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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 20 — Oct. 2, 2006
  • pp: 9113–9119
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Realization of woodpile structure using optical interference holography

Yee Kwong Pang, Jeffrey Chi Wai Lee, Cheuk Ting Ho, and Wing Yim Tam  »View Author Affiliations


Optics Express, Vol. 14, Issue 20, pp. 9113-9119 (2006)
http://dx.doi.org/10.1364/OE.14.009113


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Abstract

We report the use of a (4+1)-beam optical interference holography technique to fabricate woodpile structures in photo-resists. The configuration consists of 4 linearly polarized side beams arranged symmetrically around a circularly polarized central beam with all the beams from the same half space, making it easily accessible experimentally. The fabricated woodpile structures are in good agreement with model simulations. Furthermore, woodpiles with the diamond symmetry are also obtained by exploiting the shrinkage of the photo-resists. Bandgaps in the visible range are also observed for the samples with and without the correct stacking of the woodpile structures.

© 2006 Optical Society of America

1. Introduction

Holographic lithography, a method combining the techniques of multiple beam interference and photolithography to record the interference pattern in photo-resist, provides some unique advantages. For example, it requires only simple experimental setups, and more importantly, various structures (e.g. quasi-periodic [24

24. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003). [CrossRef]

25

25. X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006). [CrossRef]

] and chiral structures [26

26. Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005). [CrossRef] [PubMed]

]) are feasible by using different beam configurations. This method has thus attracted much interest since the realization of the FCC structure using the interference of four non-planar coherent beams [19

19. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000). [CrossRef] [PubMed]

23

23. X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003). [CrossRef]

]. Furthermore double-exposure holographic lithography has also been used to fabricate the woodpile structure in the infrared range [29

29. S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003). [CrossRef]

]. Recently, several groups have suggested that the diamond structure could be fabricated using 4-beam configurations [30

30. D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (2003). [CrossRef]

36

36. O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004). [CrossRef]

]. However, these configurations require either impractical beam arrangements or elliptical polarizations that are hard to implement experimentally [30

30. D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (2003). [CrossRef]

36

36. O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004). [CrossRef]

]. A recent attempt to fabricate the diamond structure using a (3+1)-beam configuration (3 linearly polarized side beams and one circularly polarized central beam), to simulate a double-exposure for two FCC structures, was debatable [37

37. Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005). [CrossRef]

38

38. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

]. One of us has proposed recently that the woodpile and diamond structures can be obtained using a 5-beam optical interference holography with the beams from the same half space as compared to other configurations in which the interfering beams are counter-propagating from both half spaces [38

38. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

]. In this communication, we report the use of a (4+1)-beam interference configuration to fabricate the woodpile structure in photo-resist using one single exposure. The configuration is basically the “umbrella” arrangement with 4 linearly polarized side beams arranged symmetrically around a circularly polarized central beam [38

38. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

]. The fabricated woodpile structures, in submicron scales, are in good agreement with model simulations. Furthermore, they also exhibit bandgaps in the visible range.

2. Model

The wave vectors of the (4+1)-beam configuration for the woodpile structure shown in Fig. 1(a) can be represented by[38

38. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

]

[k0=k(0,0,1)k1=k(sinφ,0,cosφ)k2=k(0,sinφ,cosφ)k3=k(sinφ,0,cosφ)k4=k(0,sinφ,cosφ)],
(1)

where k=2π/λ for λ=488 nm, the wavelength of the light source. Here φ is the angle between the side beams k i and the central beam k 0. The central beam is circularly polarized with electric field given by E0=E02(1,i,0) while the side beams are linearly polarized with electric fields normal to the plane of incidence. Given Eq. (1), the intensity distribution of the (4+1)-beam interference can be expressed as[38

38. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

]

