Abstract

We demonstrate the construction of diamond photonic crystal structures by the translation of a multi-beam interference pattern. Using phase shift of each beam, the double-exposed interference patterns can be aligned in the [111] direction for a face-centered cubic (FCC) and [210] direction for a body-centered cubic (BCC), respectively, producing diamond D from FCC and BCC-diamond like structure from BCC. The present result shows that the complete bandgap has been retained with slight deviation from ideal diamond symmetry.

©2005 Optical Society of America

1. Introduction

Photonic crystals (PCs) are called a semiconductor of light and can be used to confine, manipulate and guide photons, which are desired for the next-generation optical circuits. Recently, multibeam interference lithography has been developed and holds promise in the PC fabrication over colloidal assembly,1 direct writing,2–4 and multi-layer process5 because it produces 3D structure with controlled lattice and unit atoms in a large area by single exposure and is compatible with conventional photolithography.6

To date, among the proposed 3D PC structures, diamond networks have been known as the most optimized structure for having a large and complete photonic bandgaps (PBGs). Moreover, the PBG is robust enough to allow some structural modification within diamond symmetry,7 This makes diamond structures especially attractive over other symmetries since it allows application of a wide range of approaches to fabricate them conveniently, including Yablonobite by direct drilling,8 woodpile (<100>-diamond) by layer-by-layer fabrication,9 <110>-diamond by layer-by-layer followed by reactive ion etching,10 spiral diamond made by GLAD.11 In the case of holographic lithography, it has been reported that four interfering beams can be assembled to create the level-set D (diamond) and G (gyroid) structures, and body-centered cubic (BCC) diamond.12–15 All of these structures possess a PBG with larger than 20% between the 2nd and 3rd bands for a refractive index of n=3.6, close to the largest yet calculated.16

In this letter, we demonstrate the translation of 3D interference patterns to construct two types of diamond structures. Since the diamond symmetry can be alternatively achieved by two simple FCC or BCC sublattices, displaced along [111] direction or [210] direction, respectively, the superposition of the interference pattern and the shifted pattern could approximate the corresponding diamond structures. Specifically, we demonstrate phase-induced translation of simple FCC and BCC interference pattern. Then, we investigate the PBGs of two superimposed interference patterns of FCC and BCC, displaced in aforementioned directions. In practice, this method can be achieved by using double-exposure holographic lithography with phase shift to produce polymeric structures.17,18 The double-exposure with phase shift is preferred over multiplexed holography because of the alignment process.19 Compared to the previously reported results based on single-exposure of four-beam interference by controlling the polarization of each beam,13,14 our method provide much improved contrast of the diamond interference. The high pattern contrast is crucial for practical fabrication of photoresist structures with clearly defined and completely opened pores.20,21 Furthermore, this method can be flexible by simply changing the intensity of each exposure, resulting in F4¯3m from FCC interference pattern, which has two different PBGs.16

2. Translation of FCC or BCC interference patterns by phase shift

To construct 3D structures, four-beam interference has been widely used. The intensity distribution of the interference field of four mutually coherent laser beams can be described by Fourier superposition and can be written as

I=n=14En2+m<n4EnEmεn·εm*cos[(knkm)·r+(ϕn0ϕm0)].

where En, εn, kn and ϕn are the amplitude, the unit polarization vector, the wave vector, and the phase of the nth beam, respectively. Here, we control the phase of each beam (i.e., relative phase difference) to shift the interference pattern in a certain direction. In experiment, the phase shift can be produced by phase retarders such as wave-plates,17 Kerr cells and Pockels cells. When the relative phase difference in Eq. (1) is changed by (ϕn - ϕm), the interference term, Inm is described by

Inm=EnEmεn·εm*cos[(knkm)·r+(ϕn0ϕm0)+(ϕnϕm)].

Meanwhile, since the interference term translated by r′ in space can be described by,

Inm=EnEmεn·εm*cos[(knkm)·(r+r)+(ϕn0ϕm0)].

The relationship between the spatial translation in a certain direction and the phase shift can be obtained by comparing Eqs. (2) and (3) and given by

(ϕnϕm)=(knkm)·r.

Then, the phase shift of each beam, which induces the translation of the interference pattern, can be determined by Eq. (4) of each interference term.

