Abstract

We present a characterization technique of wide-area sub-wavelength structures. The optical bench is based on lateral shearing interferometry, which allows an accurate complex transmittance (phase and amplitude) measurement. The experimental validation is made in the long-wavelength infrared domain; more precisely we work in the integrated 8–9 µm spectral range. Measurements of the transmitted amplitude and phase shift reveal a good agreement with respectively experimental results based on Fourier Transform infrared spectrometry, and theoretical simulations.

© 2008 Optical Society of America

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  3. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
    [CrossRef]
  4. G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïdar, "Large-area dielectric and metallic free-standing gratings for mid-infrared optical filters," J. Vac. Sci. Technol. B (submitted).
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    [CrossRef]
  13. A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161,403 (2002).
    [CrossRef]
  14. 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, 659107 (2006).
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    [CrossRef] [PubMed]
  28. P. Champert, V. Couderc, and A. Barthelemy, "1.5-2.0-μm multiwatt continuum generation in dispersion-shifted fiber by use of high-power continuous-wave fiber source," IEEE Photon. Technol. Lett. 16, 2445-2447 (2004).
    [CrossRef]
  29. C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, "Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals," Opt. Lett. 33, 165-167 (2008).
    [CrossRef] [PubMed]

2008 (1)

2006 (5)

W. L. Barnes, "Surface plasmon-polariton length scales: a route to sub-wavelength optics," J. Opt. A: Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

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, 659107 (2006).
[CrossRef]

S. Velghe, N. Guerineau, R. Haıdar, B. Toulon, S. Demoustier, and J. Primot, "Two-color multi-wave lateral shearing interferometry for segmented wave-front measurements," Opt. Express 24, 9699 (2006), http://www.opticsinfobase.org/abstract.cfm?id=116369.
[CrossRef]

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, "Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs," Opt. Lett. 31, 71-73 (2006).
[CrossRef] [PubMed]

2005 (4)

2004 (2)

P. Champert, V. Couderc, and A. Barthelemy, "1.5-2.0-μm multiwatt continuum generation in dispersion-shifted fiber by use of high-power continuous-wave fiber source," IEEE Photon. Technol. Lett. 16, 2445-2447 (2004).
[CrossRef]

R. Haıdar, N. Forget, P. Kupecek, and E. Rosencher, "Fresnel phase matching for three-wave mixing in isotropic semiconductors," J. Opt. Soc. Am. B 21, 1522-1534 (2004).
[CrossRef]

2002 (1)

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161,403 (2002).
[CrossRef]

2000 (2)

J. Primot and N. Guérineau, "Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard," Appl. Opt. 39, 5715-5720 (2000).
[CrossRef]

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

1999 (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

1995 (1)

1993 (1)

1991 (1)

1990 (1)

D. Malacara, "Analysis of the interferometric Ronchi test," Appl. Opt 29, 3633-3637 (1990).
[CrossRef] [PubMed]

1986 (1)

1982 (1)

1956 (1)

S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).

Astilean, S.

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

Barbara, A.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161,403 (2002).
[CrossRef]

Bardou, N.

C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, "Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals," Opt. Lett. 33, 165-167 (2008).
[CrossRef] [PubMed]

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïdar, "Large-area dielectric and metallic free-standing gratings for mid-infrared optical filters," J. Vac. Sci. Technol. B (submitted).

Barnes, W. L.

W. L. Barnes, "Surface plasmon-polariton length scales: a route to sub-wavelength optics," J. Opt. A: Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

Barthelemy, A.

P. Champert, V. Couderc, and A. Barthelemy, "1.5-2.0-μm multiwatt continuum generation in dispersion-shifted fiber by use of high-power continuous-wave fiber source," IEEE Photon. Technol. Lett. 16, 2445-2447 (2004).
[CrossRef]

Billaudeau, C.

Bliss, D.

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental Demonstration of Near-Infrared Negative-Index Metamaterials," Phys. Rev. Lett. 95, 137,404 (2005).
[CrossRef]

Bustarret, E.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161,403 (2002).
[CrossRef]

Cai, W.

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, 659107 (2006).
[CrossRef]

G. Vincent, R. Haïdar, S. Collin, N. Guérineau, J. Primot, E. Cambril, and J.-L. Pelouard, "Realization of sinusoidal transmittances with sub-wavelength metallic structures," J. Opt. Soc. Am. B (to be published).

Champert, P.

P. Champert, V. Couderc, and A. Barthelemy, "1.5-2.0-μm multiwatt continuum generation in dispersion-shifted fiber by use of high-power continuous-wave fiber source," IEEE Photon. Technol. Lett. 16, 2445-2447 (2004).
[CrossRef]

Chanteloup, J.-C.

