Abstract

Extraordinary optical absorption (EOA) can be obtained by plasmonic surface structuring. However, studies that compare the performance of these plasmonic devices with similar structured dielectric devices are rarely found in the literature. In this work we show different methods to enhance the EOA by optimizing the geometry of the surface structuring for both plasmonic and dielectric devices, and the optimized performances are compared. Two different problem types with periodic structures are considered. The first case shows that strips of silicon on a surface can increase the absorption in an underlying silicon layer for certain optical wavelengths compared to metal strips. It is then demonstrated that by topology optimization it is possible to generate nonintuitive surface designs that perform even better than the simple strip designs for both silicon and metals. These results indicate that in general it is important to compare the absorption performance of plasmonic devices with similarly structured dielectric devices in order to find the best possible solution.

© 2013 Optical Society of America

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    [CrossRef]

2012 (4)

M. B. Dühring, N. A. Mortensen, and O. Sigmund, “Plasmonic versus dielectric enhancement in thin-film solar cells,” Appl. Phys. Lett. 100, 211914 (2012).
[CrossRef]

K. Q. Le, A. Abass, B. Maes, P. Bienstman, and A. Alù, “Comparing plasmonic and dielectric gratings for absorption enhancement in thin-film organic solar cells,” Opt. Express 20, A39–A50 (2012).
[CrossRef]

A. Polman, and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[CrossRef]

K. S. Friis, and O. Sigmund, “Robust topology design of periodic grating surfaces,” J. Opt. Soc. Am. B 29, 2935–2943 (2012).
[CrossRef]

2011 (1)

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[CrossRef]

2010 (6)

M. B. Dühring, O. Sigmund, and T. Feurer, “Design of photonic-bandgap fibers by topology optimization,” J. Opt. Soc. Am. B 27, 51–58 (2010).
[CrossRef]

K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidiscip. Optim. 42, 483–493 (2010).
[CrossRef]

J. A. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” J. Opt. Soc. Am. B 27, 1828–1832 (2010).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

2009 (2)

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef]

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

2008 (3)

2007 (1)

F. J. G. de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

2006 (3)

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Num. Methods Eng. 65, 975–1001 (2006).
[CrossRef]

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photon. Technol. Lett. 18, 850–852 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (2)

O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Philos. Trans. R. Soc. A 361, 1001–1019 (2003).
[CrossRef]

U. Basu and A. K. Chopra, “Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation,” Comput. Methods Appl. Mech. Eng. 192, 1337–1375 (2003).
[CrossRef]

1999 (1)

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108–2120 (1999).
[CrossRef]

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

A. D. Rakic, A. B. Djurišic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[CrossRef]

1994 (1)

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Eng. 1, 71–105 (1994).
[CrossRef]

1988 (1)

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods.Appl. Mech.Eng. 71, 197–224 (1988).
[CrossRef]

1987 (1)

K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Num. Methods Eng. 24, 359–373 (1987).
[CrossRef]

1985 (1)

Abass, A.

Alù, A.

Andkjær, J. A.

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Atwater, H. A.

A. Polman, and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef]

Basu, U.

U. Basu and A. K. Chopra, “Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation,” Comput. Methods Appl. Mech. Eng. 192, 1337–1375 (2003).
[CrossRef]

Bendsøe, M. P.

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods.Appl. Mech.Eng. 71, 197–224 (1988).
[CrossRef]

M. P. Bendsøe and O. Sigmund, Topology Optimization—Theory, Methods and Applications (Springer-Verlag, 2003).

Bienstman, P.

Borel, P. I.

Brongersma, M. L.

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef]

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

Bruus, H.

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Num. Methods Eng. 65, 975–1001 (2006).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Cao, L. Y.

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Catchpole, K. R.

Chandran, A.

Chopra, A. K.

U. Basu and A. K. Chopra, “Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation,” Comput. Methods Appl. Mech. Eng. 192, 1337–1375 (2003).
[CrossRef]

Cox, S. J.

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108–2120 (1999).
[CrossRef]

Cozens, J. R.

R. R. Syms and J. R. Cozens, Optical Guided Waves and Devices (McGraw-Hill, 1992).

de Abajo, F. J. G.

F. J. G. de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

Derkacs, D.

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Diaz, A. R.

K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidiscip. Optim. 42, 483–493 (2010).
[CrossRef]

Djurišic, A. B.

Dobson, D. C.

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108–2120 (1999).
[CrossRef]

Dühring, M. B.

M. B. Dühring, N. A. Mortensen, and O. Sigmund, “Plasmonic versus dielectric enhancement in thin-film solar cells,” Appl. Phys. Lett. 100, 211914 (2012).
[CrossRef]

M. B. Dühring, O. Sigmund, and T. Feurer, “Design of photonic-bandgap fibers by topology optimization,” J. Opt. Soc. Am. B 27, 51–58 (2010).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Elazar, J. M.

Fan, P.

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Fan, S.

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef]

Feurer, T.

Frandsen, L. H.

