Abstract

In this paper, a general version of coupled-mode theory for frequency-domain scattering problems in integrated optics is proposed. As a prerequisite, a physically reasonable field template is required, that typically combines modes of the optical channels in the structure with coefficient functions of in principle arbitrary coordinates. Upon 1-D discretizations of these amplitude functions into finite elements, a Galerkin procedure reduces the problem to a system of linear equations in the element coefficients, where given input amplitudes are included. Smooth approximate solutions are obtained by solving the system in a least squares sense. The versatility of the approach is illustrated by means of a series of 2-D examples, including a perpendicular crossing of waveguides, and a grating-assisted rectangular resonator. As an Appendix, we show that, alternatively, a similar procedure can be derived by variational means, i.e., by restricting a suitable functional representation of the full 2-D/3-D vectorial scattering problem (with transparent influx boundary conditions for inhomogeneous exterior) to the respective field templates.

© 2007 IEEE

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  1. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
  2. W. P. Huang, "Coupled mode theory for optical waveguides: An overview," J. Opt. Soc. Amer. A, Opt. Image Sci. 11, 963-983 (1994).
  3. Selected Papers on Coupled-Mode Theory in Guided-Wave Optics (SPIE Opt. Eng. Press, 1993).
  4. S. L. Chuang, "A coupled mode formulation by reciprocity and a variational principle," J. Lightw. Technol. LT-5, 5-15 (1987).
  5. D. R. Rowland, J. D. Love, "Evanescent wave coupling of whispering gallery modes of a dielectric cylinder," Proc. Inst. Electr. Eng., J 140, 177-188 (1993).
  6. K. R. Hiremath, R. Stoffer, M. Hammer, "Modeling of circular integrated optical microresonators by 2-D frequency-domain coupled mode theory," Opt. Commun. 257, 277-297 (2006).
  7. R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, J. tyroký, "Cylindrical integrated optical microresonators: Modeling by 3-D vectorial frequency domain coupled mode theory," Opt. Commun. 256, 46-67 (2005).
  8. M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, P. Hertel, "Radiatively coupled waveguide polarization splitter simulated by wave-matching based coupled mode theory," Opt. Quantum Electron. 31, 877-891 (1999).
  9. J. B. Nicolau, E. van Groesen, "Hybrid analytical–numeric method for light through a bounded planar dielectric structure ," J. Nonlinear Opt. Phys. Mater. 14, 161-176 (2005).
  10. E. W. C. van Groesen, J. Molenaar, Continuum Modeling in the Physical Sciences (SIAM, 2007).
  11. A. Sopaheluwakan, Characterization and Simulation of Localized States in Optical Structures Ph.D. dissertation Univ. TwenteEnschedeThe Netherlands (2006).
  12. M. Lohmeyer, R. Stoffer, "Integrated optical cross strip polarizer concept," Opt. Quantum Electron. 33, 413-431 (2001).
  13. M. Hammer, "Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics," Opt. Commun. 235, 285-303 (2004).
  14. M. Hammer, METRIC—Mode expansion tools for 2D rectangular integrated optical circuits http://www.math.utwente.nl/~hammerm/Metric/.
  15. M. Hammer, "Resonant coupling of dielectric optical waveguides via rectangular microcavities: The coupled guided mode perspective," Opt. Commun. 214, 155-170 (2002).
  16. M. Hammer, D. Yudistira, R. Stoffer, "Modeling of grating assisted standing wave microresonators for filter applications in integrated optics," Opt. Quantum Electron. 36, 25-42 (2004).

2006 (1)

K. R. Hiremath, R. Stoffer, M. Hammer, "Modeling of circular integrated optical microresonators by 2-D frequency-domain coupled mode theory," Opt. Commun. 257, 277-297 (2006).

2005 (2)

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, J. tyroký, "Cylindrical integrated optical microresonators: Modeling by 3-D vectorial frequency domain coupled mode theory," Opt. Commun. 256, 46-67 (2005).

J. B. Nicolau, E. van Groesen, "Hybrid analytical–numeric method for light through a bounded planar dielectric structure ," J. Nonlinear Opt. Phys. Mater. 14, 161-176 (2005).

