Abstract

We show that diffraction-suppressed propagation of light can be achieved in one-dimensional multilayer metal-dielectric structure, leading to high-resolution imaging through metallodielectric nanofilms.

©2006 Optical Society of America

1. Introduction

Wave diffraction is one of the fundamental phenomena associated with propagation of a finite-size beam. Diffraction is a geometric effect that spreads the transverse profile of the beam and thus limits spatial resolution. When the size of the object is comparable to the wavelength of light, the diffractive spreading blurs the image of the object after propagation. In 1987, a class of Bessel-beam solutions of the homogeneous Helmholtz equation was found to be “nondiffracting” [1, 2] in the sense that the central spot of the beam stays localized at the expense of side-lobes that spread with propagation. With recent advances in photonic research there is a growing interest in diffraction management using planar waveguide arrays [3] and photonic crystals [4]–[7]. The existence of photonic bands not only controls transmission frequencies, but also deeply affects the spatial dynamics of the beams, leading to nondiffracting beams [5] and superlensing phenomena in high-dimensional photonic crystals [8]–[9]. Subwavelength super-resolution imaging was also demonstrated with a thin silver film [10]–[13] as an alternative experimental proof of the “perfect lens” [14] concept with left-handed materials (LHM). In the above-mentioned studies, the physical mechanism of superlensing is negative refraction and recovery of evanescent components. Matched impedance is required to minimize the interference with reflection waves. In this paper, we show that nondiffracting beams can also exist in properly designed low-dimensional periodic structures, i.e. 1D multilayer alternating metallic and dielectric (MD) materials, leading to high-resolution imaging through the MD medium. In our case, the physical mechanism of high-resolution imaging is rather distinct from that of the LHM imaging. Here, the high-resolution imaging of the small object is the result of diffraction-suppressed propagation, a consequence of photonic engineering in a multilayer metallodielectric medium. Thus, the matched impedance is not required. By managing photonic bands, we will show that a nearly flat diffraction curve can be designed into a properly engineered metallodielectric medium. Hence, the beam field has little diffraction upon propagation within the MD medium, leading to a higher spatial resolution than would be obtained with propagation in free space of the same distance.

2. Diffraction curves

The MD composite consists of alternating layers of dielectric and metallic materials of layer thickness d 1 and d 2, respectively [15]. The metallic and dielectric layers are stacked along the z direction. We assume the permeability is constant (μ 1 = μ 2 = 1) for both dielectric and metallic materials and the permittivity is constant for the dielectric material (ϵ 1). We use the Drude model for metals with the dispersion given by ϵ 2(ω) = 1 - ωp 2/(ω 2 + iγω), where ωp is the plasma frequency and γ is the damping factor. To analyze the effect of photonic bands on the wave diffraction, it is sufficient to consider two-dimensional waves E(x,z) propagating along the z direction. Analogous to dispersion, diffraction is a phenomenon where different spatial frequencies kx accumulate different phases upon propagation. In free space, the phase is simply given by

ϕkxz=kzz=z(ωc)2kx2.

For multilayer periodic MD medium, the propagation modes are Bloch waves. Thus, the phase accumulation upon propagation is given by KB(kx)z, where KB is the Bloch wave number that is a function of transverse spatial components. The diffraction relation of the MD medium is a function of the wavelength, material parameters, and thickness of the layers, and can be obtained directly from the dispersion relation [15]:

cos(KBd)=cosh(α1d1)cosh(α2d2)+α12ε22+α22ε122α1α2ε1ε2sinh(α1d1)sinh(α2d2),

where αi 2 = kx 2 - (ω/c)2 ϵiμi, (i = 1,2). The existence of the Bloch modes requires that |cos(KBd)| ≤ 1. Within the MD media, the Bloch modes represent propagation waves when αi 2 < 0 and evanecent waves when αi 2 > 0. The diffraction curve, KB versus kx, can be derived directly from Eq. (2). The diffraction relation is much more complicated for the MD medium than that for free space Eq. (1). Our studies show that the diffraction in the MD medium can be either faster or slower than that in free space depending on the parameters. One important feature of the MD stack is that in the absence of material losses, evanscent waves can be coupled and transmitted from the top to the bottom layers regardless of the total thickness of the stack as long as the thickness of each layer is thin enough [15, 19]. The plasma frequency of metals can be as low as 3.5 fs-1 [16] and as high as 13 fs-1 [17]. Typically, the damping factor is much smaller than the plasma frequency, γ ~ 0.01ωp [16, 18]. By properly choosing parameters with realistic values, a nearly flat diffraction curve in the MD medium can be achieved. Figure 1 compares the diffraction curve of the MD medium with that of free space. The flat diffraction curve in the MD composite means that the phase accumulation upon propagation has the same rate for different spatial frequencies. Hence, the light propagation in the MD medium experiences much less diffraction than propagation in free space.

 figure: Fig. 1.

