Abstract

We report on a study of the wave propagation and refraction in a 2D square-lattice photonic crystal for the first two photonic bands as well as the coupling of the external waves and criteria for flat-lens focusing. Microwave experiments and numerical simulations are performed. Main results concern the transition from positive to negative refraction below the first band gap, the flat-lens focusing using a novel criterion, viz. the constancy of the ratio of the tangents of the incident and refracted angle. Focusing results for medium (≈ 10) and ultra-large dielectric contrast (≈ 100) are presented. In the latter case focusing with a spot size below one wavelength at distances several wavelengths behind the photonic crystal is achieved.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
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2005

S. Foteinopoulou and C.M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165,112 (2005).
[CrossRef]

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045,111 (2005).
[CrossRef]

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596 (2005).
[CrossRef] [PubMed]

2004

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, 165,119 (2004).
[CrossRef]

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

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, 205,125 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

P. Vodo, P. V. Parimi, W. T. Lu, S. Sridhar, and R. Win, "Microwave photonic crystal with tailor-made negative refractive index," Appl. Phys. Lett. 85, 1858 (2004).
[CrossRef]

2003

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045,115 (2003).
[CrossRef]

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative Refraction by Photonic Crystals," Nature 423, 604 (2003).
[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, 207,401 (2003).
[CrossRef]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in Media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107,402 (2003).
[CrossRef]

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245,110 (2003).

2002

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201,104 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

2000

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, 10,696 (2000).
[CrossRef]

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

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Alici, K. B.

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, 205,125 (2004).
[CrossRef]

Aydin, K.

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, 205,125 (2004).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative Refraction by Photonic Crystals," Nature 423, 604 (2003).
[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, 207,401 (2003).
[CrossRef]

Busch, K.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

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, 207,401 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative Refraction by Photonic Crystals," Nature 423, 604 (2003).
[CrossRef] [PubMed]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

Diem, M.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Economou, E. N.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in Media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107,402 (2003).
[CrossRef]

Foteinopoulou, S.

S. Foteinopoulou and C.M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165,112 (2005).
[CrossRef]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in Media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107,402 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative Refraction by Photonic Crystals," Nature 423, 604 (2003).
[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, 207,401 (2003).
[CrossRef]

Gajic, R.

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596 (2005).
[CrossRef] [PubMed]

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Garcia-Martin, A.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Gösele, U.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Griol, A.

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, 165,119 (2004).
[CrossRef]

Guven, K.

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, 205,125 (2004).
[CrossRef]

He, S.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045,111 (2005).
[CrossRef]

Hingerl, K.

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596 (2005).
[CrossRef] [PubMed]

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045,115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201,104 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045,115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201,104 (2002).
[CrossRef]

Koch, W.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Kuchar, F.

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596 (2005).
[CrossRef] [PubMed]

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Li, Z. Y.

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245,110 (2003).

Lin, L. L.

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245,110 (2003).

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

P. Vodo, P. V. Parimi, W. T. Lu, S. Sridhar, and R. Win, "Microwave photonic crystal with tailor-made negative refractive index," Appl. Phys. Lett. 85, 1858 (2004).
[CrossRef]

Lu, Z.

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045,115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201,104 (2002).
[CrossRef]

Marti, J.

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, 165,119 (2004).
[CrossRef]

Martinez, A.

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, 165,119 (2004).
[CrossRef]

Meisel, D. C.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Meisels, R.

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596 (2005).
[CrossRef] [PubMed]

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Miguez, H.

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, 165,119 (2004).
[CrossRef]

Murakowski, J.

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

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, 10,696 (2000).
[CrossRef]

Ozbay, E.

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, 205,125 (2004).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative Refraction by Photonic Crystals," Nature 423, 604 (2003).
[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, 207,401 (2003).
[CrossRef]

Parimi, P. V.

