Abstract

We study the scattering of waveguided light by a single hole in a dielectric slab with FDTD simulations and investigate two scattering processes: two dimensional (2D) scattering into slab modes and three-dimensional (3D) scattering into the surroundings. We find that 2D scattering typically dominates over the 3D losses. We find important quantitative differences between the single hole scattering and the case of scattering from an infinite Mie cylinder. Additionally, we find that a hole cannot be simply modelled as a dipolar object even in the limit of small scatterers (Rayleigh approximation). This is visible from the angular dependence of the 2D scattered intensity. We discuss the relevance of our findings in the modeling of two dimensional random scattering media.

© 2015 Optical Society of America

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References

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2014 (3)

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref] [PubMed]

S. F. Liew, S. M. Popoff, A. P. Mosk, W. L. Vos, and H. Cao, “Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport,” Phys. Rev. B 89, 224202 (2014).
[Crossref]

2013 (2)

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

2012 (2)

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11, 1017–1022 (2012).
[PubMed]

L. Labont, C. Vanneste, and P. Sebbah, “Localized mode hybridization by fine tuning of two-dimensional random media,” Opt. Lett. 37, 1946–1948 (2012).
[Crossref]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

2009 (1)

J. L. O’Brien, A. Furusawa, and J. Vukovi, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

2005 (3)

J. Venermo and A. Sihvola, “Dielectric polarizability of circular cylinder,” J. Electrostat. 63, 101–117 (2005).
[Crossref]

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[Crossref]

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

2004 (1)

2003 (2)

2002 (1)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quant. Electron. 34, 195–203 (2002).
[Crossref]

2000 (2)

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

1998 (2)

H. P. Urbach and G. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57, 3913 (1998).
[Crossref]

A. Kirchner, K. Busch, and C. M. Soukoulis, “Transport properties of random arrays of dielectric cylinders,” Phys. Rev. B 57, 277–288 (1998).
[Crossref]

1997 (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (1997).
[Crossref]

1993 (1)

1992 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[Crossref]

1990 (1)

R. Ruppin, “Electromagnetic scattering from finite dielectric cylinders,” J. Phys. D: Appl. Phys. 23, 757 (1990).
[Crossref]

Albrecht, S. M.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Andreani, L. C.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Ates, S.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Baets, R.

W. Bogaerts, P. Bienstman, and R. Baets, “Scattering at sidewall roughness in photonic crystal slabs,” Opt. Lett. 28, 689–691 (2003).
[Crossref] [PubMed]

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quant. Electron. 34, 195–203 (2002).
[Crossref]

Benisty, H.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Bienstman, P.

W. Bogaerts, P. Bienstman, and R. Baets, “Scattering at sidewall roughness in photonic crystal slabs,” Opt. Lett. 28, 689–691 (2003).
[Crossref] [PubMed]

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quant. Electron. 34, 195–203 (2002).
[Crossref]

Bogaerts, W.

W. Bogaerts, P. Bienstman, and R. Baets, “Scattering at sidewall roughness in photonic crystal slabs,” Opt. Lett. 28, 689–691 (2003).
[Crossref] [PubMed]

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quant. Electron. 34, 195–203 (2002).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles(John Wiley and Sons Inc., 1983), 10th ed.

Bonato, C.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Boscolo, S.

Bouwmeester, D.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Braud, A.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[Crossref]

Burresi, M.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref] [PubMed]

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11, 1017–1022 (2012).
[PubMed]

Busch, K.

A. Kirchner, K. Busch, and C. M. Soukoulis, “Transport properties of random arrays of dielectric cylinders,” Phys. Rev. B 57, 277–288 (1998).
[Crossref]

Cao, H.

S. F. Liew, S. M. Popoff, A. P. Mosk, W. L. Vos, and H. Cao, “Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport,” Phys. Rev. B 89, 224202 (2014).
[Crossref]

Cassagne, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Conley, G. M.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref] [PubMed]

Fan, S.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vukovi, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

Gerace, D.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Hagemeier, J.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles(John Wiley and Sons Inc., 1983), 10th ed.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Wiley and Sons, Inc., 1999).

Jacobs, S.

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

Javadi, A.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[Crossref]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

Jouanin, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Karalis, A.

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

Kim, H.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Kirchner, A.

A. Kirchner, K. Busch, and C. M. Soukoulis, “Transport properties of random arrays of dielectric cylinders,” Phys. Rev. B 57, 277–288 (1998).
[Crossref]

Koenderink, A. F.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[Crossref]

Krauss, T. F.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Labilloy, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Labont, L.

