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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 9 — May. 2, 2005
  • pp: 3348–3354
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Square spiral 3D photonic bandgap crystals at telecommunications frequencies

Martin O. Jensen and Michael J. Brett  »View Author Affiliations


Optics Express, Vol. 13, Issue 9, pp. 3348-3354 (2005)
http://dx.doi.org/10.1364/OPEX.13.003348


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Abstract

We present evidence of complete, three-dimensional photonic bandgaps in obliquely deposited thin films with a porous microstructure of tetragonally arranged square spirals. We further present a capability to engineer the bandgap center to wavelengths as low as 1.65 µm, with bandgap widths of up to 10.9%. Using new deposition methods that provide detailed control over the photonic crystal dimensions and morphology, this approach allows advanced photonic crystal architectures to be realized over large scales with uncomplicated fabrication technology.

© 2005 Optical Society of America

1. Introduction

Kennedy et al. demonstrated the first fabrication of square spiral PBC thin film structures using GLAD [12

12. S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of tetragonal square spiral photonic crystals,” Nano Lett. 2, 59–62 (2002). [CrossRef]

], and subsequently provided optical characterization of the structures [13

13. S. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photonics and Nanostructures 1, 37–42 (2003). [CrossRef]

]. Based on reflectance spectra, they found evidence of a photonic bandgap centered at 2.7 µm in a silicon GLAD thin film of square spirals arranged in a square array with a period of 1.0 µm. Yet, the optical data did not confirm the presence of a complete bandgap in all three dimensions, and the bandgap was smaller than expected due to structural disorder. Seet et. al. recently presented the fabrication of precise square spiral PBC structures in SU-8 resist using two-photon laser writing, and provided optical results indicating stop bands at mid infrared frequencies. However, although this technique is flexible and permits the incorporation of various crystal defects, the approach is time consuming and yields only small-scale crystals on the order of tens of micrometers. Furthermore, the use of two-photon laser writing restricts the crystal material to photoresists with low refractive indices, thus reducing the potential bandgap effect and limiting the range of achievable stop band frequencies [14

14. L. L. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, “Three-dimensional spiral-architecture photonic crystals obtained by direct laser writing,” Adv. Mat. 17, 541–545 (2005). [CrossRef]

].

In this paper we present methods to improve the microstructure and uniformity of GLAD-based PBCs, and demonstrate new optical measurements that deliver the most conclusive evidence yet of a complete, 3D bandgap in the square spiral architecture, at a higher frequency and with a larger bandgap than previously reported.

2. Fabrication

The GLAD thin film deposition method works by collinear vapor impingement at highly oblique angles relative to the substrate normal (typically greater than 75°). In the absence of substrate heating, geometrical shadowing becomes the dominant film growth mechanism and leads to extremely voided film structures with mean densities below 40% of bulk values [15

15. K. J. Robbie and M. J. Brett, “Method of depositing shadow sculpted thin films,” U. S. Patent 5,866,204, 2 February 1999.

,16

16. D. Vick, L. J. Friedrich, S. K. Dew, M. J. Brett, K. Robbie, M. Seto, and T. Smy, “Self-shadowing and surface diffusion effects in obliquely deposited thin films,” Thin Solid Films 339, 88–94 (1999). [CrossRef]

]. Furthermore, the lack of significant surface or bulk diffusion causes the initial substrate nuclei to evolve into a columnar microstructure. Through computer controlled substrate rotation, the basic columns can be engineered into a variety of unique shapes, including square spirals.

To obtain the periodic spiral arrangement necessary for a photonic crystal, a topography of vapor intercepting seeds must first be prepared on the substrate to enforce nucleation at predetermined sites. We have employed direct write lithography to obtain complete design freedom for easy fabrication of various prototype substrate topographies, while maintaining sub micrometer resolution. Our best results were obtained with a Heidelberg DWL 200 laser direct write lithography system, where careful optimization of the krypton-ion laser and beam optics enabled us to produce highly uniform arrays of substrate seeds in Clariant AZ-1518 resist with resolutions better than 250 nm over areas as large as 40 mm2 [17

17. M. O. Jensen and M. J. Brett, “Periodically structured glancing angle deposition thin films,” IEEE Trans. Nanotechnol. 4, 269–277 (2005). [CrossRef]

].

