A finite-difference frequency-domain method for full-vectroial mode solutions of anisotropic optical waveguides with an arbitrary permittivity tensor
Optics Express, Vol. 17, Issue 8, pp. 5965-5979 (2009)
http://dx.doi.org/10.1364/OE.17.005965
Acrobat PDF (971 KB)
Abstract
A new finite-difference frequency-domain (FDFD) method based eigenvalue algorithm is developed for analyzing anisotropic optical waveguides with an arbitrary permittivity tensor. Yee’s mesh is employed in the FD formulation along with perfectly matched layer (PML) absorption boundary conditions. A standard eigenvalue matrix equation is successfully derived through considering simultaneously four transverse field components. The new algorithm is first applied to the mode solution of a proton-exchanged LiNbO_{3} optical waveguide and the results agree with those obtained using a full-vectorial finite-element beam propagation method. Then, the algorithm is used to study modes on a liquid-crystal optical waveguide with arbitrary molecular director orientation. This arbitrary orientation may cause the loss of transverse-axis symmetries of the waveguide with symmetric background structure. Asymmetric mode-field profiles under such situations are clearly demonstrated in the numerical examples.
© 2009 Optical Society of America
1. Introduction
1. C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, “Full-vectorial mode calculations by finite difference method,” Proc. Inst. Electr. Eng. 141, 281–286 (1994). [CrossRef]
2. P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–494 (1994). [CrossRef]
3. G. R. Hadley, “High-accuracy finite-difference equations for dielectric waveguide analysis I: Uniform regions and dielectric interfaces,” J. Lightwave Technol. 20, 1210–1218 (2002). [CrossRef]
8. T. Ando, H. Nakayama, S. Numata, J. Yamauchi, and H. Nakano, “Eigenmode analysis of optical waveguides by a Yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface,” J. Lightwave Technol. 20, 1627–1634 (2002). [CrossRef]
11. L. Thylen and D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982). [CrossRef] [PubMed]
15. A. B. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Lightwave Technol. 26, 1423–1431 (2008). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
17. F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media”, IEEE Microwave Guid. Wave Lett. 8, 223V–225 (1998). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
2. Formulation
10. C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express , 12, 6165V–6177 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6165. [CrossRef]
10. C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express , 12, 6165V–6177 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6165. [CrossRef]
9. 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]
17. F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media”, IEEE Microwave Guid. Wave Lett. 8, 223V–225 (1998). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
18. R. Mittra and U. Pekel, “A new look an the perfectly matched layer PML concept for the reflectionless absorption of electromagnetic waves,” IEEE Microwave Guid. Wave Lett. 5, 84–86 (1995). [CrossRef]
3. Numerical examples
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
16. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
10. C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express , 12, 6165V–6177 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6165. [CrossRef]
10. C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express , 12, 6165V–6177 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6165. [CrossRef]
4. Conclusion
Acknowledgments
References and links
1. | C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, “Full-vectorial mode calculations by finite difference method,” Proc. Inst. Electr. Eng. 141, 281–286 (1994). [CrossRef] |
2. | P. Lüsse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12, 487–494 (1994). [CrossRef] |
3. | G. R. Hadley, “High-accuracy finite-difference equations for dielectric waveguide analysis I: Uniform regions and dielectric interfaces,” J. Lightwave Technol. 20, 1210–1218 (2002). [CrossRef] |
4. | G. R. Hadley, “High-accuracy finite-difference equations for dielectric waveguide analysis II: Dielectric corners,” J. Lightwave Technol. 20, 1219–1231 (2002). [CrossRef] |
5. | P. J. Chiang, C. L. Wu, C. H. Teng, C. S. Yang, and H. C. Chang, “Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations,” IEEE J. Quantum Electron. 44, 56–66, (2008). [CrossRef] |
6. | N. Thomas, P. Sewell, and T. M. benson, “A new full-vectorial higher order finite-difference scheme for the modal analysis of rectangular dielectric waveguides,” J. Lightwave Technol. 25, 2563–2570 (2007). [CrossRef] |
7. | K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966). |
8. | T. Ando, H. Nakayama, S. Numata, J. Yamauchi, and H. Nakano, “Eigenmode analysis of optical waveguides by a Yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface,” J. Lightwave Technol. 20, 1627–1634 (2002). [CrossRef] |
9. | 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] |
10. | C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express , 12, 6165V–6177 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6165. [CrossRef] |
