Abstract

We demonstrate image transfer by a cascaded stack consisting of two and three triangular-lattice photonic crystal slabs separated by air. The quality of the image transfered by the stack is sensitive to the air/photonic crystal interface termination and the frequency. Depending on the frequency and the surface termination, the image can be transfered by the stack with very little deterioration of the resolution, that is the resolution of the final image is approximately the same as the resolution of the image formed behind one single photonic crystal slab.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

Am. J. Phys.

A. Bers, "Note on group velocity and energy propagation", Am. J. Phys. 68, 482 - 484 (2000).
[CrossRef]

Appl. Phys. Lett.

J.B. Brock, A.A. Houck, and I.L. Chuang, "Focusing inside negative index materials," Appl. Phys. Lett. 85, 2472 - 2474 (2004).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, 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, "Improved superlensing in two-dimensional photonic crystals with a basis," Appl. Phys. Lett. 86, 061105 (2005).
[CrossRef]

IRE

P.E. Mayes, G.A. Deschamps, and W.T. Patton, "Backward-wave radiation from periodic structures and application to the design of frequency-independent antennas," Proc. IRE 49, 962 - 963 (1961).

J. Appl. Phys.

A.A. Oliner and T. Tamir, "Backward waves on isotropic plasma slabs," J. Appl. Phys. 33, 231 - 233 (1962).
[CrossRef]

J. of Electromagn. Waves and Appl.

I.V. Lindell and S. Ilvonen, "Waves in a slab of uniaxial BW medium," J. of Electromagn. Waves and Appl. 16, 303 - 318 (2002).
[CrossRef]

J. Zhejiang Univ. SCI

S. He and Z. Ruan, "A completely open cavity realized with photonic crystal wedges," J. Zhejiang Univ. SCI 6A, 355 - 357 (2005).
[CrossRef]

Laser Phys.

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, K.B. Alici, and K. Guven, "Highly directive radiation and negative refraction using photonic crystals," Laser Phys. 15, 217 - 224 (2005).

London Math. Soc.

H. Lamb, "On group-velocity," Proc. London Math. Soc. 1, 473 - 479(1904).
[CrossRef]

Microw. Opt. Tech. Lett.

I.V. Lindell, S.A. Tretyakov, K.I. Nikoskinen, and S. Ilvonen, "BW media- media with negative parameters, capable of supporting backward waves," Microw. Opt. Tech. Lett. 31, 129 - 133 (2001).
[CrossRef]

Nature

H.C. Pocklington, "Growth of a wave-group when the group-velocity is negative," Nature 71, 607 - 608 (1905).
[CrossRef]

New Journal of Physics

S. He, Y. Jin, Z. Ruan, and J. Kuang, "On subwavelength and open resonators involving metamaterials of negative refraction index," New Journal of Physics 7, 210 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quant. Electr.

M. Notomi, "Negative refraction in photonic crystals," Opt. Quant. Electr. 34, 133 - 143 (2002).
[CrossRef]

Opt. Spectrosc.

R.A. Silin, "Possibility of creating plane-parallel lenses," Opt. Spectrosc. (USSR) 44, 109 - (1978). [Translation from the original Russian version in Opt. Spektrosk. 44, 189 - 191 (1978).]

Phys. Rev. B

A. Martinez, H. Miguez, A. Griol, and J. Marti, "Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens," Phys. Rev. B 69, 165119 (2004).
[CrossRef]

K. Guven, K. Aydin, K.B. Alici, C.M. Soukoulis and E. Ozbay, "Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens," Phys. Rev. B 70, 205125 (2004).
[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]

C. Luo, S.G. Johnson, J.D. Joannopoulos, J.B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

X. Zhang, "Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens," Phys. Rev. B 70, 195110 (2004).
[CrossRef]

X. Wang and K. Kempa, "Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs," Phys. Rev. B 71, 085101 (2005).
[CrossRef]

Phys. Rev. E

R.W. Ziolkowski, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

J.S. Kole, M.T. Figge, and H. De Raedt, "Unconditionally stable algorithms to solve the time-dependent Maxwell equations," Phys. Rev. E 64, 066705 (2001).
[CrossRef]

P.F. Loschialpo, D.L. Smith, D.W. Forester, F.J. Rachford, and J. Schelleng, "Electromagnetic waves focused by a negative-index planar lens," Phys. Rev. E 67, 025602 (2003).
[CrossRef]

P.F. Loschialpo, D.W. Forester, D.L. Smith, F.J. Rachford, and C. Monzon, "Optical properties of an ideal homogeneous causal left-handed material slab," Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Phys. Rev. Lett.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

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

S. Foteinopoulou, E.N. Economou, and C.M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Phys. Today

J.B. Pendry and D.R. Smith, "Reversing light with negative refraction," Phys. Today 57, 37 - 43 (2004).
[CrossRef]

Sov. Phys. Usp.

V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and µ," Sov. Phys. Usp. 10, 509 - 514 (1968). [Translation from the original Russion version in Usp. Fiz. Nauk. 92, 517 - 526 (1967). This year was mislabeled in the translation as 1964.].
[CrossRef]

Other

A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edition, (Artech House, MA USA, 2005).

R.G.E. Hutter, Beam and wave electronics in microwave tubes, (Van Nostrand, Princeton, NJ, 1960), p.220.

J.L. Altman, Microwave circuits, (Van Nostrand, Princeton, NJ, 1964), chap.7, p.304.

R.E. Collin, Foundations for vmicrowave engineering, (McGraw-Hill, New York, 1966).

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Figures (4)

Fig. 1.
Fig. 1.

Left: Equifrequency surface plot of TM modes for a triangular lattice photonic crystal consisting of air holes with a radius of r = 0.4a, drilled in a dielectric medium (ε = 12.96, μ = 1) for the frequency range f = 0.26 - 0.33. The first Brillouin zone of a triangular lattice (dotted line) and the symmetry points are also shown. Right: Effective refractive index as a function of the angle θ of the incoming wave vector k for the frequency range f = 0.26 - 0.33.

Fig. 2.
Fig. 2.

Left: Intensity of the electric field of a TM wave with frequency f = 0.299, generated by a point source placed in front of a cascaded stack composed of two PhC slabs with an air layer in between. For the description of the imaging system we refer to the text. The blue lines indicate the propagation directions according to Snell’s law for a homogeneous slab with = -1. Intensities are plotted on a log10 scale. The field intensities are scaled between 0 and 1. Because the transmitted intensity is low, the intensities are scaled different for the regions to the left of the stack, in between the slabs, behind the stack and inside the slabs. Right: Amplitude of the electric field. The electric field amplitudes are plotted on a linear scale ranging from -1 to +1 (blue: Negative values, red: Positive values) and are scaled different for the regions to the left of the stack, in between the slabs, behind the stack and inside the slabs.

Fig. 3.
Fig. 3.

Same as the left panel of Fig. 2 for f = 0.300 (left) and for air/PhC interfaces that are not cut (right).

Fig. 4.
Fig. 4.

Same as the left panel of Fig. 2 for a cascaded stack with three PhC slabs. For the description of the imaging system we refer to the text.

Equations (1)

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J ( r , t ) = n θ ( t ) δ ( r r 0 ) sin ωt ,

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