Abstract

A way to perform sampling of the evanescent spectrum of an object is considered by using a photonic bandgap (PBG). The coupling between the scattered field from the object and the PBG is discussed, showing a connection of the guide modes with selected spectral components of the scattering object in free space. Some useful examples have been discussed, showing good agreement between numerical results and theoretical previsions.

© 2012 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
  2. S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
    [CrossRef]
  3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef]
  4. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed sub-wavelength imaging using metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  5. P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
    [CrossRef]
  6. L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
    [CrossRef]
  7. L. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121(2008).
    [CrossRef]
  8. A. Mandatori and M. Bertolotti, “Spectral properties for 1D multilayer systems and application to super resolution,” J. Eur. Opt. Soc. 6, 11004 (2011).
    [CrossRef]
  9. J. Lekner, Theory of Reflection of Electromagnetic and Particle Waves (Nijhoff/Kluwer/Springer1987).

2011 (1)

A. Mandatori and M. Bertolotti, “Spectral properties for 1D multilayer systems and application to super resolution,” J. Eur. Opt. Soc. 6, 11004 (2011).
[CrossRef]

2008 (1)

L. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121(2008).
[CrossRef]

2007 (1)

L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

2006 (2)

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed sub-wavelength imaging using metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

2005 (1)

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[CrossRef]

2000 (1)

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

Belov, P. A.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Bertolotti, M.

A. Mandatori and M. Bertolotti, “Spectral properties for 1D multilayer systems and application to super resolution,” J. Eur. Opt. Soc. 6, 11004 (2011).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Gao, L.

L. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121(2008).
[CrossRef]

L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

Hao, Y.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

He, S.

L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

Lekner, J.

J. Lekner, Theory of Reflection of Electromagnetic and Particle Waves (Nijhoff/Kluwer/Springer1987).

Li, B.

L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

Mandatori, A.

A. Mandatori and M. Bertolotti, “Spectral properties for 1D multilayer systems and application to super resolution,” J. Eur. Opt. Soc. 6, 11004 (2011).
[CrossRef]

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed sub-wavelength imaging using metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

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

Ramakrishna, S. A.

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[CrossRef]

Shi, L.

L. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121(2008).
[CrossRef]

L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed sub-wavelength imaging using metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed sub-wavelength imaging using metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

J. Eur. Opt. Soc. (1)

A. Mandatori and M. Bertolotti, “Spectral properties for 1D multilayer systems and application to super resolution,” J. Eur. Opt. Soc. 6, 11004 (2011).
[CrossRef]

Phys. Rev. B (4)

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed sub-wavelength imaging using metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

L. Shi and L. Gao, “Subwavelength imaging from a multilayered structure containing interleaved nonspherical metal-dielectric composites,” Phys. Rev. B 77, 195121(2008).
[CrossRef]

Phys. Rev. Lett. (1)

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

Rep. Prog. Phys. (1)

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

J. Lekner, Theory of Reflection of Electromagnetic and Particle Waves (Nijhoff/Kluwer/Springer1987).

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Figures (13)

Fig. 1.
Fig. 1.

Scheme for the substitution of the object with an equivalent inhomogeneous layer.

Fig. 2.
Fig. 2.

Scheme of the system and propagation paths of the field’s spectral components.

Fig. 3.
Fig. 3.

Scattering object beside the PBG.

Fig. 4.
Fig. 4.

Spectral comparison at kx=kx1=1.442k0 between the numerical curves for the two cases of the field on plane E produced by the object alone and by the object+PBG. Bold curves are dotted when referred to the system of Fig. 5(c), dashed for the system of Fig. 5(b), and solid for the system of Fig. 5(a). The thin curve corresponds to the theoretical behavior for the object alone without PBG.

Fig. 5.
Fig. 5.

Different examples of objects-PBG systems under analysis; the refractive index of the objects is n=6.

Fig. 6.
Fig. 6.

Schematic of the PBG without losses.

Fig. 7.
Fig. 7.

Transmission spectrum for the PBG of Fig. 6 under TE illumination.

Fig. 8.
Fig. 8.

Comparison of the object scattering spectra with and without the PBG.

Fig. 9.
Fig. 9.

Phase of the scattered field spectrum evaluated in C plane of Fig. 3 at kx=kx1=1.442k0. Dotted line refers to the system of Fig. 5(c), dashed line to the one of Fig. 5(b), and solid line to the one of Fig. 5(a).

Fig. 10.
Fig. 10.

Spectral comparison at kx=kx1=1.4266k0 of numerical curves calculated with PBG and objects with the theoretical ones calculated with objects only. The bold curves are dashed for the system of Fig. 5(b) and solid for the system of Fig. 5(a). The thin lines refer to the theoretical calculation for the objects alone.

Fig. 11.
Fig. 11.

Schematic of the all-dielectric PBG with bearing layers.

Fig. 12.
Fig. 12.

Spectral comparison at kx=kx1=1.4655k0 between the numerical curves for the two cases of objects with and without PBG. As for Fig. 4, bold curves are dotted when referred to the system of Fig. 5(c), dashed for the system of Fig. 5(b), and solid for the system of Fig. 5(a). The thin ones correspond to the theoretical behavior for the systems without PBG.

Fig. 13.
Fig. 13.

Reflection spectrum of the PBG: dashdot with refractive index n1=i4 and n2=4, dashed with refractive index n1=2.6 and n2=3, solid with refractive index n1=1.2 and n2=2.3. Using bearing layers, the polarization is always TE.

Tables (3)

Tables Icon

Table 1. Proof of the Invariance of |β|

Tables Icon

Table 2. Proof of the Invariance of β

Tables Icon

Table 3. Values of β for α=0.05

Equations (9)

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ES(kx)=12πS(kx;kx)EP(kx)dkx,
{ER(kx)=RB(kx)EP(kx)ET(kx)=TB(kx)EP(kx),
Ei,B(kx)=TA(kx,0)Ei,
[RB(kx1)RA(kx,kx1)+RB(kx1)*RA(kx,kx1)],
[TB(kx1)δ(kxkx1)+TB(kx1)*δ(kx+kx1)]
Eout=Ei(I+R¯+R¯2+)(TA(kx1)TB(kx1)δ(kxkx1)TA(kx1)*TB(kx1)*δ(kx+kx1)),
R¯=(RB(kx1)RA(kx1,kx1)RB(kx1)*RA(kx1,kx1)RB(kx1)RA(kx1,kx1)RB(kx1)*RA(kx1,kx1)).
Eout=Ei(IR¯)1(TA(kx1)TB(kx1)δ(kxkx1)TA(kx1)*TB(kx1)*δ(kx+kx1)).
Eout=Ei(TA(kx1)TB(kx1)δ(kxkx1)TA(kx1)*TB(kx1)*δ(kx+kx1)).

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