Abstract

Self-collimation of tightly localized laser beams demonstrated in periodic media relies on a perfect-matched rephasing of the Fourier constituents of the wavefield induced by a plane isofrequency curve. An alternate way paved for the achievement of such a phase matching condition developed a suitable spatial filtering in order to select those frequencies experiencing the same phase velocity projected over a given orientation. In principle this procedure is valid for complex structured metamaterials. However, a great majority of studies have focused on free-space propagation leading to the well-known Bessel beams. This paper is devoted to the analysis of this sort of nondiffracting beams traveling in one-dimensional metallic-dielectric photonic crystals. Specifically we present a family of localized radiation modes in multilayered periodic media, where in-phase superposition of p-polarized waves leads to radiative confinement around the beam axis. Excitation of surface plasmon polaritons yields an enhanced localization normally to the interfaces. Subwavelength beam widths along an infinitely long distance might potentially be obtained.

© 2010 Optical Society of America

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2010 (1)

2009 (2)

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

2008 (3)

2006 (6)

A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A 39, 5227–5231 (2006).
[Crossref]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[Crossref]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

C. J. Zapata-Rodríguez and A. Sánchez-Losa, “Three-dimensional field distribution in the focal region of low-Fresnel-number axicons,” J. Opt. Soc. Am. A 23, 3016–3026 (2006).
[Crossref]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[Crossref]

2005 (2)

2004 (4)

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclassical Opt. 6, 477–481 (2004).
[Crossref]

S. V. Kukhlevsky and M. Mechler, “Diffraction-free subwavelength-beam optics at nanometer scale,” Opt. Commun. 231, 35–43 (2004).
[Crossref]

D. N. Chigrin, “Radiation pattern of a classical dipole in a photonic crystal: Photon focusing,” Phys. Rev. E 70, 056611 (2004).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapó, K. Janssens, and O. Samek, “Enhanced transmission versus localization of a light pulse by a subwavelength metal slit,” Phys. Rev. B 70, 195428 (2004).
[Crossref]

2003 (7)

J. Amako, D. Sawaki, and E. Fujii, “Microstructuring transparent materials by use of nondiffracting ultrashort pulse beams generated by diffractive optics,” J. Opt. Soc. Am. B 20, 2562–2568 (2003).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

D. N. Chigrin, S. Enoch, C. M. Sotomayor-Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[Crossref]

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

2002 (3)

P. Pääkkönen, J. Tervo, P. Vahimaa, J. Turunen, and F. Gori, “General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields,” Opt. Express 10, 949–959 (2002).
[PubMed]

K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002).
[Crossref]

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

2000 (2)

1999 (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[Crossref]

1998 (3)

1997 (3)

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[Crossref]

Z. L. Horváth, M. Erdélyi, G. Szabó, Z. Bor, F. K. Tittel, and J. R. Cavallaro, “Generation of nearly nondiffracting Bessel beams with a Fabry–Perot interferometer,” J. Opt. Soc. Am. A 14, 3009–3013 (1997).
[Crossref]

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[Crossref]

1996 (1)

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[Crossref]

1995 (1)

Z. Bouchal and M. Olivik, “Non-diffracting vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[Crossref]

1989 (3)

1987 (2)

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

1977 (1)

1954 (1)

Alici, K. B.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Amako, J.

Andrés, P.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[Crossref]

Bajer, J.

Bertolotti, M.

Bor, Z.

Bouchal, Z.

Braverman, B.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Caglayan, H.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Cavallaro, J. R.

Chigrin, D. N.

D. N. Chigrin, “Radiation pattern of a classical dipole in a photonic crystal: Photon focusing,” Phys. Rev. E 70, 056611 (2004).
[Crossref]

D. N. Chigrin, S. Enoch, C. M. Sotomayor-Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003).
[Crossref] [PubMed]

Christodoulides, D. N.

O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. 30, 2611–2613 (2005).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

Ciattoni, A.

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[Crossref]

Cojocaru, C.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[Crossref]

Csapo, L.

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Csapó, L.

S. V. Kukhlevsky, M. Mechler, L. Csapó, K. Janssens, and O. Samek, “Enhanced transmission versus localization of a light pulse by a subwavelength metal slit,” Phys. Rev. B 70, 195428 (2004).
[Crossref]

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Elsaesser, T.

Enoch, S.

Erdélyi, M.

