Abstract

The inverse design of a three-dimensional nanophotonic resonator is presented. The design methodology is computationally fast (10 minutes on a standard desktop workstation) and utilizes a 2.5-dimensional approximation of the full three-dimensional structure. As an example, we employ the proposed method to design a resonator which exhibits a mode volume of 0.32(λ/n)3 and a quality factor of 7063.

© 2011 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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  4. K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. Mag. 14, 302–307 (1966).
    [CrossRef]
  5. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
  6. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein are preparing a manuscript to be called, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” http://www.stanford.edu/~boyd/papers/distr_opt_stat_learning_admm.html .
  7. Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, “Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,” ACM Trans. Math. Software 35(3), 2 (2009).
  8. M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming , version 1.21. http://cvxr.com/cvx , January 2011.
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    [CrossRef] [PubMed]
  10. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of Q-factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
    [CrossRef]

2010 (1)

2009 (1)

Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, “Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,” ACM Trans. Math. Software 35(3), 2 (2009).

2005 (1)

2004 (1)

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

2002 (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of Q-factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

2000 (2)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–749 (2000).
[CrossRef]

U. Inan and A. Inan, Electromagnetic Waves (Prentice Hall, 2000), p. 296.

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. Mag. 14, 302–307 (1966).
[CrossRef]

Boyd, S.

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

Chen, Y.

Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, “Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,” ACM Trans. Math. Software 35(3), 2 (2009).

Davis, T. A.

Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, “Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,” ACM Trans. Math. Software 35(3), 2 (2009).

Englund, D.

Fushman, I.

Hager, W. W.

Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, “Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,” ACM Trans. Math. Software 35(3), 2 (2009).

Inan, A.

U. Inan and A. Inan, Electromagnetic Waves (Prentice Hall, 2000), p. 296.

Inan, U.

U. Inan and A. Inan, Electromagnetic Waves (Prentice Hall, 2000), p. 296.

Loncar, M.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of Q-factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

Lu, J.

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of Q-factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–749 (2000).
[CrossRef]

Rajamanickam, S.

Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, “Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,” ACM Trans. Math. Software 35(3), 2 (2009).

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of Q-factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

Vandenberghe, L.

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

Vuckovic, J.

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. Mag. 14, 302–307 (1966).
[CrossRef]

ACM Trans. Math. Software (1)

Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, “Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,” ACM Trans. Math. Software 35(3), 2 (2009).

IEEE J. Quantum Electron. (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of Q-factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. Mag. (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. Mag. 14, 302–307 (1966).
[CrossRef]

Opt. Express (2)

Proc. IEEE (1)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–749 (2000).
[CrossRef]

Other (4)

U. Inan and A. Inan, Electromagnetic Waves (Prentice Hall, 2000), p. 296.

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

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein are preparing a manuscript to be called, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” http://www.stanford.edu/~boyd/papers/distr_opt_stat_learning_admm.html .

M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming , version 1.21. http://cvxr.com/cvx , January 2011.

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