## Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. II. Numerical analysis

JOSA A, Vol. 23, Issue 6, pp. 1478-1487 (2006)

http://dx.doi.org/10.1364/JOSAA.23.001478

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### Abstract

We present numerical implementation and verification of a rigorous full-vector, integral-equation formulation suitable for analyzing modal characteristics of complex, two-dimensional (2D) rectangular-like dielectric waveguides. By dividing the waveguide into vertical slices, a system of integral equations we call vector-coupled transverse-mode integral equations (VCTMIE) is derived. The entire electromagnetic mode fields are completely determined by one-dimensional unknown field functions on the slice interfaces. To further reduce numerical computation, we expand these functions in terms of the guiding modes of a slab waveguide with a large normalized frequency. Through orthogonal projection the resulting nonlinear eigenvalue and eigenvector matrix formulation enables us to obtain the effective mode index with

© 2006 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(130.0130) Integrated optics : Integrated optics

(230.4170) Optical devices : Multilayers

(230.7370) Optical devices : Waveguides

**ToC Category:**

Optical Devices

**History**

Original Manuscript: August 26, 2005

Revised Manuscript: December 4, 2005

Manuscript Accepted: December 8, 2005

**Citation**

Hung-Wen Chang and Tso-Lun Wu, "Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. II. Numerical analysis," J. Opt. Soc. Am. A **23**, 1478-1487 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-6-1478

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### References

- H. W. Chang, T. L. Wu, and M. H. Sheng, "Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. I. Mathematical formulation," J. Opt. Soc. Am. A 23, 1468-1477 (2006). [CrossRef]
- R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000). [CrossRef]
- E. A. Marcatili, "Dielectric rectangular waveguide and dielectric coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2103 (1969).
- J. E. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133-2160 (1969).
- S. F. Tsao, S. M. Chang, H. W. Chang, "Vectorial modal analysis of 2D dielectric waveguides by simple orthogonal basis," in Proceedings of Optics and Photonics Taiwan 2003 (National Taipei University of Technology, 2003), pp. 94-96.
- C. C. Huang, C.-C. Huang, and J. Y. Yang, "An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition," J. Lightwave Technol. 21, 2284-2296 (2003). [CrossRef]
- P. C. Waterman, "New formulations of acoustic scattering," J. Acoust. Soc. Am. 45, 1417-1429 (1969). [CrossRef]
- M. H. Sheng and H. W. Chang, "Accurate first-order leaky-wave analysis of antiresonant reflecting optical waveguides," Appl. Opt. 44, 751-764 (2005). [CrossRef] [PubMed]
- N. Kikuchi, Y. Shibata, H. Okamoto, Y. Kanaguchi, S. Oku, Y. Kondo, and Y. Tohmori, "Monolithically integrated 100-channel WDM channel selector employing low-crosstalk AWG," IEEE Photon. Technol. Lett. 16, 2481-2483 (2004). [CrossRef]
- M. Kohtoku, T. Hirono, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, "Control of higher order leaky modes in deep-ridged waveguides and application to low-crosstalk arrayed waveguide gratings," J. Lightwave Technol. 22, 499-508 (2004). [CrossRef]
- T. L. Wu and H. W. Chang, "Guiding mode expansion of a TE and TM transverse-mode integral equation for dielectric slab waveguides with an abrupt termination," J. Opt. Soc. Am. A 18, 2823-2832 (2001). [CrossRef]
- 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). [CrossRef]
- D. U. Li and H. C. Chang, "Full-vectorial finite element modal analysis of bounded and unbounded waveguides," in Proceedings of Asia Pacific Microwave Conference 2001 (National Taiwan University, 2001), pp. 376-379.
- Y. C. Chiang, Y. P. Chiou, and H. C. Chang, "Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles," J. Lightwave Technol. 20, 1609-1618 (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]
- N. Thomas, "Finite-difference methods for the modal analysis of dielectric waveguides with rectangular corners," Ph.D thesis(University of Nottingham, UK, 2004).
- A. S. Sudbo, "Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?" J. Lightwave Technol. 10, 418-419 (1992). [CrossRef]
- W. W. Lui, C.-L. Xu, W.-P. Huang, K. Yokoyama, and S. Seki, "Full-vectorial mode analysis with considerations of field singularities at corners of optical waveguides," J. Lightwave Technol. 17, 1509-1513 (1999). [CrossRef]
- T. Lu and D. Yevick, "Comparative evaluation of a novel series approximation for electromagnetic fields at dielectric corners with boundary element method applications," J. Lightwave Technol. 22, 1426-1432 (2004). [CrossRef]

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