Abstract

It is shown that broad-band antireflection coatings with extra large angular range can be designed based on the concept of reflectionless potentials. Numerical calculations for inhomogeneous films with or without substrate demonstrate the above capabilities for both TE and TM polarizations. The design possibilities are infinite and the underlying concept does not rely on standard use of quarter wave plates. Suitable inhomogeneous layers on both sides of a lossless thin dielectric film can thus render it invisible.

© 2007 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. Philippe Lalanne and G Michael Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology8, 53–56 (1997).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  8. J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).
  9. P. G. Drazin, et al, Solitons- An Introduction, 2nd edition (Cambridge University Press, Cambridge, 1989) Ch.3.
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  18. A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
    [Crossref]

2007 (1)

2006 (4)

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

G. W. Milton and N. A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance”, Proceedings London Royal Society A 462, 3027–3059 (2006).
[Crossref]

2005 (2)

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanisms of light transmission through metallic films”, Phys. Rev. Lett. 95, 067403 (2005).
[Crossref]

J. W. Lee, M. A. Seo, J. Y. Sohn, Y. H. Ahn, and D. S. Kim, “Invisible plasmonic meta-materials through impedance matching to vacuum,” Opt. Express 13, 10681–10687 (2005).
[Crossref] [PubMed]

2004 (1)

2002 (1)

S. Zaitsu, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[Crossref]

2001 (1)

1997 (1)

Q. Tanga, S. Ogura, M. Yamasaki, and K. Kikuchi, “Experimental study on intermediate and gradient index dielectric thin films by a novel reactive sputtering method,” J. Vac. Sci. Technol. A 15, 2670–2672 (1997).
[Crossref]

1988 (1)

N. Kiriushcheva and S. Kuzmin, “Scattering of a Gaussian wave packet by a reflectionless potential,” Am. J. Phys. 66, 867–872 (1988).
[Crossref]

1984 (1)

1980 (1)

J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).

1978 (1)

H. B. Thacker, C. Quigg, and J. L. Rosner, “Inverse scattering problem for quarkonium systems. I. One-dimensional formalism and methodology,” Phys. Rev. D 18, 274–286 (1978).
[Crossref]

1956 (1)

I. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503–1508 (1956).
[Crossref]

Aarik, J.

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

Ahn, Y. H.

Blanco, L. A.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanisms of light transmission through metallic films”, Phys. Rev. Lett. 95, 067403 (2005).
[Crossref]

Borisov, A. G.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanisms of light transmission through metallic films”, Phys. Rev. Lett. 95, 067403 (2005).
[Crossref]

Dobrowolski, J. A.

Drazin, P. G.

P. G. Drazin, et al, Solitons- An Introduction, 2nd edition (Cambridge University Press, Cambridge, 1989) Ch.3.

Garcia de Abajo, F. J.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanisms of light transmission through metallic films”, Phys. Rev. Lett. 95, 067403 (2005).
[Crossref]

Gomez-Santos, G.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanisms of light transmission through metallic films”, Phys. Rev. Lett. 95, 067403 (2005).
[Crossref]

Guenneau, S.

Jitsuno, T.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[Crossref]

Kasikov, A.

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

Kay, I.

I. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503–1508 (1956).
[Crossref]

Kikuchi, K.

Q. Tanga, S. Ogura, M. Yamasaki, and K. Kikuchi, “Experimental study on intermediate and gradient index dielectric thin films by a novel reactive sputtering method,” J. Vac. Sci. Technol. A 15, 2670–2672 (1997).
[Crossref]

Kikuta, H.

Kim, D. S.

Kintaka, K.

Kiriushcheva, N.

N. Kiriushcheva and S. Kuzmin, “Scattering of a Gaussian wave packet by a reflectionless potential,” Am. J. Phys. 66, 867–872 (1988).
[Crossref]

Kuzmin, S.

N. Kiriushcheva and S. Kuzmin, “Scattering of a Gaussian wave packet by a reflectionless potential,” Am. J. Phys. 66, 867–872 (1988).
[Crossref]

Kwong, W.

J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).

Lee, J. W.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

Mandar, H.

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

Milton, G. W.

G. W. Milton and N. A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance”, Proceedings London Royal Society A 462, 3027–3059 (2006).
[Crossref]

Mizutani, A.

Moppel, M.

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

Moses, H. E.

I. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503–1508 (1956).
[Crossref]

Nakano, H.

Nakatsuka, M.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[Crossref]

Nicolet, A.

Nicorovici, N. A.

G. W. Milton and N. A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance”, Proceedings London Royal Society A 462, 3027–3059 (2006).
[Crossref]

Nishii, J.