Following substrate topography preparation, the only other step in the fabrication of a square spiral PBC structure is the GLAD process itself. For all the PBC structures described here we used a CHA Instruments e-beam evaporator fitted with a motorized dual axis substrate holder for adjustment of the required substrate tilt and rotation. All PBC structures were deposited using silicon, whose low absorption and high dielectric constant are well suited for PBC purposes. Typical deposition pressures were 0.4 mPa, with deposition rates on the order of 1 to 2 nm/s.

Traditionally, square spiral GLAD films have been deposited by simply rotating the substrate 90° at regular intervals, with four such turns constituting one complete winding of the square spiral [12

12. S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of tetragonal square spiral photonic crystals,” Nano Lett. 2, 59–62 (2002). [CrossRef]

]. However, this approach implies aligning the unit vectors of the tetragonal lattice of substrate surface seeds with the incidence direction of the collimated vapor. Since the GLAD process relies solely on geometrical shadowing, and such shadowing occurs only in the plane spanned by the vapor incidence direction and the substrate normal, there is then no control over the film microstructure perpendicular to the vapor incidence direction. The result is broadening of the spiral arms, distortion of the arm cross-section, and bifurcation of the spirals at the square spiral corners, which degrade the optical characteristics of the PBC structure [13

13. S. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photonics and Nanostructures 1, 37–42 (2003). [CrossRef]

].

In order to eliminate these growth effects we developed two new substrate motion algorithms for GLAD square spiral film deposition. The so-called PhiSweep algorithm –previously described in ref. [18

18. M. O. Jensen and M. J. Brett, “Porosity engineering in glancing angle deposition thin films,” Appl. Phys. A 80, 763–768 (2005). [CrossRef]

] –works by oscillating the substrate from side to side about a central axis, thus decoupling the spiral growth direction (the central oscillation axis) from the vapor incidence direction. This approach significantly suppresses spiral arm broadening and cross-sectional distortion, thus yielding a much more uniform PBC structure.

Even better film microstructures were obtained by the second new substrate motion algorithm, in which the substrate is rotated to introduce a slight but permanent misalignment between the vapor incidence angle and the substrate seed lattice. Although this misalignment represents a minor distortion of the ideal square spiral PBC architecture, it also breaks the shadowing anisotropy within the growing GLAD film and hence eliminates almost all of the aforementioned growth problems. Figure 1 shows examples of the resulting film structures, in this case for silicon GLAD films deposited at a vapor incidence angle of 85° onto soda lime glass substrates with a 0.74 µm period tetragonal lattice of seeds. The morphology of these GLAD films is very close to the ideal square spiral PBC architecture described by Toader and John [7

7. O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic bandgap crystals,” Science 292, 1133–1135 (2001). [CrossRef] [PubMed]

,8

8. O. Toader and S. John, “Square spiral photonic bandgap crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002). [CrossRef]

].

Fig. 1. Scanning electron micrographs of silicon square spiral thin films deposited using the GLAD technique. The tetragonal arrangement required for the square spiral PBC architecture is achieved by preparing the substrates with a periodic topography of small seeds prior to deposition.

3. Optical characteristics

In the wavelength range of a photonic bandgap, an otherwise transparent material must feature simultaneous high reflectance and low transmittance. However, transmittance measurements have not been performed in any previously published reports on GLAD-based square spiral PBCs. We therefore examined the photonic bandgap response of the improved square spiral GLAD films using a Thermo Nicolet Nexus 670 Fourier transform infrared (FTIR) spectrometer, with a resolution of 1 nm and a beam spot size of approximately 1 mm. A typical transmittance spectrum is shown in Fig. 2. This spectrum was obtained at normal light incidence on the film previously shown in Fig. 1(a), and was corrected for losses in the soda lime glass substrate. The GLAD film was 10.5 µm thick, and had a volume fill factor of 0.21. A band of low transmittance is clearly observed for the wavelength range 1.4 µm to 2.1 µm. Since the GLAD films still contain minor imperfections relative to the ideal square spiral PBC structure, random scattering over the spot size leads to some transmission inside the stop band, as well as to tapering of the high wavelength band edge. The small fringes at the bottom of the stop band are caused by interference in the GLAD film, with the fringe separation given by the film thickness and the effective dielectric constant of the film (taking the high porosity and slight silicon dioxide content of the film into account).

Fig. 2. Transmittance spectrum of the periodic square spiral GLAD film previously shown in Fig. 1(a). The low-transmittance band from 1.4 µm to 2.1 µm overlaps with the high-reflectance bands shown in Fig. 3, and is indicative of the presence of a photonic bandgap.

For the same GLAD PBC sample, Fig. 3 shows a series of FTIR reflectance spectra with external angles of incidence from 30 to 60°. (With the instrument used here, reflectance measurements at 0° could not be performed.) Each reflectance measurement was performed against a matching reference sample of aperiodic silicon GLAD square spirals. This method was preferred over absolute measurements against an “ideal” reference (such as a polished gold surface), since absolute measurements would blend the intrinsic spectral features of the high porosity silicon GLAD film with the spectral response attributable to the 3D periodic structure of square spirals, and hence prevent isolation of the photonic bandgap characteristics. In consequence, the obtained PBC spectra are relative rather than absolute, and may exhibit reflectance values larger than 100% (the reflectance of the reference samples was 60–70 %). At every incidence angle in Fig. 3, a distinct high-reflectance band is observed. These bands overlap each other as well as the transmission stop band in Fig. 2, and they maintain their position even as the angle of incidence is altered. Indeed, the high frequency bandgap edges for the 45 and 60° spectra coincide perfectly with the normal incidence transmittance spectrum for the same PBC in Fig. 2. Meanwhile, the more blurred low frequency edge of the transmittance spectrum, caused by increased scattering in this measurement setup, may misleadingly indicate a lower frequency bandgap center than is true.

Fig. 3. Reflectance spectra for the same square spiral GLAD PBC as examined in Fig. 2, for various external light incidence angles. The photonic bandgap position remains constant, indicating that the bandgap is complete with respect to crystal direction.

The simultaneous high reflectance and low transmittance, and the invariance of the stop band frequencies with respect to the light incidence direction, are fundamental and required evidence in support of GLAD square spiral PBCs having complete, three-dimensional photonic bandgaps.

Since the crystal directions probed here correspond to the Γ-Z-R-X plane in the irreducible Brillouin zone of the tetragonal square spiral PBC, it is likely that the pinched high frequency edge of the 30° reflectance spectrum shown in Fig. 3 results from the similar high frequency pinch in the theoretical PBC dispersion relation in the Γ-R crystal direction [12

12. S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of tetragonal square spiral photonic crystals,” Nano Lett. 2, 59–62 (2002). [CrossRef]

]. We also probed the azimuthal dependence of the reflectance, in the Γ-Z-A-M plane (spectra not included here), and still found the photonic bandgap maintained, but now with the bandgap center tending slightly toward a higher frequency location (in continued accordance with theory [12

12. S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of tetragonal square spiral photonic crystals,” Nano Lett. 2, 59–62 (2002). [CrossRef]

]).

Finally, in order for a photonic bandgap to be complete, the bandgap must be maintained for all polarizations of the impinging light. Figure 4 shows reflectance spectra for different polarizations for the previously discussed GLAD square spiral PBC, at an external light incidence angle of 30°. A high reflectance region is maintained for both s and p and the intermediate polarization directions (although for p polarized light the reflectance is abnormally low due to the measurement setup), and the position of this stop band is invariant to the polarization direction. The impact of light polarization was also investigated at other angles of light incidence, with the bandgap location still found to remain constant irrespective of the polarization direction. This shows that a complete bandgap exists for all polarizations, and is the first experimental verification of a GLAD square spiral photonic bandgap being complete. It also emphasizes the advantage of 3D PBCs over 2D PBCs, with the latter in many cases yielding bandgaps for only one polarization.

Fig. 4. Reflectance spectra for a square spiral GLAD PBC for different linear polarizations of the impinging light (s, p, and intermediate polarizations). The measurements were performed at an external light incidence angle of 30°. The photonic bandgap remains in place for all polarizations, indicating that it is a complete bandgap.

We also sought to confirm that the spectral features indeed derive from the tetragonal arrangement of square spirals, and not just from some inherent artifact of the substrate, the substrate seed topography, or the material making up the GLAD sample. We thus analyzed each of the sample constituents, and investigated the response of an identical GLAD sample without the substrate seed topography, consisting of randomly arranged silicon square spirals. For both reflectance and transmittance measurements we found that no individual or composite part of the GLAD square spiral sample system was able to account for the spectral stop band observations. That is, coinciding high reflectance and low transmittance bands were found only for the periodic, tetragonally arranged square spiral GLAD films. This validates that the observed spectral features – such as the opacity demonstrated by the spectrum in Fig. 2 – are those of photonic bandgaps introduced by the square spiral film structure.

Using a ‘full width, half maximum’ approach, the complete bandgap for the GLAD square spiral PBC examined here was found to be centered at 1.65 µm and have a bandgap width of 180 nm (or a relative width of 10.9%). When taking the volume fill factor of 0.21 of the GLAD film into account, the location of the experimental bandgap is in good agreement with the theoretical band calculations for similar square spiral PBCs previously performed by Toader and John [7

7. O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic bandgap crystals,” Science 292, 1133–1135 (2001). [CrossRef] [PubMed]

,8

8. O. Toader and S. John, “Square spiral photonic bandgap crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002). [CrossRef]

]. Furthermore, the bandgap width is near the theoretically predicted, optimized bandgap width of 12.4% for this particular square spiral structure [8

8. O. Toader and S. John, “Square spiral photonic bandgap crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002). [CrossRef]

]. However, a more detailed, quantitative comparison of the experimental data with theoretical reflectivity predictions will require dedicated numerical modeling of the new GLAD square spiral structures.

When the same ‘full width half maximum’ method is applied to the best previously published optical data for a square spiral GLAD PBC [13

13. S. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photonics and Nanostructures 1, 37–42 (2003). [CrossRef]

], a partial bandgap of 6.4% centered at 2.7 µm is found. The GLAD square spiral PBC fabricated and analyzed here thus represents a large increase in the available bandgap width, and a center frequency that is significantly higher than previously reported as well as close to the third telecommunications window at 1.55 µm.

The improved photonic bandgap properties derive from the better square spiral film structure achieved using the new GLAD substrate motion algorithms discussed above. In particular, the greater uniformity in the shape and dimensions of the spirals throughout the films reduces disorder and hence scattering in the films, and the greater control over the film microstructure makes it easier to approach the theoretically ideal square spiral PBC architecture. There is still room for enhancement of the optical quality of GLAD square spiral PBCs, however, as evidenced by the lack of complete extinction of transmission inside bandgaps and the gradually tapering rather than vertical bandgap edges.

With arbitrary substrate topographies achievable using direct write lithography, and the ability of the new GLAD substrate motion algorithms to provide greater control over the exact dimensions of the square spirals, the work presented here enables engineering of the bandgap location and width of GLAD based square spiral PBCs. We have thus successfully fabricated and analyzed a number of other GLAD square spiral films with photonic bandgaps centered from 1.7 µm to 3.2 µm. Crucially, this bandgap engineering capability is achieved simply by changing the substrate seed lattice and the deposition settings, while maintaining a fabrication approach that is much easier than any other 3D PBC technology, even for large scale crystals.

4. Conclusions

Through the development of new substrate motion algorithms, we have shown that the GLAD thin film deposition technique is capable of fabricating uniform tetragonal square spiral PBC structures. We have found evidence of complete, three-dimensional photonic bandgaps in the GLAD square spiral films, with improved bandgap widths close to the theoretical maximum. Higher bandgap frequencies than previously reported have also been achieved, approaching the near infrared telecommunications range. When taking the film volume fill factor into account, the measured bandgap center corresponds to theoretical predictions.

Beyond the optical characteristics of GLAD square spiral PBCs, their key advantage in comparison with other 3D PBC architectures is the relative ease of fabrication. With only one surface topography fabrication step and one thin film deposition step, GLAD PBC fabrication relies on well-established semiconductor technologies. Furthermore, the GLAD process offers unique possibilities for defect engineering, as required for subsequent functionalization of the PBCs. Numerical modeling has shown that GLAD based PBCs yield superior light localization for waveguiding [19

19. A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical microchip,” Phys. Rev. Lett. 90, 123901, 2004. [CrossRef]

], and methods for the introduction of intentional defects in GLAD PBCs without the need for post deposition processing have already been published [20

20. M. O. Jensen and M. J. Brett, “Functional pattern engineering in glancing angle deposition thin films,” J. Nanosci. Nanotechnol. (to be published). [PubMed]

]. GLAD square spiral PBCs thus constitute a promising approach to the eventual realization of full 3D PBC devices.

Acknowledgments

The authors acknowledge George Braybrook of the Department of Earth and Atmospheric Sciences for SEM imaging. Financial support for our research was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Alberta Informatics Circle of Research Excellence (iCORE), the Alberta Ingenuity Fund, and Micralyne, Inc.

References and Links

1.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

2.

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

3.

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, “Nanofabricated three dimensional photonic crystal operating at optical wavelengths,” Phys. Scripta T68, 17–20 (1996). [CrossRef]

4.

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, Nature394, 251–253 (1998). [CrossRef]

5.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. E. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, Nature405, 437–440 (2000). [CrossRef] [PubMed]

6.

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999). [CrossRef]

7.

O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic bandgap crystals,” Science 292, 1133–1135 (2001). [CrossRef] [PubMed]

8.

O. Toader and S. John, “Square spiral photonic bandgap crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002). [CrossRef]

9.

K. Robbie, M. J. Brett, and A. Lakhtakia, “Chiral sculptured thin films,” Nature 384, 616 (1996). [CrossRef]

10.

K. Robbie and M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997). [CrossRef]

11.

K. Robbie, J. C. Sit, and M. J. Brett, “Advanced techniques for glancing angle deposition,” J. Vac. Sci. Technol. B 16, 1115–1122 (1998). [CrossRef]

12.

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, “Fabrication of tetragonal square spiral photonic crystals,” Nano Lett. 2, 59–62 (2002). [CrossRef]

13.

S. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photonics and Nanostructures 1, 37–42 (2003). [CrossRef]

14.

L. L. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, “Three-dimensional spiral-architecture photonic crystals obtained by direct laser writing,” Adv. Mat. 17, 541–545 (2005). [CrossRef]

15.

K. J. Robbie and M. J. Brett, “Method of depositing shadow sculpted thin films,” U. S. Patent 5,866,204, 2 February 1999.

16.

D. Vick, L. J. Friedrich, S. K. Dew, M. J. Brett, K. Robbie, M. Seto, and T. Smy, “Self-shadowing and surface diffusion effects in obliquely deposited thin films,” Thin Solid Films 339, 88–94 (1999). [CrossRef]

17.

M. O. Jensen and M. J. Brett, “Periodically structured glancing angle deposition thin films,” IEEE Trans. Nanotechnol. 4, 269–277 (2005). [CrossRef]

18.

M. O. Jensen and M. J. Brett, “Porosity engineering in glancing angle deposition thin films,” Appl. Phys. A 80, 763–768 (2005). [CrossRef]

19.

A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical microchip,” Phys. Rev. Lett. 90, 123901, 2004. [CrossRef]

20.

M. O. Jensen and M. J. Brett, “Functional pattern engineering in glancing angle deposition thin films,” J. Nanosci. Nanotechnol. (to be published). [PubMed]

OCIS Codes
(160.4670) Materials : Optical materials
(220.4000) Optical design and fabrication : Microstructure fabrication
(290.4210) Scattering : Multiple scattering
(310.1860) Thin films : Deposition and fabrication
(310.6860) Thin films : Thin films, optical properties

ToC Category:
Research Papers

History
Original Manuscript: March 22, 2005
Revised Manuscript: April 18, 2005
Published: May 2, 2005

Citation
Martin Jensen and Michael Brett, "Square spiral 3D photonic bandgap crystals at telecommunications frequencies," Opt. Express 13, 3348-3354 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-9-3348


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References

  1. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  2. S. John, �??Strong localization of photonic in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, �??Nanofabricated three dimensional photonic crystal operating at optical wavelengths,�?? Phys. Scripta T68, 17-20 (1996). [CrossRef]
  4. 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, Nature 394, 251-253 (1998). [CrossRef]
  5. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. E. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, Nature 405, 437-440 (2000). [CrossRef] [PubMed]
  6. S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B 60, 5751-5758 (1999). [CrossRef]
  7. O. Toader and S. John, �??Proposed square spiral microfabrication architecture for large three-dimensional photonic bandgap crystals,�?? Science 292, 1133-1135 (2001). [CrossRef] [PubMed]
  8. O. Toader and S. John, �??Square spiral photonic bandgap crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,�?? Phys. Rev. E 66, 016610 (2002). [CrossRef]
  9. K. Robbie, M. J. Brett, and A. Lakhtakia, �??Chiral sculptured thin films,�?? Nature 384, 616 (1996). [CrossRef]
  10. K. Robbie and M. J. Brett, �??Sculptured thin films and glancing angle deposition: Growth mechanics and applications,�?? J. Vac. Sci. Technol. A 15, 1460-1465 (1997). [CrossRef]
  11. S. R. Kennedy, M. J. Brett, O. Toader, and S. John, �??Fabrication of tetragonal square spiral photonic crystals,�?? Nano Lett. 2, 59-62 (2002). [CrossRef]
  12. S. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, �??Optical properties of a three-dimensional silicon square spiral photonic crystal,�?? Photonics and Nanostructures 1, 37-42 (2003). [CrossRef]
  13. L. L. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, �??Three-dimensional spiral-architecture photonic crystals obtained by direct laser writing,�?? Adv. Mat. 17, 541-545 (2005). [CrossRef]
  14. K. J. Robbie and M. J. Brett, �??Method of depositing shadow sculpted thin films,�?? U. S. Patent 5,866,204, 2 February 1999.
  15. D. Vick, L. J. Friedrich, S. K. Dew, M. J. Brett, K. Robbie, M. Seto, and T. Smy, �??Self-shadowing and surface diffusion effects in obliquely deposited thin films,�?? Thin Solid Films 339, 88-94 (1999). [CrossRef]
  16. M. O. Jensen and M. J. Brett, �??Periodically structured glancing angle deposition thin films,�?? IEEE Trans. Nanotechnol. 4, 269-277 (2005). [CrossRef]
  17. M. O. Jensen and M. J. Brett, �??Porosity engineering in glancing angle deposition thin films,�?? Appl. Phys. A 80, 763-768 (2005). [CrossRef]
  18. A. Chutinan, S. John, and O. Toader, �??Diffractionless flow of light in all-optical microchip,�?? Phys. Rev. Lett. 90, 123901, 2004. [CrossRef]
  19. M. O. Jensen and M. J. Brett, �??Functional pattern engineering in glancing angle deposition thin films,�?? J. Nanosci. Nanotechnol. (to be published). [PubMed]
  20. K. Robbie, J. C. Sit, and M. J. Brett, �??Advanced techniques for glancing angle deposition,�?? J. Vac. Sci. Technol. B 16, 1115-1122 (1998).

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