Fig. 1. Diffraction curves of the MD medium (solid blue) and free space (dashed green). The KB is the Bloch wave number and refers to the MD medium. The kz is the wave number in the z direction and refers to the free space. The kx is the wave number in the x direction. The values of ϵ 1 = 2.66, ωp = 5.8 fs-1, γ = 0.06 fs-1, d 1 = 100 nm, and d 2 = 60 nm, where d = d 1 +d 2. The wavelength λ = 632 nm and this yields ϵ 2 = -2.7802 +i0.076. This wavelength is used for all the plots.

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3. Diffraction-supressed imaging

Diffraction-suppressed propagation leads to high-resolution imagery. In a linear space-invariant optical system, the wave propagation acts as a spatial filter and is characterized by the optical transfer function (OTF). Let a two-dimensional object be placed at the plane z = 0 where the size of the object is comparable to the wavelength of light. Consider the propagation of light from the plane z = 0 to a parallel plane at a distance Z, the field distribution U(x,y, Z) is related to the field at the first plane U(x,y,0) through

UxyZ=1{H(fx,fy){U(x,y,0)}},

where the ℱ represents the Fourier transform, and the H(fx, fy) is the OTF of the propagation from the plane z = 0 to the plane z = Z. The fx and fy are spatial frequencies in the x and y directions, respectively. In near-field imaging, both propagating and evanescent components must be considered. For free space propagation, the H(fx, fy) is simply given by the propagation of the angular spectrum of plane waves including evanescent components. Shown in Fig. 2 is the propagation through the MD medium which has thickness L. The MD stack is placed at distance L 1 from the object plane (z = 0) on the left and distance L 2 from the image plane (z = Z) on the right. The total propagation distance Z = L 1 +L+ L 2 comprises two free-space regions and the MD medium. The OTF is given by cascading two free-space propagations and the propagation through the MD stack. The end surfaces of the MD medium are truncated such that the MD stack possesses mirror symmetry [19]. We consider TM polarization since only TM polarization can excite surface plasmons that assist the transmission of high spatial components through the MD stack. For our geometry, there is no coupling between TM and TE polarizations, and the TE polarized fields do not play a role in the imaging process as discussed in this work. The OTF of the MD stack for the TM polarization is computed by using transfer-matrix method (TMM) [15, 19] that includes both propagating and evanescent components. Note that the TMM has built-in vector nature of the electromagnetic fields and the method inherently takes into account multiple reflections at all boundary interfaces. The boundary conditions at all interfaces between metal and dielectric layers are automatically satisfied in the TMM.

 figure: Fig. 2.

Fig. 2. Schematic of light propagation through the MD medium. The thickness of the MD stack is L. The distances of the object and image planes to the MD stack are L 1 and L 2, respectively. The total propagation distance Z =L 1 +L+L 2.

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 figure: Fig. 3.

Fig. 3. Intensity distribution of two slits after propagating a distance Z through the MD stack (solid blue) and through free space (dashed green). L 1 = L 2 = 300 nm. L = 3200 nm. The MD stack has 20 periods of the metal-dielectric layers. The period d = 160 nm. The other parameters are the same as those in Fig. 1.

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To show how the diffraction affects image quality, assume the object comprises two slits of width 1μm and separated by 3μm. Figure 3 compares the intensity distribution at the plane z = Z with and without the MD stack. In the absence of the MD stack, the image is blurred by the central intensity peak coming from diffraction-induced constructive interference, since the width of the slits broadens due to the diffraction. In the presence of the MD stack, the diffraction is suppressed and the two slits can be clearly resolved. To demonstrate diffraction-suppressed high-resolution imaging, we use a two-dimensional object of letter ‘H’ as shown in Fig. 4. The image of letter ‘H’ after propagating a distance Z is given by Fig. 5 with and without the MD stack. In the presence of the MD stack, a clear image is obtained as the result of nondiffracting propagation inside the MD medium. In contrast, the image is blurred after propagating through free space of the same distance.

 figure: Fig. 4.

Fig. 4. Two-dimensional object of letter ‘H’ placed at the plane z = 0.

