Abstract

A computationally-fast inverse design method for nanophotonic structures is presented. The method is based on two complementary convex optimization problems which modify the dielectric structure and resonant field respectively. The design of one- and two-dimensional nanophotonic resonators is demonstrated and is shown to require minimal computational resources.

© 2010 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Yee, "Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media," IEEE Trans. Antennas Propag. Mag. 14, 302-307 (1966).
    [CrossRef]
  2. M. Albani and P. Bernardi, "A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form," IEEE Trans. Microwave Theory Tech. 22, 446-450 (1974).
    [CrossRef]
  3. J. M. Gerardy and M. Ausloos, "Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. The long-wavelength limit," Phys. Rev. B 22, 4950-4959 (1979).
    [CrossRef]
  4. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009).
    [CrossRef]
  5. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 1-11 (2002).
  6. Y. Akahane, T. Asano, B. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
    [CrossRef]
  7. A. Gondarenko and M. Lipson, "Low modal volume dipole-like dielectric slab resonator," Opt. Express 16, 17689-17694 (2008).
    [CrossRef]
  8. A. Hakansson and J. Sanchez-Dehesa, "Inverse designed photonic crystal de-multiplex waveguide coupler," Opt. Express 13, 5440-5449 (2005).
    [CrossRef]
  9. P. Borel, A. Harpth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, "Topology optimization and fabrication of photonic crystal structures," Opt. Express 12, 1996-2001 (2004).
    [CrossRef]
  10. D. Englund, I. Fushman, and J. Vuckovic. "General Recipe for Designing Photonic Crystal Cavities," Opt. Express 12, 59615975 (2005).
  11. CHOLMOD software package, accessed via MatLab.
  12. Intel Core 2 Quad 2.5GHz, 8Gb RAM.
  13. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwells equations in a planewave basis," Opt. Express 8, 967-970 (1999).
  14. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
  15. M. Grant and S. Boyd, CVX: MatLab software for disciplined convex programming, http://stanford.edu/~boyd/cvx, June 2009.
  16. K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
    [CrossRef]
  17. B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
    [CrossRef]
  18. K. Rivoire, Z. Lin, F. Hatami, W. Ted Masselink, and J. Vuckovic, "Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power," Opt. Express 17, 22609-22615 (2009).
    [CrossRef]

2009 (2)

2008 (1)

2006 (1)

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

2005 (4)

B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

D. Englund, I. Fushman, and J. Vuckovic. "General Recipe for Designing Photonic Crystal Cavities," Opt. Express 12, 59615975 (2005).

Y. Akahane, T. Asano, B. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef]

A. Hakansson and J. Sanchez-Dehesa, "Inverse designed photonic crystal de-multiplex waveguide coupler," Opt. Express 13, 5440-5449 (2005).
[CrossRef]

2004 (1)

2002 (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 1-11 (2002).

1999 (1)

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwells equations in a planewave basis," Opt. Express 8, 967-970 (1999).

1979 (1)

J. M. Gerardy and M. Ausloos, "Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. The long-wavelength limit," Phys. Rev. B 22, 4950-4959 (1979).
[CrossRef]

1974 (1)

M. Albani and P. Bernardi, "A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form," IEEE Trans. Microwave Theory Tech. 22, 446-450 (1974).
[CrossRef]

1966 (1)

K. Yee, "Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media," IEEE Trans. Antennas Propag. Mag. 14, 302-307 (1966).
[CrossRef]

Akahane, Y.

B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef]

Albani, M.

M. Albani and P. Bernardi, "A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form," IEEE Trans. Microwave Theory Tech. 22, 446-450 (1974).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef]

B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Ausloos, M.

J. M. Gerardy and M. Ausloos, "Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. The long-wavelength limit," Phys. Rev. B 22, 4950-4959 (1979).
[CrossRef]

Badolato, A.

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Bernardi, P.

M. Albani and P. Bernardi, "A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form," IEEE Trans. Microwave Theory Tech. 22, 446-450 (1974).
[CrossRef]

Borel, P.

Deotare, P.

P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Englund, D.

D. Englund, I. Fushman, and J. Vuckovic. "General Recipe for Designing Photonic Crystal Cavities," Opt. Express 12, 59615975 (2005).

Frandsen, L.

Frank, I.

P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Fushman, I.

D. Englund, I. Fushman, and J. Vuckovic. "General Recipe for Designing Photonic Crystal Cavities," Opt. Express 12, 59615975 (2005).

Gerardy, J. M.

J. M. Gerardy and M. Ausloos, "Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. The long-wavelength limit," Phys. Rev. B 22, 4950-4959 (1979).
[CrossRef]

Gondarenko, A.

Hakansson, A.

Harpth, A.

Hatami, F.

Hennessy, K.

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Hogerle, C.

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Hu, E.

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Imamoglu, A.

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Jensen, J.

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwells equations in a planewave basis," Opt. Express 8, 967-970 (1999).

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwells equations in a planewave basis," Opt. Express 8, 967-970 (1999).

Khan, M.

P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Kristensen, M.

Lin, Z.

Lipson, M.

Loncar, M.

P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 1-11 (2002).

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 1-11 (2002).

McCutcheon, M.

P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef]

B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Rivoire, K.

Sanchez-Dehesa, J.

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 1-11 (2002).

Shi, P.

Sigmund, O.

Song, B.

Song, B. -S.

B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Ted Masselink, W.

Vuckovic, J.

K. Rivoire, Z. Lin, F. Hatami, W. Ted Masselink, and J. Vuckovic, "Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power," Opt. Express 17, 22609-22615 (2009).
[CrossRef]

D. Englund, I. Fushman, and J. Vuckovic. "General Recipe for Designing Photonic Crystal Cavities," Opt. Express 12, 59615975 (2005).

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 1-11 (2002).

Yee, K.

K. Yee, "Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media," IEEE Trans. Antennas Propag. Mag. 14, 302-307 (1966).
[CrossRef]

Appl. Phys. Lett. (2)

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, "Tuning photonic nanocavities by atomic force microscope nano-oxidation," Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

IEEE Trans. Antennas Propag. Mag. (1)

K. Yee, "Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media," IEEE Trans. Antennas Propag. Mag. 14, 302-307 (1966).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. Albani and P. Bernardi, "A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form," IEEE Trans. Microwave Theory Tech. 22, 446-450 (1974).
[CrossRef]

Nat. Mater. (1)

B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Opt. Express (7)

Phys. Rev. B (1)

J. M. Gerardy and M. Ausloos, "Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. The long-wavelength limit," Phys. Rev. B 22, 4950-4959 (1979).
[CrossRef]

Phys. Rev. E (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 1-11 (2002).

Other (4)

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).

M. Grant and S. Boyd, CVX: MatLab software for disciplined convex programming, http://stanford.edu/~boyd/cvx, June 2009.

CHOLMOD software package, accessed via MatLab.

Intel Core 2 Quad 2.5GHz, 8Gb RAM.

Cited By

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

Alert me when this article is cited.


Metrics