First, we consider the translation of the simple FCC interference pattern with Fm3¯m space group.22 This structure has been demonstrated with four beams: one set of two coplanar beams interfere with another set whose plane is perpendicular to the first. This requires a substrate that is transparent at the light’s wavelength and a prism to compensate for the refraction at the air-photoresist interface.22 When the initial phase of each beam is set at zero in Eq. (2), the interference pattern can be expressed as:

Inm~cos[2πd(xy+z)+(ϕ1ϕ3)]+cos[2πd(x+y+z)+(ϕ1ϕ4)]
+cos[2πd(xy+z)+(ϕ2ϕ3)]+cos[2πd(x+y+z)+(ϕ2ϕ4)]

where d is the lattice constant. In order to translate the interference pattern in [111] direction by βd/4π as shown in Fig. 1(a), phase differences are calculated from Eq. (4) and given by (ϕ 1 -ϕ 3) = β, (ϕ 1-ϕ 4) = 3β, (ϕ 2 -ϕ 3) = -β, and (ϕ 2 -ϕ 4) = β. Then, the phases of four beams relative to the initial zero value are ϕ 1 = 3β, ϕ 2 = β, ϕ 3 = 2β, and ϕ 1 = 0.

For BCC interference pattern, the beam configurations for m3¯m symmetry of the unit atoms.are described as:

Inm~cos[4πd(y+z)+(ϕ1ϕ2)]+cos[4πd(x+y)+(ϕ1ϕ3)]
+cos[4πd(x+z)+(ϕ1ϕ4)]+cos[4πd(xz)+(ϕ2ϕ3)]
+cos[4πd(xy)+(ϕ2ϕ4)]+cos[4πd(y+z)+(ϕ3ϕ4)]

which has an Im3¯m space group of the BCC lattice. Likewise in the FCC, the translation of the interference pattern by βd/4π(2,1,0) (see Fig. 1(b)) can be achieved by solving Eq. (2). The phase differences are given by (ϕ 1 -ϕ 2 ) = β, (ϕ 1 -ϕ 3) = 3β, (ϕ 1 -ϕ 4) = 2β, (ϕ 2 -ϕ 3) = 2β, (ϕ 2 -ϕ 4) = β, and (ϕ 3 -ϕ 4) = -β. Finally, the phases of four beams relative to the initial zero value are ϕ 1 = 3β, ϕ 2 = 2β, ϕ 3 = 0, and ϕ 4 = β.

 figure: Fig. 1.

Fig. 1. Translation of (a) FCC interference pattern in the [111]direction and (b) BCC interference in the [210] direction.

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3. Superimposition of interference patterns with phase shift

With these pattern shifts, the double-exposed interference patterns can be described by the superposition of all exposed patterns. Figs. 2(a), 2(b) and 2(c) show the relative position of two FCC lattices (red for the initial pattern and blue for the shifted one), described by Eq. (5) for β = 0.80π, 1.00π and 1.16π, respectively. Then, the translations are 0.20d, 0.25d and 0.29d,all in [111] direction. The level surfaces of the double-exposed FCC interference patterns are reproduced in Figs. 2(d)–2(f) for their respective cases.

 figure: Fig. 2.

Fig. 2. The relative position of the FCC interference pattern (red) and the shifted pattern (blue) in the [111] direction by (a) 0.20d(1,1,1), (b) 0.25d(1,1,1), and (c) 0.29d(1,1,1). The level surface of each double-exposed FCC interference pattern with a filling fraction of 0.22 is shown in (d -f) for their respective cases.

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Remarkably, overall exposures make a local connection between the atoms formed in each exposure. For the FCC, the superposition of interference patterns with the translation by 0.25d describes the level surface of diamond D structure (see Fig. 2(e)) and given by

Inm~cos[2πd(xy+z)]+cos[2πd(x+y+z)]
+cos[2πd(xy+z)]+cos[2πd(x+y+z)]
+sin[2πd(xy+z)]sin[2πd(x+y+z)]
sin[2πd(xy+z)]+sin[2πd(x+y+z)]

It is noteworthy that this equation contains 8 terms instead of 4 terms reported in the literature in describing the same type of diamond D. These additional terms provide higher contrast of the interference pattern.7,14 Considering the intensity profile along [111] direction (see Fig. 3), the contrast defined by difference between maximum and minimum intensities is 8 for 8-term D in contrast to 4√2 for 4-term D. In practical applications of interference lithography, low contrast interference cannot produce well-defined photoresist pattern with completely opened, porous structure due to the homogeneous background of acid generation.20

 figure: Fig. 3.

