Efficient finite difference analysis of microstructured optical fibers
Optics Express, Vol. 13, Issue 25, pp. 10349-10359 (2005)
http://dx.doi.org/10.1364/OPEX.13.010349
Acrobat PDF (120 KB)
Abstract
A new technique of numerical analysis of microstructured optical fibers is presented. The technique combines a standard 2D finite difference equations with the discrete function expansion. By doing this one gets a matrix eigenvalue problem of a smaller size and a simple formulation of radiation boundary condition. The new algorithm was tested for the microstructures of different types and excellent agreement of the obtained results with other methods was achieved.
© 2005 Optical Society of America
1. Introduction
1 . P. Russell , “ Photonic Crystal Fibers ,” Science 299 , 358 – 362 ( 2003 ). [CrossRef] [PubMed]
2 . C. Kerbage and B. J. Eggleton , ” Numerical analysis and experimental design of tunable birefringence in microstruc-tured optical fiber ,” Opt. Express 10 , 246 – 255 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-5-246 . [PubMed]
3 . T.P. White , R.C. McPhedran , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Confinement losses in microstructured optical fibers ,” Opt. Lett. 26 , 1660 – 1662 ( 2001 ). [CrossRef]
4 . T.P. White , B.T. Kuhlmey , R.C. McPhedran , D. Maystre , R. Ranversez , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Multipole method for microstructured optical fibers. I. Formulation ,” J. Opt. Soc. Am. B 19 , 2322 – 2330 ( 2002 ). [CrossRef]
5 . D. Ferrarini , L. Vincetti , M. Zoboli , A. Cucinotta , and S. Selleri , “ Leakage properties of photonic crystal fibers ,” Opt. Express 10 , 1314 – 1319 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314 . [PubMed]
6 . H.P. Uranus and H.J.W.M. Hoekstra , “ Modeling of microstructured waveguides using a finite-element-based vecto-rial mode solver with transparent boundary conditions ,” Opt. Express 12 , 2795 – 2809 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2795 . [CrossRef] [PubMed]
7 . Z. Zhu and T.G. Brown , “ Full-vectorial finite-difference analysis of microstructured optical fibers ,” Opt. Express 10 , 853 – 864 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853 . [PubMed]
8 . Shangping Guo , Feng Wu , Sacharia Albin , Hsiang Tai , and Robert S. Rogowski , “ Loss and dispersion analysis of microstructured fibers by finite-difference method ,” Opt. Express 12 , 3341 – 3352 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341 . [CrossRef] [PubMed]
9 . J.P. Berenger , “ A perfectly matched layer for the absorption of electromagnetic waves ,” J. Comput. Phys. 114 , 185 – 200 ( 1994 ). [CrossRef]
5 . D. Ferrarini , L. Vincetti , M. Zoboli , A. Cucinotta , and S. Selleri , “ Leakage properties of photonic crystal fibers ,” Opt. Express 10 , 1314 – 1319 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314 . [PubMed]
8 . Shangping Guo , Feng Wu , Sacharia Albin , Hsiang Tai , and Robert S. Rogowski , “ Loss and dispersion analysis of microstructured fibers by finite-difference method ,” Opt. Express 12 , 3341 – 3352 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341 . [CrossRef] [PubMed]
11 . H. Rogier and D. De Zutter , “ Berenger and Leaky Modes in Microstrip Substrates Terminated by a Perfectly Matched Layer ,” IEEE Trans. Microwave Theory Tech. 49 , 712 – 715 ( 2001 ). [CrossRef]
12 . A. Bayliss , M. Gunzburger , and E. Turkel , “ Boundary conditions for the numerical solution of elliptic equations in exterior regions ,” SIAM J. Appl. Math. 42 , 430 – 451 ( 1982 ). [CrossRef]
6 . H.P. Uranus and H.J.W.M. Hoekstra , “ Modeling of microstructured waveguides using a finite-element-based vecto-rial mode solver with transparent boundary conditions ,” Opt. Express 12 , 2795 – 2809 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2795 . [CrossRef] [PubMed]
2. Formulation
2.1. Yee’s mesh
2.2. Effective dielectric constants
14 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD analysis of dielectric resonators with curved surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
