Abstract

A hollow waveguide array with subwavelength dimensions is demonstrated as a polarization converter. An individual waveguide in the array has a rectangular cross-section, which leads to an anisotropy of propagation constants and therefore to a phase shift between vertical and horizontal field components upon propagation. The hollow waveguide array was fabricated by a two-photon polymerization process followed by electrochemical deposition of gold. The fabricated array consists of about 2000×2500 hollow waveguide cells, each with dimensions of 1150nm×930nm and height of 2 μm. With these dimensions, the structure can, for example, be used at a wavelength of 1550 nm. Other wavelengths and phase shifts are accessible by changing the dimensions of the cross-section and the height. Since the widths of individual waveguides are variable, space-variant operation can be implemented.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (1)

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

2015 (2)

S. F. Helfert, A. Edelmann, and J. Jahns, “Hollow waveguide as polarization converting elements: a theoretical study,” J. Eur. Opt. Soc. 10, 15006 (2015).
[Crossref]

N. Yu and F. Capasso, “Optical metasurfaces and prospect of their applications including fiber optics,” J. Lightwave Technol. 33, 2344–2358 (2015).
[Crossref]

2014 (2)

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

J. B. Mueller, J. Fischer, F. Mayer, M. Kadic, and M. Wegener, “Polymerization kinetics in three-dimensional direct laser writing,” Adv. Mater. 26, 6566–6571 (2014).
[Crossref]

2013 (3)

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

M. Malinauskas, M. Farsari, A. Piskarskas, and S. Juodkazis, “Ultrafast laser nanostructuring of photopolymers: a decade of advances,” Phys. Rep. 533, 1–31 (2013).
[Crossref]

A. K. Kaveev, G. I. Kropotov, E. V. Tsygankova, I. A. Tzibizov, S. D. Ganichev, S. N. Danilov, P. Olbrich, C. Zoth, E. G. Kaveeva, A. I. Zhdanov, A. A. Ivanov, R. Z. Deyanov, and B. Redlich, “Terahertz polarization conversion with quartz waveplate sets,” Appl. Opt. 52, B60–B69 (2013).
[Crossref]

2012 (2)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9nm feature size,” Nat. Commun. 4, 2061 (2012).
[Crossref]

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

2011 (2)

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

T. Kämpfe and O. Parriaux, “Depth-minimized, large period half-wave corrugation for linear to radial and azimuthal polarization transformation by grating-mode phase management,” J. Opt. Soc. Am. A 28, 2235–2242 (2011).
[Crossref]

2007 (2)

2003 (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Space-variant polarization-state manipulation with computer-generated subwavelength gratings,” Proc. SPIE,  4984, 171–185 (2003).
[Crossref]

2002 (1)

1983 (1)

Bacher, A.

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

Becker, J.

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

Biener, G.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Space-variant polarization-state manipulation with computer-generated subwavelength gratings,” Proc. SPIE,  4984, 171–185 (2003).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[Crossref]

Bomzon, Z.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

Cao, W.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Cao, Y.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9nm feature size,” Nat. Commun. 4, 2061 (2012).
[Crossref]

Capasso, F.

Case, S. K.

Chen, H.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Clarke, D. R.

Clausnitzer, T.

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves, Series of Electromagnetic Waves (IEEE, 1991).

Cong, L.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Danilov, S. N.

Deyanov, R. Z.

Dmitriev, S.

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

Edelmann, A.

S. F. Helfert, A. Edelmann, and J. Jahns, “Hollow waveguide as polarization converting elements: a theoretical study,” J. Eur. Opt. Soc. 10, 15006 (2015).
[Crossref]

Enger, R. C.

Evans, R. A.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9nm feature size,” Nat. Commun. 4, 2061 (2012).
[Crossref]

Farsari, M.

M. Malinauskas, M. Farsari, A. Piskarskas, and S. Juodkazis, “Ultrafast laser nanostructuring of photopolymers: a decade of advances,” Phys. Rep. 533, 1–31 (2013).
[Crossref]

Fischer, J.

J. B. Mueller, J. Fischer, F. Mayer, M. Kadic, and M. Wegener, “Polymerization kinetics in three-dimensional direct laser writing,” Adv. Mater. 26, 6566–6571 (2014).
[Crossref]

Frölich, A.

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

Gan, Z.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9nm feature size,” Nat. Commun. 4, 2061 (2012).
[Crossref]

Ganichev, S. D.

Gansel, J. K.

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

Ghadyani, Z.

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

Gu, J.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Gu, M.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9nm feature size,” Nat. Commun. 4, 2061 (2012).
[Crossref]

Han, J.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Harder, I.

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

Hasman, E.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Space-variant polarization-state manipulation with computer-generated subwavelength gratings,” Proc. SPIE,  4984, 171–185 (2003).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[Crossref]

Helfert, S. F.

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

S. F. Helfert, A. Edelmann, and J. Jahns, “Hollow waveguide as polarization converting elements: a theoretical study,” J. Eur. Opt. Soc. 10, 15006 (2015).
[Crossref]

S. F. Helfert and J. Jahns, “Structured illumination of hollow waveguide arrays using the Talbot self-imaging,” in EOS Topical Meeting on Diffractive Optics, Joensuu, Finnland (2017).

Hong, M. H.

Ivanov, A. A.

Jahns, J.

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

S. F. Helfert, A. Edelmann, and J. Jahns, “Hollow waveguide as polarization converting elements: a theoretical study,” J. Eur. Opt. Soc. 10, 15006 (2015).
[Crossref]

S. F. Helfert and J. Jahns, “Structured illumination of hollow waveguide arrays using the Talbot self-imaging,” in EOS Topical Meeting on Diffractive Optics, Joensuu, Finnland (2017).

Jakobs, P.

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

Juodkazis, S.

M. Malinauskas, M. Farsari, A. Piskarskas, and S. Juodkazis, “Ultrafast laser nanostructuring of photopolymers: a decade of advances,” Phys. Rep. 533, 1–31 (2013).
[Crossref]

Kadic, M.

J. B. Mueller, J. Fischer, F. Mayer, M. Kadic, and M. Wegener, “Polymerization kinetics in three-dimensional direct laser writing,” Adv. Mater. 26, 6566–6571 (2014).
[Crossref]

Kämpfe, T.

Kaschke, J.

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

Kaveev, A. K.

Kaveeva, E. G.

Kleiner, V.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Space-variant polarization-state manipulation with computer-generated subwavelength gratings,” Proc. SPIE,  4984, 171–185 (2003).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[Crossref]

Kley, E.-B.

Kropotov, G. I.

Lai, W. J.

Latzel, M.

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

Leuchs, G.

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

Li, Y.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Lim, B. C.

Lim, Y. L.

Lindlein, N.

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

Ma, H.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Malinauskas, M.

M. Malinauskas, M. Farsari, A. Piskarskas, and S. Juodkazis, “Ultrafast laser nanostructuring of photopolymers: a decade of advances,” Phys. Rep. 533, 1–31 (2013).
[Crossref]

Mayer, F.

J. B. Mueller, J. Fischer, F. Mayer, M. Kadic, and M. Wegener, “Polymerization kinetics in three-dimensional direct laser writing,” Adv. Mater. 26, 6566–6571 (2014).
[Crossref]

Mueller, J. B.

J. B. Mueller, J. Fischer, F. Mayer, M. Kadic, and M. Wegener, “Polymerization kinetics in three-dimensional direct laser writing,” Adv. Mater. 26, 6566–6571 (2014).
[Crossref]

Niv, A.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Space-variant polarization-state manipulation with computer-generated subwavelength gratings,” Proc. SPIE,  4984, 171–185 (2003).
[Crossref]

Olbrich, P.

Parriaux, O.

Phua, P. B.

Piskarskas, A.

M. Malinauskas, M. Farsari, A. Piskarskas, and S. Juodkazis, “Ultrafast laser nanostructuring of photopolymers: a decade of advances,” Phys. Rep. 533, 1–31 (2013).
[Crossref]

Qu, S.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Redlich, B.

Rusina, O.

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

Seiler, T.

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

She, A.

Shian, S.

Singh, R.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Teo, H. H.

Thiel, M.

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

Tian, Z.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Tiaw, K. S.

Tishchenko, A.

Tsygankova, E. V.

Tünnermann, A.

Tzibizov, I. A.

Wang, J.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Wegener, M.

J. B. Mueller, J. Fischer, F. Mayer, M. Kadic, and M. Wegener, “Polymerization kinetics in three-dimensional direct laser writing,” Adv. Mater. 26, 6566–6571 (2014).
[Crossref]

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

Xu, Z.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Yan, M.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Yu, N.

Zhang, A.

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

Zhang, S.

Zhang, W.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Zhang, X.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

Zhdanov, A. I.

Zoth, C.

