Abstract

In this paper, a new method based on the complex images technique is presented for analysis of 2-D periodic devices such as waveguides, directional couplers, and coupled cavity waveguides (CCW). The main idea of this method lies in representing the infinite summation of the periodic Green's functions of such kind of structures in terms of finite terms of complex images. The electric field integral equation has been used to formulate the problem and the method of moments has been applied afterward for solving the equation. The method has been used successfully in the analysis of different waveguides, directional couplers, and CCWs in both rectangular and triangular lattices. Fast convergence, simple formulations, and flexibility of the method in analyzing different structures are the main advantages of the proposed method.

© 2009 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. E. Yablonovitch, "Photonic bandgap structure," J. Opt. Soc. Amer. B 10, 283-295 (1993).
  2. S. Kawakami, "Analytically solvable model of photonic crystal structures and novel phenomena," J. Lightw. Technol. 20, 1644-1650 (2002).
  3. W. Axmann, P. Kuchment, L. Kunyansky, "Asymptotic methods for thin high-contrast two-dimensional PBG materials," J. Lightw. Technol. 17, 1996-2007 (1999).
  4. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
  5. H. Benisty, C. Weisbuch, M. Agio, M. Kafesaki, C. M. Soukoulis, M. Qiu, M. Swillo, A. Karlsson, B. Jaskorzynska, A. Talneau, J. Moosburger, M. Kamp, A. Forchell, R. Ferrini, R. Houdre, U. Oesterle, "Models and measurements for the transmission of submicron-width waveguide bends defined in two-dimensional photonic crystals," IEEE J. Quantum Electron. 38, 770-785 (2002).
  6. M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightw. Technol. 19, 1970-1975 (2001).
  7. S. Boscolo, M. Midrio, C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 1, 47-53 (2002).
  8. C. Jin, S. Han, X. Meng, B. Cheng, D. Zhang, "Demultiplexer using directly resonant tunneling between point defects and waveguides in a photonic crystal," J. Appl. Phys. 91, 4771-4773 (2002).
  9. N. J. Florous, K. Saitoh, M. Koshiba, "Modeling of two-dimensional photonic crystal resonant cavities incorporating elliptically shaped dielectric cylinders," IEEE Photon. Technol. Lett. 17, 2316-2318 (2005).
  10. B. Denecker, F. Olyslager, L. Knockaert, D. De Zutter, "Generation of FDTD subcell equations by means of reduced order modeling," IEEE Trans. Antennas Propag. 51, 1806-1817 (2003).
  11. H. Derudder, D. De Zutter, F. Olyslager, "A new way to analyze waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).
  12. P. Bienstman, R. Baets, "Optical modeling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
  13. C. Hafner, "Multiple multipole program computation of periodic structures," J. Opt. Soc. Am. A 12, 1057-1067 (1995).
  14. Moreno, D. Erni, C. Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Phys. Rev. B 65, 5120-5130 (2002).
  15. M. G. Khazinsky, A. R. McGurn, "Green's function method for waveguide and single impurity methods in 2-D photonic crystals: H-polarization," Phys. Lett. 237, 175-182 (1998).
  16. D. Pissoort, E. Michielssen, F. Olyslager, D. De Zutter, "Fast analysis of 2-D electromagnetic crystal devices using a periodic Green function approach," J. Lightw. Technol. 23, 2294-2308 (2005).
  17. R. Collin, Field Theory of Guided Waves (McGraw-Hill, 1991).
  18. S. Singh, W. F. Richards, J. R. Zinecker, D. R. Wilton, "Accelerating the convergence of series representing the free space periodic Green's function," IEEE Trans. Antennas Propag. 38, 1958-1962 (1990).
  19. R. Lampe, P. Klock, P. Mayes, "Integral transforms useful for the accelerated summation of periodic free-space Green's function," IEEE Trans. Microw. Theory Tech. 33, 734-736 (1985).
  20. Y. L. Chow, J. J. Yang, D. G. Fang, G. E. Howard, "A closed-form spatial Green's function for the thick microstrip substrate," IEEE Trans. Microw. Theory Tech. 39, 588-592 (1991).
  21. Y. Hua, T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag. 37, 229-234 (1989).
  22. M. Yuan, T. K. Sarkar, "Computation of the Sommerfeld integral tails using the matrix pencil method," IEEE Trans. Antennas Propag. 54, 1358-1362 (2006).
  23. A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, A. Scherer, "Role of distributed Bragg reflection in photonic-crystal optical waveguides," Phys. Rev. B 64, 1102-1105 (2001).
  24. A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, A. Scherer, "Properties of the slab modes in photonic crystal optical waveguides," J. Lightw. Technol. 18, 1554-1564 (2000).
  25. S. G. Johnson, P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
  26. I. Vorobeichil, M. Orenstein, "Intermediate-mode assisted optical directional couplers via embedded periodic structures," IEEE J. Quantum Electron. 34, 1772-1781 (1998).
  27. A. Yariv, Y. Xu, R. K. Lee, A. Scherer, "Coupled-resonator optical waveguide: A proposal and analysis," Opt. Lett. 24, 711-713 (1999).
  28. M. Soljacic, J. D. Joannopoulos, "Enhancement of nonlinear effect using photonic crystals," Nature 3, 211-219 (2004).
  29. M. Soljacic, C. Luo, J. D. Joannopoulos, S. Fan, "Non-linear photonic crystal micro-devices for optical integration," Opt. Lett. 28, 637-639 (2003).
  30. E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, "Simulation of photonic band gaps in metal rod lattices for microwave applications," J. Appl. Phys. 91, 960-968 (2002).