Friis, K. S.

Fuchi, K.

K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidiscip. Optim. 42, 483–493 (2010).
[CrossRef]

Ganapati, V.

O. D. Miller, V. Ganapati, and E. Yablonovitch, “Inverse design of a nano-scale surface texture for light trapping,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CF2J.2.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Hall, D. G.

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Harpøth, A.

Hirayama, K.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photon. Technol. Lett. 18, 850–852 (2006).
[CrossRef]

Jensen, J. S.

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[CrossRef]

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22, 1191–1198 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, J. S. Jensen, P. Shi, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004).
[CrossRef]

O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Philos. Trans. R. Soc. A 361, 1001–1019 (2003).
[CrossRef]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Kikuchi, N.

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods.Appl. Mech.Eng. 71, 197–224 (1988).
[CrossRef]

Kristensen, M.

Le, K. Q.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Lim, S. H.

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Liu, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Maes, B.

Majewski, M. L.

Mar, W.

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Matheu, P.

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Michaleris, P.

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Eng. 1, 71–105 (1994).
[CrossRef]

Miller, O. D.

O. D. Miller, V. Ganapati, and E. Yablonovitch, “Inverse design of a nano-scale surface texture for light trapping,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CF2J.2.

Mortensen, N. A.

M. B. Dühring, N. A. Mortensen, and O. Sigmund, “Plasmonic versus dielectric enhancement in thin-film solar cells,” Appl. Phys. Lett. 100, 211914 (2012).
[CrossRef]

Nishiwaki, S.

J. A. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” J. Opt. Soc. Am. B 27, 1828–1832 (2010).
[CrossRef]

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photon. Technol. Lett. 18, 850–852 (2006).
[CrossRef]

Nomura, T.

J. A. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” J. Opt. Soc. Am. B 27, 1828–1832 (2010).
[CrossRef]

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photon. Technol. Lett. 18, 850–852 (2006).
[CrossRef]

Okkels, F.

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Num. Methods Eng. 65, 975–1001 (2006).
[CrossRef]

Olesen, L. H.

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Num. Methods Eng. 65, 975–1001 (2006).
[CrossRef]

Ouedraogo, R.

K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidiscip. Optim. 42, 483–493 (2010).
[CrossRef]

Pala, R. A.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

Polman, A.

A. Polman, and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16, 21793–21800 (2008).
[CrossRef]

Rakic, A. D.

Riishede, J.

Rothwell, E.

K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidiscip. Optim. 42, 483–493 (2010).
[CrossRef]

Sato, K.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photon. Technol. Lett. 18, 850–852 (2006).
[CrossRef]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Shi, P.

Sigmund, O.

K. S. Friis, and O. Sigmund, “Robust topology design of periodic grating surfaces,” J. Opt. Soc. Am. B 29, 2935–2943 (2012).
[CrossRef]

M. B. Dühring, N. A. Mortensen, and O. Sigmund, “Plasmonic versus dielectric enhancement in thin-film solar cells,” Appl. Phys. Lett. 100, 211914 (2012).
[CrossRef]

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[CrossRef]

J. A. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” J. Opt. Soc. Am. B 27, 1828–1832 (2010).
[CrossRef]

M. B. Dühring, O. Sigmund, and T. Feurer, “Design of photonic-bandgap fibers by topology optimization,” J. Opt. Soc. Am. B 27, 51–58 (2010).
[CrossRef]

J. Riishede and O. Sigmund, “Inverse design of dispersion compensating optical fibres using topology optimization,” J. Opt. Soc. Am. B 25, 88–97 (2008).
[CrossRef]

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22, 1191–1198 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, J. S. Jensen, P. Shi, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004).
[CrossRef]

O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Philos. Trans. R. Soc. A 361, 1001–1019 (2003).
[CrossRef]

M. P. Bendsøe and O. Sigmund, Topology Optimization—Theory, Methods and Applications (Springer-Verlag, 2003).

Svanberg, K.

K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Num. Methods Eng. 24, 359–373 (1987).
[CrossRef]

Syms, R. R.

R. R. Syms and J. R. Cozens, Optical Guided Waves and Devices (McGraw-Hill, 1992).

Temme, A.

K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidiscip. Optim. 42, 483–493 (2010).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Tortorelli, D. A.

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Eng. 1, 71–105 (1994).
[CrossRef]

Tsuji, Y.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photon. Technol. Lett. 18, 850–852 (2006).
[CrossRef]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Vasudev, A. P.

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Veronis, G.

Weller-Brophy, L. A.

White, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef]

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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Yablonovitch, E.

O. D. Miller, V. Ganapati, and E. Yablonovitch, “Inverse design of a nano-scale surface texture for light trapping,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CF2J.2.

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D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Yu, Z.