7 . Z. Zhu and T.G. Brown , “ Full-vectorial finite-difference analysis of microstructured optical fibers ,” Opt. Express 10 , 853 – 864 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853 . [PubMed]
14 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD analysis of dielectric resonators with curved surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
14 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD analysis of dielectric resonators with curved surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
14 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD analysis of dielectric resonators with curved surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
2.3. Discrete function expansion method
15 . M. Mrozowski , “ A Hybrid PEE-FDTD Algorithm for Accelerated Time Domain Analysis of Electromagnetic Waves ,” IEEE Microwave and Guided Wave Letters 4 , 323 – 325 ( 1994 ). [CrossRef]
16 . M. Mrozowski , M. Okoniewski , and M.A. Stuchly , “ A hybrid PEE-FDTD method for efficient field modeling in cyllindrical coordinates ,” Electronics Letters 32 , 194 – 195 ( 1996 ). [CrossRef]
17 . M. Wiktor and M. Mrozowski ,“ Efficient Analysis of Waveguide Components Using a Hybrid PEE-FDFD Algorithm ,” IEEE Microwave and Wireless Components Letters 13 , 396 – 398 ( 2003 ). [CrossRef]
2.4. Radiation condition
3. Numerical results
4 . T.P. White , B.T. Kuhlmey , R.C. McPhedran , D. Maystre , R. Ranversez , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Multipole method for microstructured optical fibers. I. Formulation ,” J. Opt. Soc. Am. B 19 , 2322 – 2330 ( 2002 ). [CrossRef]
3 . T.P. White , R.C. McPhedran , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Confinement losses in microstructured optical fibers ,” Opt. Lett. 26 , 1660 – 1662 ( 2001 ). [CrossRef]
4 . T.P. White , B.T. Kuhlmey , R.C. McPhedran , D. Maystre , R. Ranversez , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Multipole method for microstructured optical fibers. I. Formulation ,” J. Opt. Soc. Am. B 19 , 2322 – 2330 ( 2002 ). [CrossRef]
20 . N.A. Issa and L. Poladian , “ Vector Wave Expansion Method for Leaky Modes of Microstructured Optical Fibers ,” J. Lightwave Technol. 21 , 1005 – 1012 ( 2003 ). [CrossRef]
20 . N.A. Issa and L. Poladian , “ Vector Wave Expansion Method for Leaky Modes of Microstructured Optical Fibers ,” J. Lightwave Technol. 21 , 1005 – 1012 ( 2003 ). [CrossRef]
6 . H.P. Uranus and H.J.W.M. Hoekstra , “ Modeling of microstructured waveguides using a finite-element-based vecto-rial mode solver with transparent boundary conditions ,” Opt. Express 12 , 2795 – 2809 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2795 . [CrossRef] [PubMed]
8 . Shangping Guo , Feng Wu , Sacharia Albin , Hsiang Tai , and Robert S. Rogowski , “ Loss and dispersion analysis of microstructured fibers by finite-difference method ,” Opt. Express 12 , 3341 – 3352 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341 . [CrossRef] [PubMed]
3 . T.P. White , R.C. McPhedran , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Confinement losses in microstructured optical fibers ,” Opt. Lett. 26 , 1660 – 1662 ( 2001 ). [CrossRef]
4 . T.P. White , B.T. Kuhlmey , R.C. McPhedran , D. Maystre , R. Ranversez , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Multipole method for microstructured optical fibers. I. Formulation ,” J. Opt. Soc. Am. B 19 , 2322 – 2330 ( 2002 ). [CrossRef]
8 . Shangping Guo , Feng Wu , Sacharia Albin , Hsiang Tai , and Robert S. Rogowski , “ Loss and dispersion analysis of microstructured fibers by finite-difference method ,” Opt. Express 12 , 3341 – 3352 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341 . [CrossRef] [PubMed]
6 . H.P. Uranus and H.J.W.M. Hoekstra , “ Modeling of microstructured waveguides using a finite-element-based vecto-rial mode solver with transparent boundary conditions ,” Opt. Express 12 , 2795 – 2809 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2795 . [CrossRef] [PubMed]
7 . Z. Zhu and T.G. Brown , “ Full-vectorial finite-difference analysis of microstructured optical fibers ,” Opt. Express 10 , 853 – 864 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853 . [PubMed]
