Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods

Journal of Computational Physics

Volumn 229, Issue 10, 2010, Pages 3706-3725

  Mena, H ^a   Nguyen, N C ^b   Freund, R M ^c   Parrilo, P A ^d   Peraire, J ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b Massachusetts Institute of Technology   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d Department of Electrical Engineering and Computer Science   (United States)

Author keywords

Bandgap optimization; Photonic crystals; Semidefinite programming; Subspace methods

Indexed keywords

CONVEX OPTIMIZATION; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; PHOTONIC BAND GAP; STRUCTURAL OPTIMIZATION;

BANDGAP OPTIMIZATION; EIGENVALUE PROBLEM; LARGE-SCALES; OPTIMISATIONS; OPTIMIZATION PROBLEMS; SEMI-DEFINITE PROGRAM (SDP); SEMI-DEFINITE PROGRAMMING; SUBSPACE METHOD; TWO-DIMENSIONAL PHOTONIC CRYSTALS; WAVE VECTOR;

ENERGY GAP;

EID: 77956407041     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.01.023     Document Type: Article

References (28)

1. F. Alizadeh, Interior point methods in semidefinite programming with applications to combinatorial optimization, SIAM Journal on Optimization 5 (1) (1995) 13-51.
2. F. Alizadeh, J.P.A. Haeberly, M.L. Overton, Primal-dual interior-point methods for semidefinite programming: convergence rates, stability and numerical results, SIAM Journal on Optimization 8 (3) (1998) 746-768.
3. F. Bloch, Über die quantenmechanik der elektronen in kristallgittern, Zeitschrift für Physik A Hadrons and Nuclei 52 (7) (1929) 555-600.
4. M. Burger, S.J. Osher, E. Yablonovitch, Inverse problem techniques for the design of photonic crystals, IEICE Transactions on Electronics E Series C 87, 258-265.
5. E. Cances, C. LeBris, N.C. Nguyen, Y. Maday, A.T. Patera, G.S.H. Pau, Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry, in: Proceedings of the Workshop for High-dimensional Partial Differential Equations in Science and Engineering (Montreal), vol. 41, 2007, pp. 15-57.
6. A. Charnes, W.W. Cooper, Programming with linear functionals, Naval Research Logistics Quarterly 9 (1962).
7. S.J. Cox, D.C. Dobson, Band structure optimization of two-dimensional photonic crystals in H-polarization, Journal of Computational Physics 158 (2) (2000) 214-224.
8. B.D. Craven, B. Mond, The dual of a fractional linear program, Journal of Mathematical Analysis and Applications 42 (3) (1973) 507-512.
9. M. Doosje, B.J. Hoenders, J. Knoester, Photonic bandgap optimization in inverted fcc photonic crystals, Journal of the Optical Society of America B 17 (4) (2000) 600-606.
10. S. Fan, J.D. Joannopoulos, J.N. Winn, A. Devenyi, J.C. Chen, R.D. Meade, Guided and defect modes in periodic dielectric waveguides, Journal of the Optical Society of America B 12 (7) (1995) 1267-1272.
11. S. Fan, P. Villeneuve, J. Joannopoulos, H. Haus, Channel drop filters in photonic crystals, Optics Express 3 (1) (1998) 4-11.
12. G. Floquet, Sur les equations differentielles lineaires a coefficients periodiques, Ann De L'ecole Normale Superieure 2 (12) (1883) 47-88.
13. J.D. Joannopoulos, S.G. Johnson, J.N. Winn, R.D. Meade, Photonic Crystals: Molding the Flow of Light, Princeton University Press, 2008.
14. S. John, Strong localization of photons in certain disordered dielectric superlattices, Physical Review Letters 58 (23) (1987) 2486-2489.
15. C.Y. Kao, S. Osher, E. Yablonovitch, Maximizing band gaps in two-dimensional photonic crystals by using level set methods, Applied Physics B: Lasers and Optics 81 (2) (2005) 235-244.
16. Y. Nesterov, A. Nemirovskii, Interior-point polynomial algorithms in convex programming, SIAM Studies in Applied Mathematics 13 (1994).
17. G.S.H. Pau, Reduced-basis method for band structure calculations, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 76 (4) (2007) 046704.
18. L. Rayleigh, On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure, Philosophical Magazine 24 (147) (1887) 145-159.
19. O. Sigmund, K. Hougaard, Geometric properties of optimal photonic crystals, Physical Review Letters 100 (15) (2008) 153904.
20. O. Sigmund, J.S. Jensen, Systematic design of phononic band-gap materials and structures by topology optimization, Philosophical Transactions: Mathematical, Physical and Engineering Sciences (2003) 1001-1019.
21. M. Soljacic, S.G. Johnson, M. Ibanescu, Y. Fink, J.D. Joannopoulos, Optimal bistable switching in nonlinear photonic crystals, Physical Review E 66 (2002) 055601.
22. R.H. Tütüncü, K.C. Toh, M.J. Todd, Solving semidefinite-quadratic-linear programs using SDPT3, Mathematical Programming 95 (2) (2003) 189-217.
23. L. Vandenberghe, S. Boyd, Semidefinite programming, SIAM Review 38 (1) (1996) 49-95.
24. H. Weyl, Symmetry, Princeton University Press, 1952.
25. H. Wolkowicz, R. Saigal, L. Vandenberghe, Handbook of Semidefinite Programming: Theory, Algorithms, and Applications, Kluwer Academic Publishers, 2000.
26. E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics, Physical Review Letters 58 (20) (1987) 2059-2062.
27. X.L. Yang, L.Z. Cai, Y.R. Wang, C.S. Feng, G.Y. Dong, X.X. Shen, X.F. Meng, Y. Hu, Optimization of band gap of photonic crystals fabricated by holographic lithography, EPL-Europhysics Letters 81 (1) (2008) 14001.
28. M.F. Yanik, S. Fan, Stopping and storing light coherently, Physical Review A 71 (1) (2005) 013803. Jan.