P. Vodo, P. V. Parimi, W. T. Lu, S. Sridhar, and R. Win, "Microwave photonic crystal with tailor-made negative refractive index," Appl. Phys. Lett. 85, 1858 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045,115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201,104 (2002).
[CrossRef]

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

Pereira, S.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Prather, D.

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

Qiu, M.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045,111 (2005).
[CrossRef]

Radovanovic, J.

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Ruan, Z.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045,111 (2005).
[CrossRef]

Schilling, J.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Schneider, G.

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

Schuetz, C.

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Shi, S.

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

Soukoulis, C. M.

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, 205,125 (2004).
[CrossRef]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in Media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107,402 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative Refraction by Photonic Crystals," Nature 423, 604 (2003).
[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, 207,401 (2003).
[CrossRef]

Soukoulis, C.M.

S. Foteinopoulou and C.M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165,112 (2005).
[CrossRef]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

P. Vodo, P. V. Parimi, W. T. Lu, S. Sridhar, and R. Win, "Microwave photonic crystal with tailor-made negative refractive index," Appl. Phys. Lett. 85, 1858 (2004).
[CrossRef]

Stampfl, J.

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Thylen, L.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045,111 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vodo, P.

P. Vodo, P. V. Parimi, W. T. Lu, S. Sridhar, and R. Win, "Microwave photonic crystal with tailor-made negative refractive index," Appl. Phys. Lett. 85, 1858 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

von Freymann, G.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Wegener, M.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Wehrspohn, R. B.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Win, R.

P. Vodo, P. V. Parimi, W. T. Lu, S. Sridhar, and R. Win, "Microwave photonic crystal with tailor-made negative refractive index," Appl. Phys. Lett. 85, 1858 (2004).
[CrossRef]

Woesz, A.

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Xiao, S.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045,111 (2005).
[CrossRef]

Zarbakhsh, J.

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Appl. Phys. Lett.

P. Vodo, P. V. Parimi, W. T. Lu, S. Sridhar, and R. Win, "Microwave photonic crystal with tailor-made negative refractive index," Appl. Phys. Lett. 85, 1858 (2004).
[CrossRef]

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Gösele, "Diffraction properties of two-dimensional photonic crystals," Appl. Phys. Lett. 83, 614 (2003).
[CrossRef]

Nature

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative Refraction by Photonic Crystals," Nature 423, 604 (2003).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

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, 205,125 (2004).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045,115 (2003).
[CrossRef]

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B 71, 045,111 (2005).
[CrossRef]

Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245,110 (2003).

S. Foteinopoulou and C.M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165,112 (2005).
[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, 10,696 (2000).
[CrossRef]

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, 165,119 (2004).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201,104 (2002).
[CrossRef]

Phys. Rev. Lett.

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

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127,401 (2004).
[CrossRef]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in Media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107,402 (2003).
[CrossRef]

Z. Lu, J. Murakowski, C. Schuetz, S. Shi, G. Schneider, and D. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction atMicrowave Frequencies," Phys. Rev. Lett. 95, 153,901 (2005).
[CrossRef]

Phys.Rev. Lett.

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, 207,401 (2003).
[CrossRef]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Z. Metallk.

R. Gajic, F. Kuchar, R. Meisels, J. Radovanovic, K. Hingerl, J. Zarbakhsh, J. Stampfl, and A. Woesz, "Physical and materials aspects of photonic crystals for microwaves and millimetre waves," Z. Metallk. 95, 618 (2004).

Other

"FullWAVE," RSoft Design Group, Inc. http://www.rsoftdesign.com

"BandSOLVE," RSoft Design Group, Inc. http://www.rsoftdesign.com

S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," cond-mat/0212434v1 (2002).

G. Eleftheriades and K. Balmain, Negative-Refraction Metamaterials (Wiley, 2003).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).

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Figures (10)

Fig. 1.
Fig. 1.

