Abstract

We use transformation optics to demonstrate 2D silicon nanolenses, with wavelength-independent focal point. The lenses are designed and fabricated with dimensions ranging from 5.0 µm x 5.0 µm to 20 µm x 20 µm. According to numerical simulations the lenses are expected to focus light over a broad wavelength range, from 1.30 μm to 1.60 μm. Experimental results are presented from 1.52 µm to 1.61 µm.

© 2010 OSA

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  1. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  2. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
    [CrossRef] [PubMed]
  3. T. Matsumoto, K. S. Eom, and T. Baba, “Focusing of light by negative refraction in a photonic crystal slab superlens on silicon-on-insulator substrate,” Opt. Lett. 31(18), 2786–2788 (2006).
    [CrossRef] [PubMed]
  4. T. Asatsuma and T. Baba, “Aberration reduction and unique light focusing in a photonic crystal negative refractive lens,” Opt. Express 16(12), 8711–8719 (2008).
    [CrossRef] [PubMed]
  5. J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
    [CrossRef]
  6. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
    [CrossRef] [PubMed]
  7. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
    [CrossRef]
  8. D.-H. Kwon and D. H. Werner, “Flat focusing lens designs having minimized reflection based on coordinate transformation techniques,” Opt. Express 17(10), 7807–7817 (2009).
    [CrossRef] [PubMed]
  9. C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
    [CrossRef]
  10. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  11. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  12. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
    [CrossRef]
  13. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
    [CrossRef] [PubMed]
  14. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
    [CrossRef]
  15. W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, “Design of oblate cylindrical perfect lens using coordinate transformation,” Opt. Express 16(11), 8094–8105 (2008).
    [CrossRef] [PubMed]
  16. D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
    [CrossRef] [PubMed]

2009 (4)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

D.-H. Kwon and D. H. Werner, “Flat focusing lens designs having minimized reflection based on coordinate transformation techniques,” Opt. Express 17(10), 7807–7817 (2009).
[CrossRef] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[CrossRef] [PubMed]

2008 (6)

W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, “Design of oblate cylindrical perfect lens using coordinate transformation,” Opt. Express 16(11), 8094–8105 (2008).
[CrossRef] [PubMed]

T. Asatsuma and T. Baba, “Aberration reduction and unique light focusing in a photonic crystal negative refractive lens,” Opt. Express 16(12), 8711–8719 (2008).
[CrossRef] [PubMed]

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[CrossRef]

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[CrossRef]

2007 (1)

2006 (3)

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

T. Matsumoto, K. S. Eom, and T. Baba, “Focusing of light by negative refraction in a photonic crystal slab superlens on silicon-on-insulator substrate,” Opt. Lett. 31(18), 2786–2788 (2006).
[CrossRef] [PubMed]

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Asatsuma, T.

Baba, T.

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Cui, J.

Du, C.

Eom, K. S.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Kundtz, N.

Kwon, D.-H.

Lee, H.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Li, Z.-Y.

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

Lin, L.

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Liu, Y.-Z.

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

Liu, Z.

Luo, X.

Matsumoto, T.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[CrossRef]

Qiu, M.

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

Ribbing, C. G.

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

Roberts, D. A.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Smith, D. R.

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Sun, C.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Tian, J.

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

Tsang, M.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[CrossRef]

Tsitsas, N. L.

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[CrossRef]

Valagiannopoulos, C. A.

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[CrossRef]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Wang, W.

Werner, D. H.

Xiong, Y.

Yan, M.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

Yan, W.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

Yang, X.

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, D.-Z.

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. Tian, M. Yan, M. Qiu, C. G. Ribbing, Y.-Z. Liu, D.-Z. Zhang, and Z.-Y. Li, “Direct characterization of focusing light by negative refraction in a photonic crystal flat lens,” Appl. Phys. Lett. 93(19), 191114–191901 (2008).
[CrossRef]

Electromagnetics (1)

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[CrossRef]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B (2)

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Science (3)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Design of focusing wavelength-independent medium. (a) Conventional medium (b) Engineered medium by transformation optics, where the paths (blue lines) converge to a focal spot (FS). The arrows indicate the incident and transmitted light. The engineered medium (b) concentrates the output into a narrower region (focal spot).

Fig. 2
Fig. 2

(a) Lens with continuous refractive index distribution. (b) Lens with discrete index profile, black color represents air-holes and brown, silicon.

Fig. 3
Fig. 3

Amplitude of the field for lens with dimensions 20 µm x 20 µm, and with homogeneous index distribution (as in Fig. 2(a)): (a) λ = 1.30 µm, (b) λ = 1.55 µm.

Fig. 4
Fig. 4

Amplitude of the field for lens with dimensions 20 µm x 20 µm, and with discrete index distribution (as shown in Fig. 2(b)): (a) λ = 1.30 µm, (b) λ = 1.55 µm.

Fig. 5
Fig. 5

Power intensity distribution for a lens with discrete index refraction and focal spot equal to 35% of the width. Lens dimension: (a) 5 μm x 5 μm, (b) 10 μm x 10 μm.

Fig. 6
Fig. 6

Scanning electron microscope of a fabricated lens with dimension 10 µm x 10 µm. 80nm air-holes are etched in SOI wafer with varying density determine the distribution of the effective index of the lens. The distribution of the air holes is given by the design shown in Fig. 2(b). Also shown are SEMs of the incoming edge area and in the focusing edge area.

Fig. 7
Fig. 7

(a) SEM of the lens; NSOM images for 20 µm x 20 µm lens dimension, FS = 7µm, for three different input wavelengths: (b) λ = 1.52 µm (c) λ = 1.55 µm (d) λ = 1.61 µm. The plots in green represent the power intensity measured at the output of the sample.

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