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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 1301–1309
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Asymmetric light reflectance effect in AAO on glass

Kai Huang, Yangjuan Li, Zhiming Wu, Cheng Li, Hongkai Lai, and Junyong Kang  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 1301-1309 (2011)
http://dx.doi.org/10.1364/OE.19.001301


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Abstract

Asymmetric light reflectance effect was observed in an anodic aluminum oxide on glass structure. The transmitted light from two sides of the films show the same colors, whereas the reflected light from two sides show complementary colors. The spectra analysis demonstrates that this asymmetric light reflectance effect can be ascribed to the asymmetric geometric structure of nanoscale aluminum networks. This effect may result in applications in many fields, especially in optical communication.

© 2011 OSA

1. Introduction

Anodic aluminum oxide (AAO) films with periodic nanopore lattice are widely used as templates or masks in the fabrication of mesostructures [1

1. C. R. Martin, “Nanomaterials: a membrane-based synthetic approach,” Science 266(5193), 1961–1966 (1994). [CrossRef] [PubMed]

5

5. L. Pu, Y. Shi, J. M. Zhu, X. M. Bao, R. Zhang, and Y. D. Zheng, “Electrochemical lithography: fabrication of nanoscale Si tips by porous anodization of Al/Si wafer,” Chem. Commun. (Camb.) (8): 942–943 (2004). [CrossRef]

]. AAO films also act as insulator hosts to sustain the functional material in many situations. Moreover, the employment of AAO as photonic crystal demonstrates its value in optical applications [6

6. H. Masuda, M. Ohya, H. Asoh, M. Nakao, M. Nohtomi, and T. Tamamura, “Photonic crystal using anodic porus alumina,” Jpn. J. Appl. Phys. 38(Part 2, No. 12A), L1403–L1405 (1999). [CrossRef]

,7

7. O. Takayama and M. Cada, “Two-dimensional metallo-dielectric photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett. 85(8), 1311–1313 (2004). [CrossRef]

].

AAO films have been fabricated by a variety of methods, such as two-step anodization, imprint, electron beam lithography, and other methods [8

8. H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina,” Science 268(5216), 1466–1468 (1995). [CrossRef] [PubMed]

12

12. J. Choi, K. Nielsch, M. Reiche, R. B. Wehrspohn, and U. Gösele, “Fabrication of monodomain alumina pore arrays with an interpore distance smaller than the lattice constant of the imprint stamp,” J. Vac. Sci. Technol. B 21(2), 763–766 (2003). [CrossRef]

]. Single or multi-layer optical thin films fabricated on a variety of substrates are widely used in technical areas, such as creation of anti-reflection films [13

13. H. A. Macleod, in Thin film optical filters, (McGrwa-Hill, New York, 1989).

15

15. A. I. Mahan, “An Early Exact Solution for the Reflectance of Reflection- Increasing and Reflection-Reducing Films,” J. Opt. Soc. Am. 42(4), 259–262 (1952). [CrossRef]

], reflection-increasing films [15

15. A. I. Mahan, “An Early Exact Solution for the Reflectance of Reflection- Increasing and Reflection-Reducing Films,” J. Opt. Soc. Am. 42(4), 259–262 (1952). [CrossRef]

,16

16. A. Suzuki, “Effect of Multiply Charged Ions on the Refractive Index of Titanium Oxide Films and an Application to Decorative Films,” Jpn. J. Appl. Phys. 39(Part 1, No. 3A), 1295–1298 (2000).

], distributed Bragg reflectors (DBR) [17

17. P. Yeh, in Optical Waves in Layered Media, (Wiley, New York, 1988).

,18

18. C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002). [CrossRef] [PubMed]

], and others. For most optical film structures, reflected and transmitted light show complementary colors. At the wavelength of the peaks in transmission, the reflectance normally shows valleys.