Lagendijk, A.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[Crossref]

Lei, M.

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Liew, S. F.

S. F. Liew, S. M. Popoff, A. P. Mosk, W. L. Vos, and H. Cao, “Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport,” Phys. Rev. B 89, 224202 (2014).
[Crossref]

Liu, J.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Lodahl, P.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Madsen, K. H.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Maradudin, A. A.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (1997).
[Crossref]

McNab, S.

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[Crossref]

Midrio, M.

Moll, N.

Mosk, A. P.

S. F. Liew, S. M. Popoff, A. P. Mosk, W. L. Vos, and H. Cao, “Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport,” Phys. Rev. B 89, 224202 (2014).
[Crossref]

Novikov, I. V.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (1997).
[Crossref]

O’Brien, J. L.

J. L. O’Brien, A. Furusawa, and J. Vukovi, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Petroff, P. M.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Popoff, S. M.

S. F. Liew, S. M. Popoff, A. P. Mosk, W. L. Vos, and H. Cao, “Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport,” Phys. Rev. B 89, 224202 (2014).
[Crossref]

Povinelli, M. L.

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

Pratesi, F.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref] [PubMed]

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[Crossref]

Riboli, F.

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11, 1017–1022 (2012).
[PubMed]

Rikken, G.

H. P. Urbach and G. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57, 3913 (1998).
[Crossref]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Ruppin, R.

R. Ruppin, “Electromagnetic scattering from finite dielectric cylinders,” J. Phys. D: Appl. Phys. 23, 757 (1990).
[Crossref]

Sebbah, P.

Shchegrov, A. V.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (1997).
[Crossref]

Shen, Y.

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Sihvola, A.

J. Venermo and A. Sihvola, “Dielectric polarizability of circular cylinder,” J. Electrostat. 63, 101–117 (2005).
[Crossref]

Smith, C. J. M.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Soljai, M.

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

Soukoulis, C. M.

A. Kirchner, K. Busch, and C. M. Soukoulis, “Transport properties of random arrays of dielectric cylinders,” Phys. Rev. B 57, 277–288 (1998).
[Crossref]

Stobbe, S.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Taillaert, D.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quant. Electron. 34, 195–203 (2002).
[Crossref]

Thon, S. M.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Urbach, H. P.

H. P. Urbach and G. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57, 3913 (1998).
[Crossref]

van Exter, M. P.

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Vanneste, C.

Venermo, J.

J. Venermo and A. Sihvola, “Dielectric polarizability of circular cylinder,” J. Electrostat. 63, 101–117 (2005).
[Crossref]

Villeneuve, P. R.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Vlasov, Y.

Vos, W. L.

S. F. Liew, S. M. Popoff, A. P. Mosk, W. L. Vos, and H. Cao, “Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport,” Phys. Rev. B 89, 224202 (2014).
[Crossref]

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[Crossref]

Vukovi, J.

J. L. O’Brien, A. Furusawa, and J. Vukovi, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

Vynck, K.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref] [PubMed]

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11, 1017–1022 (2012).
[PubMed]

Weisbuch, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

Wiersma, D. S.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref] [PubMed]

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11, 1017–1022 (2012).
[PubMed]

Xu, M.

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Xu, Y.

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Yablonovitch, E.

Yeo, I.

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

Zhang, H.

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Zhang, X.

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Zhu, H.

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Zutter, D. D.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quant. Electron. 34, 195–203 (2002).
[Crossref]

Appl. Phys. B (1)

S. G. Johnson, M. L. Povinelli, M. Soljai, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81, 283–293 (2005).
[Crossref]

Appl. Phys. Lett. (2)

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[Crossref]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[Crossref]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

J. Electrostat. (1)

J. Venermo and A. Sihvola, “Dielectric polarizability of circular cylinder,” J. Electrostat. 63, 101–117 (2005).
[Crossref]

J. Lightwave Technol. (1)

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

J. Phys. D: Appl. Phys. (1)

R. Ruppin, “Electromagnetic scattering from finite dielectric cylinders,” J. Phys. D: Appl. Phys. 23, 757 (1990).
[Crossref]

Nat. Mater. (1)

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11, 1017–1022 (2012).
[PubMed]

Nat. Photonics (1)