Chettiar, U. K.

Collin, S.

C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, "Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals," Opt. Lett. 33, 165-167 (2008).
[CrossRef] [PubMed]

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, 659107 (2006).
[CrossRef]

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïdar, "Large-area dielectric and metallic free-standing gratings for mid-infrared optical filters," J. Vac. Sci. Technol. B (submitted).

G. Vincent, R. Haïdar, S. Collin, N. Guérineau, J. Primot, E. Cambril, and J.-L. Pelouard, "Realization of sinusoidal transmittances with sub-wavelength metallic structures," J. Opt. Soc. Am. B (to be published).

Couderc, V.

P. Champert, V. Couderc, and A. Barthelemy, "1.5-2.0-μm multiwatt continuum generation in dispersion-shifted fiber by use of high-power continuous-wave fiber source," IEEE Photon. Technol. Lett. 16, 2445-2447 (2004).
[CrossRef]

Demoustier, S.

S. Velghe, N. Guerineau, R. Haıdar, B. Toulon, S. Demoustier, and J. Primot, "Two-color multi-wave lateral shearing interferometry for segmented wave-front measurements," Opt. Express 24, 9699 (2006), http://www.opticsinfobase.org/abstract.cfm?id=116369.
[CrossRef]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Dong, X.

Drachev, V. P.

Du, C.

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental Demonstration of Near-Infrared Negative-Index Metamaterials," Phys. Rev. Lett. 95, 137,404 (2005).
[CrossRef]

Fejer, M. M.

Forget, N.

Freischlad, K. R.

Gao, H.

García-Vidal, F. J.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Guerineau, N.

S. Velghe, N. Guerineau, R. Haıdar, B. Toulon, S. Demoustier, and J. Primot, "Two-color multi-wave lateral shearing interferometry for segmented wave-front measurements," Opt. Express 24, 9699 (2006), http://www.opticsinfobase.org/abstract.cfm?id=116369.
[CrossRef]

Guérineau, N.

J. Primot and N. Guérineau, "Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard," Appl. Opt. 39, 5715-5720 (2000).
[CrossRef]

G. Vincent, R. Haïdar, S. Collin, N. Guérineau, J. Primot, E. Cambril, and J.-L. Pelouard, "Realization of sinusoidal transmittances with sub-wavelength metallic structures," J. Opt. Soc. Am. B (to be published).

Haidar, R.

S. Velghe, N. Guerineau, R. Haıdar, B. Toulon, S. Demoustier, and J. Primot, "Two-color multi-wave lateral shearing interferometry for segmented wave-front measurements," Opt. Express 24, 9699 (2006), http://www.opticsinfobase.org/abstract.cfm?id=116369.
[CrossRef]

R. Haıdar, N. Forget, P. Kupecek, and E. Rosencher, "Fresnel phase matching for three-wave mixing in isotropic semiconductors," J. Opt. Soc. Am. B 21, 1522-1534 (2004).
[CrossRef]

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, 659107 (2006).
[CrossRef]

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïdar, "Large-area dielectric and metallic free-standing gratings for mid-infrared optical filters," J. Vac. Sci. Technol. B (submitted).

G. Vincent, R. Haïdar, S. Collin, N. Guérineau, J. Primot, E. Cambril, and J.-L. Pelouard, "Realization of sinusoidal transmittances with sub-wavelength metallic structures," J. Opt. Soc. Am. B (to be published).

Harris, J. S.

Hugonin, J.

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

Ina, H.

Kildishev, A. V.

Kobayashi, S.

Koliopoulos, C. L.

Kuo, P. S.

Kupecek, P.

Lalanne, P.

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

Linden, S.

G. Dolling, C. Enkrich, M. Wegener, C. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Lopez-Rios, T.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161,403 (2002).
[CrossRef]

Luo, X.

Malacara, D.

D. Malacara, "Analysis of the interferometric Ronchi test," Appl. Opt 29, 3633-3637 (1990).
[CrossRef] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental Demonstration of Near-Infrared Negative-Index Metamaterials," Phys. Rev. Lett. 95, 137,404 (2005).
[CrossRef]

Möller, K.

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

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental Demonstration of Near-Infrared Negative-Index Metamaterials," Phys. Rev. Lett. 95, 137,404 (2005).
[CrossRef]

Palamaru, M.

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

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental Demonstration of Near-Infrared Negative-Index Metamaterials," Phys. Rev. Lett. 95, 137,404 (2005).
[CrossRef]

Pardo, F.