In this study, we show an asymmetric light reflectance phenomenon observed in AAO films fabricated on glass substrate. For the films reported in this study, light at incidence from the AAO side reflects and transmits light in complementary colors. However, light at incidence from the glass side results in nearly identical colors. The spectra analysis demonstrates that when light is incident from the glass side, the wavelengths of the peaks in transmission and the reflectance are nearly the same. This asymmetric light reflectance effect can be ascribed to the asymmetrical geometric structure of nanoscale aluminum networks. We believe this effect can be used in many fields, especially in optical communication.

2. Experimental

Transparent glass wafers were used as substrates. They were cleaned by acetone and ethanol ultrasonic cleaning method, then dipped in chromic acid for 12 h. Then, a thermal evaporation coat was employed to deposit 500–550 nm of highly pure aluminum (99.999%) film on the glass substrate. The aluminum film was then treated with one-step anodization process at 5 °C in a homemade anodization cell to obtain nanoporous AAO films. The anodization process was performed in 0.3 M oxalic acid solution at 10–60 V. The oxidation process was terminated after the current fell to background value and remained stable for an extended time. For comparison, a highly pure aluminum foil was treated with one-step anodization process at 5 °C for 10 min. The anodization process was performed in 0.3 M oxalic acid solution at 40 V. After anodization, part of the aluminum residue was removed by CuSO4 solution for transmission and reflectance spectra test. The other part of aluminum residue of the same sample was protected by nail polish (Maybelline). Subsequently, the nail polish was carefully removed by acetone.

We also employed Ta2O5 on quartz wafer as a substrate to investigate the origin of asymmetric light reflectance effect. A layer of approximately 320 nm Ta2O5 was electron-beam-evaporated on a quartz wafer. Thereafter, highly pure aluminum film was thermally evaporated onto the Ta2O5 on quartz substrate. The aluminum film was then anodized at 5 °C in 0.3 M oxalic acid solution at 10 V. The oxidation process was terminated after the current fell to background value and remained stable for an extended time. After anodization process, the produced AAO film was removed by wet chemical etching in a mixture of phosphoric acid (6 wt%) and chromic acid (1.8 wt%) at 60 °C for 3 h.

The optical characterizations of transmittance and reflectance spectra were performed using UV-Vis-NIR spectrophotometer (Varian Cary 2000), and the transmission and reflectance spectra were obtained in the spectral range of 200–800 nm.

3. Results and discussion

Figure 1
Fig. 1 Photographs of the glass after complete formation of AAO under 10 V: (a) Reflectance photograph of the glass taken from the front; (b) Reflectance photograph of the glass taken from the back; (c) Transmittance photograph of the glass taken from the front; (d) Transmittance photograph of the glass taken from the back.
presents the photographs of glass after complete formation of AAO under 10 V. Figures 1(a) and 1(b) present the reflective photographs of glass after complete formation of AAO film shot from the front (AAO side) and the back (glass substrate side), respectively. The camera and the light source were placed at the same side of the samples. The glass shown in Fig. 1(a) represents the color red and the glass shown in Fig. 1(b) represents the color green. Figures 1(c) and 1(d) represent the transmittal photographs of the glass shot from the front and the back, respectively. Samples were placed in the middle of the camera and the light source. The colors of the glasses are similar. That is, for the reflectance situation, the reflected light shows complementary colors. At the situation of transmittance, the transmitted light presents similar colors.

Figure 2(a)
Fig. 2 (a) Reflectance and transmittance spectra of AAO on glass under 10 V. The testing conditions are noted in the figure with the same colors as the curves; (b) Sketch of optical path lengths of the reflectance and the transmittance when light incidence is from two sides.
shows the reflectance and transmittance spectra of the sample shown in Fig. 1. All the spectra exhibit patterns of interference fringes. Absorption below 350 nm can be observed in the transmittance spectra tested from both sides and the reflectance spectrum tested from the back. This absorption can be ascribed to the absorption of the glass substrate. The transmittance spectra tested from the front and the back are nearly the same. However, the reflectance peaks and valleys from the fringes presented in the reflectance spectra tested from the two sides are nearly opposite. These spectra agree well with the asymmetric light reflectance phenomenon shown in Fig. 1.