Ogura, S.

Q. Tanga, S. Ogura, M. Yamasaki, and K. Kikuchi, “Experimental study on intermediate and gradient index dielectric thin films by a novel reactive sputtering method,” J. Vac. Sci. Technol. A 15, 2670–2672 (1997).
[Crossref]

Pars, M.

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

Pendry, J. B.

Poitras, D.

Quigg, C.

J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).

H. B. Thacker, C. Quigg, and J. L. Rosner, “Inverse scattering problem for quarkonium systems. I. One-dimensional formalism and methodology,” Phys. Rev. D 18, 274–286 (1978).
[Crossref]

Rosner, J. L.

J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).

H. B. Thacker, C. Quigg, and J. L. Rosner, “Inverse scattering problem for quarkonium systems. I. One-dimensional formalism and methodology,” Phys. Rev. D 18, 274–286 (1978).
[Crossref]

Sankur, H.

Schonfeld, J. F.

J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Seo, M. A.

Shabanov, S. V.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanisms of light transmission through metallic films”, Phys. Rev. Lett. 95, 067403 (2005).
[Crossref]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Sohn, J. Y.

Southwell, W. H.

Tanga, Q.

Q. Tanga, S. Ogura, M. Yamasaki, and K. Kikuchi, “Experimental study on intermediate and gradient index dielectric thin films by a novel reactive sputtering method,” J. Vac. Sci. Technol. A 15, 2670–2672 (1997).
[Crossref]

Thacker, H. B.

J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).

H. B. Thacker, C. Quigg, and J. L. Rosner, “Inverse scattering problem for quarkonium systems. I. One-dimensional formalism and methodology,” Phys. Rev. D 18, 274–286 (1978).
[Crossref]

Uustare, T.

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

Yamanaka, T.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[Crossref]

Yamasaki, M.

Q. Tanga, S. Ogura, M. Yamasaki, and K. Kikuchi, “Experimental study on intermediate and gradient index dielectric thin films by a novel reactive sputtering method,” J. Vac. Sci. Technol. A 15, 2670–2672 (1997).
[Crossref]

Zaitsu, S.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[Crossref]

Zolla, F.

Am. J. Phys. (1)

N. Kiriushcheva and S. Kuzmin, “Scattering of a Gaussian wave packet by a reflectionless potential,” Am. J. Phys. 66, 867–872 (1988).
[Crossref]

Ann. Phys. (1)

J. F. Schonfeld, W. Kwong, J. L. Rosner, C. Quigg, and H. B. Thacker, “On the convergence of reflectionless approximation to confining potentials,” Ann. Phys. 12, 1–28 (1980).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. Zaitsu, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[Crossref]

J. Appl. Phys. (1)

I. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503–1508 (1956).
[Crossref]

J. Phys. D: Appl. Phys. (1)

A. Kasikov, J. Aarik, H. Mandar, M. Moppel, M. Pars, and T. Uustare, “Refractive index gradients in TiO2 thin films grown by atomic layer deposition,” J. Phys. D: Appl. Phys. 39, 54–60 (2006).
[Crossref]

J. Vac. Sci. Technol. A (1)

Q. Tanga, S. Ogura, M. Yamasaki, and K. Kikuchi, “Experimental study on intermediate and gradient index dielectric thin films by a novel reactive sputtering method,” J. Vac. Sci. Technol. A 15, 2670–2672 (1997).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. D (1)

H. B. Thacker, C. Quigg, and J. L. Rosner, “Inverse scattering problem for quarkonium systems. I. One-dimensional formalism and methodology,” Phys. Rev. D 18, 274–286 (1978).
[Crossref]

Phys. Rev. Lett. (1)

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanisms of light transmission through metallic films”, Phys. Rev. Lett. 95, 067403 (2005).
[Crossref]

Proceedings London Royal Society A (1)

G. W. Milton and N. A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance”, Proceedings London Royal Society A 462, 3027–3059 (2006).
[Crossref]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

Other (2)

P. G. Drazin, et al, Solitons- An Introduction, 2nd edition (Cambridge University Press, Cambridge, 1989) Ch.3.

Philippe Lalanne and G Michael Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology8, 53–56 (1997).

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Figures (9)

Fig. 1.
Fig. 1.

Intensity reflection coefficient R as a function of angle of incidence θ for the inhomogeneous film (see text for a description) (a) without or (b) with the substrate at λ=1.06µm. The insets show the refractive index profiles.

Fig. 2.
Fig. 2.

Intensity reflection coefficient R as a function of angle of incidence θ for the inhomogeneous film (see text for a description) (a) without or (b) with the substrate at λ=1.55µm. The insets show the refractive index profiles.