Esarey, E.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[Crossref]

Fagerholm, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[Crossref]

Friberg, A. T.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[Crossref]

A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
[Crossref] [PubMed]

Fujii, E.

Gori, F.

Griebner, U.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

Grunwald, R.

Hafizi, B.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[Crossref]

Hartmann, H. -J.

Herrero, R.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[Crossref]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[Crossref]

Holm, S.

S. Holm, “Bessel and conical beams and approximation with annular arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 712–718 (1998).
[Crossref]

Horváth, Z. L.

Huttunen, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[Crossref]

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Indebetouw, G.

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Janner, K.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclassical Opt. 6, 477–481 (2004).
[Crossref]

Janssens, K.

S. V. Kukhlevsky, M. Mechler, L. Csapó, K. Janssens, and O. Samek, “Enhanced transmission versus localization of a light pulse by a subwavelength metal slit,” Phys. Rev. B 70, 195428 (2004).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Joannopoulos, J. D.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Jüptner, W.

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

Kebbel, V.

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

Kowalczyk, M.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[Crossref]

Kukhlevsky, S. V.

G. Nyitray, V. Mathew, and S. V. Kukhlevsky, “Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources,” Opt. Commun. 281, 1082–1086 (2008).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapó, K. Janssens, and O. Samek, “Enhanced transmission versus localization of a light pulse by a subwavelength metal slit,” Phys. Rev. B 70, 195428 (2004).
[Crossref]

S. V. Kukhlevsky and M. Mechler, “Diffraction-free subwavelength-beam optics at nanometer scale,” Opt. Commun. 231, 35–43 (2004).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Kuntz, K. B.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Kuzmiak, V.

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[Crossref]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinenann, 1984).

Laporta, P.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclassical Opt. 6, 477–481 (2004).
[Crossref]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

Leizer, A.

Li, Z.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Li, Z. -Y.

Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[Crossref]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinenann, 1984).

Lin, L. -L.

Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[Crossref]

Lobino, M.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Longhi, S.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclassical Opt. 6, 477–481 (2004).
[Crossref]

Lu, Z.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

Lvovsky, A. I.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Manela, O.

Maradudin, A. A.

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[Crossref]

Martin, O. J. F.

Martínez-Corral, M.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[Crossref]

Mathew, V.

G. Nyitray, V. Mathew, and S. V. Kukhlevsky, “Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources,” Opt. Commun. 281, 1082–1086 (2008).
[Crossref]

McLeod, J. H.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Mechler, M.

S. V. Kukhlevsky and M. Mechler, “Diffraction-free subwavelength-beam optics at nanometer scale,” Opt. Commun. 231, 35–43 (2004).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapó, K. Janssens, and O. Samek, “Enhanced transmission versus localization of a light pulse by a subwavelength metal slit,” Phys. Rev. B 70, 195428 (2004).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Miret, J. J.

Morgan, D. P.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[Crossref]

Mugnai, D.

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref] [PubMed]

Murakowski, J. A.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

Nibbering, E. T. J.

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

Novitsky, A. V.

A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A 39, 5227–5231 (2006).
[Crossref]

Novitsky, D. V.

A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A 39, 5227–5231 (2006).
[Crossref]

Nyitray, G.

G. Nyitray, V. Mathew, and S. V. Kukhlevsky, “Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources,” Opt. Commun. 281, 1082–1086 (2008).
[Crossref]

Olivik, M.

Z. Bouchal and M. Olivik, “Non-diffracting vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[Crossref]

Ozbay, E.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Pääkkönen, P.

Palma, C.

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[Crossref]

Pessina, E. M.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinenann, 1984).

Porras, M. A.

Prather, D. W.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Ramakrishna, S. A.

Ranfagni, A.

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref] [PubMed]

Reivelt, K.

K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002).
[Crossref]

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

Ruggeri, R.

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref] [PubMed]

Ruschin, S.

Saari, P.

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002).
[Crossref]

Salomaa, M. M.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[Crossref]

Samek, O.

S. V. Kukhlevsky, M. Mechler, L. Csapó, K. Janssens, and O. Samek, “Enhanced transmission versus localization of a light pulse by a subwavelength metal slit,” Phys. Rev. B 70, 195428 (2004).
[Crossref]

Sánchez-Losa, A.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

Sawaki, D.

Schneider, G. J.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

Schuetz, C. A.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

Segev, M.

Serrat, C.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[Crossref]

Shi, S.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
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Soljacic, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
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Sotomayor-Torres, C. M.

Sprangle, P.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
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Staliunas, K.

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
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K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
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Szabó, G.

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
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Tandon, S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
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Tayeb, G.

Tervo, J.

Tittel, F. K.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

Trull, J.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
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Turunen, J.

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Yariv, A.

Yeh, P.

Youn, S. H.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
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Ziolkowski, R. W.

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
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Appl. Phys. Lett. (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
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IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

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J. Mod. Opt. (1)

Z. Bouchal and M. Olivik, “Non-diffracting vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
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J. Opt. B: Quantum Semiclassical Opt. (1)

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclassical Opt. 6, 477–481 (2004).
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J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (9)

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C. J. Zapata-Rodríguez and A. Sánchez-Losa, “Three-dimensional field distribution in the focal region of low-Fresnel-number axicons,” J. Opt. Soc. Am. A 23, 3016–3026 (2006).
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J. Opt. Soc. Am. B (2)

J. Phys. A (1)

A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A 39, 5227–5231 (2006).
[Crossref]

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
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Nature Mater. (1)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Opt. Commun. (4)

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[Crossref]

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[Crossref]

S. V. Kukhlevsky and M. Mechler, “Diffraction-free subwavelength-beam optics at nanometer scale,” Opt. Commun. 231, 35–43 (2004).
[Crossref]

G. Nyitray, V. Mathew, and S. V. Kukhlevsky, “Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources,” Opt. Commun. 281, 1082–1086 (2008).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Lett. A (1)

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Phys. Rev. A (2)

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
[Crossref] [PubMed]

Phys. Rev. B (3)

Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[Crossref]

S. V. Kukhlevsky, M. Mechler, L. Csapó, K. Janssens, and O. Samek, “Enhanced transmission versus localization of a light pulse by a subwavelength metal slit,” Phys. Rev. B 70, 195428 (2004).
[Crossref]

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[Crossref]

Phys. Rev. E (7)

D. N. Chigrin, “Radiation pattern of a classical dipole in a photonic crystal: Photon focusing,” Phys. Rev. E 70, 056611 (2004).
[Crossref]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[Crossref]

K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002).
[Crossref]

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[Crossref]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[Crossref]

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[Crossref]

Phys. Rev. Lett. (4)

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006).
[Crossref] [PubMed]

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Other (5)

A. E. Siegman, Lasers (University Science Books, 1986).

H.E.Hernández-Figueroa, M.Zamboni-Rached, and E.Recami, eds., Localized Waves (Wiley, 2008).
[Crossref]

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinenann, 1984).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

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Figures (11)

Fig. 1
Fig. 1

Schematic geometry of the planar-nano-layer-based medium.

Fig. 2
Fig. 2

Dispersion equation at ω = 3.4 × 10 15   rad / s for a periodic media as presented in Fig. 1 with w = 5 × 10 8   m and p = 4.5 × 10 7   m . The red (straight) line marks the boundary of homogeneous- and evanescent-wave regimes in the dielectric, k p = 7.711 . The points in yellow determine the cutoff normalized frequencies k p of values ( A ) 8.737, ( B ) 8.503, ( C ) 8.301, ( D ) 7.899, ( E ) 5.126, and ( F ) 4.571.

Fig. 3
Fig. 3

Isofrequency curves at different propagation constants β c < β < β max are shown for the (a) first and (b) second sheets of the dispersion curve. Contour lines are labeled following the normalization β p .

Fig. 4
Fig. 4

Behavior of the complex amplitude (left column) and argument (right column) of the wave function h K at different values of k and positive K corresponding to the first (top), second (middle), and third (bottom) bands.

Fig. 5
Fig. 5

Contour plot of the intensity | h x | 2 in the x y plane corresponding to a localized diffraction-free beam of normalized propagation constant β p = 8.503 and transverse frequency γ p = 2.008 leading to ( k p ) max = 8.737 . Intensity distributions along the coordinate axes are shown at the top and left sides. Inset: Isofrequency curve where shaded region corresponds to the excited spatial bandwidth.

Fig. 6
Fig. 6

(a) Solutions k x of Eq. (15), K s = 0 , associated with different propagation constants β of the wavefields, in the layered structure of Fig. 1. (b) Azimuthal angle ϕ in the plane k x K that corresponds to each solution of the aforementioned self-guiding condition.