Figure 3
Fig. 3 SEM images of the microstructure of the samples: (a) Top surface of the sample anodized at 10 V; (b) Remaining aluminum of the sample anodized at 10 V; (c) Remaining aluminum of the sample anodized at 60 V; (d) Cross-sectional view of the sample anodized at 10V.
shows the SEM images of the microstructure of the samples. The pores can be clearly seen in the image of the surface of the sample shown in Fig. 1 [Fig. 3(a)]. The average diameter of the pores is approximately 10 nm. The most interpore distance is approximately 25~35nm, corresponding to a formation voltage of 10 V. Figures 3(b) and 3(c) present the SEM images of the remaining aluminum of the sample anodized at 10 V and 60 V, respectively. The AAO films on the glass were removed by the mixed solution of phosphoric acid (6 wt%) and chromic acid (1.8 wt%). A layer of remaining aluminum can be observed on glass substrate. The remaining aluminum presents a network-like shape. The average distance of the hollows in the aluminum networks is approximately 30 nm. This network-like shape can be observed clearly on the sample anodized at 60 V, of which the interpore distance is rather big. From the cross-sectional SEM imagine [Fig. 3(d)], the thickness of the AAO film is approximately 610 nm.

Under thin-film estimation, the fringe maxima in the spectra are described by the relationships as
mλ1=2nλ1L   and   (m+1)λ2=2nλ2L
(1)
where m is the interference order of the fringe maxima, which contains information of optical path length difference and reflection-phase shift, and nλ is the effective refractive index at wavelength λ. The symbols λ1 and λ2 are the wavelengths of two neighboring fringe maxima at the interference order of m and m + 1, respectively. The band gap of the AAO film is rather big; therefore, nλ can be regarded as a constant at the long-wavelength region. Thus, the relationship of m value and the λ1, λ2 can be given by

λ1/λ2=(m+1)/m
(2)

A series of samples were prepared under different anodizing voltages. Table 1

Table 1. Wavelengths of the fringe maxima and the m values calculated by wavelength

table-icon
View This Table
presents the m value calculated by two fringe maxima at the longest wavelength in the reflectance spectrum of the samples (anodized at 10, 20, 40, and 60 V, respectively). The parameters listed in Table 1 show that the m value of the fringe maxima in the reflectance spectra is an integer when the light is incident from the front and half-integer when the light is incident from the back, regardless of anodizing voltage. The thickness of the films (L) can be calculated using formula (1). For sample anodized at 10 V, λ1 is 646nm, corresponding to a thickness of 598 nm; λ2 is 487 nm, corresponding a thickness of 601 nm. These results agree well with the film thickness measured by the SEM image.

Assuming the angle of the incident light is 0°, when light is incident from the front, part of the incident light reflects at the top surface of the AAO film. The other part of the light refracts into the AAO films and then reflects at the bottom surface of the AAO film. These two beams result in reflectance fringes [Fig. 2(b)]. The effective refractive index of AAO films is approximately 1.62 [19

19. K. Huang, L. Pu, Y. Shi, P. Han, R. Zhang, and Y. D. Zheng, “Photoluminescence oscillations in porous alumina films,” Appl. Phys. Lett. 89(20), 201118 (2006). [CrossRef]

], which is bigger than the refractive index of the air. Thus, there is a half-wave loss [20

20. M. Born, and E. Wolf, in Principles of Optics, (Cambridge, 2003)

] between reflected and incident light, and the reflection-phase shift at the top surface of the AAO films is π. The measured reflectance spectra demonstrate that the phase difference of the light reflected at the front surface and the bottom surface is at integer multiples of 2π. Thus, it can be deduced that the reflection-phase shift at the bottom surface of the AAO film is π as well.

