Abstract

We develop a generalized formalism for describing the propagation of an electromagnetic wave along the z-direction of a dielectric medium. The derivation is achieved by casting the 2-D transverse part of the Maxwell equations in a Schrodinger-like form whose Hamiltonian is identified to be pseudo-Hermitian. The developed formalism is combined with the variational principle to derive a set of nonorthogonal coupled-mode theory which is slightly different from that derived using the same variational principle but with the 3-D Maxwell equations. By showing that the 3-D variational approach suffers from a mode-expansion incompatibility issue that is absent in our 2-D case, we conclude that our nonorthogonal coupled-mode theory is more rigorous. Owing to the complexity of the second-order error of the propagation constant as revealed by further analysis, it is found that our nonorthogonal coupled-mode theory may not necessarily be more accurate in practice. The developed pseudo-Hermitian formalism may provide a good framework for the analysis and design of various integrated optical devices.

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  1. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1992).
  2. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  3. T. Tamir, Integrated Optics (Springer-Verlag, 1982).
  4. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
  5. E. Merzbacher, Quantum Mechanics (Wiley, 1997).
  6. A. Mostafazadeh, "Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian," J. Math. Phys. 43, 205-214 (2002).
  7. A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," IEEE J. Lightw. Technol. 3, 1135-1146 (1985).
  8. W. Streifer, M. Osinski, A. Hardy, "Reformulation of the coupled mode theory of multiwaveguide systems," IEEE J. Lightw. Technol. 5, 1-4 (1987).
  9. H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," IEEE J. Lightw. Technol. 5, 16-23 (1987).
  10. H. A. Haus, W. P. Huang, "Coupled-mode theory," Proc. IEEE 79, 1505-1518 (1991).

2002 (1)

A. Mostafazadeh, "Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian," J. Math. Phys. 43, 205-214 (2002).

1991 (1)

H. A. Haus, W. P. Huang, "Coupled-mode theory," Proc. IEEE 79, 1505-1518 (1991).

1987 (2)

W. Streifer, M. Osinski, A. Hardy, "Reformulation of the coupled mode theory of multiwaveguide systems," IEEE J. Lightw. Technol. 5, 1-4 (1987).

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," IEEE J. Lightw. Technol. 5, 16-23 (1987).

1985 (1)

A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," IEEE J. Lightw. Technol. 3, 1135-1146 (1985).

IEEE J. Lightw. Technol. (1)

W. Streifer, M. Osinski, A. Hardy, "Reformulation of the coupled mode theory of multiwaveguide systems," IEEE J. Lightw. Technol. 5, 1-4 (1987).

IEEE J. Lightw. Technol. (2)

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," IEEE J. Lightw. Technol. 5, 16-23 (1987).

A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," IEEE J. Lightw. Technol. 3, 1135-1146 (1985).

J. Math. Phys. (1)

A. Mostafazadeh, "Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian," J. Math. Phys. 43, 205-214 (2002).

Proc. IEEE (1)

H. A. Haus, W. P. Huang, "Coupled-mode theory," Proc. IEEE 79, 1505-1518 (1991).

Other (5)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1992).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 1984).

T. Tamir, Integrated Optics (Springer-Verlag, 1982).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

E. Merzbacher, Quantum Mechanics (Wiley, 1997).

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