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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 17 — Aug. 22, 2005
  • pp: 6454–6459
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Colloidal photonic crystal cladded optical fibers: Towards a new type of photonic band gap fiber

Jianzhao Li, Peter R. Herman, Christopher E. Valdivia, Vladimir Kitaev, and Geoffrey A. Ozin  »View Author Affiliations


Optics Express, Vol. 13, Issue 17, pp. 6454-6459 (2005)
http://dx.doi.org/10.1364/OPEX.13.006454


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Abstract

A facile approach of fabricating a new type of hollow photonic band gap fibers is proposed. Templates for generating such fibers are demonstrated by a complete and uniform coating of a standard silica optical fiber (125 μm diameter) with a three-dimensional colloidal photonic crystal through isothermal heating evaporation induced self-assembly. The photonic crystal cylindrical annulus is characterized by optical and scanning electron microscopy, and is found to yield a 1.4-μm stop band by optical reflection and transmission spectroscopy. The results also demonstrate a practical means of enveloping macro- or micro-curved surfaces with three-dimensional photonic crystals, a task that is geometrically challenging by other photonic crystal fabrication methods.

© 2005 Optical Society of America

1. Introduction

Traditional silica optical fibers have been exploited in widely diverse applications such as telecommunication, sensing, optical imaging, material processing, medical diagnostics and surgery. Nevertheless, there are two inherent drawbacks with such optical fibers. The first is associated with the optical properties of the solid core where absorption, scattering and dispersion limit long distance signal transmission and prevent the delivery of high intensity ultrashort laser pulses. The second drawback is the low refractive index contrast (∆n ~ 5×10-3) of silica waveguides that causes large bending loss when small radius turns are required in compact integrated optical systems. One promising approach to overcome these two limitations are photonic band gap fibers (PBGFs) having hollow core guiding structures. Here, light in a particular frequency range, called the photonic band gap or stop band, is reflected by a surrounding photonic crystal medium [1

1. See, for example, J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light (Princeton University Press, Princeton, 1995).

]. One type of hollow-core PBGF is made by drawing a preform of an ordered stack of silica capillaries to generate a two-dimensional photonic crystal having periodically distributed airhole columns [2–4

2. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995). [CrossRef]

]. The other type of PBGF is a Bragg fiber that uses periodic concentric dielectric structures coated on the inside surface of a hollow core to form a one-dimensional photonic crystal reflector [5–8

5. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998). [CrossRef] [PubMed]

].

In this report, we introduce a method of fabricating a new type of PBGF which is based on three-dimensional (3-D) photonic crystals. The procedure to generate such PBGFs involves first making an annular template by coating a cylindrical silica fiber with a silica colloidal photonic crystal, which we report here. By infiltrating the colloidal crystal with silicon in the interstitial spaces by chemical vapor deposition (CVD), and etching away chemically the silica photonic crystal template together with the supporting silica fiber, one then finally obtains a novel air-core waveguide with a 3-D cladding photonic crystal (3DCPC).

2. Experiment

A standard single-mode silica optical fiber (Corning, SMF-28) was selected as an ideal cylindrical substrate for the colloidal crystal coating because of the good optical quality of its outer surface. One end of the fiber stripped of its buffer was inserted into a zirconia fiber ferrule for the convenience of handling. Prior to the coating, the 125-μm diameter silica fiber was cleaned in an ultrasonic bath first using water and then ethanol for 1 and 3 minutes, respectively. Silica microspheres were deposited onto the fiber using a previously described procedure of isothermal heating evaporation induced self-assembly (IHEISA) [9

9. S. Wong, V. Kitaev, and G.A. Ozin, “Colloidal Crystal Films: Advances in Universality and Perfection,” J. Amer. Chem. Soc. 125, 15589–15598 (2003). [CrossRef]

]. Briefly, the cleaned fibers were immersed vertically into a cylindrical vial with ethanol dispersion of monodispersed silica microspheres with polydispersity <1.5%. The vial was heated to 79.8°C to evaporate ethanol and create uniform highly-ordered coatings. The silica microspheres used for coating had a diameter of 640 nm and were synthesized from smaller seeds (~175 nm diameter) following the re-growth approach reported by Giesche [10

10. H. Giesche, “Synthesis of monodispersed silica powders II. Controlled growth reaction and continuous production process,” J. Eur. Ceramic Soc. 14, 205–214 (1994). [CrossRef]

]. By varying microsphere concentration in the colloidal dispersion, the coating thickness could be controlled ranging from a monolayer to tens of microsphere layers.

