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

1. V.G. Veselago, �??The electrodynamics of substances with simultaneously negative values of permittivity and permeability,�?? Sov. Phys. Usp. 10, 509 (1968). [CrossRef]
2. 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]
3. 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]
4. 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]
5. R.A. Shelby, D.R. Smith, S. Schultz, �??Experimental verification of a negative index of refraction,�?? Science 292, 77-79 (2001). [CrossRef] [PubMed]
6. 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]
7. 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]
8. M. Notomi, �??Negative refraction in photonic crystals,�?? Opt. Quantum Electron. 34, 133-143 (2002). [CrossRef]
9. 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]
10. J.B. Pendry, �??Negative refraction makes a perfect lens,�?? Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
11. 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]
12. 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]
13. 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]
14. Z. Lu, S. Shi, C.A. Schuetz, D.W. Prather, �??Experimental demonstration of negative refraction imaging in both amplitude and phase,�?? Opt. Express, 13, 2007-2012 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2007">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2007</a>. [CrossRef] [PubMed]
15. 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.
16. 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]
17. X. Ao, and S. He, �??Three-dimensional photonic crystal of negative refraction achieved by interference lithography,�?? Opt. Lett. 29, 2542-2544(2004). [CrossRef] [PubMed]
18. 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.
19. S. G. Johnson, and J.D. Joannopoulos, �??Block-iterative frequency-dormain methods for Maxwell�??s equations in a planewave basis,�?? Opt. Express 8, 173-190 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>. [CrossRef] [PubMed]
20. 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]
21. J.W. Goodman, Introduction to Fourier Optics, pp. 57-58, McGraw-Hill Companies, Inc. 1996.
22. V.A. Podolskiy, and E.E. Narimanov, �??Near-sight superlens,�?? Opt. Lett. 30, 75 (2005). [CrossRef] [PubMed]

Appl. Phys. Lett.

• 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

• 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

• 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

• Z. Lu, S. Shi, C.A. Schuetz, D.W. Prather, �??Experimental demonstration of negative refraction imaging in both amplitude and phase,�?? Opt. Express, 13, 2007-2012 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2007">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2007</a>. [CrossRef] [PubMed]
• S. G. Johnson, and J.D. Joannopoulos, �??Block-iterative frequency-dormain methods for Maxwell�??s equations in a planewave basis,�?? Opt. Express 8, 173-190 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>. [CrossRef] [PubMed]

Opt. Lett.

• V.A. Podolskiy, and E.E. Narimanov, �??Near-sight superlens,�?? Opt. Lett. 30, 75 (2005). [CrossRef] [PubMed]
• X. Ao, and S. He, �??Three-dimensional photonic crystal of negative refraction achieved by interference lithography,�?? Opt. Lett. 29, 2542-2544(2004). [CrossRef] [PubMed]

Opt. Quantum Electron.

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

Phys. Rev. B

• 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.

• 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.
• 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]
• 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]

Science

• 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.

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

Other

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

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