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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 22797–22808

Analytic solutions for spectral properties of superstructure, Gaussian-apodized and phase shift gratings with short- or long-period

Xiangkai Zeng and Kuai Liang  »View Author Affiliations

Optics Express, Vol. 19, Issue 23, pp. 22797-22808 (2011)

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The analytic solutions (AS) for the spectral properties of short- and long-period waveguide gratings with the effects of discrete phase shift (PS), Gaussian-apodization (GA) and superstructure are presented in this paper, which are derived from the Fourier mode coupling (FMC) theory proposed recently. The spectral properties include the reflectivity of short-period gratings, and the transmission of long-period gratings. The calculated spectra based on the analytic solutions are achieved and compared with measured cases and that on the transfer matrix (TM) method, in the case of changing grating parameters. The AS-based calculation requires the average time of several milliseconds at common PC, and the AS-based efficiency is improved up to ~6700 times the TM-based one. The comparisons have confirmed that the FMC-based analytic solutions are suitable for the real-time and accurate analyses of some non-uniform waveguide gratings.

© 2011 OSA

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(230.0230) Optical devices : Optical devices
(070.7345) Fourier optics and signal processing : Wave propagation
(230.7408) Optical devices : Wavelength filtering devices

ToC Category:
Diffraction and Gratings

Original Manuscript: July 11, 2011
Revised Manuscript: September 28, 2011
Manuscript Accepted: October 4, 2011
Published: October 26, 2011

Xiangkai Zeng and Kuai Liang, "Analytic solutions for spectral properties of superstructure, Gaussian-apodized and phase shift gratings with short- or long-period," Opt. Express 19, 22797-22808 (2011)

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  1. Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14(26), 12644–12654 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12644 . [CrossRef] [PubMed]
  2. C. Wang and J. Yao, “Photonic generation of chirped microwave pulses using superimposed chirped fiber Bragg gratings,” IEEE Photon. Technol. Lett. 20(11), 882–884 (2008). [CrossRef]
  3. Y. Tang, Z. Wang, L. Wosinski, U. Westergren, and S. He, “Highly efficient nonuniform grating coupler for silicon-on-insulator nanophotonic circuits,” Opt. Lett. 35(8), 1290–1292 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-8-1290 . [CrossRef] [PubMed]
  4. B. Lin, S. C. Tjin, H. Zhang, D. Tang, J. Hao, B. Dong, and S. Liang, “Switchable dual-wavelength single-longitudinal-mode erbium-doped fiber laser using an inverse-Gaussian apodized fiber Bragg grating filter and a low-gain semiconductor optical amplifier,” Appl. Opt. 49(36), 6855–6860 (2010), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-36-6855 . [CrossRef] [PubMed]
  5. J. L. Rebola and A. V. T. Cartaxo, “Performance optimization of Gaussian apodized fiber Bragg grating filters in WDM Systems,” J. Lightwave Technol. 20(8), 1537–1544 (2002), http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-20-8-1537 . [CrossRef]
  6. Q. Ye, R. Huang, Q. Xu, H. Cai, R. Qu, and Z. Fang, “Numerical investigation of ultrashort complex pulse generation based on pulse shaping using a superstructure fiber Bragg grating,” J. Lightwave Technol. 27(13), 2449–2456 (2009), http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-27-13-2449 . [CrossRef]
  7. X. Chen, J. Yao, F. Zeng, and Z. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17(7), 1390–1392 (2005). [CrossRef]
  8. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]
  9. M. Yamada and K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26(16), 3474–3478 (1987). [CrossRef] [PubMed]
  10. L. A. Weller-Brophy and D. G. Hall, “Analysis of waveguide gratings: application of Rouard’s method,” J. Opt. Soc. Am. A 2(6), 863–871 (1985). [CrossRef]
  11. H. Kogelnik, “Filter response of nonuniform almost-periodic structure,” Bell Syst. Tech. J. 55, 109–126 (1976).
  12. E. Mazzetto, C. G. Someda, J. A. Acebron, and R. Spigler, “The fractional Fourier transform in the analysis and synthesis of fiber Bragg gratings,” Opt. Quantum Electron. 37(8), 755–787 (2005). [CrossRef]
  13. J. J. Liau, N. H. Sun, S. C. Lin, R. Y. Ro, J. S. Chiang, C. L. Pan, and H. W. Chang, “A new look at numerical analysis of uniform fiber Bragg gratings using coupled mode theory,” Prog. Electromag. Res., PIER 93, 385–401 (2009). [CrossRef]
  14. E. Peral and J. Capmany, “Generalized Bloch wave analysis for fiber and waveguide gratings,” J. Lightwave Technol. 15(8), 1295–1302 (1997). [CrossRef]
  15. A. Bouzid and M. A. G. Abushagur, “Scattering analysis of slanted fiber gratings,” Appl. Opt. 36(3), 558–562 (1997). [CrossRef] [PubMed]
  16. L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(6), 4758–4767 (1993). [CrossRef] [PubMed]
  17. G. D. Marshall, R. J. Williams, N. Jovanovic, M. J. Steel, and M. J. Withford, “Point-by-point written fiber-Bragg gratings and their application in complex grating designs,” Opt. Express 18(19), 19844–19859 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-19-19844 . [CrossRef] [PubMed]
  18. R. J. Espejo, M. Svalgaard, and S. D. Dyer, “Characterizing fiber Bragg grating index profiles to improve the writing process,” IEEE Photon. Technol. Lett. 18(21), 2242–2244 (2006). [CrossRef]
  19. X. K. Zeng and Y. J. Rao, “Theory of Fourier mode coupling for fiber Bragg gratings,” Acta. Phys. Sin. 59, 8597–8606 (2010).
  20. X. K. Zeng and Y. J. Rao, “Theory of Fourier mode coupling for long-period fiber gratings,” Acta. Phys. Sin. 59, 8607–8614 (2010).
  21. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962). [CrossRef]
  22. A. P. Zhang, B. O. Guan, X. M. Tao, and H. Y. Tam, “Mode coupling in superstructure fiber Bragg grating,” IEEE Photon. Technol. Lett. 14(4), 489–491 (2002). [CrossRef]
  23. B. O. Guan, H. Y. Tam, X. M. Tao, and X. Y. Dong, “Simultaneous Strain and Temperature Measurement Using a Superstructure Fiber Bragg Grating,” IEEE Photon. Technol. Lett. 12(6), 675–677 (2000). [CrossRef]

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