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 figure: Fig. 5.

Fig. 5. Image of letter ‘H’ after propagating a distance Z through the MD stack (left) and through air (right). The MD stack has 5 periods of the metal-dielectric layers. The thickness of the stack L = 800 nm. L 1 = L 2 = 100 nm. The other paramters are the same as those in Fig. 1.

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4. Summary

We have shown that diffraction-suppressed high-resolution image can be achieved through the multilayer metallodielectric medium. Nearly diffraction-free beams can exist in properly designed low-dimensional metallodielectric photonic materials. This work suggests that it is possible to provide another degree of freedom for designing high-resolution optical systems to improve diffraction-induced image degradation.

Acknowledgments

This work is supported by Office of Naval Research (ONR) Independent Laboratory In-house Research and Independent Applied Research funds.

References and links

01. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987). [CrossRef]   [PubMed]  

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

03. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000). [CrossRef]   [PubMed]  

04. S. Longhi and D. Janner, “Diffraction and localization in low-dimensional photonic bandgaps,” Opt. Lett. 29, 2653 (2004). [CrossRef]   [PubMed]  

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

06. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett. 30, 2894 (2005). [CrossRef]   [PubMed]  

07. H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004). [CrossRef]  

08. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003). [CrossRef]  

09. C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003). [CrossRef]  

10. N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science 308, 534 (2005). [CrossRef]   [PubMed]  

11. N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003). [CrossRef]  

12. D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Submicron imaging with a planar silver lens,” Appl. Phys. Lett. 844403 (2004). [CrossRef]  

13. D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 132127 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2127. [CrossRef]   [PubMed]  

14. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000). [CrossRef]   [PubMed]  

15. S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13, 4113 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4113. [CrossRef]   [PubMed]  

16. S. Sena Akarca-Biyikli, Irfan Bulu, and Ekmel Ozbay, “Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,” Appl. Phys. Lett. 85, 1098 (2004). [CrossRef]  

17. W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134 (2000). [CrossRef]  

18. M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998). [CrossRef]  

19. S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005). [CrossRef]  

References

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  1. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987).
    [Crossref] [PubMed]
  2. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651 (1987).
    [Crossref]
  3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
    [Crossref] [PubMed]
  4. S. Longhi and D. Janner, “Diffraction and localization in low-dimensional photonic bandgaps,” Opt. Lett. 29, 2653 (2004).
    [Crossref] [PubMed]
  5. O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. 30, 2611 (2005).
    [Crossref] [PubMed]
  6. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett. 30, 2894 (2005).
    [Crossref] [PubMed]
  7. H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
    [Crossref]
  8. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
    [Crossref]
  9. C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
    [Crossref]
  10. N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science 308, 534 (2005).
    [Crossref] [PubMed]
  11. N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
    [Crossref]
  12. D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Submicron imaging with a planar silver lens,” Appl. Phys. Lett. 844403 (2004).
    [Crossref]
  13. D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 132127 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2127.
    [Crossref] [PubMed]
  14. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [Crossref] [PubMed]
  15. S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13, 4113 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4113.
    [Crossref] [PubMed]
  16. S. Sena Akarca-Biyikli, Irfan Bulu, and Ekmel Ozbay, “Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,” Appl. Phys. Lett. 85, 1098 (2004).
    [Crossref]
  17. W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134 (2000).
    [Crossref]
  18. M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
    [Crossref]
  19. S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
    [Crossref]

2005 (6)

2004 (4)

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Submicron imaging with a planar silver lens,” Appl. Phys. Lett. 844403 (2004).
[Crossref]

S. Sena Akarca-Biyikli, Irfan Bulu, and Ekmel Ozbay, “Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,” Appl. Phys. Lett. 85, 1098 (2004).
[Crossref]

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
[Crossref]

S. Longhi and D. Janner, “Diffraction and localization in low-dimensional photonic bandgaps,” Opt. Lett. 29, 2653 (2004).
[Crossref] [PubMed]

2003 (3)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
[Crossref]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

2000 (3)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134 (2000).
[Crossref]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
[Crossref] [PubMed]

1998 (1)

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
[Crossref]

1987 (2)

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

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

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
[Crossref] [PubMed]

Blaikie, R. J.

Bloemer, M. J.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
[Crossref]

Bowden, C. M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
[Crossref]

Bulu, Irfan

S. Sena Akarca-Biyikli, Irfan Bulu, and Ekmel Ozbay, “Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,” Appl. Phys. Lett. 85, 1098 (2004).
[Crossref]

Chen, C.-C.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
[Crossref]

Chien, H.-T.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
[Crossref]

Christodoulides, D. N.