3. Results

The IHEISA procedure provided uniform colloidal crystal coatings of several centimeters in length on the surface of an optical fiber. A microscope image of a ~3-cm long colloidal-coated fiber is shown Fig. 1(a), followed by three scanning electron microscopy (SEM) images in Fig. 1(b) to 1(d) recorded at increasing magnification and with different viewing angles. A continuous, uniform and highly-ordered hexagonal close-packed colloidal crystal structure with [111] crystallographic direction normal to the curved surface can be clearly observed. No dislocations or defects were discernable upon inspection of the coated fiber by rotating it around its axis. The images confirm the growth of a high quality 3DCPC film that conforms to the fiber surface, demonstrating the extension of the IHEISA process from flat [9

9. S. Wong, V. Kitaev, and G.A. Ozin, “Colloidal Crystal Films: Advances in Universality and Perfection,” J. Amer. Chem. Soc. 125, 15589–15598 (2003). [CrossRef]

,11

11. J. Li, L. E. Ladan, P. R. Herman, V. Kitaev, and G. A. Ozin, “Colloidal photonic crystal mirrors for high-resolving-power Fabry-Perots,” in Technical Digest of Conference on Lasers and Electro-Optics (CLEO), CTuDD2 (San Francisco, CA, May 16–24, 2004).

] to curved substrates.

Fig. 1. A standard silica optical fiber of 125-μm diameter coated with silica microspheres: optical microscope image of a 3-cm coated fiber (a), and scanning electron microscope images at various magnifications (b – d).

Figure 2 compares optical microscope images of a bare fiber (a) and a photonic crystal cladded fiber (b) observed in reflection mode. The axial uniformity together with the symmetric color distribution from the fiber top to the fiber edges further attests to the high quality of the 3DCPC, which spectrally shifts the stop band with the viewing angle around the fiber.

Fig. 2. Optical microscopy images of a bare (a) and a photonic crystal cladded (b) optical fiber of 125-νm diameter.

In order to quantitatively characterize the 3DCPC, both reflection and transmission spectra were investigated. The reflection spectrum was obtained using a Fourier-transform-infrared (FTIR) spectrometer (BOMAN MB-157 2E). A ~10 μm by ~50 μm source beam (perpendicular and parallel to the fiber axis, respectively) from the FTIR spectrometer was projected through a microscope objective and aligned to meet the 3DCPC-coated fiber surface at normal incidence. Fig. 3 presents a typical normalized reflection spectrum. The peak reflection at ~1385-nm wavelength exactly matches the centre of the stop band expected for a colloidal photonic crystal made of 640-nm silica microspheres and probed in the [111] crystallographic direction. Fabry-Perot interference resonances are also seen outside the stop band that originate with Fresnel reflection from the outer and inner surfaces of the 3DCPC. The spectrum is invariant along the length of the fiber and attests to the uniform thickness and good optical quality of the 3DCPC film. The ~180-400 nm fringe-to-fringe spacing provides a ~5 μm estimate for the 3DCPC film thickness which coincides with that revealed by SEM cross section images.

Fig. 3. Normal incidence reflection spectrum produced by the colloidal photonic crystal cladded fibers as shown in Fig. 1.

Figure 4 (top) illustrates the fiber coupling arrangement used for recording transmission spectra through the full cross-section of the colloidal-crystal-cladded fiber. This geometry was previously applied by Eggleton and coworkers [12

12. H. C. Nguyen, P. Domachuk, B. J. Eggleton, M. J. Steel, M. Straub, M. Gu, and M. Sumetsky, “New slant on photonic crystal fibers,” Opt. Express 12, 1528–1539 (2004), http://www.opticsexpress.or g/abstract.cfm?URI=OPEX-12-8-1528. [CrossRef] [PubMed]

] for probing the transmission spectrum transversely of a 2D-photonic-crystal-based holey PBGF. Two cleaved SMF-28 fibers were aligned for butt-coupling and then slightly separated to accommodate our photonic crystal cladded fiber. Light from a broadband LED source (Agilent, 83427A) was coupled into one fiber and transmission was collected by the second fiber for detection by an optical spectrum analyzer (Ando, AQ6317B). Fig. 4 (bottom) displays a characteristic 3DCPC transmission spectrum, which was normalized against the transmission spectrum recorded with direct butt-coupling of the two probe fibers. A moderately strong transmission dip of ~8 dB at ~1385 nm wavelength coincides with the photonic band gap expected for the 640-nm microspheres. However, unlike the spectral recordings in Reference [12

