## Circuit model for mode extraction in lossy/lossless photonic crystal waveguides |

JOSA B, Vol. 29, Issue 1, pp. 170-177 (2012)

http://dx.doi.org/10.1364/JOSAB.29.000170

Enhanced HTML Acrobat PDF (702 KB)

### Abstract

An approximate circuit model is proposed for mode extraction in two-dimensional photonic crystal waveguides. The dispersion equation governing the complex propagation constant of the photonic crystal waveguide is then related to the resonance condition in the proposed circuit model. In this fashion, a scalar complex transcendental equation is given for mode extraction. To avoid searching for the complex roots of the derived scalar dispersion equation, however, the real and imaginary parts of the sought-after propagation constant are extracted by using the physical resonance condition and its corresponding quality factor in the here-proposed circuit model, respectively. All the necessary conditions for the accuracy of the proposed circuit model are discussed, and some numerical examples are given. It is fortunate that the proposed model can be applied for accurate mode extraction in most of the applications. Both major polarizations are considered.

© 2011 Optical Society of America

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(130.0130) Integrated optics : Integrated optics

(130.5296) Integrated optics : Photonic crystal waveguides

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: May 17, 2011

Revised Manuscript: August 26, 2011

Manuscript Accepted: October 18, 2011

Published: December 16, 2011

**Citation**

Nasim Habibi, Amin Khavasi, Mehdi Miri, and Khashayar Mehrany, "Circuit model for mode extraction in lossy/lossless photonic crystal waveguides," J. Opt. Soc. Am. B **29**, 170-177 (2012)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-1-170

Sort: Year | Journal | Reset

### References

- S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000). [CrossRef]
- C. Sauvan, P. Lalanne, J. C. Rodier, J. P. Hugonin, and A. Talneau, “Accurate modeling of line-defect photonic crystal waveguides,” IEEE Photon. Technol. Lett. 15, 1243–1245 (2003). [CrossRef]
- K. Yasumoto, H. Jia, and K. Sun, “Rigorous analysis of two-dimensional photonic crystal waveguide,” Radio Sci. 40, 1–7 (2005). [CrossRef]
- P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, “An efficient approach toward guided mode extraction in two-dimensional photonic crystals,” Opt. Commun. 281, 2826–2833 (2008). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
- P. G. Ciarlet, The Finite Element Method for Elliptic Problems (Society for Industrial and Applied Mathematics, 2002).
- A. Khelif, B. Djafari-Rouhani, J. O. Vasseur, P. A. Deymier, Ph. Lambin, and L. Dobrzynski, “Transmittivity through straight and stublike waveguides in a two-dimensional phononic crystal,” Phys. Rev. B 65, 174308 (2002). [CrossRef]
- P. Sarrafi and K. Mehrany, “Fast convergent and unconditionally stable Galerkin’s method with adaptive Hermite–Gauss expansion for guided-mode extraction in two-dimensional photonic crystal based waveguides,” J. Opt. Soc. Am. B 26, 169–175 (2009). [CrossRef]
- E. Istrate and E. H. Sargent, “Photonic crystal waveguide analysis using interface boundary conditions,” IEEE J. Quantum Electron. 41, 461–467 (2005). [CrossRef]
- R. Sorrentino, “Transverse resonance technique,” in Numerical Techniques for Microwave and Millimeter—Wave Passive Structures, T. Itoh, ed. (Wiley, 1989), Chap. 1L.
- T. Rozzi and M. Mongiardo, Open Electromagnetic Waveguides (The Institution of Electrical Engineers, 1997), pp. 135–141.
- W. Kuang, W. J. Kim, A. Mock, and J. O’Brien, “Propagation loss of line-defect photonic crystal slab waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1183–1195 (2006). [CrossRef]
- A. Khavasi, N. Habibi, A. H. Hosseinnia, and K. Mehrany, “A transmission line model for extraction of defect modes in two-dimensional photonic crystals,” in 2010 International Conference on Photonics (ICP) (IEEE, 2010), pp. 1–3.
- M. Miri, A. Khavasi, K. Mehrany, and B. Rashidian, “Transmission line model to design matching stage for light coupling into two-dimensional photonic crystals,” Opt. Lett. 35, 115–117 (2010). [CrossRef]
- S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1965).
- E. Loewen and E. Popov, Diffraction Gratings and Applications (Dekker, 1997).
- A. Khavasi, A. K. Jahromi, and K. Mehrany, “Longitudinal Legendre polynomial expansion of electromagnetic fields for analysis of arbitrary-shaped gratings,” J. Opt. Soc. Am. A 25, 1564–1573 (2008). [CrossRef]
- G. Lifante, Integrated Photonics Fundamentals (Wiley, 2003).
- A. Agrawal and J. H. Lang, Foundations of Analog and Digital Electronic Circuits (Elsevier, 2005).
- Z. Szabó, G. Kádár, and J. Volk, “Band gaps in photonic crystals with dispersion,” Int. J. Comput. Math. Electr. Electron. Eng. (COMPEL) 24, 521–533 (2005). [CrossRef]
- A. H. Hosseinnia, “Migration of eigenmodes in photonic and quantum-well structures,” MSc thesis (Sharif University of Technology, 2008).
- E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reﬂection pole method and wavevector density method,” J. Lightwave Technol. 17, 929–941(1999). [CrossRef]
- Y. Zhao and Y. Hao, “Finite-difference time-domain study of guided modes in nano-plasmonic waveguides,” IEEE Trans. Antennas Propag. 55, 3070–3077 (2007). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.