Fig. 3. Intensity profile of 8-term and 4-term interference patterns along [111] direction

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Meanwhile, instead of diamond D, this method can simply construct F4¯3m , with the different intensity of each exposure, which possesses dual complete PBGs.14

In Figs. 4(a), 4(b) and 4(c), the position of two BCC lattices (red for the initial pattern and blue for the shifted one), described by Eq. (6) are shown for β = 0.40π, 0.50π and 1.16π, respectively. Then, the translations are 0.20d, 0.25d and 0.29d, all in [210] direction.

 figure: Fig. 4.

Fig. 4. The relative position of the BCC interference pattern (red) and the shifted pattern (blue) in the [210] direction by (a) 0.20d (1,1,1), (b) 0.25d (1,1,1), and (c) 0.29d (1,1,1). The level surface of each double-exposed BCC interference pattern with a filling fraction of 0.20 is shown in (d-f) for their respective cases.

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The level surfaces of the double-exposed BCC interference patterns are reproduced in Figs. 4(d)–4(f) for their respective cases. For the BCC-based structure, shift of interference pattern into [210] by 0.25d constructs a BCC diamond-like structure with diamond D symmetry in the body-centered tetragonal unit cell (see Fig 4(e)).7 From Eq. (6), the level surface of this structure can be expressed by

Inm~cos[4πd(x+y)]+cos[4πd(y+z)]
+cos[4πd(y+z)]+cos[4πd(xy)]
+sin[4πd(x+y)]sin[4πd(y+z)]
sin[4πd(y+z)]sin[4πd(xy)]

4. Bandgap of superimposed FCC and BCC interference patterns

In Fig. 5, we calculate the PBG of the double-exposed FCC as a function of the degree of phase shift. The polymeric structure by interference lithography can be used as a template to deposit high refractive index materials.23 The PCs with a refractive index of 3.45 produced from FCC-based structure show a complete PBG between the 2nd and 3rd bands. The volume fraction is optimized to achieve a maximum PBG at each point, ranging from 0.22 to 0.26. The bandgap width has a local maximum at a translation of 0.25d(1,1,1) with diamond D symmetry defined in Eq. (6). They show a complete PBG with the gap-midgap ratio as large as 25%, which is comparable to the previous results.12 Meanwhile, the complete PBG appears when the degree of the pattern translation is varied from 0.18 to 0.30. The relatively large PBG is retained within the deviation from diamond D (See Fig 3, these structures possess the PBG width above 10%). Therefore, this method is feasible even with the experimental error during translation. Likewise the FCC case, we calculate PBG of BCC-based structure as shown in Fig. 5. The optimized volume fraction for a maximum PBG is found 0.20 for the normalized pattern shift of 0.25, and the optimal volume fraction is increased to 0.30 for the upper and lower bounds of the phase shift in Fig. 5. The bandgap width reaches a maximum, at which the gap-midgap ratio is 22%, for a translation of 0.25d(2,1,0) with BCC diamond-like structure defined in Eq. (8).15

 figure: Fig. 5.

Fig. 5. Complete PBG of double-exposed (a) FCC and (b) BCC interference patterns as a function of the normalized pattern shift in [111] and [210], respectively.

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4. Conclusion

In summary, we propose a double exposure technique that translates interference patterns by phase shift. The superposition of two interference patterns constructs partially overlapped structures, whereas the two unit atoms in the basis are connected with each other. We demonstrate that translation in both the [111] direction for FCC and the [210] direction for BCC, respectively, can produce diamond D and BCC diamond-like structure, respectively. Such structures show a large complete PBG between 2nd and 3rd bands, in agreement with the literature results. The large bandgap is retained within the accepted variation in the degree of translation. Compared to the single-exposed diamond D structures, the present double-exposed structure has a better contrast of the interference pattern, which is necessary to their practical realization in interference lithography.

Acknowlegments

We would like to thank David N. Sharp in Oxford University and Steven G. Johnson in MIT for their help with the photonic bandgap calculation. This work was supported by the “National R&D Project for Nano Science and Technology” of the Ministry of Commerce, Industry and Energy, the BK21 program, and the CUPS-ERC, Office of Naval Research (ONR) through the MURI program (Grant # E-21-6WG-G2), and the Korea Research Foundation Postdoctoral Fellowship (Grant # KRF-2005-000-10299) for JHM.

References and links

1 . S. H. Park , D. Qin , and Y. Xia , “ Crystallization of mesoscale particles over large areas ,” Adv. Mater. 10 , 1028 – 1032 ( 1998 ). [CrossRef]  

2 . G. M. Gratson , M. J. Xu , and J. A. Lewis , “ Microporiodis structures - Direct writing of three-dimensional webs ,” Nature 428 , 386 – 386 ( 2004 ). [CrossRef]   [PubMed]  

3 . M. Deubel , 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]   [PubMed]  

4 . S. Kawata , H. B. Sun , T. Tanaka , and K. Takada , “ Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption ,” Nature 412 , 697 – 698 ( 2001 ). [CrossRef]   [PubMed]  

5 . S. Noda , N. Yamamoto , and A. Sasaki , “ New realization method for three-dimensional photonic crystal in optical wavelength region ,” Jpn. J. Appl. Phys. 35 (7B), L909 – L912 ( 1996 ). [CrossRef]  

6 . 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]  

7 . M. Maldovan and E. L. Thomas , “ Diamond-structured photonic crystals ,” Nat. Mater. 3 (9), 593 – 600 ( 2004 ). [CrossRef]   [PubMed]  

8 . E. Yablonovitch , T. J. 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]  

9 . K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun. 89 , 413 – 416 ( 1994 ). [CrossRef]  

10 . S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett. 65 , 1466 – 1468 ( 1994 ). [CrossRef]  

11 . 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]  

12 . M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B 65 , 165123 ( 2002 ). [CrossRef]  

13 . 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. A 20 , 948 – 954 ( 2003 ). [CrossRef]  

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

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

16 . M. Maldovan , C. K. Ullal , W. C. Carter , and E. L. Thomas , “ Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups ,” Nat. Mater. 2 (10), 664 – 667 ( 2003 ). [CrossRef]   [PubMed]  

17 . J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett. 85 , 4184 – 4186 ( 2004 ). [CrossRef]  

18 . A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op. 1 (5), L3 – L6 ( 1999 ). [CrossRef]  

19 . J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett. 82 , 1652 – 1654 ( 2003 ). [CrossRef]  

20 . 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. Mater. 14 , 2831 – 2833 ( 2002 ). [CrossRef]  

21 . J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met. 148 , 99 – 102 ( 2005 ). [CrossRef]  

22 . M. J. Escuti , J. Qi , and G. P. Crawford , “ Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals ,” Opt. Lett. 28 (7), 522 – 524 ( 2003 ). [CrossRef]   [PubMed]  

23 . N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

References

  • View by:

  1. S. H. Park , D. Qin , and Y. Xia , “ Crystallization of mesoscale particles over large areas ,” Adv. Mater.   10 , 1028 – 1032 ( 1998 ).
    [Crossref]
  2. G. M. Gratson , M. J. Xu , and J. A. Lewis , “ Microporiodis structures - Direct writing of three-dimensional webs ,” Nature   428 , 386 – 386 ( 2004 ).
    [Crossref] [PubMed]
  3. M. Deubel , 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] [PubMed]
  4. S. Kawata , H. B. Sun , T. Tanaka , and K. Takada , “ Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption ,” Nature   412 , 697 – 698 ( 2001 ).
    [Crossref] [PubMed]
  5. S. Noda , N. Yamamoto , and A. Sasaki , “ New realization method for three-dimensional photonic crystal in optical wavelength region ,” Jpn. J. Appl. Phys.   35 (7B), L909 – L912 ( 1996 ).
    [Crossref]
  6. 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]
  7. M. Maldovan and E. L. Thomas , “ Diamond-structured photonic crystals ,” Nat. Mater.   3 (9), 593 – 600 ( 2004 ).
    [Crossref] [PubMed]
  8. E. Yablonovitch , T. J. 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]
  9. K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
    [Crossref]
  10. S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett.   65 , 1466 – 1468 ( 1994 ).
    [Crossref]
  11. 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]
  12. M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B   65 , 165123 ( 2002 ).
    [Crossref]
  13. 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. A   20 , 948 – 954 ( 2003 ).
    [Crossref]
  14. D. N. Sharp , A. J. Turberfield , and R. G. Denning , “ Holographic photonic crystals with diamond symmetry ,” Phys. Rev. B   68 , 205102 ( 2003 ).
    [Crossref]
  15. O. Toader , T. Y. M. Chan , and S. John , “ Photonic band gap architectures for holographic lithography ,” Phys. Rev. Lett.   92 (4), 043905 ( 2004 ).
    [Crossref] [PubMed]
  16. M. Maldovan , C. K. Ullal , W. C. Carter , and E. L. Thomas , “ Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups ,” Nat. Mater.   2 (10), 664 – 667 ( 2003 ).
    [Crossref] [PubMed]
  17. J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett.   85 , 4184 – 4186 ( 2004 ).
    [Crossref]
  18. A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
    [Crossref]
  19. J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett.   82 , 1652 – 1654 ( 2003 ).
    [Crossref]
  20. 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. Mater.   14 , 2831 – 2833 ( 2002 ).
    [Crossref]
  21. J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
    [Crossref]
  22. M. J. Escuti , J. Qi , and G. P. Crawford , “ Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals ,” Opt. Lett.   28 (7), 522 – 524 ( 2003 ).
    [Crossref] [PubMed]
  23. N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