The refractive index of glass is approximately 1.52, which is smaller than the effective refractive index of the AAO film. Therefore, there is no reason for the reflection-phase shift at the bottom surface of the AAO film to occur at the interface of the AAO film and glass. Figure 4(a)
Fig. 4 (a) Reflectance spectra versus transmittance spectra of AAO film without aluminum residue; (b) Reflectance spectrum of AAO film with aluminum residue versus reflectance and transmittance spectrum of AAO film without aluminum residue; (c) Sketch of optical path lengths of the reflectance tested at the region with and without aluminum residue.
shows the reflectance and transmittance spectra of the AAO film oxidized using an aluminum foil. A part of the aluminum residue [21

21. H. Masuda and M. Satoh, “Fabrication of Gold Nanodot Array Using Anodic Porous Alumina as an Evaporation Mask,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L126–L129 (1996). [CrossRef]

] under the AAO film was removed [Fig. 4(c)]. The interference fringes in the transmittance spectra, whereas the light is incident from both sides are nearly similar. However, unlike the reflectance spectra of the AAO on glass, the interference fringes in the reflectance spectra test from two sides show similar fringe shapes and are opposite to the fringes in the transmittance spectra. The m value calculated by the method mentioned above demonstrates that there is a phase difference at half-integer multiples of 2π between the light reflecting at the top and bottom surfaces of the AAO films. This is because of the presence of a reflection-phase shift of π at the top surface of AAO film and the absence of a reflection-phase shift at the bottom surface of AAO film. However, the reflectance spectrum of the same AAO sample without removing the aluminum residue illustrates the opposite fringe maxima and minima compared with the reflectance spectrum with the aluminum residue removed [Fig. 4(b)]. The m value demonstrates that when there is aluminum residue, the phase difference of the top and bottom surfaces is at integer multiples of 2π. It has been reported that there is aluminum residue on the glass substrate [22

22. H. Asoh, M. Matsuo, M. Yoshihama, and S. Ono, “Transfer of nanoporous pattern of anodic porous aluimna into Si substrate,” Appl. Phys. Lett. 83(21), 4408–4410 (2003). [CrossRef]

,23

23. P. G. Miney, P. E. Colavita, M. V. Schiza, R. J. Priore, F. G. Haibach, and M. L. Myrick, “Growth and characterization of a porous aluminum oxide film formed on an electrically insulating support,” Electrochem. Solid-State Lett. 6(10), B42–B45 (2003). [CrossRef]

]. The aluminum residue presents self-ordered aluminum networks on glass substrates [Fig. 3(b)]. Thus, we can conclude that the reflection-phase shift of π at the bottom surface of AAO film on glass occurs when the light reflects at the interface of the AAO film and the aluminum residue networks between the AAO film and the glass substrate.

The reflectance spectra when light is incident from the back can be similarly discussed. A part of the incident light reflects at the interface of the glass and the AAO film [Fig. 2(b)]. Meanwhile, a reflection-phase shift of π occurs. The other part of the light refracts into the AAO film and then reflects at the interface of the AAO film and the air. No reflection-phase shift occurs. Thus, the phase difference between the two light beams is at half-integer multiples of 2π. Considering that the refractive index of the glass is smaller than the effective refractive index of the AAO film, this reflection-phase shift of π at the interface of the glass and the AAO film can be caused by either the aluminum networks or the interface of the glass and the AAO film. Figure 5(a)
Fig. 5 (a) Reflectance spectra versus transmittance spectra of Ta2O5 on quartz film without aluminum residue networks; (b) Reflectance spectra versus transmittance spectra of Ta2O5 on quartz film with aluminum residue networks; (c) Schematic representation of the aluminum residue networks/Ta2O5/quartz wafer structure.
presents the reflectance and transmittance spectra of a quartz wafer covered with a Ta2O5 layer. Figure 5(b) presents the reflectance and transmittance spectra of the same sample when the aluminum networks have been fabricated above it [Fig. 5(c)]. Obviously, these spectra do not present the asymmetric light reflect effect, indicating that the bottom surface of the aluminum networks does not engender reflection-phase shift. We can assume that the reflection-phase shift is caused by the geometric structure of the aluminum networks, rather than the material property. As for the geometric structure of the aluminum networks, in Fig. 5(c), the cross-sectional structure of the aluminum networks can be regarded as a triangle-like shape. We suppose that the asymmetric light reflectance effect is caused by the asymmetric cross-sectional structure of the triangle aluminum networks. This asymmetric cross-sectional structure likely induces asymmetric scattering or absorption of light from different orientations. But the interaction of the light and the aluminum networks need further investigation.

