Abstract

Digital holographic microscopy (DHM) has been successfully applied for the first time to characterize the radiative out-of-plane emission properties of a superdirective device. Complementarily to near-field microscopy, DHM allows us to reconstruct the beam in the far-field region. The angular dispersion of the light beam radiated from a grating composed of air and anti-air metamaterial has been determined, and the proposed technique has highlighted a collimation degree higher than 0.04°, as already evaluated in a previous work. Further considerations on the retrieved phase map of the beam in the acquisition plane are presented.

© 2012 Optical Society of America

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  1. J. Pendry and S. Ramakrishna, J. Phys. Condens. Matter 15, 6345 (2003).
    [CrossRef]
  2. V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
    [CrossRef]
  3. M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
    [CrossRef]
  4. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
    [CrossRef]
  5. S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef]
  6. V. Mocella, P. Dardano, L. Moretti, and I. Rendina, Opt. Express 15, 6605 (2007).
    [CrossRef]
  7. V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, Opt. Express 18, 25068 (2010).
    [CrossRef]
  8. G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
    [CrossRef]
  9. B. Javidi, S. Yeom, I. Moon, and M. Daneshpanah, Opt. Express 14, 3806 (2006).
    [CrossRef]
  10. G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
    [CrossRef]
  11. Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
    [CrossRef]
  12. Y. Lim, S. Lee, and B. Lee, Opt. Express 19, 5202 (2011).
    [CrossRef]
  13. R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004).
    [CrossRef]
  14. M. Notomi, Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  15. C. Wagner, S. Seebacher, W. Osten, and W. Juptner, Appl. Opt. 38, 4812 (1999).
    [CrossRef]
  16. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  17. L. Yu and L. Cai, J. Opt. Soc. Am. A 18, 1033 (2001).
    [CrossRef]

2011 (1)

2010 (3)

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, Opt. Express 18, 25068 (2010).
[CrossRef]

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

2009 (1)

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

2008 (1)

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

2007 (1)

2006 (2)

B. Javidi, S. Yeom, I. Moon, and M. Daneshpanah, Opt. Express 14, 3806 (2006).
[CrossRef]

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

2004 (2)

R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

2003 (1)

J. Pendry and S. Ramakrishna, J. Phys. Condens. Matter 15, 6345 (2003).
[CrossRef]

2002 (1)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

1999 (1)

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Balduzzi, D.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Cabrini, S.

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, Opt. Express 18, 25068 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Cai, L.

Chang, A. S. P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Coppola, G.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Daneshpanah, M.

Dardano, P.

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, Opt. Express 18, 25068 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

V. Mocella, P. Dardano, L. Moretti, and I. Rendina, Opt. Express 15, 6605 (2007).
[CrossRef]

De Nicola, S.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Dhuey, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Di Caprio, G.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Engheta, N.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Ferraro, P.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Finizio, A.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Galli, A.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Gioffré, M.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grilli, S.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Guerin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Hahn, J.

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

Harteneck, B.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Iodice, M.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Javidi, B.

Juptner, W.

Kim, H.

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

Kim, S.

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

Lee, B.

Y. Lim, S. Lee, and B. Lee, Opt. Express 19, 5202 (2011).
[CrossRef]

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

Lee, S.

Lim, Y.

Y. Lim, S. Lee, and B. Lee, Opt. Express 19, 5202 (2011).
[CrossRef]

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

Mocella, V.

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, Opt. Express 18, 25068 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

V. Mocella, P. Dardano, L. Moretti, and I. Rendina, Opt. Express 15, 6605 (2007).
[CrossRef]

Moon, I.

Moretti, L.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

V. Mocella, P. Dardano, L. Moretti, and I. Rendina, Opt. Express 15, 6605 (2007).
[CrossRef]

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Olynick, D.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Osten, W.

Park, J.

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

Pendry, J.

J. Pendry and S. Ramakrishna, J. Phys. Condens. Matter 15, 6345 (2003).
[CrossRef]

Puglisi, R.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Ramakrishna, S.

J. Pendry and S. Ramakrishna, J. Phys. Condens. Matter 15, 6345 (2003).
[CrossRef]

Rendina, I.

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, Opt. Express 18, 25068 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

V. Mocella, P. Dardano, L. Moretti, and I. Rendina, Opt. Express 15, 6605 (2007).
[CrossRef]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Saffioti, N.

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Seebacher, S.

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Wagner, C.

Yeom, S.

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Yu, L.

Ziolkowski, R. W.

R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004).
[CrossRef]

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (2)

G. Di Caprio, M. Gioffré, N. Saffioti, S. Grilli, P. Ferraro, R. Puglisi, D. Balduzzi, A. Galli, and G. Coppola, IEEE J. Sel. Top. Quantum Electron. 16, 833 (2010).
[CrossRef]

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, IEEE J. Sel. Top. Quantum Electron. 46, 300 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. Condens. Matter (1)

J. Pendry and S. Ramakrishna, J. Phys. Condens. Matter 15, 6345 (2003).
[CrossRef]

Meas. Sci. Technol. (1)

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Opt. Express (4)

Phys. Rev. B (1)

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Phys. Rev. E (1)

R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (5)

Fig. 1.
Fig. 1.

Optical setup. In the inset a scanning electron microscope image of the PhC structure is shown.

Fig. 2.
Fig. 2.

(a) Acquired hologram; the reconstructed (b) intensity and (c) phase maps.

Fig. 3.
Fig. 3.

(a) Reconstructed optical field from a 3D point of view; (b) sections of the beam at different reconstruction distances.

Fig. 4.
Fig. 4.

(a) XZ and (b) YZ cross sections of the intensity distribution.

Fig. 5.
Fig. 5.

(a) Unwrapped phase map and (b) phase profiles corresponding to the Y positions 1.5 mm, 2.1 mm, 2.7 mm, 3.3 mm, and 3.9 mm.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Γ(ξ,n)=Γ(x,y)g(xξ,yη)dxdy,
g(x,y)=exp[ikz]iλzexp[ik2z(x2+y2)],
F[Γprop]=F[Γin]G,
G(n,m)=exp{i2πλ1λ2(n+N2Δx22dλ)N2Δx2λ2(m+N2Δy22dλ)N2Δy2}.

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