Conforti, M.

De Angelis, C.

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
[Crossref]

Durnin, J.

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

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

Eberly, J. H.

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

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
[Crossref] [PubMed]

Elson, J. M.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science 308, 534 (2005).
[Crossref] [PubMed]

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

Feng, S.

Janner, D.

Joannopoulos, J. D.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

Johnson, S. G.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

Kuo, C.-H.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
[Crossref]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science 308, 534 (2005).
[Crossref] [PubMed]

Locatelli, A.

Longhi, S.

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
[Crossref]

Luo, C.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

Manela, O.

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
[Crossref]

Melville, D. O. S.

Miceli, J. J.

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

Modotto, D.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
[Crossref] [PubMed]

Overfelt, P. L.

Ozbay, Ekmel

S. Sena Akarca-Biyikli, Irfan Bulu, and Ekmel Ozbay, “Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,” Appl. Phys. Lett. 85, 1098 (2004).
[Crossref]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
[Crossref]

Pendry, J. B.

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

Pethel, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
[Crossref]

Preist, T. W.

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134 (2000).
[Crossref]

Sambles, R. J.

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134 (2000).
[Crossref]

Scalora, M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures.” J. Appl. Phys. 83, 2377 (1998).
[Crossref]

Segev, M.

Sena Akarca-Biyikli, S.

S. Sena Akarca-Biyikli, Irfan Bulu, and Ekmel Ozbay, “Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,” Appl. Phys. Lett. 85, 1098 (2004).
[Crossref]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
[Crossref] [PubMed]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
[Crossref]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science 308, 534 (2005).
[Crossref] [PubMed]

Tan, W. C.

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134 (2000).
[Crossref]

Tang, H.-T.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
[Crossref]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
[Crossref]

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D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Submicron imaging with a planar silver lens,” Appl. Phys. Lett. 844403 (2004).
[Crossref]

Ye, Z.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
[Crossref]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science 308, 534 (2005).
[Crossref] [PubMed]

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

Appl. Phys. Lett. (3)

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Submicron imaging with a planar silver lens,” Appl. Phys. Lett. 844403 (2004).
[Crossref]

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Nature (London) (1)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (4)

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70113101 (2004).
[Crossref]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134 (2000).
[Crossref]

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[Crossref]

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Science (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science 308, 534 (2005).
[Crossref] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1. Diffraction curves of the MD medium (solid blue) and free space (dashed green). The KB is the Bloch wave number and refers to the MD medium. The kz is the wave number in the z direction and refers to the free space. The kx is the wave number in the x direction. The values of ϵ 1 = 2.66, ωp = 5.8 fs-1, γ = 0.06 fs-1, d 1 = 100 nm, and d 2 = 60 nm, where d = d 1 +d 2. The wavelength λ = 632 nm and this yields ϵ 2 = -2.7802 +i0.076. This wavelength is used for all the plots.
Fig. 2.
Fig. 2. Schematic of light propagation through the MD medium. The thickness of the MD stack is L. The distances of the object and image planes to the MD stack are L 1 and L 2, respectively. The total propagation distance Z =L 1 +L+L 2.
Fig. 3.
Fig. 3. Intensity distribution of two slits after propagating a distance Z through the MD stack (solid blue) and through free space (dashed green). L 1 = L 2 = 300 nm. L = 3200 nm. The MD stack has 20 periods of the metal-dielectric layers. The period d = 160 nm. The other parameters are the same as those in Fig. 1.
Fig. 4.
Fig. 4. Two-dimensional object of letter ‘H’ placed at the plane z = 0.
Fig. 5.
Fig. 5. Image of letter ‘H’ after propagating a distance Z through the MD stack (left) and through air (right). The MD stack has 5 periods of the metal-dielectric layers. The thickness of the stack L = 800 nm. L 1 = L 2 = 100 nm. The other paramters are the same as those in Fig. 1.

Equations (3)

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ϕ k x z = k z z = z ( ω c ) 2 k x 2 .
cos ( K B d ) = cosh ( α 1 d 1 ) cosh ( α 2 d 2 ) + α 1 2 ε 2 2 + α 2 2 ε 1 2 2 α 1 α 2 ε 1 ε 2 sinh ( α 1 d 1 ) sinh ( α 2 d 2 ) ,
U x y Z = 1 { H ( f x , f y ) { U ( x , y , 0 ) } } ,

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