11. | L. Thylen and D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982). [CrossRef] [PubMed] |
12. | C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, “A full-vectorial beam propagation method for anisotropic waveguides,” J. Lightwave Technol. 12, 1926–1931 (1994). [CrossRef] |
13. | C. L. D. S. Sobrinho and A. J. Giarola, “Analysis of biaxially anisotropic dielectric waveguides with Gaussian-Gaussian index of refraction profiles by the finite-difference method,” IEE Proc.-H 140, 224–230 (1993). |
14. | P. Lüsse, K. Ramm, and H.-G. Unger, “Vectorial eigenmode calculation for anisotropic planar optical waveguides,” Electron. Lett. 32, 38–39 (1996). [CrossRef] |
15. | A. B. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Lightwave Technol. 26, 1423–1431 (2008). [CrossRef] |
16. | K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef] |
17. | F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media”, IEEE Microwave Guid. Wave Lett. 8, 223V–225 (1998). [CrossRef] |
18. | R. Mittra and U. Pekel, “A new look an the perfectly matched layer PML concept for the reflectionless absorption of electromagnetic waves,” IEEE Microwave Guid. Wave Lett. 5, 84–86 (1995). [CrossRef] |
19. | P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley and Sons, Inc., New York, 1999). |
OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.3720) Optical devices : Liquid-crystal devices
(230.7370) Optical devices : Waveguides
(260.2110) Physical optics : Electromagnetic optics
ToC Category:
Physical Optics
History
Original Manuscript: January 28, 2009
Revised Manuscript: March 18, 2009
Manuscript Accepted: March 18, 2009
Published: March 30, 2009
Citation
Ming-yun Chen, Sen-ming Hsu, and Hung-Chun Chang, "A finite-difference frequency-domain method for full-vectroial mode solutions of anisotropic optical waveguides with arbitrary permittivity tensor," Opt. Express 17, 5965-5979 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-5965
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References
- C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," Proc. Inst. Electr. Eng. 141, 281-286 (1994). [CrossRef]
- P. L¨usse, P. Stuwe, J. Schule, and H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by a new finite difference method," J. Lightwave Technol. 12, 487-494 (1994). [CrossRef]
- G. R. Hadley, "High-accuracy finite-difference equations for dielectric waveguide analysis I: Uniform regions and dielectric interfaces," J. Lightwave Technol. 20, 1210-1218 (2002). [CrossRef]
- G. R. Hadley, "High-accuracy finite-difference equations for dielectric waveguide analysis II: Dielectric corners," J. Lightwave Technol. 20, 1219-1231 (2002). [CrossRef]
- P. J. Chiang, C. L. Wu, C. H. Teng, C. S. Yang, and H. C. Chang, "Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations," IEEE J. Quantum Electron. 44, 56-66, (2008). [CrossRef]
- N. Thomas, P. Sewell, and T. M. benson, "A new full-vectorial higher order finite-difference scheme for the modal analysis of rectangular dielectric waveguides," J. Lightwave Technol. 25, 2563-2570 (2007). [CrossRef]
- K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
- T. Ando, H. Nakayama, S. Numata, J. Yamauchi, and H. Nakano, "Eigenmode analysis of optical waveguides by a Yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface," J. Lightwave Technol. 20, 1627-1634 (2002). [CrossRef]
- 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]
- C. P. Yu, and H. C. Chang, "Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers," Opt. Express, 12, 6165V-6177 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6165. [CrossRef]
- L. Thylen and D. Yevick, "Beam propagation method in anisotropic media," Appl. Opt. 21, 2751-2754 (1982). [CrossRef] [PubMed]
- C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, "A full-vectorial beam propagation method for anisotropic waveguides," J. Lightwave Technol. 12, 1926-1931 (1994). [CrossRef]
- C. L. D. S. Sobrinho and A. J. Giarola, "Analysis of biaxially anisotropic dielectric waveguides with Gaussian-Gaussian index of refraction profiles by the finite-difference method," IEE Proc.-H 140, 224-230 (1993).
- P. Lüsse, K. Ramm, and H.-G. Unger, "Vectorial eigenmode calculation for anisotropic planar optical waveguides," Electron. Lett. 32, 38-39 (1996). [CrossRef]
- A. B. Fallahkhair, K. S. Li, and T. E. Murphy, "Vector finite difference modesolver for anisotropic dielectric waveguides," J. Lightwave Technol. 26, 1423-1431 (2008). [CrossRef]
- K. Saitoh, and M. Koshiba, "Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides," J. Lightwave Technol. 19, 405-413 (2001). [CrossRef]
- F. L. Teixeira and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microwave Guid. Wave Lett. 8, 223V-225 (1998). [CrossRef]
- R. Mittra and U. Pekel, "A new look an the perfectly matched layer PML concept for the reflectionless absorption of electromagnetic waves," IEEE Microwave Guid. Wave Lett. 5, 84-86 (1995). [CrossRef]
- P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley and Sons, Inc., New York, 1999).
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