12. H. C. Nguyen, P. Domachuk, B. J. Eggleton, M. J. Steel, M. Straub, M. Gu, and M. Sumetsky, “New slant on photonic crystal fibers,” Opt. Express 12, 1528–1539 (2004), http://www.opticsexpress.or g/abstract.cfm?URI=OPEX-12-8-1528. [CrossRef] [PubMed]

] or the reflection spectrum in Fig. 3, the transmission stop band spectrum is modulated with equally spaced fringes of ~2-dB amplitude and ~5-nm peak-to-peak spacing. This spacing corresponds to the free spectral range, c/2nd, of etalon-like multi-reflections between the photonic crystal cladded walls of the fiber [11

11. J. Li, L. E. Ladan, P. R. Herman, V. Kitaev, and G. A. Ozin, “Colloidal photonic crystal mirrors for high-resolving-power Fabry-Perots,” in Technical Digest of Conference on Lasers and Electro-Optics (CLEO), CTuDD2 (San Francisco, CA, May 16–24, 2004).

]. Here, c is the light speed in vacuum, n is the silica refractive index (~1.45) and d is the fiber diameter (~125 μm). Although large optical cavity losses are expected because of the cylindrical mirror geometry, this observation of Fabry-Perot fringes is another good indication of a highly uniform and complete photonic crystal coating all around the fiber. Reflection and transmission spectral recordings such as in Fig. 3 and 4 did not vary when probing the 3-cm long photonic crystal cladded fiber at random axial positions or with azimuthal rotation of the fiber.

Fig. 4. Experimental arrangement (top) for recording the transverse transmission spectrum of the photonic crystal cladded fiber and a representative transmission spectrum (bottom) normalized to that without insertion of the photonic crystal cladded fiber. SMF: single-mode fiber; PCF: photonic crystal fiber.

4. Discussion

Although a cylindrical fiber has been successfully cladded with a high quality colloidal photonic crystal, this 3DCPC does not possess a complete photonic band gap where omnidirectional light of any polarization can be reflected. For ideal waveguiding, the present 3DCPC structure presents a promising template for inversion with silicon to complete the photonic band gap [13

13. A. Blanco, E. Chomski, S. Grabchak, M Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000). [CrossRef] [PubMed]

,14

14. Y. A. Vlasov, X. Bo, J. C. Sturn, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001). [CrossRef] [PubMed]

]. For example, a previously reported procedure is presently being modified to infiltrate the silica colloid with silicon using CVD. Wet chemical etching with hydrofluoric acid (HF) will then remove the silica templating colloids to provide an omnidirectional photonic bandgap crystal [13

13. A. Blanco, E. Chomski, S. Grabchak, M Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000). [CrossRef] [PubMed]

,14

14. Y. A. Vlasov, X. Bo, J. C. Sturn, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001). [CrossRef] [PubMed]

] For the present geometry, the HF etching step also removes the supporting silica optical fiber to leave behind a novel all-silicon hollow-core waveguide that traps and guides light within completely cylindrical porous walls. Such fiber configuration promises to provide efficient optical guiding as presently available step-index or holey photonic band gap fibers. In addition, with the added novelty of being constructed with micro-porous walls that efficiently reflect light internally in the hollow core while transmitting or adsorbing gases, liquids, and nano-particulates, it is also promising for new application opportunities such as optical sensing or spectrally tunable waveguiding.

The reported approach of producing colloidal photonic crystal cladding is reasonably expected to extend to fibers with larger or smaller diameter provided the diameter is far beyond the sphere size, for example, 10-20 μm for ~500-nm spheres. The results shown in this paper also suggest that high quality self-assembled coatings of colloidal photonic crystals can be extended to other regularly or irregularly curved surfaces for non-waveguiding applications (thermal shielding for example), providing novel optical components for free-space and other optical beams. For these new application directions, colloidal chemistry provides a method for generating photonic crystals directly on curved surfaces that is faster and more flexible than other well-developed techniques including lithographic processes or nonlithographic woodpile techniques [15–20

15. J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997). [CrossRef]

], which so far have been solely used for flat substrates.