2005 (1)

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

2004 (5)

J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett.   85 , 4184 – 4186 ( 2004 ).
[Crossref]

G. M. Gratson , M. J. Xu , and J. A. Lewis , “ Microporiodis structures - Direct writing of three-dimensional webs ,” Nature   428 , 386 – 386 ( 2004 ).
[Crossref] [PubMed]

M. Deubel , 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] [PubMed]

M. Maldovan and E. L. Thomas , “ Diamond-structured photonic crystals ,” Nat. Mater.   3 (9), 593 – 600 ( 2004 ).
[Crossref] [PubMed]

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

2003 (5)

M. Maldovan , C. K. Ullal , W. C. Carter , and E. L. Thomas , “ Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups ,” Nat. Mater.   2 (10), 664 – 667 ( 2003 ).
[Crossref] [PubMed]

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. A   20 , 948 – 954 ( 2003 ).
[Crossref]

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

J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett.   82 , 1652 – 1654 ( 2003 ).
[Crossref]

M. J. Escuti , J. Qi , and G. P. Crawford , “ Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals ,” Opt. Lett.   28 (7), 522 – 524 ( 2003 ).
[Crossref] [PubMed]

2002 (2)

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B   65 , 165123 ( 2002 ).
[Crossref]

2001 (2)

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]

S. Kawata , H. B. Sun , T. Tanaka , and K. Takada , “ Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption ,” Nature   412 , 697 – 698 ( 2001 ).
[Crossref] [PubMed]

2000 (1)

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]

1999 (1)

A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
[Crossref]

1998 (1)

S. H. Park , D. Qin , and Y. Xia , “ Crystallization of mesoscale particles over large areas ,” Adv. Mater.   10 , 1028 – 1032 ( 1998 ).
[Crossref]

1996 (1)

S. Noda , N. Yamamoto , and A. Sasaki , “ New realization method for three-dimensional photonic crystal in optical wavelength region ,” Jpn. J. Appl. Phys.   35 (7B), L909 – L912 ( 1996 ).
[Crossref]

1994 (2)

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett.   65 , 1466 – 1468 ( 1994 ).
[Crossref]

1991 (1)

E. Yablonovitch , T. J. 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]

Aizenberg, J.

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

Berger, V.

A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
[Crossref]

Biswas, R.

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

Busch, K.

M. Deubel , 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] [PubMed]

Campbell, M.

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]

Carter, W. C.

M. Maldovan , C. K. Ullal , W. C. Carter , and E. L. Thomas , “ Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups ,” Nat. Mater.   2 (10), 664 – 667 ( 2003 ).
[Crossref] [PubMed]

M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B   65 , 165123 ( 2002 ).
[Crossref]

Chaikin, P. M.

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

Chan, C. T.

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

Chan, T. Y. M.

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

Chang, W.-S.

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett.   85 , 4184 – 4186 ( 2004 ).
[Crossref]

Chelnokov, A.

A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
[Crossref]

Courtois, J. Y.

A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
[Crossref]

Crawford, G. P.

M. J. Escuti , J. Qi , and G. P. Crawford , “ Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals ,” Opt. Lett.   28 (7), 522 – 524 ( 2003 ).
[Crossref] [PubMed]

J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett.   82 , 1652 – 1654 ( 2003 ).
[Crossref]

Denning, R. G.

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

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]

Deubel, M.

M. Deubel , 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] [PubMed]

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Escuti, M. J.

Fan, S. H.

S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett.   65 , 1466 – 1468 ( 1994 ).
[Crossref]

Fontecchio, A. K.

J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett.   82 , 1652 – 1654 ( 2003 ).
[Crossref]

Freymann, G. Von

M. Deubel , 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] [PubMed]

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Gmitter, T. J.

E. Yablonovitch , T. J. 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]

Gratson, G. M.

G. M. Gratson , M. J. Xu , and J. A. Lewis , “ Microporiodis structures - Direct writing of three-dimensional webs ,” Nature   428 , 386 – 386 ( 2004 ).
[Crossref] [PubMed]

Harrison, M. T.

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]

Hermatschweiler, M.

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Ho, K. M.

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

Joannopoulos, J. D.

S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett.   65 , 1466 – 1468 ( 1994 ).
[Crossref]

John, S.

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

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]

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Kawata, S.

S. Kawata , H. B. Sun , T. Tanaka , and K. Takada , “ Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption ,” Nature   412 , 697 – 698 ( 2001 ).
[Crossref] [PubMed]

Lee, S.-K.

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

Leung, K. M.

E. Yablonovitch , T. J. 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]

Lewis, J. A.

G. M. Gratson , M. J. Xu , and J. A. Lewis , “ Microporiodis structures - Direct writing of three-dimensional webs ,” Nature   428 , 386 – 386 ( 2004 ).
[Crossref] [PubMed]

Lourtioz, J. M.

A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
[Crossref]

Maldovan, M.

M. Maldovan and E. L. Thomas , “ Diamond-structured photonic crystals ,” Nat. Mater.   3 (9), 593 – 600 ( 2004 ).
[Crossref] [PubMed]

M. Maldovan , C. K. Ullal , W. C. Carter , and E. L. Thomas , “ Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups ,” Nat. Mater.   2 (10), 664 – 667 ( 2003 ).
[Crossref] [PubMed]

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. A   20 , 948 – 954 ( 2003 ).
[Crossref]

M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B   65 , 165123 ( 2002 ).
[Crossref]

Meade, R. D.

S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett.   65 , 1466 – 1468 ( 1994 ).
[Crossref]

Megens, M.

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

Moon, J. H.

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett.   85 , 4184 – 4186 ( 2004 ).
[Crossref]

Noda, S.

S. Noda , N. Yamamoto , and A. Sasaki , “ New realization method for three-dimensional photonic crystal in optical wavelength region ,” Jpn. J. Appl. Phys.   35 (7B), L909 – L912 ( 1996 ).
[Crossref]

Ozin, G. A.

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Park, S. H.

S. H. Park , D. Qin , and Y. Xia , “ Crystallization of mesoscale particles over large areas ,” Adv. Mater.   10 , 1028 – 1032 ( 1998 ).
[Crossref]

Pereira, S.

M. Deubel , 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] [PubMed]

Perez-Willard, F.

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Pine, D. J.

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett.   85 , 4184 – 4186 ( 2004 ).
[Crossref]

Qi, J.

J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett.   82 , 1652 – 1654 ( 2003 ).
[Crossref]

M. J. Escuti , J. Qi , and G. P. Crawford , “ Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals ,” Opt. Lett.   28 (7), 522 – 524 ( 2003 ).
[Crossref] [PubMed]

Qin, D.

S. H. Park , D. Qin , and Y. Xia , “ Crystallization of mesoscale particles over large areas ,” Adv. Mater.   10 , 1028 – 1032 ( 1998 ).
[Crossref]

Rowson, S.

A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
[Crossref]

Russel, W. B.

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

Sasaki, A.

S. Noda , N. Yamamoto , and A. Sasaki , “ New realization method for three-dimensional photonic crystal in optical wavelength region ,” Jpn. J. Appl. Phys.   35 (7B), L909 – L912 ( 1996 ).
[Crossref]

Sharp, D. N.

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

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]

Sigalas, M.

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

Small, A.

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

Soukoulis, C. M.

M. Deubel , 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] [PubMed]

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band-gaps in 3-dimensions -New layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

Sousa, M. E.

J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett.   82 , 1652 – 1654 ( 2003 ).
[Crossref]

Sun, H. B.

