Abstract

Anodic aluminum oxide (AAO) films with different pore sizes were prepared to modulate the effective refractive index and birefringence. To investigate the relationship between the refractive index and the pore size of the AAO film, optical constants were obtained using a prism coupler with various lasers. With experimental results, the dispersion curve of alumina itself without pores was extracted using a theoretical anisotropic model. We demonstrated that AAO films could offer a wide range of refractive index and birefringence values for optical device applications. Furthermore, index profiles as a function of the thickness of the AAO films were obtained by inverse Wentzel- Kramer-Brillouin approximation to examine the optical homogeneity.

© 2011 Optical Society of America

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2010 (2)

T. D. Lazzara, A. Lau, and W. Knoll, J. Nanosci. Nanotechnol. 10, 4293 (2010).
[CrossRef] [PubMed]

M. Shaban, H. Hamdy, F. Shahin, J. Park, and S. W. Ryu, J. Nanosci. Nanotechnol. 10, 3380 (2010).
[CrossRef] [PubMed]

2009 (2)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, Nat. Photon. 3, 461 (2009).
[CrossRef]

Y. W. Jung, J. S. Byun, D. H. Woo, and Y. D. Kim, Thin Solid Films 517, 3726 (2009).
[CrossRef]

2008 (2)

J. Wang, C. W. Wang, Y. Li, and W. M. Liu, Thin Solid Films 516, 7689 (2008).
[CrossRef]

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

2006 (1)

W. Lee, R. Ji, U. Gosele, and K. Nielsch, Nat. Mater. 5, 741(2006).
[CrossRef] [PubMed]

2004 (1)

K. H. A. Lau, L. S. Tan, K. Tamada, M. S. Sander, and W. Knoll, J. Phys. Chem. B 108, 10812 (2004).
[CrossRef]

2001 (1)

E. Dogheche, P. Ruterana, and F. Omnes, J. Appl. Phys. 90, 4411 (2001).
[CrossRef]

1998 (1)

J. De Laet, H. Terryn, and J. Vereecken, Thin Solid Films 320, 241 (1998).
[CrossRef]

1994 (1)

1989 (1)

1981 (1)

G. E. Thompson and G. C. Wood, Nature 290, 230 (1981).
[CrossRef]

1979 (1)

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

1973 (1)

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Byun, J. S.

Y. W. Jung, J. S. Byun, D. H. Woo, and Y. D. Kim, Thin Solid Films 517, 3726 (2009).
[CrossRef]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, Nat. Photon. 3, 461 (2009).
[CrossRef]

Chen, J.

De Laet, J.

J. De Laet, H. Terryn, and J. Vereecken, Thin Solid Films 320, 241 (1998).
[CrossRef]

Dogheche, E.

E. Dogheche, P. Ruterana, and F. Omnes, J. Appl. Phys. 90, 4411 (2001).
[CrossRef]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, Nat. Photon. 3, 461 (2009).
[CrossRef]

Gosele, U.

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

W. Lee, R. Ji, U. Gosele, and K. Nielsch, Nat. Mater. 5, 741(2006).
[CrossRef] [PubMed]

Hamdy, H.

M. Shaban, H. Hamdy, F. Shahin, J. Park, and S. W. Ryu, J. Nanosci. Nanotechnol. 10, 3380 (2010).
[CrossRef] [PubMed]

Hillebrand, R.

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

Hottier, F.

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Ji, R.

W. Lee, R. Ji, U. Gosele, and K. Nielsch, Nat. Mater. 5, 741(2006).
[CrossRef] [PubMed]

Jung, Y. W.

Y. W. Jung, J. S. Byun, D. H. Woo, and Y. D. Kim, Thin Solid Films 517, 3726 (2009).
[CrossRef]

Kim, Y. D.

Y. W. Jung, J. S. Byun, D. H. Woo, and Y. D. Kim, Thin Solid Films 517, 3726 (2009).
[CrossRef]

Knoll, W.

T. D. Lazzara, A. Lau, and W. Knoll, J. Nanosci. Nanotechnol. 10, 4293 (2010).
[CrossRef] [PubMed]

K. H. A. Lau, L. S. Tan, K. Tamada, M. S. Sander, and W. Knoll, J. Phys. Chem. B 108, 10812 (2004).
[CrossRef]

Lau, A.

