
  21. J. J. Campbell, "Application of the solutions of certain boundary value problems to the symmetrical four-port junction and specially truncated bends in parallel-plate waveguides and balanced strip-transmission lines," IEEE Trans. Microwave Theory Tech. MTT-16, 165-176 (1968). [CrossRef]
  22. R. Levy, "Analysis and synthesis of waveguide multi-aperture directional couplers," IEEE Trans. Microwave Theory Tech. MTT-16, 995-1006 (1968). [CrossRef]
  23. G. P. Riblet, "A coupling theorem for matched symmetrical two-branch four-port networks," IEEE Trans. Circuits Syst. CAS-25, 145-148 (1978). [CrossRef]
  24. O. Schwelb and R. Antepyan, "Conservation laws for distributed four-ports," IEEE Trans. Microwave Theory Tech. MTT-33, 157-160 (1985). [CrossRef]
  25. J. Esteban and J. M. Rebollar, "Generalized scattering matrix of generalized two-port discontinuities: application to four-port and nonsymmetric six-port couplers," IEEE Trans. Microwave Theory Tech. 39, 1725-1734 (1991). [CrossRef]
  26. K. Araki and Y. Naito, "On the properties of lossless reciprocal 4-port circuits with reflection symmetry," IEEE Trans. Circuits Syst. 39, 155-161 (1992). [CrossRef]
  27. H.-C. Lu and T.-H. Chu, "Multiport scattering matrix measurement using a reduced-port network analyzer," IEEE Trans. Microwave Theory Tech. 51, 1525-1533 (2003). [CrossRef]
  28. J. Martens, D. V. Judge, and J. A. Bigelow, "Uncertainties associated with many-port (>4) S-parameter measurements using a four-port vector network analyzer," IEEE Trans. Microwave Theory Tech. 52, 1361-1368 (2004). [CrossRef]
  29. C. B. Fafadia, "Thick linear optical lattice filters," Master's thesis (University of Texas at Dallas, 2003).
  30. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991). [CrossRef]
  31. F. R. Gantmacher, The Theory of Matrices (Chelsea, 1977), Vol. 1.
  32. F. D. Murnaghan, The Unitary and Rotation Groups (Spartan, 1962).
  33. R. P. Stanley, Enumerative Combinatorics (Cambridge U. Press, 1999), Vol. 2. [CrossRef]
  34. P. Lounesto, Clifford Algebras and Spinors (Cambridge U. Press, 2001). [CrossRef]
  35. Ulf Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited