Abstract

We introduce an optical nanostructure device made of one dimensional photonic crystal (1DPC) with a graded-index defect layer, which has the ability of producing frequency dependent twisted beam shapes. The defect layer’s refractive index distribution function changes in r and φ directions in cylindrical coordinate. The rays passing through different transverse positions of an introduced structure experience different optical pathways. Thus, the defect mode has transverse dependency and twisted shapes have been generated in transmitted spectrum (phase and amplitude). The incident beam frequency is a factor that can engineer the obtained twisted beam shape. This study demonstrates the ability of the PC structures to produce controllable spiral light beam shapes.

© 2014 Optical Society of America

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    [CrossRef]
  7. V. V. Rumyantsev and A. Schwartzman, J Electr. Electron. Syst. 1, 2 (2013).
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  8. D. Gagnon, J. Dumont, and L. J. Dubé, J. Opt. Soc. Am. A 29, 2673 (2012).
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  9. F. M. Dickey, Opt. Photon. News 14(4), 30 (2003).
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  10. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
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  11. M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2014

K. Jamshidi-Ghaleh and F. Bayat, IEEE Photon. Technol. Lett. 26, 440 (2014).
[CrossRef]

K. Jamshidi-Ghaleh and F. Bayat, Prog. Electromagn. Res. M 34, 63 (2014).
[CrossRef]

2013

V. V. Rumyantsev and A. Schwartzman, J Electr. Electron. Syst. 1, 2 (2013).
[CrossRef]

2012

D. Gagnon, J. Dumont, and L. J. Dubé, J. Opt. Soc. Am. A 29, 2673 (2012).
[CrossRef]

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[CrossRef]

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, Phys. Rev. Lett. 109, 33903 (2012).
[CrossRef]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Opt. Lett. 37, 2136 (2012).
[CrossRef]

2010

O. Rasoga and D. Dragoman, Appl. Opt. 49, 2161 (2010).
[CrossRef]

E. Lotfi, K. Jamshidi-Ghaleh, F. Moslem, and H. Masalehdan, Eur. Phys. J. D 60, 369 (2010).
[CrossRef]

2009

A. Banerjee, Prog. Electromagnet. Res. Lett. 11, 129 (2009).
[CrossRef]

C.-J. Wu, B.-H. Chu, and M.-T. Weng, J. Electromagn. Waves Appl. 23, 129 (2009).
[CrossRef]

M. S. Kovačević, A. Djordjevich, and D. Nikezić, Opt. Appl. 39267 (2009).

2007

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2004

2003

F. M. Dickey, Opt. Photon. News 14(4), 30 (2003).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

T. W. Smith and G. E. Wnek, Proc. SPIE 5051, 389 (2003).
[CrossRef]

1999

M. Kharitonov, N. Shatokhina, T. Sultanov, V. Zubov, and W. Staude, J. Russ. Laser Res. 20, 171 (1999).
[CrossRef]

1998

Z.-Y. Li, J. Wang, and B.-Y. Gu, Phys. Rev. B 58, 3721 (1998).
[CrossRef]

1996

H. Laabs and B. Ozygus, Opt. Laser Technol. 28, 213 (1996).
[CrossRef]

1994

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

1991

1987

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

1966

1885

J. W. Strutt, Proc. London Math. Soc 17, 4 (1885).

Andreasen, J.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, Phys. Rev. Lett. 109, 33903 (2012).
[CrossRef]

Arie, A.

Arnold, C. B.

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[CrossRef]

Bachelard, N.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, Phys. Rev. Lett. 109, 33903 (2012).
[CrossRef]

Banerjee, A.

A. Banerjee, Prog. Electromagnet. Res. Lett. 11, 129 (2009).
[CrossRef]

Bayat, F.

K. Jamshidi-Ghaleh and F. Bayat, IEEE Photon. Technol. Lett. 26, 440 (2014).
[CrossRef]

K. Jamshidi-Ghaleh and F. Bayat, Prog. Electromagn. Res. M 34, 63 (2014).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (CUP Archive, 1999).

Brett, M. J.

Brown, B. R.

Chu, B.-H.

C.-J. Wu, B.-H. Chu, and M.-T. Weng, J. Electromagn. Waves Appl. 23, 129 (2009).
[CrossRef]

Dickey, F. M.

F. M. Dickey, Opt. Photon. News 14(4), 30 (2003).
[CrossRef]

Djordjevich, A.

M. S. Kovačević, A. Djordjevich, and D. Nikezić, Opt. Appl. 39267 (2009).

Dragoman, D.

Dubé, L. J.

Dumont, J.

Duocastella, M.

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[CrossRef]

Gagnon, D.

Gigan, S.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, Phys. Rev. Lett. 109, 33903 (2012).
[CrossRef]

Gu, B.-Y.

Z.-Y. Li, J. Wang, and B.-Y. Gu, Phys. Rev. B 58, 3721 (1998).
[CrossRef]

Hawkeye, M. M.

Herman, R. M.

Jamshidi-Ghaleh, K.

K. Jamshidi-Ghaleh and F. Bayat, Prog. Electromagn. Res. M 34, 63 (2014).
[CrossRef]

K. Jamshidi-Ghaleh and F. Bayat, IEEE Photon. Technol. Lett. 26, 440 (2014).
[CrossRef]

E. Lotfi, K. Jamshidi-Ghaleh, F. Moslem, and H. Masalehdan, Eur. Phys. J. D 60, 369 (2010).
[CrossRef]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Juwiler, I.

Kharitonov, M.

M. Kharitonov, N. Shatokhina, T. Sultanov, V. Zubov, and W. Staude, J. Russ. Laser Res. 20, 171 (1999).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Kovacevic, M. S.

M. S. Kovačević, A. Djordjevich, and D. Nikezić, Opt. Appl. 39267 (2009).

Laabs, H.

H. Laabs and B. Ozygus, Opt. Laser Technol. 28, 213 (1996).
[CrossRef]

Li, Z.-Y.

Z.-Y. Li, J. Wang, and B.-Y. Gu, Phys. Rev. B 58, 3721 (1998).
[CrossRef]

Lohmann, A. W.

Lotfi, E.

E. Lotfi, K. Jamshidi-Ghaleh, F. Moslem, and H. Masalehdan, Eur. Phys. J. D 60, 369 (2010).
[CrossRef]

Masalehdan, H.

E. Lotfi, K. Jamshidi-Ghaleh, F. Moslem, and H. Masalehdan, Eur. Phys. J. D 60, 369 (2010).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Moslem, F.

E. Lotfi, K. Jamshidi-Ghaleh, F. Moslem, and H. Masalehdan, Eur. Phys. J. D 60, 369 (2010).
[CrossRef]

Nikezic, D.

M. S. Kovačević, A. Djordjevich, and D. Nikezić, Opt. Appl. 39267 (2009).

Ozygus, B.

H. Laabs and B. Ozygus, Opt. Laser Technol. 28, 213 (1996).
[CrossRef]

Pendry, J. B.

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

Rasoga, O.

Rumyantsev, V. V.

V. V. Rumyantsev and A. Schwartzman, J Electr. Electron. Syst. 1, 2 (2013).
[CrossRef]

Schwartzman, A.

V. V. Rumyantsev and A. Schwartzman, J Electr. Electron. Syst. 1, 2 (2013).
[CrossRef]

Sebbah, P.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, Phys. Rev. Lett. 109, 33903 (2012).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Shapira, A.

Shatokhina, N.

M. Kharitonov, N. Shatokhina, T. Sultanov, V. Zubov, and W. Staude, J. Russ. Laser Res. 20, 171 (1999).
[CrossRef]

Shiloh, R.

Sit, J. C.

Smith, T. W.

T. W. Smith and G. E. Wnek, Proc. SPIE 5051, 389 (2003).
[CrossRef]

Staude, W.

M. Kharitonov, N. Shatokhina, T. Sultanov, V. Zubov, and W. Staude, J. Russ. Laser Res. 20, 171 (1999).
[CrossRef]

Strutt, J. W.

J. W. Strutt, Proc. London Math. Soc 17, 4 (1885).

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Sultanov, T.

M. Kharitonov, N. Shatokhina, T. Sultanov, V. Zubov, and W. Staude, J. Russ. Laser Res. 20, 171 (1999).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

van Popta, A. C.

Wang, J.

Z.-Y. Li, J. Wang, and B.-Y. Gu, Phys. Rev. B 58, 3721 (1998).
[CrossRef]

Weng, M.-T.

C.-J. Wu, B.-H. Chu, and M.-T. Weng, J. Electromagn. Waves Appl. 23, 129 (2009).
[CrossRef]

Wiggins, T. A.

Wnek, G. E.

T. W. Smith and G. E. Wnek, Proc. SPIE 5051, 389 (2003).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (CUP Archive, 1999).

Wu, C.-J.

C.-J. Wu, B.-H. Chu, and M.-T. Weng, J. Electromagn. Waves Appl. 23, 129 (2009).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, in Confined Electrons and Photons (Springer, 1995), pp. 885–898.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals, (Wiley, 1984), Vol. 5.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals, (Wiley, 1984), Vol. 5.

Zubov, V.

M. Kharitonov, N. Shatokhina, T. Sultanov, V. Zubov, and W. Staude, J. Russ. Laser Res. 20, 171 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Eur. Phys. J. D

E. Lotfi, K. Jamshidi-Ghaleh, F. Moslem, and H. Masalehdan, Eur. Phys. J. D 60, 369 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

K. Jamshidi-Ghaleh and F. Bayat, IEEE Photon. Technol. Lett. 26, 440 (2014).
[CrossRef]

J Electr. Electron. Syst.

V. V. Rumyantsev and A. Schwartzman, J Electr. Electron. Syst. 1, 2 (2013).
[CrossRef]

J. Electromagn. Waves Appl.

C.-J. Wu, B.-H. Chu, and M.-T. Weng, J. Electromagn. Waves Appl. 23, 129 (2009).
[CrossRef]

J. Mod. Opt.

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. Russ. Laser Res.

M. Kharitonov, N. Shatokhina, T. Sultanov, V. Zubov, and W. Staude, J. Russ. Laser Res. 20, 171 (1999).
[CrossRef]

Laser Photon. Rev.

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[CrossRef]

Nat. Phys.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Opt. Appl.

M. S. Kovačević, A. Djordjevich, and D. Nikezić, Opt. Appl. 39267 (2009).

Opt. Laser Technol.

H. Laabs and B. Ozygus, Opt. Laser Technol. 28, 213 (1996).
[CrossRef]

Opt. Lett.

Opt. Photon. News

F. M. Dickey, Opt. Photon. News 14(4), 30 (2003).
[CrossRef]

Phys. Rev. B

Z.-Y. Li, J. Wang, and B.-Y. Gu, Phys. Rev. B 58, 3721 (1998).
[CrossRef]

Phys. Rev. Lett.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, Phys. Rev. Lett. 109, 33903 (2012).
[CrossRef]

Proc. London Math. Soc

J. W. Strutt, Proc. London Math. Soc 17, 4 (1885).

Proc. SPIE

T. W. Smith and G. E. Wnek, Proc. SPIE 5051, 389 (2003).
[CrossRef]

Prog. Electromagn. Res. M

K. Jamshidi-Ghaleh and F. Bayat, Prog. Electromagn. Res. M 34, 63 (2014).
[CrossRef]

Prog. Electromagnet. Res. Lett.

A. Banerjee, Prog. Electromagnet. Res. Lett. 11, 129 (2009).
[CrossRef]

Other

E. Yablonovitch, in Confined Electrons and Photons (Springer, 1995), pp. 885–898.

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (CUP Archive, 1999).

A. Yariv and P. Yeh, Optical Waves in Crystals, (Wiley, 1984), Vol. 5.

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Figures (5)

Fig. 1.
Fig. 1.

Profile of the normalized refractive index distribution function proposed for the defect layer versus normalized transverse Cartesian coordinates of x/x0 and y/y0.

Fig. 2.
Fig. 2.

Behavior of the ray path inside the graded-index defect layer for two incident rays in xy (a) and xz (b) planes.

Fig. 3.
Fig. 3.

4D illustration of the transmission at the transmittance spectrum of the 1DPC structure with proposed graded-index defect layer under the irradiation of the plane wave beam versus the normalized frequency ω/ω0 and the normalized distances of x/x0 and y/y0 in the first band gap. (The fourth dimension, which is transmission, is shown in color). The white region in the middle is the band gap, and the curved plane in it represents the defect mode.

Fig. 4.
Fig. 4.

4D representation of the defect mode illustrated in Fig. 3.

Fig. 5.
Fig. 5.

Surfaces of constant phase (φ=0) as it propagates for the incident frequency tuned to be ω=1.09ω0. (a) Top view of the phase of the transmitted wave on the output plane versus the normalized y/y0 and x/x0 directions for the incident frequency tuned to be (b) ω=ω0 and (c) ω=1.09ω0.

Equations (5)

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

dds(ndxds)=nx
dds(ndyds)=ny.
Mj(ω)=[coskjdjinjsinkjdjinjsinkjdjcoskjdj],
M(r,ω)=[MA(ω)MB(ω)]4MC(r,ω)[MA(ω)MB(ω)]4=[m11(r,ω)m12(r,ω)m21(r,ω)m22(r,ω)].
t(r,ω)=2[m22(r,ω)+m11(r,ω)][m12(r,ω)+m21(r,ω)].

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