T. D. Lazzara, A. Lau, and W. Knoll, J. Nanosci. Nanotechnol. 10, 4293 (2010).
[CrossRef] [PubMed]

Lau, K. H. A.

K. H. A. Lau, L. S. Tan, K. Tamada, M. S. Sander, and W. Knoll, J. Phys. Chem. B 108, 10812 (2004).
[CrossRef]

Lazzara, T. D.

T. D. Lazzara, A. Lau, and W. Knoll, J. Nanosci. Nanotechnol. 10, 4293 (2010).
[CrossRef] [PubMed]

Lee, W.

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

W. Lee, R. Ji, U. Gosele, and K. Nielsch, Nat. Mater. 5, 741(2006).
[CrossRef] [PubMed]

Li, Y.

J. Wang, C. W. Wang, Y. Li, and W. M. Liu, Thin Solid Films 516, 7689 (2008).
[CrossRef]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, Nat. Photon. 3, 461 (2009).
[CrossRef]

Liu, W. M.

J. Wang, C. W. Wang, Y. Li, and W. M. Liu, Thin Solid Films 516, 7689 (2008).
[CrossRef]

Miyagi, M.

Mu, X.

Nielsch, K.

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

W. Lee, R. Ji, U. Gosele, and K. Nielsch, Nat. Mater. 5, 741(2006).
[CrossRef] [PubMed]

Omnes, F.

E. Dogheche, P. Ruterana, and F. Omnes, J. Appl. Phys. 90, 4411 (2001).
[CrossRef]

Park, J.

M. Shaban, H. Hamdy, F. Shahin, J. Park, and S. W. Ryu, J. Nanosci. Nanotechnol. 10, 3380 (2010).
[CrossRef] [PubMed]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, Nat. Photon. 3, 461 (2009).
[CrossRef]

Ruterana, P.

E. Dogheche, P. Ruterana, and F. Omnes, J. Appl. Phys. 90, 4411 (2001).
[CrossRef]

Ryu, S. W.

M. Shaban, H. Hamdy, F. Shahin, J. Park, and S. W. Ryu, J. Nanosci. Nanotechnol. 10, 3380 (2010).
[CrossRef] [PubMed]

Saito, M.

Sander, M. S.

K. H. A. Lau, L. S. Tan, K. Tamada, M. S. Sander, and W. Knoll, J. Phys. Chem. B 108, 10812 (2004).
[CrossRef]

Schwirn, K.

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

Shaban, M.

M. Shaban, H. Hamdy, F. Shahin, J. Park, and S. W. Ryu, J. Nanosci. Nanotechnol. 10, 3380 (2010).
[CrossRef] [PubMed]

Shahin, F.

M. Shaban, H. Hamdy, F. Shahin, J. Park, and S. W. Ryu, J. Nanosci. Nanotechnol. 10, 3380 (2010).
[CrossRef] [PubMed]

Shao, Z.

Steinhart, M.

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

Tamada, K.

K. H. A. Lau, L. S. Tan, K. Tamada, M. S. Sander, and W. Knoll, J. Phys. Chem. B 108, 10812 (2004).
[CrossRef]

Tan, L. S.

K. H. A. Lau, L. S. Tan, K. Tamada, M. S. Sander, and W. Knoll, J. Phys. Chem. B 108, 10812 (2004).
[CrossRef]

Terryn, H.

J. De Laet, H. Terryn, and J. Vereecken, Thin Solid Films 320, 241 (1998).
[CrossRef]

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Thompson, G. E.

G. E. Thompson and G. C. Wood, Nature 290, 230 (1981).
[CrossRef]

Torge, R.

Ulrich, R.

Vereecken, J.

J. De Laet, H. Terryn, and J. Vereecken, Thin Solid Films 320, 241 (1998).
[CrossRef]

Wang, C. W.

J. Wang, C. W. Wang, Y. Li, and W. M. Liu, Thin Solid Films 516, 7689 (2008).
[CrossRef]

Wang, J.