2006 (1)

M. Yuan, T. K. Sarkar, "Computation of the Sommerfeld integral tails using the matrix pencil method," IEEE Trans. Antennas Propag. 54, 1358-1362 (2006).

2005 (2)

N. J. Florous, K. Saitoh, M. Koshiba, "Modeling of two-dimensional photonic crystal resonant cavities incorporating elliptically shaped dielectric cylinders," IEEE Photon. Technol. Lett. 17, 2316-2318 (2005).

D. Pissoort, E. Michielssen, F. Olyslager, D. De Zutter, "Fast analysis of 2-D electromagnetic crystal devices using a periodic Green function approach," J. Lightw. Technol. 23, 2294-2308 (2005).

2004 (1)

M. Soljacic, J. D. Joannopoulos, "Enhancement of nonlinear effect using photonic crystals," Nature 3, 211-219 (2004).

2003 (2)

M. Soljacic, C. Luo, J. D. Joannopoulos, S. Fan, "Non-linear photonic crystal micro-devices for optical integration," Opt. Lett. 28, 637-639 (2003).

B. Denecker, F. Olyslager, L. Knockaert, D. De Zutter, "Generation of FDTD subcell equations by means of reduced order modeling," IEEE Trans. Antennas Propag. 51, 1806-1817 (2003).

2002 (6)

S. Boscolo, M. Midrio, C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 1, 47-53 (2002).

C. Jin, S. Han, X. Meng, B. Cheng, D. Zhang, "Demultiplexer using directly resonant tunneling between point defects and waveguides in a photonic crystal," J. Appl. Phys. 91, 4771-4773 (2002).

S. Kawakami, "Analytically solvable model of photonic crystal structures and novel phenomena," J. Lightw. Technol. 20, 1644-1650 (2002).

H. Benisty, C. Weisbuch, M. Agio, M. Kafesaki, C. M. Soukoulis, M. Qiu, M. Swillo, A. Karlsson, B. Jaskorzynska, A. Talneau, J. Moosburger, M. Kamp, A. Forchell, R. Ferrini, R. Houdre, U. Oesterle, "Models and measurements for the transmission of submicron-width waveguide bends defined in two-dimensional photonic crystals," IEEE J. Quantum Electron. 38, 770-785 (2002).

