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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 25 — Sep. 1, 2000
  • pp: 4629–4637

Analysis and design of almost-periodic vertical-grating-assisted codirectional coupler filters with nonuniform duty ratios

Gia-Wei Chern and Lon. A. Wang  »View Author Affiliations


Applied Optics, Vol. 39, Issue 25, pp. 4629-4637 (2000)
http://dx.doi.org/10.1364/AO.39.004629


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Abstract

A systematic approach to the analysis of almost-periodic vertical-grating-assisted codirectional couplers with nonuniform duty ratios is presented. The Poisson sum formula is used to expand rigorously a nonuniform rectangular grating into a quasi-Fourier series, and local grating parameters such as period, width, and duty ratio can be defined unambiguously in such a procedure. On the basis of this expansion the coupled-local-mode formulation is the most natural extension for the analysis of such a nonuniform grating-assisted codirectional coupler filter. By transformation of the coupled-local-mode equations into the Zakharov–Shabat system the Gel’fand–Levintan–Marchenko inverse-scattering method is then used to synthesize special grating-assisted codirectional coupler filters. The design is illustrated by two typical examples: One is a third-order Butterworth filter, and the other is a linear filter.

© 2000 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(130.2790) Integrated optics : Guided waves
(230.7400) Optical devices : Waveguides, slab

History
Original Manuscript: January 24, 2000
Revised Manuscript: May 17, 2000
Published: September 1, 2000

Citation
Gia-Wei Chern and Lon. A. Wang, "Analysis and design of almost-periodic vertical-grating-assisted codirectional coupler filters with nonuniform duty ratios," Appl. Opt. 39, 4629-4637 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-25-4629


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References

  1. D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. Part II: grating-assisted couplers,” J. Lightwave Technol. 5, 268–273 (1987). [CrossRef]
  2. I. Kim, R. C. Alferness, L. L. Buhl, U. Koren, B. I. Miller, M. G. Young, M. A. Newkirk, M. D. Chien, T. L. Koch, G. Raybon, C. A. Burrus, “InGaAs/InGaAsP MQW optical amplifier integrated with grating-assisted vertical-coupler noise filter,” IEEE Photon. Technol. Lett. 5, 1319–1321 (1993). [CrossRef]
  3. W. Vanderbauwhede, I. Moerman, P. Van Daele, P. Demeester, “Wavelength tuning by quantum well electrorefraction in a grating-assisted vertical coupler filter with InGaAsP/InAlGaAs MQW waveguide,” Opt. Quantum Electron. 28, 583–590 (1996). [CrossRef]
  4. H. Sakata, “Analysis of wavelength-selective photodetectors based on grating-assisted forward coupling,” J. Lightwave Technol. 11, 560–566 (1993). [CrossRef]
  5. Y. H. Jan, G. A. Fish, L. A. Coldren, S. P. DenBaars, “Demonstration of InP–InGaAsP vertical grating-assisted codirectional coupler filters and receivers with tapered coupling coefficient distributions,” IEEE Photon. Technol. Lett. 9, 994–996 (1997). [CrossRef]
  6. R. C. Alferness, P. S. Cross, “Filter characteristics of codirectionally coupled waveguides with weighted coupling,” IEEE J. Quantum Electron. 14, 843–847 (1978). [CrossRef]
  7. H. Sakata, “Sidelobe suppression in grating-assisted wavelength-selective couplers,” Opt. Lett. 17, 463–465 (1992). [CrossRef] [PubMed]
  8. M. Yamada, K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26, 3474–3478 (1987). [CrossRef] [PubMed]
  9. M. Matsuhara, K. O. Hill, A. Watanabe, “Optical-waveguide filters: synthesis,” J. Opt. Soc. Am. 65, 804–809 (1975). [CrossRef]
  10. G. H. Song, S. Y. Shin, “Design of corrugated waveguide filters by the Gel’fand–Levitan–Marchenko inverse-scattering method,” J. Opt. Soc. Am. A 2, 1905–1915 (1985). [CrossRef]
  11. K. A. Winick, “Design of grating-assisted waveguide couplers with weighted coupling,” J. Lightwave Technol. 9, 1481–1492 (1991). [CrossRef]
  12. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Elsevier, New York, 1969).
  13. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 48, 109–126 (1976). [CrossRef]
  14. P. N. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 466.
  15. A. Ishimaru, “Theory of unequally spaced arrays,” IRE Trans. Antennas Propag. 10, 691–702 (1963). [CrossRef]
  16. V. E. Zakharov, A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).
  17. H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, New York, 1975), Chap. 2.
  18. C. H. Henry, L. F. Johnson, R. A. Logan, D. P. Clarke, “Determination of the refractive index of InGaAsP epitaxial layers by mode line luminescence spectroscopy,” IEEE J. Quantum Electron. 21, 1887–1892 (1985). [CrossRef]
  19. G. H. Song, “Theory of symmetry in optical filter responses,” J. Opt. Soc. Am. A 11, 2027–2037 (1994). [CrossRef]

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