J. Wang, C. W. Wang, Y. Li, and W. M. Liu, Thin Solid Films 516, 7689 (2008).
[CrossRef]

X. Mu, X. Yue, J. Chen, J. Wang, and Z. Shao, Appl. Opt. 33, 3227 (1994).
[CrossRef] [PubMed]

Woo, D. H.

Y. W. Jung, J. S. Byun, D. H. Woo, and Y. D. Kim, Thin Solid Films 517, 3726 (2009).
[CrossRef]

Wood, G. C.

G. E. Thompson and G. C. Wood, Nature 290, 230 (1981).
[CrossRef]

Yue, X.

ACS Nano (1)

K. Schwirn, W. Lee, R. Hillebrand, M. Steinhart, K. Nielsch, and U. Gosele, ACS Nano 2, 302 (2008).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (1)

E. Dogheche, P. Ruterana, and F. Omnes, J. Appl. Phys. 90, 4411 (2001).
[CrossRef]

J. Nanosci. Nanotechnol. (2)

M. Shaban, H. Hamdy, F. Shahin, J. Park, and S. W. Ryu, J. Nanosci. Nanotechnol. 10, 3380 (2010).
[CrossRef] [PubMed]

T. D. Lazzara, A. Lau, and W. Knoll, J. Nanosci. Nanotechnol. 10, 4293 (2010).
[CrossRef] [PubMed]

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

J. Phys. Chem. B (1)

K. H. A. Lau, L. S. Tan, K. Tamada, M. S. Sander, and W. Knoll, J. Phys. Chem. B 108, 10812 (2004).
[CrossRef]

Nat. Mater. (1)

W. Lee, R. Ji, U. Gosele, and K. Nielsch, Nat. Mater. 5, 741(2006).
[CrossRef] [PubMed]

Nat. Photon. (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, Nat. Photon. 3, 461 (2009).
[CrossRef]

Nature (1)

G. E. Thompson and G. C. Wood, Nature 290, 230 (1981).
[CrossRef]

Phys. Rev. B (1)

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Thin Solid Films (3)

J. Wang, C. W. Wang, Y. Li, and W. M. Liu, Thin Solid Films 516, 7689 (2008).
[CrossRef]

J. De Laet, H. Terryn, and J. Vereecken, Thin Solid Films 320, 241 (1998).
[CrossRef]

Y. W. Jung, J. S. Byun, D. H. Woo, and Y. D. Kim, Thin Solid Films 517, 3726 (2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a)–(c) Top-view SEM images of AAO films with different pore widening process times of (a)  0 min (pore size: 26 nm ), (b)  50 min (pore size: 50 nm ), and (c)  70 min (pore size: 75 nm ). (d) Cross-sectional SEM image of AAO film with a thickness of 1.8 μm . The scale bar is 500 nm .

Fig. 2
Fig. 2

(a) Schematic depicting the prism coupling setup. (b) TM guiding mode spectrum for an AAO film with a 50 nm pore size obtained using a 532 nm wavelength.

Fig. 3
Fig. 3

(a) Dependence of the dispersion curve on the pore size of AAO films. (b) Variation of the birefringence as a function of the pore radius. (c) Dependence of the dispersion curve on the thickness of AAO films (pore radius: 13 nm ). Open circles (―○―) and closed squares (―▪―) indicate the TM and TE modes, respectively.

Fig. 4
Fig. 4

(a) Dispersion curves of alumina as a host material of AAO films. Inset: Determination of the refractive index of alumina at a wavelength of 532 nm by fitting the measured results to the theoretical anisotropy model. (b) Extraordinary refractive index profile (TM) obtained by the iWKB method for AAO films having various pore sizes.

Equations (3)

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n TE = n 1 π a 2 2 b 2 ( n 1 2 n 2 2 ) 2 n 1 ( n 1 2 + n 2 2 ) ,
n TM = n 1 π a 2 b 2 n 1 ( n 1 2 n 2 2 ) n 1 2 + n 2 2 ,
k 0 0 x m n ( x ) 2 n ( x m ) 2 d x = ( m + 3 4 ) π ,

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