I(r)=l,mEl·Em*eiqlm·ri(δlδm)
(2)

where q lm=k l-k m for l,m=0-4 and δ’s are the phases of the beams. For simplicity, we choose |E i|=1 for i=0-4. Figure 1(b) shows a woodpile structure obtained by the superposition of orthogonal x-and y-directional rods stacked and interlaced with a half rodspace shift in each plane. The x-and y-rods are obtained by the interference of beams (k 0,k 2,k 4) and (k 0,k 1,k 3), respectively. The lattice spacing [shown in Fig. 1(b)] and the shape of the rods depend on the angle φ. For diamond symmetry, the lattice ratio a/b is equal to 1/√2, corresponding to φ=70.53°. Figures 1(c) and 1(d) show woodpile structures as intensity contour surfaces obtained by Eqs. (1) and (2) for all beams with the

Fig. 1. (a). (4+1)-beam configuration for the woodpile structure. (b) Superposition of x-rods and y-rods obtained by the interference of (k 0,k 2,k 4) and (k 0,k 1,k 3), respectively. (c) Woodpile structure shown as intensity contour surfaces with a 50% cut-off by the interference of (k 0,k 1,k 2,k 3,k 4) beams with equal phases and using φ=41.8°. The structure is compressed by 40% and expanded by 10% along the z and in the xy-directions, respectively, to simulate the deformations observed in the experiment. (Same result is obtained using φ=70.53° but without the deformations as reported in Ref. [38].) The insets, upper-right (50% cut-off) and lower-right (95% cut-off), are views of the top and the unit cell of the diamond structure, respectively. (d) Contour surfaces with a 40% intensity cut-off for the 5-beam interference similar to (c) but with k 2 180° out of phase w.r.t. the other beams. The insets, upper-right (40% cut-off) and lower-right (60% cut-off), are views of the top and the unit cell, respectively.

same phases (δ‘s=0) and one beam 180° out of phase (e.g. δ2=180° and others are zero), respectively. To compare with the experimental results, the structures are simulated using the experimental incidence angle φ=41.8° with a 40% shrinkage in the z-direction and 10% expansion in the xy-directions to achieve the diamond symmetry. One obvious difference between Figs. 1(c) and (d) is that the x-and y-rods in Fig. 1(c) are correctly stacked and interlaced while in Fig. 1(d) they occupy the same z-position in each plane for the incorrect phase case. The top views (upper-right insets in Figs. 1(c) and (d)) further demonstrate the stacking of the rods in both cases. The lower-right inset of Fig. 1(c) obtained at a higher intensity cut-off, shows clearly a diamond structure for the correct phase configuration while the corresponding inset in Fig. 1(d) shows a FCC structure interlaced with z-directional rods in between. For even higher intensity cut-offs, the z-rods will disappear giving only a FCC structure. Fortunately, good woodpile/diamond structure can still be obtained for small phase difference as confirmed by 200 simulations with random-phases within which more than 50% still show visually discernible woodpile structures.

3. Experiment

Fig. 2. (a). 3D SEM image of woodpile structure. The upper-left inset shows the expanded view of the woodpile structure. (b)–(d) SEM images for the woodpile structures with a/b=0.72, 0.88, and 0.82, respectively. Note that (b) and (c) show the favorable results with the x- and y-rods properly interlaced while (d) shows the unfavorable result with the x-and y-rods in the same plane for each layer. The upper-right insets (size 1.5×1.0µm2) are the expanded front views while the lower-left insets (size 1.8×1.8µm2) are the top views of the structures. The scale bars (white) are all 1.0 µm.

The five beams with diameter 7.5 mm in Fig. 1(a) were obtained by passing an expanded beam from an argon ion laser through a template with one central hole and four side holes distributed evenly around the central hole. The beams, each with power 4.5 mW and polarization adjusted by wave plates mounted at the holes of the template, entered a four-sided truncated pyramid from the base as shown in Fig. 1(a). The central beam, converted to circular polarization by a quarter wave plate, went straight up the pyramid while the side beams reflected internally at the slanted surfaces, making an angle φ=41.8° with the central beam, and intersected at the truncated surface as shown in Fig. 1(a). Using this setup, the beams were more uniform and, more importantly, the phases of the beams were fixed because they were obtained from the same expanded beam. We used the Shell “SU8” photo-resist resin (sensitized to the 488nm line of the argon ion laser and with refractive index 1.62) as the recording medium and followed the processing procedures reported earlier.[24

24. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003). [CrossRef]

26

26. Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005). [CrossRef] [PubMed]

] The resin was spin-coated on glass substrates with almost the same refractive index as the SU8 to form ~20 µ m thick samples. The samples were heated to 90°C to remove any solvent left before exposure. The photo-resist coated sample was placed on the truncated surface of the pyramid with index-matching to reduce multiple reflections. The exposure time was 15 s. After the exposure, a post-thermal treatment at 90°C for about 30 mins was needed to complete the polymerization. Polymerization occurred only at regions where the dosage exceeded a critical value, while under-exposed regions were washed away first by bathing the sample with propylene-glycol-methyl-ether-acetate (PGMEA) for 8 hours, then rinsing with PGMEA-acetone solution, and finally with ethanol, creating a copy of the woodpile pattern. The long development time was to ensure the complete removable of the under-exposed regions and, more importantly, to enable the detachment of the sample from the substrate so that the structure at the sample-substrate side could be imaged by electron microscope.

Despite the differences in the rod stacking, all samples possess visible range bandgaps in the normal reflectance and transmittance, shown in Figs. 3(a)-3(c) for samples in Figs. 2(b)-2(d) respectively, using unpolarized light [24

24. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003). [CrossRef]

25

25. X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006). [CrossRef]

]. (We were unable to observe obvious orientational dependence of the optical spectra using polarized light. Note that the reflectance and transmittance do not add up to unit because of the absorption of the SU8 and parasitic scattering from the microstructure.) Overall, there is a bandgap around 700 nm, shifting slightly to longer wavelength, for the correct rod stacking samples in Figs. 2(b)-2(c). Despite the incorrect stacking in Fig. 2(d), the bandgap is also ~700 nm suggesting that either our samples are not good enough or the normal incidence is not sensitive enough to distinguish the difference. Unfortunately, our samples do not have uniform regions (see inset photos in Fig. 3) large enough for obtaining reliable angular dependent measurements and to warrant a quantitative comparison with calculations.

Fig. 3. (a)-(c). Normal reflectance (in blue) and transmittance (in red) for the samples in Fig. 2(b)-(d), respectively. The insets are white light reflection photos. The dashed circles (17 µm diameter) are regions where optical spectra are obtained.

To conclude, we have fabricated the woodpile structure on photo-resist using a (4+1)-beam optical interference holography. The samples resemble the simulations very well. By exploiting the shrinkage of the photo-resist, samples with the diamond lattice spacing are obtained. The woodpile structures display visible range bandgaps. Our samples, although small in size and with low dielectric contrast, could be used as templates for fabricating woodpile structures with higher dielectric contrast for complete bandgaps.

Acknowledgments

We thank C. T. Chan for helpful discussions. Support from Hong Kong RGC grants CA02/03.SC01, HKUST603303, and HKUST603405 is gratefully acknowledged.

References and Links

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C. M. Soukoulis, “Photonic band gap material,” (Kluwer, Dordrecht, 1996).

2.

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3.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

4.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic crystals,” (Princeton, 1995).

5.

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6.

J. Maddox, “Photonic band-gaps bite the dust,” Nature 348, 481 (1990). [CrossRef]

7.

E. Yablonovitch, T. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991). [CrossRef] [PubMed]

8.

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994). [CrossRef]

9.

M. Maldovan and E. L. Thomas, “Diamond-structured photonic crystal,” Nature Materials 3, 593–600 (2004). [CrossRef] [PubMed]

10.

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in Titania,” Science 281, 802–804 (1998). [CrossRef]

11.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002). [CrossRef]

12.

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005). [CrossRef]

13.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002). [CrossRef]

14.

A. Chutinan and S. Noda, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Phys. Rev. B 57, R2006–R2008 (1998). [CrossRef]

15.

O. Toader and S. John, “Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals,” Science 292, 1133–1135 (2001). [CrossRef] [PubMed]

16.