S. Kawata , H. B. Sun , T. Tanaka , and K. Takada , “ Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption ,” Nature   412 , 697 – 698 ( 2001 ).
[Crossref] [PubMed]

Takada, K.

S. Kawata , H. B. Sun , T. Tanaka , and K. Takada , “ Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption ,” Nature   412 , 697 – 698 ( 2001 ).
[Crossref] [PubMed]

Tanaka, T.

S. Kawata , H. B. Sun , T. Tanaka , and K. Takada , “ Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption ,” Nature   412 , 697 – 698 ( 2001 ).
[Crossref] [PubMed]

Tereault, N.

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Thomas, E. L.

M. Maldovan and E. L. Thomas , “ Diamond-structured photonic crystals ,” Nat. Mater.   3 (9), 593 – 600 ( 2004 ).
[Crossref] [PubMed]

M. Maldovan , C. K. Ullal , W. C. Carter , and E. L. Thomas , “ Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups ,” Nat. Mater.   2 (10), 664 – 667 ( 2003 ).
[Crossref] [PubMed]

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. A   20 , 948 – 954 ( 2003 ).
[Crossref]

M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B   65 , 165123 ( 2002 ).
[Crossref]

Toader, O.

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

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]

Turberfield, A. J.

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

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]

Ullal, C. K.

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. A   20 , 948 – 954 ( 2003 ).
[Crossref]

M. Maldovan , C. K. Ullal , W. C. Carter , and E. L. Thomas , “ Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups ,” Nat. Mater.   2 (10), 664 – 667 ( 2003 ).
[Crossref] [PubMed]

Urbas, A. M.

M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B   65 , 165123 ( 2002 ).
[Crossref]

Villeneuve, P. R.

S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett.   65 , 1466 – 1468 ( 1994 ).
[Crossref]

Wegener, M.

M. Deubel , 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] [PubMed]

N. Tereault , G. von Freymann , M. Deubel , M. Hermatschweiler , F. Perez-Willard , S. John , M. Wegener , and G. A. Ozin , “ New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates. ,” Adv. Mater. in press ( 2005 ).

Wiltzius, P.

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

Wohlgemuth, M.

Xia, Y.

S. H. Park , D. Qin , and Y. Xia , “ Crystallization of mesoscale particles over large areas ,” Adv. Mater.   10 , 1028 – 1032 ( 1998 ).
[Crossref]

Xu, M. J.

G. M. Gratson , M. J. Xu , and J. A. Lewis , “ Microporiodis structures - Direct writing of three-dimensional webs ,” Nature   428 , 386 – 386 ( 2004 ).
[Crossref] [PubMed]

Yablonovitch, E.

E. Yablonovitch , T. J. 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]

Yamamoto, N.

S. Noda , N. Yamamoto , and A. Sasaki , “ New realization method for three-dimensional photonic crystal in optical wavelength region ,” Jpn. J. Appl. Phys.   35 (7B), L909 – L912 ( 1996 ).
[Crossref]

Yang, S.

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

Yang, S.-M.

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett.   85 , 4184 – 4186 ( 2004 ).
[Crossref]

Yi, G.-R.

J. H. Moon , A. Small , G.-R. Yi , S.-K. Lee , W.-S. Chang , D. J. Pine , and S.-M. Yang , “ Patterned polymer photonic crystals using soft lithography and holographic lithography ,” Synth. Met.   148 , 99 – 102 ( 2005 ).
[Crossref]

Yufa, N.

M. Maldovan , A. M. Urbas , N. Yufa , W. C. Carter , and E. L. Thomas , “ Photonic properties of bicontinuous cubic microphases ,” Phys. Rev. B   65 , 165123 ( 2002 ).
[Crossref]

Adv. Mater. (1)

S. H. Park , D. Qin , and Y. Xia , “ Crystallization of mesoscale particles over large areas ,” Adv. Mater.   10 , 1028 – 1032 ( 1998 ).
[Crossref]

Appl. Phys. Lett. (3)

S. H. Fan , P. R. Villeneuve , R. D. Meade , and J. D. Joannopoulos , “ Design of 3-dimensional photonic crystals at submicron length scales ,” Appl. Phys. Lett.   65 , 1466 – 1468 ( 1994 ).
[Crossref]

J. H. Moon , S.-M. Yang , D. J. Pine , and W.-S. Chang , “ Multiple-exposure holographic lithography with phase shift ,” Appl. Phys. Lett.   85 , 4184 – 4186 ( 2004 ).
[Crossref]

