Abstract

We explore beam-bending properties of graded index (GRIN) waveguide with hyperbolic secant profile. The transmission efficiency and bandwidth features are extracted for GRIN photonic crystal (PC) media composed of dielectric rods. Light guiding performance of the GRIN PC medium is analyzed for 90° and 180° waveguide bends. The finite-difference time-domain method is deployed to investigate the performance of the designed GRIN waveguides. By the help of proposed photonic configuration, bending of light is achieved with a high efficiency within a broad bandwidth, which promotes the use of GRIN PC structures for efficient light-bending purposes.

© 2013 Optical Society of America

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2012 (2)

2011 (1)

2010 (3)

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Opt. Express 18, 20321 (2010).
[CrossRef]

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

2009 (1)

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

2007 (1)

2006 (1)

E. Centeno, D. Cassange, and J. P. Albert, Phys. Rev B 73, 235119 (2006).
[CrossRef]

2001 (1)

1999 (1)

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Albert, J. P.

E. Centeno, D. Cassange, and J. P. Albert, Phys. Rev B 73, 235119 (2006).
[CrossRef]

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Bermel, P.

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Cassange, D.

E. Centeno, D. Cassange, and J. P. Albert, Phys. Rev B 73, 235119 (2006).
[CrossRef]

Centeno, E.

E. Centeno, D. Cassange, and J. P. Albert, Phys. Rev B 73, 235119 (2006).
[CrossRef]

Chen, L. W.

Citrin, D. S.

Gajic, R.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Opt. Express 18, 20321 (2010).
[CrossRef]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Gao, T.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

Giden, I. H.

Gomez-Reino, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Hingerl, K.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Opt. Express 18, 20321 (2010).
[CrossRef]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Huang, T. J.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

Ibanescu, M.

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Isic, G.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Opt. Express 18, 20321 (2010).
[CrossRef]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Joannopoulos, J. D.

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Juluri, B. K.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kawashime, T.

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kiraly, B.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kurt, H.

Lin, S.-C. S.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

Lu, M.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Notomi, M.

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Oner, B. B.

Oskooi, F.

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Pazos, J.

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Roundy, D.

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Rumpf, R. C.

Sato, T.

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Turduev, M.

Vasic, B.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Opt. Express 18, 20321 (2010).
[CrossRef]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Wang, H. W.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Comput. Phys. Commun. (1)

F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

J. Appl. Phys. (1)

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, J. Appl. Phys. 108, 103505 (2010).
[CrossRef]

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

Opt. Express (5)

Phys. Rev B (1)

E. Centeno, D. Cassange, and J. P. Albert, Phys. Rev B 73, 235119 (2006).
[CrossRef]

Phys. Rev. B (1)

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Other (3)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Supplementary Material (1)

» Media 1: MOV (3306 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Schematic view of (a) GRIN PC structure with (b) HS index profile and representation of (c) 90° and (d) 180° waveguide bending by GRIN PC configurations. (Notations; OA -optical axis and P -reference point).

Fig. 2.
Fig. 2.

Transmission efficiencies for 90° and 180° waveguide bends are plotted. Shaded regions represent the operating frequency bands with high efficiencies.

Fig. 3.
Fig. 3.

Electric field snap-shots of the propagating beam at selected time steps. (a) 90° and (b) 180° waveguide bends for lower frequency region (Media 1). The arrows in the figure describe the direction of light propagation. Spatial intensity profiles of the propagating beam in (c) 90° and (d) 180° GRIN PC waveguide bends operating at the upper frequency region.

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