J. L. O’Brien, A. Furusawa, and J. Vukovi, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Opt. Commun. (1)

H. Zhang, Y. Shen, Y. Xu, H. Zhu, M. Lei, X. Zhang, and M. Xu, “Effective medium theory for two-dimensional random media composed of coreshell cylinders,” Opt. Commun. 306, 9–16 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quant. Electron. (1)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quant. Electron. 34, 195–203 (2002).
[Crossref]

Photonic Nanostruct. (1)

C. Bonato, J. Hagemeier, D. Gerace, S. M. Thon, H. Kim, L. C. Andreani, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Far-field emission profiles from L3 photonic crystal cavity modes,” Photonic Nanostruct. 11, 37–47 (2013).
[Crossref]

Phys. Rev. A (1)

H. P. Urbach and G. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57, 3913 (1998).
[Crossref]

Phys. Rev. B (5)

A. Kirchner, K. Busch, and C. M. Soukoulis, “Transport properties of random arrays of dielectric cylinders,” Phys. Rev. B 57, 277–288 (1998).
[Crossref]

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[Crossref]

K. H. Madsen, S. Ates, J. Liu, A. Javadi, S. M. Albrecht, I. Yeo, S. Stobbe, and P. Lodahl, “Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity,” Phys. Rev. B 90, 155303 (2014).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

S. F. Liew, S. M. Popoff, A. P. Mosk, W. L. Vos, and H. Cao, “Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport,” Phys. Rev. B 89, 224202 (2014).
[Crossref]

Phys. Rev. Lett. (2)

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (1997).
[Crossref]

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref] [PubMed]

Other (3)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

J. D. Jackson, Classical Electrodynamics (John Wiley and Sons, Inc., 1999).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles(John Wiley and Sons Inc., 1983), 10th ed.

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Figures (4)

Fig. 1
Fig. 1 (Left) The simulation cell is (8λ)3 in volume and surrounded by a λ-thick perfectly matching layer. (Right) The calculated Ez component of the scattered electric field in the z = 0 plane for a hole diameter d = 0.1λ and a waveguide thickness h = 0.4λ. The field is normalized to the amplitude of the incident Ez field. The red and blue dashed lines indicate the profiles of the surfaces for Poynting vector integration.
Fig. 2
Fig. 2 (Left) Calculated scattering efficiencies Q2D as function of the diameter of the hole, for a slab refractive index of n2 = 1.5. Data for TM0 (in black) are plotted for three different thicknesses h in the single-mode regime. The TE0 case (in red) is plotted only for the largest thickness. Polynomial fits Q2D = Arp were performed on data for d ≤ 0.2λ (encircled in the plot) and plotted as dotted lines. The scattering efficiencies of a Mie cylinder for TM and TE polarization, respectively shown in black and red dashed curves, have almost the same values in the examined diameters range. (Right) The ratio of Q2D and the scattering efficiency of Mie cylinder Qsca for different confinement factors (see text). The dashed line Γ4.5 is an empirical fit added to guide the eye.
Fig. 3
Fig. 3 Ratio Q3D/Q2D, quantifying the scattering losses out of the slab relative to the scattering into slab modes, as function of the hole diameter d. Results are reported for the TM mode for h = 0.40,0.32,0.25 and for the TE mode for a slab thickness of h = 0.40.
Fig. 4
Fig. 4 Normalized differential scattering cross sections σ′(θ) for TM (a–d) and TE (e–f) polarization, for Mie cylinders (a, e) and holes in slabs with n2 = 1.5 and thickness h. The differential scattering cross section are all normalized to 1 and the colorscale defines ten bands for values from 0 to 1. The grid for the vertical axis indicates the values of hole diameters used in the simulations. Ez(z = 0) for h = 0.4, d = 0.1 in TM case is shown in Fig. 1. In g) we report in polar coordinates the normalized differential scattering cross sections for holes of the same diameter d = 0.125 and slabs of three different thickness for TM polarization. The scattering in the slab geometries is more directional as compared to the corresponding Mie cylinder.

Tables (1)

Tables Icon

Table 1 Fit parameters of Q2D shown in Fig. 2. p is the exponent of the polynomial dependence of the 2D scattering efficiency from the diameter of the hole (see Eq. (4)). Γ is the confinement factor for the slab mode defined in Eq. (3).

Equations (4)

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

Q s c a = σ s c a d L = W s I i d L
Q 2 D = σ 2 D d = W 2 D I ˜ i d
Γ = s l a b S x ^ d z S x ^ d z
Q 2 D = A r p

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