J. Qi , M. E. Sousa , A. K. Fontecchio , and G. P. Crawford , “ Temporally multiplexed holographic polymer-dispersed liquid crystals ,” Appl. Phys. Lett.   82 , 1652 – 1654 ( 2003 ).
[Crossref]

Chem. Mater. (1)

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. Mater.   14 , 2831 – 2833 ( 2002 ).
[Crossref]

J. Opt. A-Pure Appl. Op. (1)

A. Chelnokov , S. Rowson , J. M. Lourtioz , V. Berger , and J. Y. Courtois , “ An optical drill for the fabrication of photonic crystals ,” J. Opt. A-Pure Appl. Op.   1 (5), L3 – L6 ( 1999 ).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Translation of (a) FCC interference pattern in the [111]direction and (b) BCC interference in the [210] direction.
Fig. 2.
Fig. 2. The relative position of the FCC interference pattern (red) and the shifted pattern (blue) in the [111] direction by (a) 0.20d(1,1,1), (b) 0.25d(1,1,1), and (c) 0.29d(1,1,1). The level surface of each double-exposed FCC interference pattern with a filling fraction of 0.22 is shown in (d -f) for their respective cases.
Fig. 3.
Fig. 3. Intensity profile of 8-term and 4-term interference patterns along [111] direction
Fig. 4.
Fig. 4. The relative position of the BCC interference pattern (red) and the shifted pattern (blue) in the [210] direction by (a) 0.20d (1,1,1), (b) 0.25d (1,1,1), and (c) 0.29d (1,1,1). The level surface of each double-exposed BCC interference pattern with a filling fraction of 0.20 is shown in (d-f) for their respective cases.
Fig. 5.
Fig. 5. Complete PBG of double-exposed (a) FCC and (b) BCC interference patterns as a function of the normalized pattern shift in [111] and [210], respectively.

Equations (17)

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I = n = 1 4 E n 2 + m < n 4 E n E m ε n · ε m * cos [ ( k n k m ) · r + ( ϕ n 0 ϕ m 0 ) ] .
I nm = E n E m ε n · ε m * cos [ ( k n k m ) · r + ( ϕ n 0 ϕ m 0 ) + ( ϕ n ϕ m ) ] .
I nm = E n E m ε n · ε m * cos [ ( k n k m ) · ( r + r ) + ( ϕ n 0 ϕ m 0 ) ] .
( ϕ n ϕ m ) = ( k n k m ) · r .
I nm ~ cos [ 2 π d ( x y + z ) + ( ϕ 1 ϕ 3 ) ] + cos [ 2 π d ( x + y + z ) + ( ϕ 1 ϕ 4 ) ]
+ cos [ 2 π d ( x y + z ) + ( ϕ 2 ϕ 3 ) ] + cos [ 2 π d ( x + y + z ) + ( ϕ 2 ϕ 4 ) ]
I nm ~ cos [ 4 π d ( y + z ) + ( ϕ 1 ϕ 2 ) ] + cos [ 4 π d ( x + y ) + ( ϕ 1 ϕ 3 ) ]
+ cos [ 4 π d ( x + z ) + ( ϕ 1 ϕ 4 ) ] + cos [ 4 π d ( x z ) + ( ϕ 2 ϕ 3 ) ]
+ cos [ 4 π d ( x y ) + ( ϕ 2 ϕ 4 ) ] + cos [ 4 π d ( y + z ) + ( ϕ 3 ϕ 4 ) ]
I nm ~ cos [ 2 π d ( x y + z ) ] + cos [ 2 π d ( x + y + z ) ]
+ cos [ 2 π d ( x y + z ) ] + cos [ 2 π d ( x + y + z ) ]
+ sin [ 2 π d ( x y + z ) ] sin [ 2 π d ( x + y + z ) ]
sin [ 2 π d ( x y + z ) ] + sin [ 2 π d ( x + y + z ) ]
I nm ~ cos [ 4 π d ( x + y ) ] + cos [ 4 π d ( y + z ) ]
+ cos [ 4 π d ( y + z ) ] + cos [ 4 π d ( x y ) ]
+ sin [ 4 π d ( x + y ) ] sin [ 4 π d ( y + z ) ]
sin [ 4 π d ( y + z ) ] sin [ 4 π d ( x y ) ]

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