Abstract

We introduce and analyze a design concept based on nonspherical solid immersion lens (SIL) geometry. We find via finite difference time domain (FDTD) simulations that elliptical solid immersion lenses (eSILs) exhibit a notably improved emission directionality compared to the standard SIL design. Large light-collection efficiencies are achieved even for small numerical apertures (NAs). For example, using a NA as low as 0.3, over 65% of the total light emitted by a dipole can be collected.

© 2014 Optical Society of America

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  6. K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
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  16. M. J. Mandella, “Collimators and collimator arrays employing ellipsoidal solid immersion lenses,” U.S. patent6,452,726 B1 (September17, 2002).
  17. S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
    [CrossRef]
  18. V. Zwiller and G. Bjork, J. Appl. Phys. 92, 660 (2002).
    [CrossRef]
  19. J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
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  22. A. W. Schell, J. Kaschke, J. Fischer, R. Henze, J. Wolters, M. Wegener, and O. Benson, Sci. Rep. 3, 1577 (2013).
    [CrossRef]
  23. D. McCloskey and J. F. Donegan, Appl. Phys. Lett. 103, 091101 (2013).
    [CrossRef]
  24. A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
    [CrossRef]
  25. In the discarded data the total energy in the simulation volume did not decline to 10−4 of the energy injected after a time of 600 fs.
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2013

A. W. Schell, J. Kaschke, J. Fischer, R. Henze, J. Wolters, M. Wegener, and O. Benson, Sci. Rep. 3, 1577 (2013).
[CrossRef]

D. McCloskey and J. F. Donegan, Appl. Phys. Lett. 103, 091101 (2013).
[CrossRef]

2011

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, Phys. Rev. Lett. 106, 096801 (2011).
[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, Rev. Sci. Instrum. 82, 071101 (2011).
[CrossRef]

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

O. Benson, Nature 480, 193 (2011).
[CrossRef]

A. W. Schell, G. Kewes, T. Schröder, J. Wolters, T. Aichele, and O. Benson, Rev. Sci. Instrum. 82, 073709 (2011).
[CrossRef]

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, New J. Phys. 13, 055017 (2011).
[CrossRef]

A. W. Schell, G. Kewes, T. Hanke, A. Leitenstorfer, R. Bratschitsch, O. Benson, and T. Aichele, Opt. Express 19, 7914 (2011).
[CrossRef]

X. W. Chen, V. Sandoghdar, and S. Götzinger, Opt. Lett. 36, 3545 (2011).
[CrossRef]

2010

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

2009

2005

B. Lounis and M. Orrit, Rep. Prog. Phys. 68, 1129 (2005).
[CrossRef]

2004

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
[CrossRef]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

2003

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

2002

W. Barnes, G. Bjork, J. Gïrard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

V. Zwiller and G. Bjork, J. Appl. Phys. 92, 660 (2002).
[CrossRef]

2001

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef]

1990

S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
[CrossRef]

Aichele, T.

A. W. Schell, G. Kewes, T. Schröder, J. Wolters, T. Aichele, and O. Benson, Rev. Sci. Instrum. 82, 073709 (2011).
[CrossRef]

A. W. Schell, G. Kewes, T. Hanke, A. Leitenstorfer, R. Bratschitsch, O. Benson, and T. Aichele, Opt. Express 19, 7914 (2011).
[CrossRef]

S. Schietinger, M. Barth, T. Aichele, and O. Benson, Nano Lett. 9, 1694 (2009).
[CrossRef]

Altintas, A.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
[CrossRef]

Ampem-Lassen, E.

Andersen, U. L.

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, Phys. Rev. Lett. 106, 096801 (2011).
[CrossRef]

Banholzer, M. J.

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, New J. Phys. 13, 055017 (2011).
[CrossRef]

Barnes, W.

W. Barnes, G. Bjork, J. Gïrard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Barth, M.

S. Schietinger, M. Barth, T. Aichele, and O. Benson, Nano Lett. 9, 1694 (2009).
[CrossRef]

Benson, O.

A. W. Schell, J. Kaschke, J. Fischer, R. Henze, J. Wolters, M. Wegener, and O. Benson, Sci. Rep. 3, 1577 (2013).
[CrossRef]

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, New J. Phys. 13, 055017 (2011).
[CrossRef]

A. W. Schell, G. Kewes, T. Schröder, J. Wolters, T. Aichele, and O. Benson, Rev. Sci. Instrum. 82, 073709 (2011).
[CrossRef]

O. Benson, Nature 480, 193 (2011).
[CrossRef]

A. W. Schell, G. Kewes, T. Hanke, A. Leitenstorfer, R. Bratschitsch, O. Benson, and T. Aichele, Opt. Express 19, 7914 (2011).
[CrossRef]

S. Schietinger, M. Barth, T. Aichele, and O. Benson, Nano Lett. 9, 1694 (2009).
[CrossRef]

Benson, T. M.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
[CrossRef]

Bjork, G.

