Inverse design of nanophotonic structures using complementary convex optimization
Optics Express, Vol. 18, Issue 4, pp. 3793-3804 (2010)
http://dx.doi.org/10.1364/OE.18.003793
Acrobat PDF (1508 KB)
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
1. Introduction
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]
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] [PubMed]
10. D. Englund, I. Fushman, and J. Vuckovic. “General Recipe for Designing Photonic Crystal Cavities,” Opt. Express 12, 5961–5975 (2005). [CrossRef]
2. Numerical setup
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]
3. Least-squares method in 1D
3.1. Least-Squares
3.2. Regularized least-squares
4. Complementary optimization in 1D
4.1. Motivation for a Complementary Optimization Strategy
4.2. Complementary optimization
4.3. Complementary optimization with bounded ε
15. M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, http://stanford.edu/∼boyd/cvx, June 2009.
5. Complementary optimization in 2D
5.1. “S” Resonator
5.2. Multi-mode inverse design
5.3. Design of waveguiding devices
6. Complementary optimization with bounded ε in 2D
6.1. Numerical method
10. D. Englund, I. Fushman, and J. Vuckovic. “General Recipe for Designing Photonic Crystal Cavities,” Opt. Express 12, 5961–5975 (2005). [CrossRef]
6.2. Circular grating resonator
7. A. Gondarenko and M. Lipson, “Low modal volume dipole-like dielectric slab resonator,” Opt. Express 16, 17689–17694 (2008). [CrossRef] [PubMed]
6.3. Beam resonator
10. D. Englund, I. Fushman, and J. Vuckovic. “General Recipe for Designing Photonic Crystal Cavities,” Opt. Express 12, 5961–5975 (2005). [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]
7. Conclusions and outlook
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]
Acknowledgements
References and links
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] [PubMed] |
7. | A. Gondarenko and M. Lipson, “Low modal volume dipole-like dielectric slab resonator,” Opt. Express 16, 17689–17694 (2008). [CrossRef] [PubMed] |
8. | A. Hakansson and J. Sanchez-Dehesa, “Inverse designed photonic crystal de-multiplex waveguide coupler,” Opt. Express 13, 5440–5449 (2005). [CrossRef] [PubMed] |
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] [PubMed] |
10. | D. Englund, I. Fushman, and J. Vuckovic. “General Recipe for Designing Photonic Crystal Cavities,” Opt. Express 12, 5961–5975 (2005). [CrossRef] |
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] |
OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.5750) Optical devices : Resonators
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(230.5298) Optical devices : Photonic crystals
ToC Category:
Optical Design and Fabrication
History
Original Manuscript: December 21, 2009
Revised Manuscript: February 2, 2010
Manuscript Accepted: February 4, 2010
Published: February 10, 2010
Citation
Jesse Lu and Jelena Vuckovic, "Inverse design of nanophotonic structures using complementary convex optimization," Opt. Express 18, 3793-3804 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3793
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References
- 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]
- 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]
- 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]
- 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).
- Y. Akahane, T. Asano, B. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005). [CrossRef] [PubMed]
- A. Gondarenko and M. Lipson, "Low modal volume dipole-like dielectric slab resonator," Opt. Express 16, 17689-17694 (2008). [CrossRef] [PubMed]
- A. Hakansson and J. Sanchez-Dehesa, "Inverse designed photonic crystal de-multiplex waveguide coupler," Opt. Express 13, 5440-5449 (2005). [CrossRef] [PubMed]
- 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] [PubMed]
- D. Englund, I. Fushman, and J. Vuckovic. "General Recipe for Designing Photonic Crystal Cavities," Opt. Express 12, 59615975 (2005). [CrossRef]
- CHOLMOD software package, accessed via MatLab.
- Intel Core 2 Quad 2.5GHz, 8Gb RAM.
- 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).
- 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.
- 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]
- B. -S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005). [CrossRef]
- 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]
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