Abstract

We report a physical mechanism leading to high phase retardation in slanted photonic nanostructures. The phenomenon is based on the waveguiding of the transverse electric polarization component inside the slanted pillars, while the transverse magnetic component is not guided. Such a mechanism leads to very high phase retardation even with shallow structures that are suitable also for lithographical mass production. We present physical principle, numerical analysis of the phenomenon and designs for half-wave retarders. As an experimental result, a slanted grating producing 177 degrees retardation and 95.5% transmission is presented.

© 2011 Optical Society of America

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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]
  3. C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
    [CrossRef]
  4. 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]
  5. T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
    [CrossRef]
  6. B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
    [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]
  8. 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]
  9. T. Levola, and P. Laakkonen, “Replicated slanted gratings with a high refractive index material for in and outcoupling of light,” Opt. Express 15, 2067–2074 (2007).
    [CrossRef] [PubMed]
  10. B. Päivänranta, N. Passilly, J. Pietarinen, P. Laakkonen, M. Kuittinen, and J. Tervo, “Low-cost fabrication of form-birefringent quarter-wave plates,” Opt. Express 16, 16334–16342 (2008).
    [CrossRef] [PubMed]

2008 (1)

2007 (3)

2004 (2)

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
[CrossRef] [PubMed]

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

2003 (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]

1993 (1)

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

1983 (1)

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

Bonod, N.

Chernov, B.

Flanders, D. C.

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

Fujita, T.

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Haggans, C. W.

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Isano, T.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Ishizuka, K.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Iwakami, N.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Jiang, J.

Kaneda, Y.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Karvinen, P.

Kostuk, R. K.

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Kuittinen, M.

Laakkonen, P.

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]

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Nordin, G. P.

Päivänranta, B.

Passilly, N.

Pietarinen, J.

Popov, E.

Suzuki, N.

T. Isano, Y. Kaneda, N. Iwakami, K. Ishizuka, and N. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Tervo, J.

Turunen, J.

Ventola, K.

Wang, B.

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]

J. Mod. Opt. (1)

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[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. Suzuki, “Fabrication of Half-wave Plates with Subwavelength Structures,” Jpn. J. Appl. Phys. 43, 5294–5296 (2004).
[CrossRef]

Opt. Express (4)

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

Schematic cross-section of a slanted-binary structure. Figure illustrates the grating parameters: period d, linewidth c, depth h and slant angle Θ, and the principle of the large phase difference arising from qualitatively different propagation properties of TE and TM polarization components.

Fig. 2
Fig. 2

Relation between the phase shifts and the grating period. Phase shifts experienced by the zeroth-order TE and TM modes inside the grating layer, the difference between the phase shifts of the modes, as well as the total phase retardation between TE and TM polarized output fields as a function of the grating period. The other properties of the grating are given on the first row of Table 1.

Fig. 3
Fig. 3

Computed phase maps of the field with three different periods. The yellow outline marks the grating profile. One black–white–black sequence corresponds to π/4 phase shift. The propagation direction of the field is from left to right. The other grating parameters are taken from the first row of Table 1.

Fig. 4
Fig. 4

(a) The fabricated example grating in a cross section SEM image. The Grating period d =410nm and the slant angle is approximately 30 degrees. (b) Measured normalized analyzer transmission as a function of analyzer orientation. The black curve (substrate) represents the incoming linearly polarized beam. The red curve represents the beam altered by the half-wave retardation of the grating.

Tables (1)

Tables Icon

Table 1 Numerically designed grating parameters that lead to half-wave retardation between TE and TM polarizations. Refractive indices of the grating and the substrate are denoted with ng and nsub, respectively; d is the grating period, f is the fill factor (linewidth/period ratio), h is the grating depth while Θ is the slant angle. The transmittances for the TE and TM polarization states are given by TTE and TTM, respectively.

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