W. Barnes, G. Bjork, J. Gïrard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

V. Zwiller and G. Bjork, J. Appl. Phys. 92, 660 (2002).
[CrossRef]

Boriskin, A. V.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
[CrossRef]

Boriskina, S. V.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
[CrossRef]

Bouwmeester, D.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Bratschitsch, R.

Busch, K.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Chen, X. W.

X. W. Chen, V. Sandoghdar, and S. Götzinger, Opt. Lett. 36, 3545 (2011).
[CrossRef]

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

Deubel, M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Donegan, J. F.

D. McCloskey and J. F. Donegan, Appl. Phys. Lett. 103, 091101 (2013).
[CrossRef]

Eghlidi, H.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

Eisaman, M. D.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, Rev. Sci. Instrum. 82, 071101 (2011).
[CrossRef]

Fan, J.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, Rev. Sci. Instrum. 82, 071101 (2011).
[CrossRef]

Fischer, J.

A. W. Schell, J. Kaschke, J. Fischer, R. Henze, J. Wolters, M. Wegener, and O. Benson, Sci. Rep. 3, 1577 (2013).
[CrossRef]

Gädeke, F.

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, New J. Phys. 13, 055017 (2011).
[CrossRef]

Ganesan, K.

Gibson, B. C.

Gïrard, J.

W. Barnes, G. Bjork, J. Gïrard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Götzinger, S.

X. W. Chen, V. Sandoghdar, and S. Götzinger, Opt. Lett. 36, 3545 (2011).
[CrossRef]

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

Hadden, J. P.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

Hagemeier, J.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Hanke, T.

Hanson, R.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Harrison, J. P.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006).

Heeres, E. C.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Henze, R.

A. W. Schell, J. Kaschke, J. Fischer, R. Henze, J. Wolters, M. Wegener, and O. Benson, Sci. Rep. 3, 1577 (2013).
[CrossRef]

Ho, Y.-L. D.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

Hollenberg, L. C.

Hossain, F. M.

Huck, A.

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, Phys. Rev. Lett. 106, 096801 (2011).
[CrossRef]

Huntington, S. T.

Jonsson, P.

W. Barnes, G. Bjork, J. Gïrard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Kaschke, J.

A. W. Schell, J. Kaschke, J. Fischer, R. Henze, J. Wolters, M. Wegener, and O. Benson, Sci. Rep. 3, 1577 (2013).
[CrossRef]

Kawata, S.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Kewes, G.

A. W. Schell, G. Kewes, T. Schröder, J. Wolters, T. Aichele, and O. Benson, Rev. Sci. Instrum. 82, 073709 (2011).
[CrossRef]

A. W. Schell, G. Kewes, T. Hanke, A. Leitenstorfer, R. Bratschitsch, O. Benson, and T. Aichele, Opt. Express 19, 7914 (2011).
[CrossRef]

Kim, H.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Kino, G. S.

S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
[CrossRef]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef]

Kukura, P.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

Kumar, S.

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, Phys. Rev. Lett. 106, 096801 (2011).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef]

Lee, K. G.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

Leitenstorfer, A.

Lettow, R.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

Lounis, B.

B. Lounis and M. Orrit, Rep. Prog. Phys. 68, 1129 (2005).
[CrossRef]

Mandella, M. J.

M. J. Mandella, “Collimators and collimator arrays employing ellipsoidal solid immersion lenses,” U.S. patent6,452,726 B1 (September17, 2002).

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
[CrossRef]

Marseglia, L.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

McCloskey, D.

D. McCloskey and J. F. Donegan, Appl. Phys. Lett. 103, 091101 (2013).
[CrossRef]

Migdall, A.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, Rev. Sci. Instrum. 82, 071101 (2011).
[CrossRef]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef]

Nosich, A. I.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006).

OBrien, J. L.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

Oosterkamp, T. H.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Orrit, M.

