Abstract

A Dove prism and an anamorphic prism pair are investigated in negative index imaging systems. An equilateral triangular prism with refractive index of 1 operates as a negative index Dove prism that inverts as well as images the incident field. A negative index anamorphic prism pair acts as a negative index imaging system with magnification. The relationship between achievable magnification and aberrations is discussed. Both prism systems can be implemented by using negative index photonic crystals, and their performance is demonstrated numerically by the finite-difference time-domain method. These negative index prism structures enhance the functionalities of negative index flat lenses and broaden the applications of negative index materials.

© 2007 Optical Society of America

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  1. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
    [CrossRef]
  3. V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
    [CrossRef]
  4. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
    [CrossRef] [PubMed]
  5. E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-Polymer photonic crystal membrane," IEEE Photonics Technol. Lett. 17, 1196-1198 (2005).
    [CrossRef]
  6. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2006 (4)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
[CrossRef]

J. Chen, C. Radu, and A. Puri, "Aberration-free negative-refractive-index lens," Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

2005 (4)

T. Matsumoto, S. Fujita, and T. Baba, "Wavelength demultiplexer consisting of photonic crystal superprism and superlens," Opt. Express 13, 10768-10776 (2005).
[CrossRef] [PubMed]

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045111 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-Polymer photonic crystal membrane," IEEE Photonics Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

2004 (3)

S. Xiao, M. Qiu, Z. Ruan, and S. He, "Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction," Appl. Phys. Lett. 85, 4269-4271 (2004).
[CrossRef]

X. Wang, Z. F. Ren, and K. Kempa, "Unrestricted superlensing in a triangular two dimensional photonic crystal," Opt. Express 12, 2919-2924 (2004).
[CrossRef] [PubMed]

D. Schurig and D. R. Smith, "Negative index lens aberrations," Phys. Rev. E 70, 065601 (2004).
[CrossRef]

2003 (2)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

2000 (4)

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic-crystal spot-size converter," Appl. Phys. Lett. 76, 268-270 (2000).
[CrossRef]

1997 (1)

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Baba, T.

Braat, J.

Cai, W.

Chen, J.

J. Chen, C. Radu, and A. Puri, "Aberration-free negative-refractive-index lens," Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

Chettiar, U. K.

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Drachev, V. P.

Engheta, N.

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Fujita, S.

He, S.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045111 (2005).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, "Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction," Appl. Phys. Lett. 85, 4269-4271 (2004).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic-crystal spot-size converter," Appl. Phys. Lett. 76, 268-270 (2000).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic-crystal spot-size converter," Appl. Phys. Lett. 76, 268-270 (2000).
[CrossRef]

Kempa, K.

Kildishev, A. V.

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic-crystal spot-size converter," Appl. Phys. Lett. 76, 268-270 (2000).
[CrossRef]

Lee, J. B.

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-Polymer photonic crystal membrane," IEEE Photonics Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Linden, S.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Matsumoto, T.

Notomi, M.

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Park, W.

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
[CrossRef]

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-Polymer photonic crystal membrane," IEEE Photonics Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Puri, A.

J. Chen, C. Radu, and A. Puri, "Aberration-free negative-refractive-index lens," Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

Qiu, M.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045111 (2005).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, "Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction," Appl. Phys. Lett. 85, 4269-4271 (2004).
[CrossRef]

Radu, C.

J. Chen, C. Radu, and A. Puri, "Aberration-free negative-refractive-index lens," Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

Ren, Z. F.

Ruan, Z.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045111 (2005).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, "Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction," Appl. Phys. Lett. 85, 4269-4271 (2004).
[CrossRef]

Salandrino, A.

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Sarychev, A. K.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic-crystal spot-size converter," Appl. Phys. Lett. 76, 268-270 (2000).
[CrossRef]

Schonbrun, E.

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
[CrossRef]

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-Polymer photonic crystal membrane," IEEE Photonics Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Schurig, D.

D. Schurig and D. R. Smith, "Negative index lens aberrations," Phys. Rev. E 70, 065601 (2004).
[CrossRef]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Smith, D. R.

D. Schurig and D. R. Smith, "Negative index lens aberrations," Phys. Rev. E 70, 065601 (2004).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Soukoulis, C. M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Summers, C. J.