Adv. Mater. (1)

J. B. Mueller, J. Fischer, F. Mayer, M. Kadic, and M. Wegener, “Polymerization kinetics in three-dimensional direct laser writing,” Adv. Mater. 26, 6566–6571 (2014).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103, 171107 (2013).
[Crossref]

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Thiel, and M. Wegener, “Tapered gold-helix mmetamaterial as improved circular polarizers,” Appl. Phys. Lett. 100, 101109 (2012).
[Crossref]

J. Appl. Phys. (1)

H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115, 154504 (2014).
[Crossref]

J. Eur. Opt. Soc. (2)

S. F. Helfert, A. Edelmann, and J. Jahns, “Hollow waveguide as polarization converting elements: a theoretical study,” J. Eur. Opt. Soc. 10, 15006 (2015).
[Crossref]

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, and I. Harder, “Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region,” J. Eur. Opt. Soc. 6, 11041 (2011).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Nat. Commun. (1)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9nm feature size,” Nat. Commun. 4, 2061 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

S. F. Helfert, T. Seiler, J. Jahns, J. Becker, P. Jakobs, and A. Bacher, “Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification,” Opt. Quantum Electron. 49, 313 (2017).
[Crossref]

Phys. Rep. (1)

M. Malinauskas, M. Farsari, A. Piskarskas, and S. Juodkazis, “Ultrafast laser nanostructuring of photopolymers: a decade of advances,” Phys. Rep. 533, 1–31 (2013).
[Crossref]

Proc. SPIE (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Space-variant polarization-state manipulation with computer-generated subwavelength gratings,” Proc. SPIE,  4984, 171–185 (2003).
[Crossref]

Other (3)

R. E. Collin, Field Theory of Guided Waves, Series of Electromagnetic Waves (IEEE, 1991).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

S. F. Helfert and J. Jahns, “Structured illumination of hollow waveguide arrays using the Talbot self-imaging,” in EOS Topical Meeting on Diffractive Optics, Joensuu, Finnland (2017).

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Figures (14)

Fig. 1.
Fig. 1. Polarization rotation in a birefringent material. Left, field components of input beam; center, field components of output beam; right, resulting polarization rotation for total fields.
Fig. 2.
Fig. 2. Electric field distribution of the lowest order modes in a rectangular hollow waveguide.
Fig. 3.
Fig. 3. Schematic drawing of the HWA with dimensions in the top view and the side view. The yellow-colored structure is the surrounding gold sidewalls. The spacing in between is air.
Fig. 4.
Fig. 4. Hollow waveguide array illuminated with a vertically polarized plane wave. The arrows indicate the direction of the electric field.
Fig. 5.
Fig. 5. Principle of a local polarization rotation. At the output of an HWA a polarization rotation occurs in the tilted cells. The arrows indicate the direction of the electric field.
Fig. 6.
Fig. 6. Electric field of the fundamental mode in a hollow waveguide. The field is essentially confined to the width of the waveguide. Calculation is done with the paramaters of Table 1.
Fig. 7.
Fig. 7. Dielectric subwavelength grating: the electric field distribution of the fundamental mode is shown. In comparison to Fig. 6, one recognizes that the field extends over several lateral periods. Calculation is done with the paramaters of Table 2.
Fig. 8.
Fig. 8. Process chain for the fabrication of the negative structure using two-photon polymerization.
Fig. 9.
Fig. 9. Scanning electron microscope image of freestanding photoresist pillars after the two-photon polymerization process and development.
Fig. 10.
Fig. 10. Process chain for the electrochemical deposition of the gold structure.
Fig. 11.
Fig. 11. Scanning electron microscope image of a hollow waveguide array.
Fig. 12.
Fig. 12. Height profile of the entire hollow waveguide array at two positions.
Fig. 13.
Fig. 13. Experimental setup: a linearly polarized laser diode illuminates the HWA. The HWA is placed in a rotatable holder for changing the rotation angle α . The angle α denotes the angle between the orientation of the electromagnetic field ( x ) and of the HWA ( x ). To measure the maximum and minimum transmitted power a linear polarizer (analyzer) and a detector are used.
Fig. 14.
Fig. 14. Measurement for degree of polarization as a function of rotation angle α with margin of error (shaded in gray).

Tables (2)

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Table 1. Hollow Waveguide Array

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Table 2. Dielectric Grating

Equations (4)

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Δ ϕ = Δ β h = ( β x β y ) h .
n eff , 10 = 1 λ 0 2 4 w x 2 ; n eff , 01 = 1 λ 0 2 4 w y 2 ,
Δ ϕ = k 0 ( n eff , 10 n eff , 01 ) h .
PG = P max P min P max + P min .

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