Two-dimensional point spread matrix of layered metal–dielectric imaging elements

doi:10.1364/JOSAA.28.000111

Two-dimensional point spread matrix of layered metal–dielectric imaging elements

Rafał Kotyński, Tomasz J. Antosiewicz, Karol Król, and Krassimir Panajotov »View Author Affiliations

JOSA A, Vol. 28, Issue 2, pp. 111-117 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000111

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Abstract

We describe the change of the spatial distribution of the state of polarization occurring during two-dimensional (2D) imaging through a multilayer and in particular through a layered metallic flat lens. Linear or circular polarization of incident light is not preserved due to the difference in the amplitude transfer functions for the TM and TE polarizations. In effect, the transfer function and the point spread function (PSF) that characterize 2D imaging through a multilayer both have a matrix form, and cross-polarization coupling is observed for spatially modulated beams with a linear or circular incident polarization. The PSF in a matrix form is used to characterize the resolution of the superlens for different polarization states. We demonstrate how the 2D PSF may be used to design a simple diffractive nanoelement consisting of two radial slits. The structure assures the separation of nondiffracting radial beams originating from two slits in the mask and exhibits an interesting property of a backward power flow in between the two rings.

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(100.6640) Image processing : Superresolution
(110.0110) Imaging systems : Imaging systems
(260.0260) Physical optics : Physical optics
(160.4236) Materials : Nanomaterials
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Materials

History
Original Manuscript: October 1, 2010
Manuscript Accepted: November 25, 2010
Published: January 11, 2011

Virtual Issues
February 2, 2011 Spotlight on Optics

Citation
Rafał Kotyński, Tomasz J. Antosiewicz, Karol Król, and Krassimir Panajotov, "Two-dimensional point spread matrix of layered metal–dielectric imaging elements," J. Opt. Soc. Am. A 28, 111-117 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-2-111

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References

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]
S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002). [CrossRef]
D. O. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134(2005). [CrossRef] [PubMed]
N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005). [CrossRef] [PubMed]
M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705(2000). [CrossRef]
H. Zhang, L. Shen, L. Ran, Y. Yuan, and J. Kong, “Layered superlensing in two-dimensional photonic crystals,” Opt. Express 14, 11178–11183 (2006). [CrossRef] [PubMed]
C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003). [CrossRef]
A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004). [CrossRef] [PubMed]
H. Zhang, H. Zhu, L. Qian, and D. Fan, “Collimations and negative refractions by slabs of 2D photonic crystals with periodically-aligned tube-type air holes,” Opt. Express 15, 3519–3530 (2007). [CrossRef] [PubMed]
K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004). [CrossRef]
D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003). [CrossRef]
B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006). [CrossRef]
S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003). [CrossRef]
E. V. Ponizovskaya and A. M. Bratkovsky, “Metallic negative index nanostructures at optical frequencies: losses and effect of gain medium,” Appl. Phys. A 87, 161–165 (2007). [CrossRef]
T. A. Fadeyeva, V. G. Shvedov, Y. V. Izdebskaya, A. V. Volyar, E. Brasselet, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Spatially engineered polarization states and optical vortices in uniaxial crystals,” Opt. Express 18, 10848–10863 (2010). [CrossRef] [PubMed]
X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010). [CrossRef] [PubMed]
Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57(2009). [CrossRef]
S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002). [CrossRef]
B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed.(Wiley, 2007).
J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25, 911–918 (2008). [CrossRef]
N. Mattiucci, D. Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: application to super-resolution,” Opt. Express 17, 17517–17529 (2009). [CrossRef] [PubMed]
R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal–dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010). [CrossRef] [PubMed]
R. Kotynski and T. Stefaniuk, “Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes,” J. Opt. A Pure Appl. Opt. 11, 015001(2009). [CrossRef]
R. Kotynski, “Fourier optics approach to imaging with sub-wavelength resolution through metal–dielectric multilayers,” Opto-Electron. Rev. 18, 366–375 (2010). [CrossRef]
B. Lee, Ph. Lalanne, and Y. Fainman, eds., “Feature Issue on Plasmonic Diffractive Optics and Imaging,” Appl. Opt. 49(7), PD01, A01–A41 (2010). [CrossRef]
A. W. Norfolk and E. J. Grace, “Reconstruction of optical fields with the quasi-discrete Hankel transform,” Opt. Express 18, 10551–10556 (2010). [CrossRef] [PubMed]
E.Palik, ed., Handbook of Optical Constants of Solids(Academic, 1998).
P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

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[1] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]

[2] S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002). [CrossRef]

[3] D. O. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134(2005). [CrossRef] [PubMed]

[4] N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005). [CrossRef] [PubMed]

[5] M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705(2000). [CrossRef]

[6] H. Zhang, L. Shen, L. Ran, Y. Yuan, and J. Kong, “Layered superlensing in two-dimensional photonic crystals,” Opt. Express 14, 11178–11183 (2006). [CrossRef] [PubMed]

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

[8] A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004). [CrossRef] [PubMed]

[9] H. Zhang, H. Zhu, L. Qian, and D. Fan, “Collimations and negative refractions by slabs of 2D photonic crystals with periodically-aligned tube-type air holes,” Opt. Express 15, 3519–3530 (2007). [CrossRef] [PubMed]

[10] K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004). [CrossRef]

[11] D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003). [CrossRef]

[12] B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006). [CrossRef]

[13] S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003). [CrossRef]

[14] E. V. Ponizovskaya and A. M. Bratkovsky, “Metallic negative index nanostructures at optical frequencies: losses and effect of gain medium,” Appl. Phys. A 87, 161–165 (2007). [CrossRef]

[15] T. A. Fadeyeva, V. G. Shvedov, Y. V. Izdebskaya, A. V. Volyar, E. Brasselet, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Spatially engineered polarization states and optical vortices in uniaxial crystals,” Opt. Express 18, 10848–10863 (2010). [CrossRef] [PubMed]

[16] X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010). [CrossRef] [PubMed]

[17] Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57(2009). [CrossRef]

[18] S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002). [CrossRef]

[19] B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed.(Wiley, 2007).

[20] J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

[21] C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25, 911–918 (2008). [CrossRef]

[22] N. Mattiucci, D. Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: application to super-resolution,” Opt. Express 17, 17517–17529 (2009). [CrossRef] [PubMed]

[23] R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal–dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010). [CrossRef] [PubMed]

[24] R. Kotynski and T. Stefaniuk, “Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes,” J. Opt. A Pure Appl. Opt. 11, 015001(2009). [CrossRef]

[25] R. Kotynski, “Fourier optics approach to imaging with sub-wavelength resolution through metal–dielectric multilayers,” Opto-Electron. Rev. 18, 366–375 (2010). [CrossRef]

[26] B. Lee, Ph. Lalanne, and Y. Fainman, eds., “Feature Issue on Plasmonic Diffractive Optics and Imaging,” Appl. Opt. 49(7), PD01, A01–A41 (2010). [CrossRef]

[27] A. W. Norfolk and E. J. Grace, “Reconstruction of optical fields with the quasi-discrete Hankel transform,” Opt. Express 18, 10551–10556 (2010). [CrossRef] [PubMed]

[28] E.Palik, ed., Handbook of Optical Constants of Solids(Academic, 1998).

[29] P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

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Two-dimensional point spread matrix of layered metal–dielectric imaging elements