Intensity versus position of the TM beam without the PhC and transmitted through the PhC at f = 36.5 GHz and Θ i = 45°. The dashed curves are low-frequency filtered and used for the determination of the peak positions. The measurement set-up is shown schematically in the inset.

Fig. 2.
Fig. 2.

Angle of refraction Θ r as a function of frequency with the angle of incidence Θ i , as the parameter based on the EFC calculations. Also included are the experimental data points for Θ i = 45° (diamonds) and Θ i = 30° (triangles) (details see section 2.1). A variation of the rod radius corresponding to that one of the rods used in the experiments is included for Θ i = 45° (dashed curve: r = 0.60 mm, all other curves: r = 0.61 mm). The full dots on the calculated curves mark n beam = -1.

Fig. 3.
Fig. 3.

Intensity versus position of the TE beam without the PhC (curves peaked near x = 0 mm) and transmitted through the PhC (curves peaked near x = -20 mm) for f = 67 GHz (second band), Θ i = 15°, and incidence on the ΓM surface of the PhC. Upper diagram experimental results. Smoothed curves are low-pass filtered. Lower diagram: from FDTD calculations.

Fig. 4.
Fig. 4.

EFCs of the second TE band with 0.5 GHz steps between 65 and 67.5 GHz. ε = 9.6. Black arrow: incident wave vector k air at 67 GHz for 15° incidence on the ΓX surface. White arrow: k phC (direction of the phase velocity). k phC is obtained using the conservation of k . Dashed arrow: group velocity, obtained from /dk in point B. The wave with a k phC at point A does not exist since the direction of v gr would not correspond to an energy flow away from the source.

Fig. 5.
Fig. 5.

Deviations of n beam from the value -1 in the upper part of the first band of a square lattice PhC with ε= 9.6 and 90 (dashed and full curve, respectively). The frequencies are chosen to give the smallest variations with respect to the incident angle, i.e. 37 GHz for ε= 9.6 and 13.05 GHz for ε= 90.

Fig. 6.
Fig. 6.

EFC in the first TM band for ε = 90 and incidence on the ΓM surface. The air circle (around Γ) and the PhC-EFC (around M) at 12.90 GHz are emphasized. The dashed ellipse corresponds to Rtan1 = 0.5. Size of semi-major axis = kair , size of semi-minor axis = kairRtan for f=12.90 GHz.

Fig. 7.
Fig. 7.

Ratio of the tangents of the refracted and incident angles (Rtan1) as a function of frequency in the first TM band for ε = 90.

Fig. 8.
Fig. 8.

Wave pattern (Ey ) for a small (= λ/10) source and propagation (TM polarization) through a PhC slab (surface parallel to ΓM, 79 rows of alternatingly 91 and 90 rods). ε= 90. λ≈23 mm. Left diagram: f = 12.90 GHz (Rtan ≈const.), right diagram: f = 13.05 GHz (nbeam ≈-1). Both frequencies lie near the upper edge of the first band. The limits of the color scale for the left diagram are larger by a factor of three. The lateral size of the source (at z = -7.5 cm for 12.90 GHz, at z = 10.4 cm for 13.05 GHz) is marked by a yellow rectangle (not to scale). Below each diagram showing focusing through the slab is a diagram for the same frequency showing the internal propagation. In the lower diagram reflection by the second surface of the PhC is inhibited by including an absorbing surface. Then, a clear internal focus appears.

Fig. 9.
Fig. 9.

Wave pattern from a small (1λ= 4.5 mm) source for incidence on the ΓX surface of a PhC slab (21 rows of 41 rods). The lateral size of the source (at z= -3 cm) is marked by a yellow rectangle. ε = 9.6. f = 66.85 GHz (second TE band, regime of negative refraction). The beam is collimated although neither the condition nbeam = -1 nor Rtan =const is fulfilled.

Fig. 10.
Fig. 10.

Phase refractive index nph vs. frequency in the second TE band. ε= 9.6. f = 66.85 GHz, marked by a vertical line, is the frequency in Fig. 9.

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