N. Yamamoto, S. Noda, and A. Sasaki, “Development of one period of a three-dimensional photonic crystal in the 5–10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 36, 1907–1911 (1997). [CrossRef]

17.

S Y Lin, J G Fleming, D L Hetherington, B K Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998). [CrossRef]

18.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003). [CrossRef]

19.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000). [CrossRef] [PubMed]

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S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002). [CrossRef]

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23.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003). [CrossRef]

24.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003). [CrossRef]

25.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006). [CrossRef]

26.

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005). [CrossRef] [PubMed]

27.

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004). [CrossRef]

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M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004). [CrossRef]

29.

S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003). [CrossRef]

30.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (2003). [CrossRef]

31.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. Han, and S. Yang, “Photonic crystals through holographic lithography: simple cubic, diamond-like, and gyroid-like structures,” Appl. Phys. Lett. 84, 5434–5436 (2004). [CrossRef]

32.

M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001). [CrossRef]

33.

C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, “Triply periodic bicontinuous structures through interference lithography: a level set approach,” J. Opt. Soc. Am. 20, 948–954 (2003). [CrossRef]

34.

D. C. Meisel, M. Wegener, and K. Busch, “Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps,” Phys. Rev. B 70, 165104-1/10 (2004). [CrossRef]

35.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band gap templating using optical interference. Lithography,” Phys. Rev. E 71, 046605-1/18 (2005). [CrossRef]

36.

O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004). [CrossRef]

37.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005). [CrossRef]

38.

W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication

ToC Category:
Holography

History
Original Manuscript: August 8, 2006
Revised Manuscript: September 20, 2006
Manuscript Accepted: September 25, 2006
Published: October 2, 2006

Citation
Yee Kwong Pang, Jeffrey Chi Lee, Cheuk Ting Ho, and Wing Yim Tam, "Realization of woodpile structure using optical interference holography," Opt. Express 14, 9113-9119 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-9113


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References

  1. C. M. Soukoulis, "Photonic band gap material," (Kluwer, Dordrecht, 1996).
  2. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  3. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  4. J. D. Joannopoulos, R. D. Meade and J. N. Winn, "Photonic crystals," (Princeton, 1995).
  5. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990). [CrossRef] [PubMed]
  6. J. Maddox, "Photonic band-gaps bite the dust," Nature 348, 481 (1990). [CrossRef]
  7. E. Yablonovitch, T. Gmitter and K. M. Leung, "Photonic band structure: The face-centered-cubic case employing nonspherical atoms," Phys. Rev. Lett. 67, 2295-2298 (1991). [CrossRef] [PubMed]
  8. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: a family of photonic crystals," Phys. Rev. B 50, 1988-1991 (1994). [CrossRef]
  9. M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystal," Nature Materials 3, 593-600 (2004). [CrossRef] [PubMed]
  10. J. E. G. J. Wijnhoven and W. L. Vos, "Preparation of photonic crystals made of air spheres in Titania," Science 281, 802-804 (1998). [CrossRef]
  11. E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López and J. Sánchez-Dehesa, "Optical study of the full photonic band gap in silicon inverse opals," Appl. Phys. Lett. 81, 4925-4927 (2002). [CrossRef]
  12. W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan and P Sheng, "Fabrication and optical characterization of gold-infiltrated silica opals," J. Phys. Condens. Matter. 17, 2177-2190 (2005). [CrossRef]
  13. F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, C. López, "Nanorobotic manipulation of microspheres for on-chip diamond architectures," Adv. Mater. 4, 1144-1147 (2002). [CrossRef]
  14. A. Chutinan and S. Noda, "Full three-dimensional photonic bandgap crystals at near- infrared wavelengths," Phys. Rev. B 57, R2006-R2008 (1998). [CrossRef]
  15. O. Toader and S. John, "Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals," Science 292, 1133-1135 (2001). [CrossRef] [PubMed]
  16. N. Yamamoto, S. Noda, and A. Sasaki, "Development of one period of a three-dimensional photonic crystal in the 5-10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques," Jpn. J. Appl. Phys. 36, 1907-1911 (1997). [CrossRef]
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