Abstract

We propose to use hybrid dielectric–metallic subwavelength structures to code complex transmittance (module and phase) in the mid-infrared wavelength range. As a demonstrator, we have designed and fabricated large-area (2mm×2mm) metallic gratings with transmittance levels ranging from 37% to 98%. Optical transmission measurements are in very good agreement with numerical computations. It demonstrates the ability to control the transmission intensity with high accuracy by the use of lateral structuration of metal at the nanoscale. A nonresonant process ensures a large spectral band. We discuss the integration of this concept to code a laterally modulated sinusoidal transmittance pattern. The phase shift induced by metal structures is analyzed. A technologically viable solution is proposed to reduce this parasitic effect in our application. Such devices allow one to obtain optical beams with a lateral, two-dimensional sinusoidal modulation and can answer the growing needs of optical wavefront analysis applications.

© 2008 Optical Society of America

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2007

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007).
[CrossRef]

2006

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

2005

2004

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A, Pure Appl. Opt. 4, S154-S160 (2002).
[CrossRef]

2000

1998

1995

1993

1992

1991

1985

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs material parameters for use in research and device applications,” J. Appl. Phys. 58, R1-R29 (1985).
[CrossRef]

Adachi, S.

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs material parameters for use in research and device applications,” J. Appl. Phys. 58, R1-R29 (1985).
[CrossRef]

Astilean, S.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möllers, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings,” Opt. Lett. 23, 1081-1083 (1998).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Cambril, E.

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings,” Opt. Lett. 23, 1081-1083 (1998).
[CrossRef]

Chavel, P.

Collin, S.

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

R. Haïdar, G. Vincent, N. Guérineau, S. Collin, S. Velghe, and J. Primot, “Wollaston prism-like devices based on blazed dielectric subwavelength gratings,” Opt. Express 13, 9941-9953 (2005).
[CrossRef] [PubMed]

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A, Pure Appl. Opt. 4, S154-S160 (2002).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Dial, O.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Farn, M. W.

Gao, X.

Garcia-Vidal, F. J.

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Guérineau, N.

Haïdar, R.

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

R. Haïdar, G. Vincent, N. Guérineau, S. Collin, S. Velghe, and J. Primot, “Wollaston prism-like devices based on blazed dielectric subwavelength gratings,” Opt. Express 13, 9941-9953 (2005).
[CrossRef] [PubMed]

Haidner, H.

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möllers, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Kipfer, P.

Lalanne, P.

Launois, H.

Lee, M. S. L.

Mait, J. N.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), p. 126.

Martin-Moreno, L.

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Möllers, K. D.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möllers, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Palamaru, M.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möllers, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Pardo, F.

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A, Pure Appl. Opt. 4, S154-S160 (2002).
[CrossRef]

Pelouard, J. L.

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A, Pure Appl. Opt. 4, S154-S160 (2002).
[CrossRef]

Pelouard, J.-L.

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

Prather, D. W.

Primot, J.

Sauvan, C.

Scherer, A.

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Sogno, L.

Stork, W.

Streibl, N.

Teissier, R.

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A, Pure Appl. Opt. 4, S154-S160 (2002).
[CrossRef]

Velghe, S.

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

R. Haïdar, G. Vincent, N. Guérineau, S. Collin, S. Velghe, and J. Primot, “Wollaston prism-like devices based on blazed dielectric subwavelength gratings,” Opt. Express 13, 9941-9953 (2005).
[CrossRef] [PubMed]

Vincent, G.

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

R. Haïdar, G. Vincent, N. Guérineau, S. Collin, S. Velghe, and J. Primot, “Wollaston prism-like devices based on blazed dielectric subwavelength gratings,” Opt. Express 13, 9941-9953 (2005).
[CrossRef] [PubMed]

Appl. Opt.

J. Appl. Phys.

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs material parameters for use in research and device applications,” J. Appl. Phys. 58, R1-R29 (1985).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möllers, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A, Pure Appl. Opt. 4, S154-S160 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Proc. SPIE

G. Vincent, R. Haïdar, S. Collin, E. Cambril, S. Velghe, J. Primot, F. Pardo, and J.-L. Pelouard, “Complex transmittance gratings based on subwavelength metallic structures,” Proc. SPIE 6195, 61951K (2006).
[CrossRef]

Other

D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), p. 126.

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Figures (9)

Fig. 1
Fig. 1

Schematic of the device coding a sinusoidal transmittance. There are two levels of approximation, one for the intensity T (obtained with a limited number of subwavelength metallic gratings on side A) and the other for the phase ψ (coded with a superposed dielectric structure on side B).

Fig. 2
Fig. 2

Sinusoidal pattern is divided into a number of domains, each domain corresponding to a geometrical extension L n and transmittance level T n . Each transmittance level is obtained with a subwavelength grating.

Fig. 3
Fig. 3

Grating that is associated with one level of transmittance. It consists of a lamellar gold grating deposited on a GaAs substrate that was previously covered with AR layers on both sides.

Fig. 4
Fig. 4

Grating transmission as a function of the slit width for TM polarization and under normal incidence at λ = 7 μ m . Excellent agreement between the calculated (solid curve) and measured (dots) results.

Fig. 5
Fig. 5

Test structure made of three subwavelength gratings. Each of them corresponds to one transmission level that has been individually measured by an FT spectrometer and compared to calculations (Fig. 4).

Fig. 6
Fig. 6

Transmission spectra of the gratings for TM polarization and under normal incidence. Approximate target wavelength ( λ = 7 μ m ) and the simulated data (dashed curve) are in good agreement with the FTIR measurements (solid curves) obtained using an FTIR spectrometer. Si 3 N 4 optical index has been taken to equal 1.98.

Fig. 7
Fig. 7

Sinusoidal pattern obtained in the 5 8 μ m spectral range by placing the gratings side-by-side.

Fig. 8
Fig. 8

Device is composed of a stepped metallic pattern (coding the transmission intensity on the front side) superposed to a stepped phase pattern (coding the phase on the back side). (a) No additional phase compensation and (b) one step of parasitic phase is compensated for [see Table 2c].

Fig. 9
Fig. 9

Top, FT spectra of the various transmittances [(a) perfect sinusoidal pattern and approximated sinusoid (b) without and (c) with phase compensation]. Bottom, propagation of the corresponding transmitted beams (light-pipes).

Tables (3)

Tables Icon

Table 1 Geometrical Extension L n and Trans mission Intensity T n of Each Domain of the Ap proximated Sinusoidal Transmittance Pattern a

Tables Icon

Table 2 Geometry and Results for a Five-Level Transmittance a, b, c

Tables Icon

Table 3 Evolution of the Quality Criteria for Various Devices (Perfect Sinusoidal Pattern and Various Compensated Approximations) a, b

Equations (1)

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f = C max C 1 .

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