2004 (2)

M. Hammer, "Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics," Opt. Commun. 235, 285-303 (2004).

M. Hammer, D. Yudistira, R. Stoffer, "Modeling of grating assisted standing wave microresonators for filter applications in integrated optics," Opt. Quantum Electron. 36, 25-42 (2004).

2002 (1)

M. Hammer, "Resonant coupling of dielectric optical waveguides via rectangular microcavities: The coupled guided mode perspective," Opt. Commun. 214, 155-170 (2002).

2001 (1)

M. Lohmeyer, R. Stoffer, "Integrated optical cross strip polarizer concept," Opt. Quantum Electron. 33, 413-431 (2001).

1999 (1)

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, P. Hertel, "Radiatively coupled waveguide polarization splitter simulated by wave-matching based coupled mode theory," Opt. Quantum Electron. 31, 877-891 (1999).

1994 (1)

W. P. Huang, "Coupled mode theory for optical waveguides: An overview," J. Opt. Soc. Amer. A, Opt. Image Sci. 11, 963-983 (1994).

1993 (1)

D. R. Rowland, J. D. Love, "Evanescent wave coupling of whispering gallery modes of a dielectric cylinder," Proc. Inst. Electr. Eng., J 140, 177-188 (1993).

1987 (1)

S. L. Chuang, "A coupled mode formulation by reciprocity and a variational principle," J. Lightw. Technol. LT-5, 5-15 (1987).

J. Lightw. Technol. (1)

S. L. Chuang, "A coupled mode formulation by reciprocity and a variational principle," J. Lightw. Technol. LT-5, 5-15 (1987).

J. Nonlinear Opt. Phys. Mater. (1)

J. B. Nicolau, E. van Groesen, "Hybrid analytical–numeric method for light through a bounded planar dielectric structure ," J. Nonlinear Opt. Phys. Mater. 14, 161-176 (2005).

J. Opt. Soc. Amer. A, Opt. Image Sci. (1)

W. P. Huang, "Coupled mode theory for optical waveguides: An overview," J. Opt. Soc. Amer. A, Opt. Image Sci. 11, 963-983 (1994).

Opt. Commun. (4)

K. R. Hiremath, R. Stoffer, M. Hammer, "Modeling of circular integrated optical microresonators by 2-D frequency-domain coupled mode theory," Opt. Commun. 257, 277-297 (2006).

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, J. tyroký, "Cylindrical integrated optical microresonators: Modeling by 3-D vectorial frequency domain coupled mode theory," Opt. Commun. 256, 46-67 (2005).

M. Hammer, "Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics," Opt. Commun. 235, 285-303 (2004).

M. Hammer, "Resonant coupling of dielectric optical waveguides via rectangular microcavities: The coupled guided mode perspective," Opt. Commun. 214, 155-170 (2002).

Opt. Quantum Electron. (3)

M. Hammer, D. Yudistira, R. Stoffer, "Modeling of grating assisted standing wave microresonators for filter applications in integrated optics," Opt. Quantum Electron. 36, 25-42 (2004).

M. Lohmeyer, R. Stoffer, "Integrated optical cross strip polarizer concept," Opt. Quantum Electron. 33, 413-431 (2001).

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, P. Hertel, "Radiatively coupled waveguide polarization splitter simulated by wave-matching based coupled mode theory," Opt. Quantum Electron. 31, 877-891 (1999).

Proc. Inst. Electr. Eng., J (1)

D. R. Rowland, J. D. Love, "Evanescent wave coupling of whispering gallery modes of a dielectric cylinder," Proc. Inst. Electr. Eng., J 140, 177-188 (1993).

Other (5)

Selected Papers on Coupled-Mode Theory in Guided-Wave Optics (SPIE Opt. Eng. Press, 1993).

E. W. C. van Groesen, J. Molenaar, Continuum Modeling in the Physical Sciences (SIAM, 2007).

A. Sopaheluwakan, Characterization and Simulation of Localized States in Optical Structures Ph.D. dissertation Univ. TwenteEnschedeThe Netherlands (2006).

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

M. Hammer, METRIC—Mode expansion tools for 2D rectangular integrated optical circuits http://www.math.utwente.nl/~hammerm/Metric/.

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