Fig. 7
Fig. 7

Transverse intensity | h x | 2 ( x , y ) for diffraction-free beams of β p = 7.899 and spatial frequencies (a) γ p = 2.552 , (b) γ p = 3.148 , and (c) γ p = 3.734 . Insets: Isofrequency curve at β p = 7.899 . The blue shade indicates the spectral window in k x under excitation. Light blue regions refer to gap-induced frustrated excitation.

Fig. 8
Fig. 8

Intensity | h x | 2 in the transverse x y plane for a nondiffracting beam of β = 10.16 μ m 1 and γ = 16.55 μ m 1 . Excitation of Bloch modes with | k x | < 5.15 μ m 1 leads to nonevanescent wavelets in the dielectric slabs so that the resulting hybrid wavefield from Eq. (3) combines Bloch constituents of different nature.

Fig. 9
Fig. 9

Transverse pattern of a nondiffracting beam with β = 9.00 μ m 1 . The beam width of the main central focus has Δ x = 109   nm and Δ y = 46   nm , going beyond the diffraction limit Δ min = 116   nm .

Fig. 10
Fig. 10

Transverse intensity | h x | 2 of a diffraction-free beam traveling in a metal-dielectric multilayer of period p = 13.2   nm . The propagation constant β = 11.4 μ m 1 is significantly lower than the maximum value achievable, β max = 595 μ m 1 , leading to extreme subwavelength localization.

Fig. 11
Fig. 11

Intensity pattern in the x y plane corresponding to a nondiffracting beam of propagation constant β = 9.00 μ m 1 and transverse frequency γ = 17.20 μ m 1 . The planar isofrequency curve induces a self-guiding effect along the y-axis providing Block waves with K = 11.9 μ m 1 . Interference fringes are caused by counter-propagating wave functions.

Equations (22)

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E ( x , y , z , t ) = e ( x , y ) exp ( i β z i ω t ) ,
H ( x , y , z , t ) = h ( x , y ) exp ( i β z i ω t ) ,
( x 2 + y 2 + ω 2 ϵ / c 2 β 2 ) h x = 0 ,
h x ( x , y ) = K a K h K ( y ) exp ( i k x x + i K y ) d k x ,
[ h K + h K ] = exp ( i K y ) T α ( y y α ) [ a α b α ] ,     for   y R α ,
T α ( y ) = [ exp ( i k y α y ) 0 0 exp ( i k y α y ) ] .
k y α = { ( ω / c ) 2 ϵ α k 2 , ( ω / c ) 2 ϵ α k 2 i k 2 ( ω / c ) 2 ϵ α , ( ω / c ) 2 ϵ α < k 2 , }
cos ( K p ) = cos [ k y d ( p w ) ] cos ( k y m w ) ( k y m 2 ϵ d 2 + k y d 2 ϵ m 2 ) 2 k y d k y m ϵ d ϵ m sin [ k y d ( p w ) ] sin ( k y m w ) .
β c = ϵ d ω / c ,
a K ± = { 1 β c 2 ( k x 2 + β 2 ) , if   | k x | < β c 2 β 2 0 , otherwise }
k = β c 2 β 2
a K = 1 γ 2 k x 2 ,     for   | k x | < γ ,
h x ( x , y = 0 ) = 2 π / 2 π / 2 cos ( γ x   cos   ϕ ) d ϕ = 2 π J 0 ( γ x ) ,
h x ( x , y ) K , k x s a K s h K s ( y ) exp ( i k x s x + i K s y ) I K s ( y ) ,
I K s ( y ) = exp [ i K s ( k x k x s ) 2 y / 2 ] d k x = 2 π | K s y |   exp [ i π 4 sgn ( K s y ) ] .
f s ( 1 f s 2 ) + f s 2 f s = 0.
h x ( x , y = 0 ) = 2 π J 0 ( γ x ) h x c 1 ( γ x ) ,
h x c 1 ( γ x ) = 2 ϕ c 1 ϕ c 1 cos ( γ x   cos   ϕ ) d ϕ = m = 0 C m ( c 1 ) J 2 m ( γ x ) ,
C m ( c 1 ) = 4 ( 1 ) m sin ( 2 m ϕ c 1 ) m ,     for   m 0 ,
h x ( x , y = 0 ) = 2 π J 0 ( γ x ) h x c 1 ( γ x ) + h x c 2 ( γ x ) ,
1 ϵ eff = w p 1 ϵ m + p w p 1 ϵ d .
p w = 1 ϵ d ϵ m .

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