Moreno, D. Erni, C. Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Phys. Rev. B 65, 5120-5130 (2002).

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, "Simulation of photonic band gaps in metal rod lattices for microwave applications," J. Appl. Phys. 91, 960-968 (2002).

2001 (3)

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, A. Scherer, "Role of distributed Bragg reflection in photonic-crystal optical waveguides," Phys. Rev. B 64, 1102-1105 (2001).

P. Bienstman, R. Baets, "Optical modeling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).

M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightw. Technol. 19, 1970-1975 (2001).

2000 (2)

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, A. Scherer, "Properties of the slab modes in photonic crystal optical waveguides," J. Lightw. Technol. 18, 1554-1564 (2000).

S. G. Johnson, P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).

1999 (2)

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, "Coupled-resonator optical waveguide: A proposal and analysis," Opt. Lett. 24, 711-713 (1999).

W. Axmann, P. Kuchment, L. Kunyansky, "Asymptotic methods for thin high-contrast two-dimensional PBG materials," J. Lightw. Technol. 17, 1996-2007 (1999).

1998 (3)

H. Derudder, D. De Zutter, F. Olyslager, "A new way to analyze waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).

M. G. Khazinsky, A. R. McGurn, "Green's function method for waveguide and single impurity methods in 2-D photonic crystals: H-polarization," Phys. Lett. 237, 175-182 (1998).

I. Vorobeichil, M. Orenstein, "Intermediate-mode assisted optical directional couplers via embedded periodic structures," IEEE J. Quantum Electron. 34, 1772-1781 (1998).

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

1995 (1)

C. Hafner, "Multiple multipole program computation of periodic structures," J. Opt. Soc. Am. A 12, 1057-1067 (1995).

1993 (1)

E. Yablonovitch, "Photonic bandgap structure," J. Opt. Soc. Amer. B 10, 283-295 (1993).

1991 (1)

Y. L. Chow, J. J. Yang, D. G. Fang, G. E. Howard, "A closed-form spatial Green's function for the thick microstrip substrate," IEEE Trans. Microw. Theory Tech. 39, 588-592 (1991).

1990 (1)

S. Singh, W. F. Richards, J. R. Zinecker, D. R. Wilton, "Accelerating the convergence of series representing the free space periodic Green's function," IEEE Trans. Antennas Propag. 38, 1958-1962 (1990).

1989 (1)

Y. Hua, T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag. 37, 229-234 (1989).

1985 (1)

R. Lampe, P. Klock, P. Mayes, "Integral transforms useful for the accelerated summation of periodic free-space Green's function," IEEE Trans. Microw. Theory Tech. 33, 734-736 (1985).

Electron. Lett. (1)

H. Derudder, D. De Zutter, F. Olyslager, "A new way to analyze waveguide discontinuities using perfectly matched layers," Electron. Lett. 34, 2138-2140 (1998).

IEEE J. Quantum Electron. (1)

H. Benisty, C. Weisbuch, M. Agio, M. Kafesaki, C. M. Soukoulis, M. Qiu, M. Swillo, A. Karlsson, B. Jaskorzynska, A. Talneau, J. Moosburger, M. Kamp, A. Forchell, R. Ferrini, R. Houdre, U. Oesterle, "Models and measurements for the transmission of submicron-width waveguide bends defined in two-dimensional photonic crystals," IEEE J. Quantum Electron. 38, 770-785 (2002).

IEEE Trans. Antennas Propag. (2)

B. Denecker, F. Olyslager, L. Knockaert, D. De Zutter, "Generation of FDTD subcell equations by means of reduced order modeling," IEEE Trans. Antennas Propag. 51, 1806-1817 (2003).

M. Yuan, T. K. Sarkar, "Computation of the Sommerfeld integral tails using the matrix pencil method," IEEE Trans. Antennas Propag. 54, 1358-1362 (2006).