7 . Z. Zhu and T.G. Brown , “ Full-vectorial finite-difference analysis of microstructured optical fibers ,” Opt. Express 10 , 853 – 864 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853 . [PubMed]
4. Conclusions
References and links
1 . | P. Russell , “ Photonic Crystal Fibers ,” Science 299 , 358 – 362 ( 2003 ). [CrossRef] [PubMed] |
2 . | C. Kerbage and B. J. Eggleton , ” Numerical analysis and experimental design of tunable birefringence in microstruc-tured optical fiber ,” Opt. Express 10 , 246 – 255 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-5-246 . [PubMed] |
3 . | T.P. White , R.C. McPhedran , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Confinement losses in microstructured optical fibers ,” Opt. Lett. 26 , 1660 – 1662 ( 2001 ). [CrossRef] |
4 . | T.P. White , B.T. Kuhlmey , R.C. McPhedran , D. Maystre , R. Ranversez , C.M. de Sterke , L.C. Botten , and M.J. Steel , “ Multipole method for microstructured optical fibers. I. Formulation ,” J. Opt. Soc. Am. B 19 , 2322 – 2330 ( 2002 ). [CrossRef] |
5 . | D. Ferrarini , L. Vincetti , M. Zoboli , A. Cucinotta , and S. Selleri , “ Leakage properties of photonic crystal fibers ,” Opt. Express 10 , 1314 – 1319 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314 . [PubMed] |
6 . | H.P. Uranus and H.J.W.M. Hoekstra , “ Modeling of microstructured waveguides using a finite-element-based vecto-rial mode solver with transparent boundary conditions ,” Opt. Express 12 , 2795 – 2809 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2795 . [CrossRef] [PubMed] |
7 . | Z. Zhu and T.G. Brown , “ Full-vectorial finite-difference analysis of microstructured optical fibers ,” Opt. Express 10 , 853 – 864 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853 . [PubMed] |
8 . | Shangping Guo , Feng Wu , Sacharia Albin , Hsiang Tai , and Robert S. Rogowski , “ Loss and dispersion analysis of microstructured fibers by finite-difference method ,” Opt. Express 12 , 3341 – 3352 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341 . [CrossRef] [PubMed] |
9 . | J.P. Berenger , “ A perfectly matched layer for the absorption of electromagnetic waves ,” J. Comput. Phys. 114 , 185 – 200 ( 1994 ). [CrossRef] |
10 . | J.P. Berenger , “ Perfectly matched layer for the FDTD solution of wave-structure. Interaction problems ,” IEEE Trans. Microwave Theory Tech. 44 , 110 – 117 ( 1996 ). |
11 . | H. Rogier and D. De Zutter , “ Berenger and Leaky Modes in Microstrip Substrates Terminated by a Perfectly Matched Layer ,” IEEE Trans. Microwave Theory Tech. 49 , 712 – 715 ( 2001 ). [CrossRef] |
12 . | A. Bayliss , M. Gunzburger , and E. Turkel , “ Boundary conditions for the numerical solution of elliptic equations in exterior regions ,” SIAM J. Appl. Math. 42 , 430 – 451 ( 1982 ). [CrossRef] |
13 . | T. Weiland , “ Verlustbehaftete Wellenleiter mit beliebiger. Randkontur und Materialverteilung ,” AEU 33 , 170 – 174 ( 1979 ). |
14 . | N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD analysis of dielectric resonators with curved surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef] |
15 . | M. Mrozowski , “ A Hybrid PEE-FDTD Algorithm for Accelerated Time Domain Analysis of Electromagnetic Waves ,” IEEE Microwave and Guided Wave Letters 4 , 323 – 325 ( 1994 ). [CrossRef] |
16 . | M. Mrozowski , M. Okoniewski , and M.A. Stuchly , “ A hybrid PEE-FDTD method for efficient field modeling in cyllindrical coordinates ,” Electronics Letters 32 , 194 – 195 ( 1996 ). [CrossRef] |
17 . | M. Wiktor and M. Mrozowski ,“ Efficient Analysis of Waveguide Components Using a Hybrid PEE-FDFD Algorithm ,” IEEE Microwave and Wireless Components Letters 13 , 396 – 398 ( 2003 ). [CrossRef] |
18 . | C.D. Meyer , “ Matrix analysis and applied linear algebra ”, SIAM , Philadelphia ( 2000 ). |
19 . | M. Wiktor and M. Mrozowski ,“ Discrete Projection for Finite Difference Methods ,” 20th Annual Review or Progress in Applied Computational Electromagnetics, Syracuse NY 2004 , Conf. proceedings, S04P08. |