In transmittance, whether the light is incident from the front or from the back, the optical path lengths are the same in the AAO film. The light reflects once at the interface of the AAO film and aluminum residue, engendering a reflection-phase shift of π, and reflects once at the interface of the AAO film and the air, engendering no reflection-phase shift [Fig. 2(b)]. Thus, the fringe maxima and minima of these two transmittance spectra show similarities, as does as reflectance spectra when the light is incident from the back.

4. Conclusion

Our results show that there is an asymmetric light reflectance effect in the AAO on glass films. Light of a specified wavelength, which is incident from front of the film, presents constructive interference in reflection and destructive interference in transmission. However, light at incidence from the back presents both constructive interference in reflection and transmission. This asymmetric light reflectance effect is caused by the geometric asymmetry of the nanoscale aluminum networks. This phenomenon might draw the attention from both fundamental and technological points of view. The demonstration of asymmetric light reflection could contribute to optical devices when combined with other optical structures, such as optical gratings, photonic crystals, and DBRs. Furthermore, theoretical analysis of the results would help to further investigate this extraordinary interference phenomenon, and fully understand the implication of these findings.

Acknowledgements

The authors are grateful to the NSFC fund of the 973 project of 2011CB301905, the National Natural Science Foundation of China under grant no. 61036003 and Natural Science Foundation of Fujian Province of no. 2008J0029, 2010J01343.

References and links

1.

C. R. Martin, “Nanomaterials: a membrane-based synthetic approach,” Science 266(5193), 1961–1966 (1994). [CrossRef] [PubMed]

2.

J. von Behren, L. Tsybeskov, and P. M. Fauchet, “Preparation and characterization of ultrathin porous silicon films,” Appl. Phys. Lett. 66(13), 1662–1664 (1995). [CrossRef]

3.

J. Li, C. Papadopoulos, and J. M. Xu, “Growing Y-junction carbon nanotubes,” Nature 402, 253–254 (1999).

4.

H. Masuda, A. Abe, M. Nakao, A. Yokoo, T. Tamamura, and K. Nishio, “Ordered mosaic nanocomposites in anodic porous alumina,” Adv. Mater. 15(2), 161–164 (2003). [CrossRef]

5.

L. Pu, Y. Shi, J. M. Zhu, X. M. Bao, R. Zhang, and Y. D. Zheng, “Electrochemical lithography: fabrication of nanoscale Si tips by porous anodization of Al/Si wafer,” Chem. Commun. (Camb.) (8): 942–943 (2004). [CrossRef]

6.

H. Masuda, M. Ohya, H. Asoh, M. Nakao, M. Nohtomi, and T. Tamamura, “Photonic crystal using anodic porus alumina,” Jpn. J. Appl. Phys. 38(Part 2, No. 12A), L1403–L1405 (1999). [CrossRef]

7.

O. Takayama and M. Cada, “Two-dimensional metallo-dielectric photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett. 85(8), 1311–1313 (2004). [CrossRef]

8.

H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina,” Science 268(5216), 1466–1468 (1995). [CrossRef] [PubMed]

9.

H. Masuda, H. Yamada, M. Satoh, H. Asoh, M. Nakao, and T. Tamamura, “Highly ordered nanochannel-array architecture in anodic alumina,” Appl. Phys. Lett. 71(19), 2770–2772 (1997). [CrossRef]

10.

H. Masuda, H. Asoh, M. Watanabe, K. Nishio, M. Nakao, and T. Tamamura, “Square and triangular nanohole array architectures in anodic alumina,” Adv. Mater. 13(3), 189–192 (2001). [CrossRef]

11.

A.-P. Li, F. Müller, and U. Gösele, “Polycrystalline and Monocrystalline Pore Arrays with. Large Interpore Distance in Anodic Alumina,” Electrochem. Solid-State Lett. 3(3), 131–134 (1999). [CrossRef]

12.

J. Choi, K. Nielsch, M. Reiche, R. B. Wehrspohn, and U. Gösele, “Fabrication of monodomain alumina pore arrays with an interpore distance smaller than the lattice constant of the imprint stamp,” J. Vac. Sci. Technol. B 21(2), 763–766 (2003). [CrossRef]

13.

H. A. Macleod, in Thin film optical filters, (McGrwa-Hill, New York, 1989).

14.

J. D. Rancourt, in Optical thin films. Users Handbook, (McGrwa-Hill, New York, 1987).

15.

A. I. Mahan, “An Early Exact Solution for the Reflectance of Reflection- Increasing and Reflection-Reducing Films,” J. Opt. Soc. Am. 42(4), 259–262 (1952). [CrossRef]

16.

A. Suzuki, “Effect of Multiply Charged Ions on the Refractive Index of Titanium Oxide Films and an Application to Decorative Films,” Jpn. J. Appl. Phys. 39(Part 1, No. 3A), 1295–1298 (2000).

17.

P. Yeh, in Optical Waves in Layered Media, (Wiley, New York, 1988).

18.

C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002). [CrossRef] [PubMed]

19.

K. Huang, L. Pu, Y. Shi, P. Han, R. Zhang, and Y. D. Zheng, “Photoluminescence oscillations in porous alumina films,” Appl. Phys. Lett. 89(20), 201118 (2006). [CrossRef]

20.

M. Born, and E. Wolf, in Principles of Optics, (Cambridge, 2003)

21.

H. Masuda and M. Satoh, “Fabrication of Gold Nanodot Array Using Anodic Porous Alumina as an Evaporation Mask,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L126–L129 (1996). [CrossRef]

22.

H. Asoh, M. Matsuo, M. Yoshihama, and S. Ono, “Transfer of nanoporous pattern of anodic porous aluimna into Si substrate,” Appl. Phys. Lett. 83(21), 4408–4410 (2003). [CrossRef]

23.

P. G. Miney, P. E. Colavita, M. V. Schiza, R. J. Priore, F. G. Haibach, and M. L. Myrick, “Growth and characterization of a porous aluminum oxide film formed on an electrically insulating support,” Electrochem. Solid-State Lett. 6(10), B42–B45 (2003). [CrossRef]

OCIS Codes
(310.6628) Thin films : Subwavelength structures, nanostructures
(080.6755) Geometric optics : Systems with special symmetry

ToC Category:
Thin Films

History
Original Manuscript: December 1, 2010
Revised Manuscript: December 24, 2010
Manuscript Accepted: December 28, 2010
Published: January 11, 2011

Citation
Kai Huang, Yangjuan Li, Zhiming Wu, Cheng Li, Hongkai Lai, and Junyong Kang, "Asymmetric light reflectance effect in AAO on glass," Opt. Express 19, 1301-1309 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1301


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References

  1. C. R. Martin, “Nanomaterials: a membrane-based synthetic approach,” Science 266(5193), 1961–1966 (1994). [CrossRef] [PubMed]
  2. J. von Behren, L. Tsybeskov, and P. M. Fauchet, “Preparation and characterization of ultrathin porous silicon films,” Appl. Phys. Lett. 66(13), 1662–1664 (1995). [CrossRef]
  3. J. Li, C. Papadopoulos, and J. M. Xu, “Growing Y-junction carbon nanotubes,” Nature 402, 253–254 (1999).
  4. H. Masuda, A. Abe, M. Nakao, A. Yokoo, T. Tamamura, and K. Nishio, “Ordered mosaic nanocomposites in anodic porous alumina,” Adv. Mater. 15(2), 161–164 (2003). [CrossRef]
  5. L. Pu, Y. Shi, J. M. Zhu, X. M. Bao, R. Zhang, and Y. D. Zheng, “Electrochemical lithography: fabrication of nanoscale Si tips by porous anodization of Al/Si wafer,” Chem. Commun. (Camb.) (8): 942–943 (2004). [CrossRef]
  6. H. Masuda, M. Ohya, H. Asoh, M. Nakao, M. Nohtomi, and T. Tamamura, “Photonic crystal using anodic porus alumina,” Jpn. J. Appl. Phys. 38(Part 2, No. 12A), L1403–L1405 (1999). [CrossRef]
  7. O. Takayama and M. Cada, “Two-dimensional metallo-dielectric photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett. 85(8), 1311–1313 (2004). [CrossRef]
  8. H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina,” Science 268(5216), 1466–1468 (1995). [CrossRef] [PubMed]
  9. H. Masuda, H. Yamada, M. Satoh, H. Asoh, M. Nakao, and T. Tamamura, “Highly ordered nanochannel-array architecture in anodic alumina,” Appl. Phys. Lett. 71(19), 2770–2772 (1997). [CrossRef]
  10. H. Masuda, H. Asoh, M. Watanabe, K. Nishio, M. Nakao, and T. Tamamura, “Square and triangular nanohole array architectures in anodic alumina,” Adv. Mater. 13(3), 189–192 (2001). [CrossRef]
  11. A.-P. Li, F. Müller, and U. Gösele, “Polycrystalline and Monocrystalline Pore Arrays with. Large Interpore Distance in Anodic Alumina,” Electrochem. Solid-State Lett. 3(3), 131–134 (1999). [CrossRef]
  12. J. Choi, K. Nielsch, M. Reiche, R. B. Wehrspohn, and U. Gösele, “Fabrication of monodomain alumina pore arrays with an interpore distance smaller than the lattice constant of the imprint stamp,” J. Vac. Sci. Technol. B 21(2), 763–766 (2003). [CrossRef]
  13. H. A. Macleod, in Thin film optical filters, (McGrwa-Hill, New York, 1989).
  14. J. D. Rancourt, in Optical thin films. Users Handbook, (McGrwa-Hill, New York, 1987).
  15. A. I. Mahan, “An Early Exact Solution for the Reflectance of Reflection- Increasing and Reflection-Reducing Films,” J. Opt. Soc. Am. 42(4), 259–262 (1952). [CrossRef]
  16. A. Suzuki, “Effect of Multiply Charged Ions on the Refractive Index of Titanium Oxide Films and an Application to Decorative Films,” Jpn. J. Appl. Phys. 39(Part 1, No. 3A), 1295–1298 (2000).
  17. P. Yeh, in Optical Waves in Layered Media, (Wiley, New York, 1988).
  18. C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002). [CrossRef] [PubMed]
  19. K. Huang, L. Pu, Y. Shi, P. Han, R. Zhang, and Y. D. Zheng, “Photoluminescence oscillations in porous alumina films,” Appl. Phys. Lett. 89(20), 201118 (2006). [CrossRef]
  20. M. Born, and E. Wolf, in Principles of Optics, (Cambridge, 2003)
  21. H. Masuda and M. Satoh, “Fabrication of Gold Nanodot Array Using Anodic Porous Alumina as an Evaporation Mask,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L126–L129 (1996). [CrossRef]
  22. H. Asoh, M. Matsuo, M. Yoshihama, and S. Ono, “Transfer of nanoporous pattern of anodic porous aluimna into Si substrate,” Appl. Phys. Lett. 83(21), 4408–4410 (2003). [CrossRef]
  23. P. G. Miney, P. E. Colavita, M. V. Schiza, R. J. Priore, F. G. Haibach, and M. L. Myrick, “Growth and characterization of a porous aluminum oxide film formed on an electrically insulating support,” Electrochem. Solid-State Lett. 6(10), B42–B45 (2003). [CrossRef]

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