## Influence of the refractive index core profile on modal scattering of terminated two-dimensional waveguides

JOSA A, Vol. 24, Issue 6, pp. 1752-1760 (2007)

http://dx.doi.org/10.1364/JOSAA.24.001752

Enhanced HTML Acrobat PDF (229 KB)

### Abstract

We examine the influence of the refractive index core profile on the modal scattering of abruptly terminated slab waveguides. The analysis is based on the integral equation method with accelerating parameters, while for the field description in the waveguide core, an appropriate Lanczos–Fourier expansion is employed. The electric-field distribution on the terminal plane, the reflection and transformation coefficient of the TE guided modes, and the far-field radiation pattern are computed. Numerical results are presented for slab waveguides with step, linear, and parabolic refractive index profiles of the core. Finally, several approximate analytical solutions are derived to study the problem in question and to explain the results obtained.

© 2007 Optical Society of America

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(230.7400) Optical devices : Waveguides, slab

(260.2110) Physical optics : Electromagnetic optics

(290.0290) Scattering : Scattering

**ToC Category:**

Optical Devices

**History**

Original Manuscript: September 13, 2006

Revised Manuscript: December 13, 2006

Manuscript Accepted: December 18, 2006

Published: May 9, 2007

**Citation**

Panagiota A. Koukoutsaki, Nikolaos F. Dasyras, Ioannis G. Tigelis, Alexander B. Manenkov, and Angelos J. Amditis, "Influence of the refractive index core profile on modal scattering of terminated two-dimensional waveguides," J. Opt. Soc. Am. A **24**, 1752-1760 (2007)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-6-1752

Sort: Year | Journal | Reset

### References

- T.Tamir, ed., Integrated Optics, 2nd ed. (Springer,1979).
- R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 1984).
- P. C. Kendall, D. A. Roberts, P. N. Robson, M. J. Adams, and M. J. Robertson, "Semiconductor laser facet reflectivities using free-space radiation modes," IEE Proc.: Optoelectron. 140, 49-55 (1993). [CrossRef]
- A. Vukovic, "Fourier transformation analysis of optoelectronics components and circuits," Ph.D. thesis (University of Nottingham, 2000), (http://www.nottingham.ac.uk/ggiemr/publications/avlowbarthesis.htm).
- A. N. Chester, S. Mastellucci, and A. M. Verga Scheggi, Optical Fiber Sensors (Martinus Nijhoff, 1967).
- A. Ishimura, Wave Propagation and Scattering in Random Media (Academic, 1978).
- J. E. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984). [CrossRef]
- F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991). [CrossRef] [PubMed]
- R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, "Surface polariton reflection and radiation at end faces," Appl. Phys. Lett. 42, 764-766 (1983). [CrossRef]
- E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993). [CrossRef]
- A. F. Gonvharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Yakovlev, "Determination of the dielectric constant of Yba2Cu3O7−δ single crystals in the 10 μm spectral range by SEW phase spectroscopy," Phys. Lett. A 133, 163-166 (1988). [CrossRef]
- K. N. Kocharyn, M. N. Afsar, Yu. H. Avetissian, R. L. Sarkissian, A. Banajanian, and I. I. Tkachov, "A novel quasi-optical resonator for the surface near-millimeter waves," IEEE Trans. Microwave Theory Tech. 47, 27-33 (1999). [CrossRef]
- C. Vassallo, "Reflectivity of multi-dielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide," J. Opt. Soc. Am. A 5, 1918-1928 (1988). [CrossRef]
- F. Fernandez and Y. Lu, Microwave and Optical Waveguide Analysis by the Finite Element Method (Research Studies, 1996).
- A. V. Brovko, A. B. Manenkov, and A. G. Rozhnev, "FDTD-analysis of the wave diffraction from dielectric waveguide discontinuities," Opt. Quantum Electron. 35, 395-406 (2003). [CrossRef]
- C. J. Smartt, T. M. Benson, and P. C. Kendall, "Free-space radiation mode method for the analysis of propagation in optical waveguide devices," IEE Proc.: Optoelectron. 140, 56-61 (1993). [CrossRef]
- A. Vucovic, P. Sewell, T. M. Benson, and P. C. Kendall, "Novel half-space radiation mode method for buried waveguide analysis," Opt. Quantum Electron. 31, 43-51 (1999). [CrossRef]
- D. N. Chien, M. Tanaka, and K. Tanaka, "Numerical simulation of an arbitrarily ended asymmetrical slab waveguide by guided-mode extracted integral equations," J. Opt. Soc. Am. A 19, 1649-1657 (2002). [CrossRef]
- I. G. Tigelis and A. B. Manenkov, "Analysis of mode scattering from an abruptly ended dielectric slab waveguide by an accelerated iteration technique," J. Opt. Soc. Am. A 17, 2249-2259 (2000). [CrossRef]
- A. B. Manenkov, G. P. Latsas, and I. G. Tigelis, "Scattering of the transverse magnetic modes from an abruptly ended strongly asymmetrical slab waveguide by an accelerated integral equation technique," J. Opt. Soc. Am. A 18, 3110-3119 (2001). [CrossRef]
- A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method," Radiophys. Quantum Electron. 25, 1050-1055 (1982). [CrossRef]
- K. Hayashi, M. Koshiba, Y. Tsuji, S. Yoneta, and R. Kaji, "Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis," J. Lightwave Technol. LT-16, 2040-2045 (1998). [CrossRef]
- P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmodes expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001). [CrossRef]
- A. B. Manenkov, T. M. Benson, P. D. Sewell, and P. C. Kendall, "Applicability of scalar theory for analysis of mode reflection from an optical dielectric waveguide end," Opt. Quantum Electron. 33, 1195-1204 (2001). [CrossRef]
- M. J. Adams, An Introduction to Optical Waveguides (Wiley, 1981).
- A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
- A. B. Manenkov, "Excitation of open homogeneous waveguides," Radiophys. Quantum Electron. 13, 578-586 (1970). [CrossRef]
- A. B. Manenkov, "Eigenmodes expansion in lossy open waveguides," Opt. Quantum Electron. 23, 621-632 (1991). [CrossRef]
- C. Lanczos, Applied Analysis (Prentice Hall, 1956).
- P. A. Koukoutsaki, I. G. Tigelis, and A. B. Manenkov, "Guided-mode analysis by the Lanczos-Fourier expansion," J. Opt. Soc. Am. A 19, 2293-2300 (2002). [CrossRef]
- N. F. Dasyras, I. G. Tigelis, A. Tsigopoulos, and A. B. Manenkov, "Calculation of radiation modes using the Lanczos-Fourier expansion," J. Opt. Soc. Am. A 21, 1740-1749 (2004). [CrossRef]
- I. G. Tigelis and A. B. Manenkov, "Scattering from an abruptly terminated asymmetrical slab waveguide," J. Opt. Soc. Am. A 16, 523-532 (1999). [CrossRef]
- D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).
- L. Lewin, Theory of Waveguides (Newness-Butterworths, 1975).
- D. Marcuse, "Gaussian approximation of the fundamental modes of graded-index fibers," J. Opt. Soc. Am. 68, 103-109 (1978). [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.