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
[CrossRef]

Thylén, L.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045111 (2005).
[CrossRef]

Tinker, M.

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-Polymer photonic crystal membrane," IEEE Photonics Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic-crystal spot-size converter," Appl. Phys. Lett. 76, 268-270 (2000).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Wang, X.

Wegener, M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Xiao, S.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045111 (2005).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, "Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction," Appl. Phys. Lett. 85, 4269-4271 (2004).
[CrossRef]

Yamashita, T.

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
[CrossRef]

Yuan, H.

Appl. Opt. (1)

Appl. Phys. Lett. (3)

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic-crystal spot-size converter," Appl. Phys. Lett. 76, 268-270 (2000).
[CrossRef]

J. Chen, C. Radu, and A. Puri, "Aberration-free negative-refractive-index lens," Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, "Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction," Appl. Phys. Lett. 85, 4269-4271 (2004).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-Polymer photonic crystal membrane," IEEE Photonics Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Nature (1)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (4)

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
[CrossRef]

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045111 (2005).
[CrossRef]

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Phys. Rev. E (1)

D. Schurig and D. R. Smith, "Negative index lens aberrations," Phys. Rev. E 70, 065601 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (2)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Three-dimensional positive index Dove prism used to invert an object of the shape of letter F. (b) Ray trace for a 2D negative index Dove prism. The base length of the prism is S. Rays originating from three point sources are presented by red, blue, and green (online) colors. The optical axis of the prism is indicated by the thick (blue online) line. Object and image planes are indicated by the light gray (online) solid lines on each side of the prism.

Fig. 2
Fig. 2

(a) FDTD simulation of the intensity distribution through a Dove prism made of a homogeneous material with n = 1 in air. Images formed by the prism ( A , B , and C ) are inverted corresponding to the objects A, B, and C. (b) FDTD simulation of a Dove prism made of negative index PC. The object is located on the optical axis of the system.

Fig. 3
Fig. 3

(a) Schematic of a positive index anamorphic prism pair used to expand the beam size from D1 to D2. The optical axis of the system is indicated by the dashed line. (b) Schematic of a negative index oblique prism, which exhibits image magnification. The apex angle of the prism is α. Object A 1 B 1 and images A 2 B 2 and A 3 B 3 are indicated by arrows. The refractive index of the prism and of the surrounding medium are n p and n s , respectively. The refraction angle of the center ray at the oblique surface is β.

Fig. 4
Fig. 4

(a) Ray trace of a negative index anamorphic prism pair. The apex angle of the prisms is 40 deg , and the indexes of the prism and the surrounding medium are 1 and 1.5, respectively. Image I1-I2 formed by the prism pair is magnified by a factor of 1.5 compared with the object O1-O2. The optical axis of the system before and after the prism pair is parallel to the z axis. The object and image planes are along the y axis. (b) Magnification of a negative index anamorphic prism pair system and its dependence on the apex angle of the prism and the refractive index of the surrounding medium. The prism has an index of 1 .

Fig. 5
Fig. 5

Aberrations represented by the transverse deviation of the rays. (a) For the prism pair system shown in Fig. 4a, aberrations for rays with various incident angles are plotted. The solid black curve indicates aberrations for an on-axis object. The dashed upper (red online) and lower (blue online) curves indicate aberrations of two off-axis objects that are placed at equal distance above and below the optical axis. (b) On-axis image aberrations change with incident angle for three prism pair systems with apex angles of 40, 50, and 60 deg . (c) Image aberrations depend on both the incident angle of the rays and the transverse distance of the object corresponding to optical axis. The prism pair system is the same as in (a).

Fig. 6
Fig. 6

FDTD simulation of a negative index prism pair system with a 40 deg apex angle. Object and image planes are indicated by two arrows. The inset shows the intensity along the object plane and the image plane by a solid (blue online) and a dashed (red online) curve, respectively. The displacements between the sources and the images are D1 and D2, where D 2 = 1.45 D 1 .

Fig. 7
Fig. 7

FDTD simulation of an anamorphic prism pair by a negative index PC. The prisms have an apex angle of 60 deg . Object and image planes are indicated by two arrows. The inset shows the intensity along the object plane and the image plane by a solid (blue online) and a dashed (red online) curve, respectively. The displacements between the sources and the images are D1 and D2, where D 2 = 3 D 1 .

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