C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, "Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals," Opt. Lett. 33, 165-167 (2008).
[CrossRef] [PubMed]

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, 659107 (2006).
[CrossRef]

Pelouard, J.-L.

C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, "Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals," Opt. Lett. 33, 165-167 (2008).
[CrossRef] [PubMed]

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, 659107 (2006).
[CrossRef]

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïdar, "Large-area dielectric and metallic free-standing gratings for mid-infrared optical filters," J. Vac. Sci. Technol. B (submitted).

G. Vincent, R. Haïdar, S. Collin, N. Guérineau, J. Primot, E. Cambril, and J.-L. Pelouard, "Realization of sinusoidal transmittances with sub-wavelength metallic structures," J. Opt. Soc. Am. B (to be published).

Pendry, J. B.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Porto, J. A.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Primot, J.

S. Velghe, N. Guerineau, R. Haıdar, B. Toulon, S. Demoustier, and J. Primot, "Two-color multi-wave lateral shearing interferometry for segmented wave-front measurements," Opt. Express 24, 9699 (2006), http://www.opticsinfobase.org/abstract.cfm?id=116369.
[CrossRef]

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, 659107 (2006).
[CrossRef]

J. Primot and N. Guérineau, "Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard," Appl. Opt. 39, 5715-5720 (2000).
[CrossRef]

J. Primot and L. Sogno, "Achromatic three-wave (or more) lateral shearing interferometer," J. Opt. Soc. Am. A 12, 2679-2685 (1995).
[CrossRef]

J. Primot, "Three-wave lateral shearing interferometer," Appl. Opt. 32, 6242-6249 (1993).
[CrossRef] [PubMed]

G. Vincent, R. Haïdar, S. Collin, N. Guérineau, J. Primot, E. Cambril, and J.-L. Pelouard, "Realization of sinusoidal transmittances with sub-wavelength metallic structures," J. Opt. Soc. Am. B (to be published).

Quémerais, P.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161,403 (2002).
[CrossRef]

Roddier, C.

Roddier, F.

Rosencher, E.

Rytov, S. M.

S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).

Sarychev, A. K.

Sauvan, C.

Shalaev, V. M.

Shi, H.

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[CrossRef] [PubMed]

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[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Generic structure of a sub-wavelength grating, and definition or the parameters h, d and w.

Fig. 2.
Fig. 2.

Geometry of the sample under study. Each square area (number from 1 to 5) is filled with a different sub-wavelength grating. The last square (number 6) is the reference square.

Fig. 3.
Fig. 3.

Illustration of the parasitic phase shift induced by the metallic sub-wavelength gratings (various opto-geometrical parameters, as indicated in table 1); horizontal black lines are located on the amplitude peak value. One can also notice the amplitude modulation from one grating to the other.

Fig. 4.
Fig. 4.

A segmented phase (a)φ(x,y) is made of two continuous, plane segments separated by a step of height h. (b) The initial phase is represented with its replica separated by the lateral shearing distance s along the x-direction. (c) The phase difference to which the interferogram is sensitive is then a h-high, s-wide crenel.

Fig. 5.
Fig. 5.

Data extraction from the interferogram, thanks to a Fourier analysis. The green square correspond to the 0th-order analysis and the red squares to the harmonics analysis. The 0th-order leads to the amplitude of the transmitted wave whereas the harmonics lead to the derivatives of the phase.

Fig. 6.
Fig. 6.

Experimental bench dedicated to LWIR domain. The QWLSI consists of the MHM grating and the detector.

Fig. 7.
Fig. 7.

Experimental interferogram (a) and the computed derivative (or difference quotient) along the y-axis (b) (or similarly x-axis). The plot (c) shows a profile of the derivative. The intensity patterns are noticeable on the interferogram.

Fig. 8.
Fig. 8.

Reconstructed amplitude (a) and phase (b) of the sample.

Fig. 9.
Fig. 9.

Comparison between the average transmissions of the five sub-wavelength gratings evaluated by QWLSI and those measured by FTIR.

Tables (2)

Tables Icon

Table 1. Values of slit widths and induced computed transmission and phase shift. The period d is 2 µm, the gold thickness is 830 nm and the working wavelength is 8µm. Notice that real index (n=2.05) is assumed for the Si3N4 layer.

Tables Icon

Table 2. Phase modulation induced by the sub-wavelength gratings: comparison between the expected results and the measured values.

Equations (2)

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

Δ φ ( x , y ) = φ ( x + s 2 , y ) φ ( x s 2 , y ) ,
φ ( x + s 2 , y ) φ ( x s 2 , y ) s φ x ;

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