Comprehensive theory of plane-wave expansion based eigenmode method for scattering-matrix analysis of photonic structures

Journal of the Optical Society of America B: Optical Physics

Volumn 26, Issue 7, 2009, Pages 1341-1350

  Krishnamurthy, Vivek ^a   Klein, Benjamin ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL DEFECTS; ELASTIC WAVES; PHOTONIC CRYSTALS; WAVE PROPAGATION;

CONVERGENCE ANALYSIS; EIGEN-MODE EXPANSION; EIGENMODE METHOD; LARGE STRUCTURES; PHOTONIC STRUCTURE; PLANE-WAVE EXPANSIONS; REFLECTION AND TRANSMISSION; SCATTERING MATRICES;

MATRIX ALGEBRA;

EID: 67849103849     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.26.001341     Document Type: Article

References (31)

1. T. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction gratings," Proc. IEEE 73, 894-937 (1985).
2. D. M. Whittaker and I. S. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
3. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001).
4. M. Dems, R. Kotynski, and K. Panajatov, "Plane-wave admittance method-a novel approach of determining the electromagnetic modes in photonic structures," Opt. Express 13, 3196-3207 (2005).
5. E. Istrate, A. A. Green, and E. H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005).
6. A. S. Sudbo, "Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides," Pure Appl. Opt. 2, 211-233 (1993).
7. K. A. Zaki, S. Chen, and C. Chen, "Modeling discontinuities in dielectric loaded waveguides," IEEE Trans. Microwave Theory Tech. 36, 1804-1810 (1988).
8. P. Bienstman, "Rigorous and efficient modeling of wavelength scale photonic components," Ph.D. dissertation (University of Gent, 2001).
9. L. Li, "Use of Fourier-series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
10. P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996).
11. P. Bienstman and R. Baets, "Rigorous and efficient optical VCSEL model based on vectorial eigenmode expansion and perfectly matched layers," IEE Proc.: Optoelectron. 149, 161-165 (2002).
12. J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St. J. Russel, and P. J. Roberts, "Robust photonic band gaps for hollow core guidance in PCF made from high index glass," Opt. Express 11, 2854-2861 (2003).
13. G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plane-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005).
14. S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 045102 (2002).
15. S. Shi, C. Chen, and D. W. Prather, "Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers," J. Opt. Soc. Am. A 21, 1769-1775 (2004).
16. S. Johnson and S. D. Joannapoulos, "Block-iterative frequency domain methods for Maxwell's equations in a plane-wave basis," Opt. Express 8, 173-190 (2001).
17. R. Kotynski, M. Dems, and K. Panajotov, "Waveguiding losses of micro-structured fibres-plane wave method revisited," Opt. Quantum Electron. 39, 469-479 (2007).
18. P. Bienstman, "Two-stage mode finder for waveguides with a 2D cross section," Opt. Quantum Electron. 36, 5-14 (2004).
19. S.-T. Peng and A. Oliner, "Guidance and leakage properties of a class of open dielectric waveguides: Part I- Mathematical formulations," IEEE Trans. Microwave Theory Tech. 29, 843-855 (1981).
20. A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and leakage properties of a class of open dielectric waveguides: Part II-New physical effects," IEEE Trans. Microwave Theory Tech. 29, 855-869 (1981).
21. A. S. Omar and K. F. Schunenmann, "Complex and backward-wave modes in inhomogeneously and anisotropically filled waveguides," IEEE Trans. Microwave Theory Tech. 35, 268-275 (1987).
22. J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 2002), pp. 233-267.
23. G. Sleijpen and H. A. van der Vorst, "A Jacobi-Davidson iteration method for linear eigenvalue problems," SIAM J. Matrix Anal. Appl. 17, 401-425 (1996).
24. D. R. Fokkema, G. L. G. Sleijpen, and H. A. van der Vorst, "Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils," SIAM J. Sci. Comput. 20, 94-125 (1998).
25. R. B. Lehoucq, D. C. Sorenson, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM Publications, 1998).
26. L. Li, "Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings," J. Opt. Soc. Am. A 11, 2829-2836 (1994).
27. S. Fan and S. D. Joannapoulos, "Analysis of guided mode resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
28. N. Yokouchi, A. J. Danner, and K. D. Choquette, "Twodimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1439-1445 (2003).
29. M. Dems, T. Czyszanowski, and K. Panajotov, "Numerical analysis of high Q-factor photonic-crystal VCSELs with plane-wave admittance method," Opt. Quantum Electron. 39, 419-426 (2007).
30. A. Furukawa, M. Hoshi, S. Sasaki, A. Matsuzono, K. Morito, and T. Baba, "High-power single-transverse-mode holey VCSELs," Proc. SPIE 5722, 183-190 (2005).
31. T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).