Abstract

We demonstrate high-efficiency half-wave retardation in diffracted light in the 2nd order Littrow mounting. The diffracting structure is a slanted crossed grating with subwavelength period in the direction of the second grating vector, which makes it possible to mix the polarization states of the input light inside the grating layer, and hence to create the half-wave retardation. We present an experimental result with 58.9 % diffraction efficiency and a near perfect half-wave retardation. We explain the effect qualitatively using the classical coupled-wave approach.

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  2. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [CrossRef]
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    [CrossRef] [PubMed]
  4. D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
    [CrossRef]
  5. T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
    [CrossRef]
  6. N. Passilly, K. Ventola, P. Karvinen, P. Laakkonen, J. Turunen, and J. Tervo, “Polarization conversion in conical diffraction by metallic and dielectric subwavelength gratings,” Appl. Opt. 46, 4258–4265 (2007).
    [CrossRef] [PubMed]
  7. N. Bonod, E. Popov, L. Li, and B. Chernov, “Unidirectional excitation of surface plasmons by slanted gratings,” Opt. Express 15, 11427–11432 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
    [CrossRef]
  10. K. Ventola, J. Tervo, P. Laakkonen, and M. Kuittinen, “High phase retardation by waveguiding in slanted photonic nanostructures,” Opt. Express 19, 241–246 (2011).
    [CrossRef] [PubMed]
  11. L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A: Pure appl. Opt. 5, 345–355 (2003).
    [CrossRef]
  12. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions”, SIAM Optim J. 9, 112–147 (1999).
    [CrossRef]
  13. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  14. S. Siitonen, P. Laakkonen, J. Tervo, and M. Kuittinen, “A double-sided grating coupler for thin light guides,” Opt. Express 15, 2008–2018 (2007).
    [CrossRef] [PubMed]

2011 (1)

2007 (5)

2004 (1)

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

2003 (2)

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A: Pure appl. Opt. 5, 345–355 (2003).
[CrossRef]

1999 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions”, SIAM Optim J. 9, 112–147 (1999).
[CrossRef]

1995 (1)

1983 (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Baets, R.

F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
[CrossRef]

Bonod, N.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Cheng, C.-C.

Chernov, B.

Fainman, Y.

Flanders, D. C.

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Isano, T.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Ishizuka, K.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Iwakami, N.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Jin, G.-F.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Kaneda, Y.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Karvinen, P.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kotlyar, M. V.

F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
[CrossRef]

Krauss, T. F.

F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
[CrossRef]

Kuittinen, M.

Laakkonen, P.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions”, SIAM Optim J. 9, 112–147 (1999).
[CrossRef]

Levola, T.

Li, L.

N. Bonod, E. Popov, L. Li, and B. Chernov, “Unidirectional excitation of surface plasmons by slanted gratings,” Opt. Express 15, 11427–11432 (2007).
[CrossRef] [PubMed]

L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A: Pure appl. Opt. 5, 345–355 (2003).
[CrossRef]

Liu, H.-T.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Passilly, N.

Popov, E.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions”, SIAM Optim J. 9, 112–147 (1999).
[CrossRef]

Scherer, A.

Siitonen, S.

Si-Li,

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Sun, P.-C.

Susuki, N.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Taillaert, D.

F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
[CrossRef]

Tervo, J.

Turunen, J.

Tyan, R.-C.

Van Laere, F.

F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
[CrossRef]

Van Thourhout, D.

F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
[CrossRef]

Ventola, K.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions”, SIAM Optim J. 9, 112–147 (1999).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions”, SIAM Optim J. 9, 112–147 (1999).
[CrossRef]

Xu, F.

Yan, Y.-B.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Yi, D.-E.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

IEEE Photon. Technol. Lett. (1)

F. Van Laere, M. V. Kotlyar, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007).
[CrossRef]

J. Opt. A: Pure appl. Opt. (1)

L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A: Pure appl. Opt. 5, 345–355 (2003).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Susuki, “Fabrication of half-wave plates with subwave-length structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Opt. Commun. (1)

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Li, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

SIAM Optim J. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions”, SIAM Optim J. 9, 112–147 (1999).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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Figures (9)

Fig. 1
Fig. 1

Schematic view on the grating geometry. Light propagates inside a waveguide, hitting the 3D grating on top surface (grating vectors gx and gy). Three propagating diffraction orders are created, and the -2nd order propagates anti-parallel to the incident beam. Polarization states are defined with polarization azimuth ψ and ellipticity β. TE and TM stand for field components perpendicular and parallel to the plane of propagation.

Fig. 2
Fig. 2

Illustration of the output polarization states corresponding to the numerical examples in table 1. Blue = row A and green = row C. The red ellipse represents the (linear) input polarization. On the left for TM-, on the right for TE-polarized input.

Fig. 3
Fig. 3

Squared amplitudes of the diffraction orders in the x-direction immediately behind the input-boundary inside the grating. Left: TM-polarized input field. Green bars correspond to the TM-parts of the plane-wave components propagating in the positive z direction, while red bars correspond to the TE-parts propagating in the negative z direction. Right: TE-polarized input field. Red bars correspond to the TE-parts of the plane-wave components propagating in the positive z direction, and blue bars correspond to the TM-parts propagating in the negative z direction.

Fig. 4
Fig. 4

Sketch of the two-wave coupling inside the grating layer with TM-polarized input. The polarization state of the TM-polarized the zero-order wave (green) remains essentially unchanged but it loses energy to the TE-polarized backward-propagating −2 order wave (red) due to the periodically modulated anisotropic material.

Fig. 5
Fig. 5

Phase difference between the output ±45° components (solid), and diffraction efficiency of the −2nd reflected order (dashed) as a function of the grating depth h. Other grating parameters are as in the first row of table 1. Input polarization is TM.

Fig. 6
Fig. 6

Cross-section SEM images of the fabricated structure. Cross-section taken in the direction of the y-axis (figure 1). The grating period dy = 500 nm.

Fig. 7
Fig. 7

Setup for the optical testing. Polarization state is determined for the input beam (red) in position B, and for the -2nd reflected order (blue) in position A.

Fig. 8
Fig. 8

Measured intensities as a function of the analyzer rotation and corresponding polarization ellipses in the analyzer plane. Measured with (a) TM-, (b) TE-, (c) 45° linear, and (d) 25° linear polarized input. Red solid = input, blue dashed = −2nd reflected order.

Fig. 9
Fig. 9

Usage of the polarization-conversion grating to enhance the incoupling efficiency to a light guide.

Tables (1)

Tables Icon

Table 1 Numerically designed grating parameters for half-wave retardation in the -2nd reflected order. (A) The optimized design, showing the diffraction efficiency R2, rotation of the polarization direction Δψ, and ellipticity β. (B) A design with a larger period dy, for easier prototype fabrication. The used wavelength is λ = 633 nm, and the substrate and grating are made of fused silica with n = 1.4569 at λ = 633 nm. Angle of incidence in both designs is the 2nd order Littrow angle, θ≃50°.

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