IEEE Trans. Microw. Theory Tech. (2)

R. Lampe, P. Klock, P. Mayes, "Integral transforms useful for the accelerated summation of periodic free-space Green's function," IEEE Trans. Microw. Theory Tech. 33, 734-736 (1985).

Y. L. Chow, J. J. Yang, D. G. Fang, G. E. Howard, "A closed-form spatial Green's function for the thick microstrip substrate," IEEE Trans. Microw. Theory Tech. 39, 588-592 (1991).

IEEE J. Quantum Electron. (2)

I. Vorobeichil, M. Orenstein, "Intermediate-mode assisted optical directional couplers via embedded periodic structures," IEEE J. Quantum Electron. 34, 1772-1781 (1998).

S. Boscolo, M. Midrio, C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 1, 47-53 (2002).

IEEE Photon. Technol. Lett. (1)

N. J. Florous, K. Saitoh, M. Koshiba, "Modeling of two-dimensional photonic crystal resonant cavities incorporating elliptically shaped dielectric cylinders," IEEE Photon. Technol. Lett. 17, 2316-2318 (2005).

IEEE Trans. Antennas Propag. (2)

S. Singh, W. F. Richards, J. R. Zinecker, D. R. Wilton, "Accelerating the convergence of series representing the free space periodic Green's function," IEEE Trans. Antennas Propag. 38, 1958-1962 (1990).

Y. Hua, T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag. 37, 229-234 (1989).

J. Appl. Phys. (1)

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, "Simulation of photonic band gaps in metal rod lattices for microwave applications," J. Appl. Phys. 91, 960-968 (2002).

J. Lightw. Technol. (2)

S. Kawakami, "Analytically solvable model of photonic crystal structures and novel phenomena," J. Lightw. Technol. 20, 1644-1650 (2002).

W. Axmann, P. Kuchment, L. Kunyansky, "Asymptotic methods for thin high-contrast two-dimensional PBG materials," J. Lightw. Technol. 17, 1996-2007 (1999).

J. Appl. Phys. (1)

C. Jin, S. Han, X. Meng, B. Cheng, D. Zhang, "Demultiplexer using directly resonant tunneling between point defects and waveguides in a photonic crystal," J. Appl. Phys. 91, 4771-4773 (2002).

J. Lightw. Technol. (3)

M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightw. Technol. 19, 1970-1975 (2001).

D. Pissoort, E. Michielssen, F. Olyslager, D. De Zutter, "Fast analysis of 2-D electromagnetic crystal devices using a periodic Green function approach," J. Lightw. Technol. 23, 2294-2308 (2005).

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, A. Scherer, "Properties of the slab modes in photonic crystal optical waveguides," J. Lightw. Technol. 18, 1554-1564 (2000).

J. Opt. Soc. Am. A (1)

C. Hafner, "Multiple multipole program computation of periodic structures," J. Opt. Soc. Am. A 12, 1057-1067 (1995).

J. Opt. Soc. Amer. B (1)

E. Yablonovitch, "Photonic bandgap structure," J. Opt. Soc. Amer. B 10, 283-295 (1993).

Nature (1)

M. Soljacic, J. D. Joannopoulos, "Enhancement of nonlinear effect using photonic crystals," Nature 3, 211-219 (2004).

Opt. Lett. (2)

Opt. Quantum Electron. (1)

P. Bienstman, R. Baets, "Optical modeling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).

Phys. Rev. B (1)

Moreno, D. Erni, C. Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Phys. Rev. B 65, 5120-5130 (2002).

Phys. Lett. (1)

M. G. Khazinsky, A. R. McGurn, "Green's function method for waveguide and single impurity methods in 2-D photonic crystals: H-polarization," Phys. Lett. 237, 175-182 (1998).

Phys. Rev. B (2)

S. G. Johnson, P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, A. Scherer, "Role of distributed Bragg reflection in photonic-crystal optical waveguides," Phys. Rev. B 64, 1102-1105 (2001).

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

Other (1)

R. Collin, Field Theory of Guided Waves (McGraw-Hill, 1991).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.