Abstract

We present the experimental demonstration of imaging by all-angle negative refraction in a 3D photonic crystal flat lens at microwave frequencies. The flat lens is made of a body-centered cubic photonic crystal (PhC) whose dispersion at the third band results in group velocity opposite to phase velocity for electromagnetic waves. We fabricated the photonic crystal following a layer-by-layer process. A microwave imaging system was established based on a vector network analyzer, where two dipoles work as the source and the detector separately. By scanning the volume around the lens with the detector dipole, we captured the image of the dipole source in both amplitude and phase. The image of two incoherent sources separated by 0.44λ showed two resolvable spots, which served to verify sub-wavelength resolution.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett. (3)

R.A. Shelby, D.R. Smith, S.C. Nemat-Nasser, S. Schultz, �??Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,�?? Appl. Phys. Lett. 78, 489 (2001).
[CrossRef]

Z. Lu, C. Chen, C.A. Schuetz, S. Shi, J.A. Murakowski, G.J. Schneider, D.W. Prather, �??Subwavelength imaging at microwave frequencies by a flat cylindrical lens using optimized negative refraction,�?? Submitted to Appl. Phys. Lett.

C. Luo, S.G. Johson, J.D. Joannopoulos, and J.B. Pendry, �??All-angle negative refraction in a three-dimensionally periodic photonic crystal,�?? Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

IEEE Trans. Microw. Theory Techniques (1)

J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, �??Magnetism from conductors and enhanced nonlinear phenomena,�?? IEEE Trans. Microw. Theory Techniques 47, 2075�??2084 (1999).
[CrossRef]

Nature (2)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, C.M. Soukoulis, �??Electromagnetic wave: negative refraction by photonic crystals,�?? Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

P.V. Parimi, W.T. Lu, P. Vodo, S. Sridhar, �??Photonic crystals: imaging by flat lens using negative refraction,�?? Nature 426, 404 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

M. Notomi, �??Negative refraction in photonic crystals,�?? Opt. Quantum Electron. 34, 133-143 (2002).
[CrossRef]

Phys. Rev. B (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, �??Superprism phenomena in photonic crystals,�?? Phys. Rev. B 58, R10096-10099 (2000).
[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]

Phys. Rev. Lett. (6)

Z. Lu, J.A. Murakowski, S. Shi, C.A. Schuetz, G. J. Schneider, and D.W. Prather, �??Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies,�?? Submitted to Phys. Rev. Lett.

K.M. Ho, C.T. Chan, and C.M. Soukoulis, �??Existence of a photonic gap in periodic dielectric structure,�?? Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

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

P.V. Parimi, W.T. Lu, P. Vodo, J. Sokoloff, J.S. Derov, S. Sridhar, �??Negative refraction and left-handed electromagnetism in microwave photonic crystals,�?? Phys. Rev. Lett. 92, 127401(4) (2004).
[CrossRef] [PubMed]

D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, �??Composite medium with simultaneously negative permeability and permittivity,�?? Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

J.B. Pendry, A.J. Holden, W.J. Stewart, I. Youngs, �??Extremely low frequency plasmons in metallic mesostructures,�?? Phys. Rev. Lett. 76, 4773�??4776 (1996).
[CrossRef] [PubMed]

Science (1)

R.A. Shelby, D.R. Smith, S. Schultz, �??Experimental verification of a negative index of refraction,�?? Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V.G. Veselago, �??The electrodynamics of substances with simultaneously negative values of permittivity and permeability,�?? Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (1)

J.W. Goodman, Introduction to Fourier Optics, pp. 57-58, McGraw-Hill Companies, Inc. 1996.

Supplementary Material (2)

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Figures (7)

Fig. 1.
Fig. 1.

(a) Conventional cubic cell of the bcc structure. (b) Three-dimensional PhC fabricated layer-by-layer (20 layers in total). Note that (101) plane works as the flat lens surface, so the lattice orientation has rotated 45° surrounding vertical axis. (c) Band structure of the bcc lattice photonic crystal.

Fig. 2.
Fig. 2.

Experimental setup for acquiring three-dimensional field distribution.

Fig. 3.
Fig. 3.

Amplitude distributions changing with the frequency (multimedia movie, 392KB).

Fig. 4.
Fig. 4.

Image of a microwave dipole achieved through the 3D PhC flat lens at image distance, d i=12mm. (b)(c). The image size full width at half maximum (FWHM) is found to be 9mm×7mm. The working frequency is f=16.4GHz (λ=18.3mm).

Fig. 5.
Fig. 5.

(a) Measured amplitude distribution. The amplitude scale on the source side varies from -41 dB (yellow) to -80 dB (black), and on the image side from -49 dB to -80 dB. (b) Phase distribution in vertical plane.

Fig. 6.
Fig. 6.

The amplitude changing along z-axis for 16.4GHz (multimedia movie, 392KB).

Fig. 7.
Fig. 7.

(a) The image (intensity) of two sources from two different vector network analyzers. (b) The intensity distribution along the white line marked on (a). The image shows two resolvable spots with distance 8mm (0.44λ,λ=18.3mm).

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