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Adv. Mater. (1)

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

M. B. Dühring, N. A. Mortensen, and O. Sigmund, “Plasmonic versus dielectric enhancement in thin-film solar cells,” Appl. Phys. Lett. 100, 211914 (2012).
[CrossRef]

Comput. Methods Appl. Mech. Eng. (1)

U. Basu and A. K. Chopra, “Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation,” Comput. Methods Appl. Mech. Eng. 192, 1337–1375 (2003).
[CrossRef]

Comput. Methods.Appl. Mech.Eng. (1)

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods.Appl. Mech.Eng. 71, 197–224 (1988).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photon. Technol. Lett. 18, 850–852 (2006).
[CrossRef]

Int. J. Num. Methods Eng. (2)

K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Num. Methods Eng. 24, 359–373 (1987).
[CrossRef]

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Num. Methods Eng. 65, 975–1001 (2006).
[CrossRef]

Inverse Probl. Eng. (1)

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Eng. 1, 71–105 (1994).
[CrossRef]

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

J. Opt. Soc. Am. B (5)

Laser Photon. Rev. (1)

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[CrossRef]

Nano Lett. (1)

L. Y. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Nat. Mater. (4)

A. Polman, and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Philos. Trans. R. Soc. A (1)

O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Philos. Trans. R. Soc. A 361, 1001–1019 (2003).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. G. de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

SIAM J. Appl. Math. (1)

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108–2120 (1999).
[CrossRef]

Struct. Multidiscip. Optim. (1)

K. Fuchi, A. R. Diaz, E. Rothwell, R. Ouedraogo, and A. Temme, “Topology optimization of periodic layouts of dielectric materials,” Struct. Multidiscip. Optim. 42, 483–493 (2010).
[CrossRef]

Other (5)

R. R. Syms and J. R. Cozens, Optical Guided Waves and Devices (McGraw-Hill, 1992).

COMSOL AB, “COMSOL reference manual for COMSOL 3.5, 3.5 edition” (COMSOL AB,Stockholm, Sweden).

Virginia Semiconductor, Inc., “Optical properties of silicon,” www.virginiasemi.com.

M. P. Bendsøe and O. Sigmund, Topology Optimization—Theory, Methods and Applications (Springer-Verlag, 2003).

O. D. Miller, V. Ganapati, and E. Yablonovitch, “Inverse design of a nano-scale surface texture for light trapping,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CF2J.2.

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Figures (5)

Fig. 1.
Fig. 1.

Periodic cell structure with period p. The strips on the surface with thickness t can consist of the four different materials Si Al, Ag, and Au. The absorbed energy is measured in Ωabs, and PMLs are added at each end of the domain.

Fig. 2.
Fig. 2.

Normalized absorption in Ωabs compared to a bare surface for strips made of the four materials Si, Al, Ag, and Au as function of the wavelength λ. The four plots are made when the sizes of the strips are optimized for the wavelength, indicated by the vertical dotted line.

Fig. 3.
Fig. 3.

Results for the structures optimized for λ=633nm: the absolute value of the magnetic field normalized to the amplitude of the incoming wave H0 for (a) Si and (b) Al strips; the logarithm to the absorption ΦH normalized to the amplitude of the incoming wave for (c) Si and (d) Al strips.

Fig. 4.
Fig. 4.

Results of the topology optimization for λ=633nm where white corresponds to air and black to solid material in the optimized designs. (a) Design with Si for t=100nm, (b) design with Si for t=200nm, (c) design with Al for t=80nm, and (d) absorption in Ωabs for the optimized designs (topopt) normalized with the absorption for a bare surface as a function of the wavelength λ.

Fig. 5.
Fig. 5.

Results of the topology optimization for λ=440, 633, and 849 nm. (a) Optimized design with Si for t=150nm, where white corresponds to air and black to Si and (b) absorption in Ωabs for the optimized designs (topopt) normalized with the absorption for a bare surface as a function of the wavelength λ. The performance is compared to that of the optimized designs (topopt) from Figs. 4(a) and 4(b).

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

1γixi(1γiAuxi)+k02Bu=0inΩ,
γ1(x1)=1jσ(x1xn)2,
ni(Auxi)2jk0ABu0=0onΓin,
ni(Auxi)+jk0ABu=0onΓout,
ni(Auxi)=0onΓ{ΓinΓout}.
u(r)=n=1Nunϕ1,n(r).
Su=f,
ΦH=ΩabsR(12[H3x1(H3x1jωεr)*+H3x2(H3x2jωεr)*]I(εr)jεr)dr,
ΦE=ΩabsR(ωε0I(εr)2E3E3*)dr.
εr(ρ)=εa+ρ(εsεa).
maxρlog(ΦH),objective function
subject to0ρ(r)1rΩd,design variable bounds.
ρ(r)=n=1Ndρnϕ2,n(r).
dΦHdρ=ΦHρ+ΦHH3RH3Rρ+ΦHH3IH3Iρ.
STλ=(ΦH3RjΦH3I)T,
ΦH3RjΦH3I=Ωo(H3x1jωεr)*I(εr)jεrϕ1,nx1+(H3x2jωεr)*I(εr)jεrϕ1,nx2dr.
dΦdρ=Φρ+R(λTSρH3).

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