20 . | N.A. Issa and L. Poladian , “ Vector Wave Expansion Method for Leaky Modes of Microstructured Optical Fibers ,” J. Lightwave Technol. 21 , 1005 – 1012 ( 2003 ). [CrossRef] |
OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.2400) Fiber optics and optical communications : Fiber properties
ToC Category:
Research Papers
Citation
P. Kowalczyk, M. Wiktor, and M. Mrozowski, "Efficient finite difference analysis of microstructured optical fibers," Opt. Express 13, 10349-10359 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-25-10349
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References
- P. Russell, "Photonic Crystal Fibers," Science 299, 358-362 (2003). [CrossRef] [PubMed]
- C. Kerbage, B. J. Eggleton, "Numerical analysis and experimental design of tunable birefringence in microstructured optical fiber," Opt. Express 10, 246-255 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-5-246">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-5-246</a>. [PubMed]
- T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, M.J. Steel, "Confinement losses in microstructured optical fibers," Opt. Lett. 26, 1660-1662 (2001). [CrossRef]
- T.P. White, B.T. Kuhlmey, R.C. McPhedran, D.Maystre, R. Ranversez, C.M. de Sterke, L.C. Botten, M.J. Steel, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002). [CrossRef]
- D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, "Leakage properties of photonic crystal fibers," Opt. Express 10, 1314-1319 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314</a>. [PubMed]
- H.P. Uranus, H.J.W.M. Hoekstra, "Modeling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions," Opt. Express 12, 2795-2809 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2795">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2795</a>. [CrossRef] [PubMed]
- Z.Zhu, T.G. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Opt. Express 10, 853-864 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853</a>. [PubMed]
- Shangping Guo, Feng Wu, Sacharia Albin, Hsiang Tai, Robert S. Rogowski,"Loss and dispersion analysis of microstructured fibers by finite-difference method," Opt. Express 12, 3341-3352 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341</a>. [CrossRef] [PubMed]
- J.P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994). [CrossRef]
- J.P. Berenger, "Perfectly matched layer for the FDTD solution of wave-structure. Interaction problems," IEEE Trans. Microwave Theory Tech. 44, 110-117 (1996).
- H. Rogier, D. De Zutter, "Berenger and Leaky Modes in Microstrip Substrates Terminated by a Perfectly Matched Layer," IEEE Trans. Microwave Theory Tech. 49, 712-715 (2001). [CrossRef]
- A. Bayliss, M. Gunzburger, E. Turkel, "Boundary conditions for the numerical solution of elliptic equations in exterior regions," SIAM J. Appl. Math. 42, 430-451 (1982). [CrossRef]
- T.Weiland, "VerlustbehafteteWellenleiter mit beliebiger. Randkontur und Materialverteilung," AEU 33, 170-174 (1979).
- N. Kaneda, B. Houshmand, T. Itoh, "FDTD analysis of dielectric resonators with curved surfaces," IEEE Trans. Microwave Theory Tech. 45, 1645-1649 (1997). [CrossRef]
- M. Mrozowski, "A Hybrid PEE-FDTD Algorithm for Accelerated Time Domain Analysis of Electromagnetic Waves," IEEE Microwave and Guided Wave Letters 4, 323-325 (1994). [CrossRef]
- M. Mrozowski, M. Okoniewski, M.A. Stuchly, "A hybrid PEE- FDTD method for efficient field modeling in cyllindrical coordinates," Electronics Letters 32, 194-195 (1996). [CrossRef]
- M. Wiktor, M. Mrozowski,"Efficient Analysis of Waveguide Components Using a Hybrid PEE-FDFD Algorithm," IEEE Microwave and Wireless Components Letters 13, 396-398 (2003). [CrossRef]
- C.D. Meyer, "Matrix analysis and applied linear algebra", SIAM, Philadelphia (2000).
- M.Wiktor, M. Mrozowski,"Discrete Projection for Finite Difference Methods," 20th Annual Review or Progress in Applied Computational Electromagnetics, Syracuse NY 2004, Conf. proceedings, S04P08.
- N.A. Issa, L. Poladian, "VectorWave Expansion Method for Leaky Modes of Microstructured Optical Fibers," J. Lightwave Technol. 21, 1005-1012 (2003). [CrossRef]
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