B. Lounis and M. Orrit, Rep. Prog. Phys. 68, 1129 (2005).
[CrossRef]

Patton, B. R.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

Pereira, S.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Petroff, P. M.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Pfaff, W.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Polyakov, S. V.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, Rev. Sci. Instrum. 82, 071101 (2011).
[CrossRef]

Prawer, S.

Rarity, J. G.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

Renn, A.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

Sandoghdar, V.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, Nat. Photonics 5, 166 (2011).
[CrossRef]

X. W. Chen, V. Sandoghdar, and S. Götzinger, Opt. Lett. 36, 3545 (2011).
[CrossRef]

Schell, A. W.

A. W. Schell, J. Kaschke, J. Fischer, R. Henze, J. Wolters, M. Wegener, and O. Benson, Sci. Rep. 3, 1577 (2013).
[CrossRef]

A. W. Schell, G. Kewes, T. Schröder, J. Wolters, T. Aichele, and O. Benson, Rev. Sci. Instrum. 82, 073709 (2011).
[CrossRef]

A. W. Schell, G. Kewes, T. Hanke, A. Leitenstorfer, R. Bratschitsch, O. Benson, and T. Aichele, Opt. Express 19, 7914 (2011).
[CrossRef]

Schietinger, S.

S. Schietinger, M. Barth, T. Aichele, and O. Benson, Nano Lett. 9, 1694 (2009).
[CrossRef]

Schröder, T.

A. W. Schell, G. Kewes, T. Schröder, J. Wolters, T. Aichele, and O. Benson, Rev. Sci. Instrum. 82, 073709 (2011).
[CrossRef]

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, New J. Phys. 13, 055017 (2011).
[CrossRef]

Sewell, P.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, Microw. Opt. Technol. Lett. 43, 515 (2004).
[CrossRef]

Shakoor, A.

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, Phys. Rev. Lett. 106, 096801 (2011).
[CrossRef]

Simpson, D. A.

Soukoulis, C. M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Stanley-Clarke, A. C.

J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010).
[CrossRef]

Sun, H. B.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Takada, K.

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Figures (6)

Fig. 1.
Fig. 1.

Elliptical solid immersion lens geometry. (a) Geometrical parameters of the eSILs. The spheroid’s two semi-axes a and b and its truncated height h. (b) Illustration of a standard SIL with parameters r=a/b=1 and s=h/(2·b)=0.5. (c) eSIL with parameters r=0.8 and s=0.75. The green arrow indicates the emitting dipole.

Fig. 2.
Fig. 2.

Angular far-field intensity distributions. (a)–(c) are far-field intensity distributions for a dipole parallel to the planar SIL surface, while the dipole in (d)–(f) is perpendicular. (a) and (d) are the distributions for a standard SIL, while (b) and (e) and (c) and (f) are for eSILs with parameters r=0.8 and s=0.875 and r=0.6, s=0.708, respectively. The color scale shows the light intensity normalized to the total intensity radiated in the upper hemisphere.

Fig. 3.
Fig. 3.

Collection efficiency of a eSIL with parameters r=0.8 and s=0.75 (black line) in comparison with a standard SIL (red/grey line). Plots in (a) and (b) are for dipoles parallel and perpendicular to the planar SIL surface, respectively. Collection efficiency is enhanced, especially for small NAs of the collections optics. All efficiencies are normalized to the intensity emitted into the upper hemisphere, i.e., the efficiency equals one for NA=1.

Fig. 4.
Fig. 4.

Collection efficiency of optimized eSIL (black line) compared with standard and Weiserstrass SILs (red/grey and green/dotted lines, respectively). (a) and (b) show the data with normalization to the total power emitted by a dipole. The plots in (a) and (b) are for dipoles parallel and perpendicular to the planar SIL surface, respectively. Note that in contrast to Fig. 3 the normalization here is to the total power radiated by the dipole.

Fig. 5.
Fig. 5.

Variations of design parameters r and s at fixed NAs. (a) and (b) show the influence of changes in the parameters for a fixed NA of 0.2 for the two different dipoles, while (c) and (d) show the influence of changes in the parameters for a NA of 0.6. Black data points correspond to cases where the data was discarded due to unwanted resonances [25].

Fig. 6.
Fig. 6.

Comparison of intensity distributions. (a) and (b) show the far-field intensity distributions perpendicular and parallel to the in-plane emitting dipole. Results for the standard SIL are shown in red, while results for eSILs with parameters r=0.8, 0.2 and s=0.88, 0.83 are shown in black and blue. The dotted red lines are Gaussian fits to the data.

Equations (1)

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x2+y2a2+z2b2=1,r=ab,s=h2·b,

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