Fig. 3.
Fig. 3.

Normal incidence intensity reflection coefficient R as a function of wavelength λ for the inhomogeneous film (see text for a description) (a) without or (b) with the substrate. The inhomogeneous film is designed at wavelength 1.06µm. The solid (dashed) lines are for the inhomogeneous film occupying -3µmz≤3µm (-2µmz≤2µm).

Fig. 4.
Fig. 4.

Normal incidence intensity reflection coefficient R as a function of wavelength λ for the inhomogeneous film (see text for a description) (a) without or (b) with the substrate. The inhomogeneous film is designed at wavelength 1.55µm. The solid (dashed) lines are for the inhomogeneous film occupying -3µmz≤3µm (-2µmz≤2µm).

Fig. 5.
Fig. 5.

Reflection coefficient R as functions of (a) angle of incidence θ for TE polarized light and (b) wavelength λ for normal incidence. The solid and dashed lines are for A 1=11,A 2=5.5 and κ1=5.5,κ2=2.25, i.e., for well separated eigenvalues and for A 1=11,A 2=5.5 and κ1=5.5,κ2=5.4, i.e., for closely spaced eigenvalues, respectively. The corresponding profiles designed at λ=1.06µm are shown in the inset.

Fig. 6.
Fig. 6.

Reflection coefficient R as functions of (a) angle of incidence θ for TM polarized light and (b) wavelength l for normal incidence. The solid, dashed and dotted lines are for the parameter sets (i) A 1=11, κ1=5.5, (ii) A 1=11, κ1=5.5, A 2=5.5, κ2=2.75, and (iii) A 1=11, κ1=5.5, A 2=5.5, κ2=2.75,A 3=2, κ3=1, respectively. The corresponding profiles designed at λ=1.06µm are shown in the inset.

Fig. 7.
Fig. 7.

Intensity reflection coefficient R as a function of angle of incidence θ for the inhomogeneous film (see text for a description) (a) without or (b) with the substrate. The inhomogeneous film (occupying -4µmz≤4µm) is designed at wavelength 1.55µm. The solid (dashed) lines are for TE (TM) polarization.

Fig. 8.
Fig. 8.

Normal incidence intensity reflection coefficient R as a function of wavelength λ for the inhomogeneous film (see text for a description) (a) without or (b) with the substrate. The inhomogeneous film is designed at wavelength 1.55µm. The solid (dashed) lines are for the inhomogeneous film occupying -4µmz≤4µm.

Fig. 9.
Fig. 9.

Intensity reflection coefficient R as a function of angle of incidence θ for the PT profile for s-polarized light at λ=1.06µm. The curves from right to left are for step-sizes 0.005, 0.01, 0.05 and 0.1 µm, respectively. The left inset shows the refractive index profile, while the right one shows the enlarged portion between 89 and 90 degrees.

Equations (13)

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d 2 d z 2 + ( k 0 2 ε ( z ) k x 2 ) = 0 ,
d 2 d z 2 d dz d ( ln ε ( z ) ) dz + ( k 0 2 ε ( z ) k x 2 ) = 0 ,
V ( z ) = k 0 2 ε s k 0 2 ε ( z ) .
E = k 0 2 ε s cos 2 θ .
d 2 ψ d z 2 + ( E V ( z ) ) ψ = 0 .
n 2 ( z ) = n s 2 V ( z ) k 0 2 ; ε s = n s 2 .
j = 1 N M ij f j ( z ) = A i e κ i z , M ij = δ ij + A i e ( κ i + κ j ) z ( κ i + κ j ) .
V ( z ) = 2 d 2 d z 2 [ log ( D ) ] .
n 2 ( z ) = n s 2 + 2 k 0 2 d 2 d z 2 [ log ( D ) ] .
D ( z ) = 1 + e 2 κ 1 z ; n 2 ( z ) = n s 2 + 2 κ 1 2 k 0 2 Sech 2 ( κ 1 z )
D ( z ) = 1 + A 1 2 κ 1 e 2 κ 1 z + A 2 2 κ 2 e 2 κ 2 z + ( κ 1 κ 2 ) 2 A 1 A 2 e 2 ( κ 1 + κ 2 ) z 4 κ 1 κ 2 ( κ 1 + κ 2 ) 2 ,
n 2 ( z ) = n s 1 2 + 2 k 0 2 d 2 d z 2 [ log ( D ) ] + n s 2 2 n s 1 2 2 [ 1 + tanh ( κ 1 z ) ] ,
κ 1 = ( π λ ) 2 ( n max 2 n s 2 ) ,

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