5. Conclusion

In conclusion, colloidal self-assembly chemistry has been extended to cladding cylindrical fibers with 3-D photonic crystals for the purpose of developing a new type of air-core optical waveguide. A suitable template for making such optical waveguides based on standard optical fibers has been fabricated and structurally and optically characterized. Additionally, the proposed fabrication scheme offers a versatile and expedient approach for enveloping or spectrally shielding a volume with macro- or micro-curved surfaces, which can not be easily achieved with other photonic crystal fabrication methods.

Acknowledgments

GAO is Government of Canada Research Chair in Materials Chemistry. The authors gratefully acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support. The authors also thank Yuankun Lin for helpful discussions.

References and links

1.

See, for example, J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light (Princeton University Press, Princeton, 1995).

2.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995). [CrossRef]

3.

J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]

4.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Size-mode photonic band gap uidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

5.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998). [CrossRef] [PubMed]

6.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999). [CrossRef]

7.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608-1-8 (2003). [CrossRef]

8.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Opt. Express 12, 1510–1517 (2004),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1510. [CrossRef] [PubMed]

9.

S. Wong, V. Kitaev, and G.A. Ozin, “Colloidal Crystal Films: Advances in Universality and Perfection,” J. Amer. Chem. Soc. 125, 15589–15598 (2003). [CrossRef]

10.

H. Giesche, “Synthesis of monodispersed silica powders II. Controlled growth reaction and continuous production process,” J. Eur. Ceramic Soc. 14, 205–214 (1994). [CrossRef]

11.

J. Li, L. E. Ladan, P. R. Herman, V. Kitaev, and G. A. Ozin, “Colloidal photonic crystal mirrors for high-resolving-power Fabry-Perots,” in Technical Digest of Conference on Lasers and Electro-Optics (CLEO), CTuDD2 (San Francisco, CA, May 16–24, 2004).

12.

H. C. Nguyen, P. Domachuk, B. J. Eggleton, M. J. Steel, M. Straub, M. Gu, and M. Sumetsky, “New slant on photonic crystal fibers,” Opt. Express 12, 1528–1539 (2004), http://www.opticsexpress.or g/abstract.cfm?URI=OPEX-12-8-1528. [CrossRef] [PubMed]

13.

A. Blanco, E. Chomski, S. Grabchak, M Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000). [CrossRef] [PubMed]

14.

Y. A. Vlasov, X. Bo, J. C. Sturn, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001). [CrossRef] [PubMed]

15.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997). [CrossRef]

16.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter-wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2061 (1994). [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.

J. G. Fleming, S. Y. Lin, I. EI-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002). [CrossRef] [PubMed]

19.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000). [CrossRef] [PubMed]

20.

S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77, 3490–3492 (2000). [CrossRef]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2340) Fiber optics and optical communications : Fiber optics components
(230.7370) Optical devices : Waveguides
(310.1620) Thin films : Interference coatings

ToC Category:
Research Papers

History
Original Manuscript: June 29, 2005
Revised Manuscript: August 5, 2005
Published: August 22, 2005

Citation
Jianzhao Li, Peter Heman, Christopher Valdivia, Vladimir Kitaev, and Geoffrey Ozin, "Colloidal photonic crystal cladded optical fibers: Towards a new type of photonic band gap fiber," Opt. Express 13, 6454-6459 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-17-6454


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References

  1. See, for example, J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light (Princeton University Press, Princeton, 1995).
  2. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, �??Full 2-D photonic bandgaps in silica/air structures,�?? Electron. Lett. 31, 1941-1943 (1995). [CrossRef]
  3. J. Broeng, T. A. Birks, and P. St. J. Russell, �??Photonic band gap guidance in optical fibers,�?? Science 282, 1476-1478 (1998). [CrossRef] [PubMed]
  4. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, �??A dielectric omnidirectional reflector,�?? Science 282, 1679-1682 (1998). [CrossRef] [PubMed]
  5. Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, E. L. Thomas, �??Guiding optical light in air using an all-dielectric structure,�?? J. Lightwave Technol. 17, 2039-2041 (1999). [CrossRef]
  6. M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, �??Analysis of mode structure in hollow dielectric waveguide fibers,�?? Phys. Rev. E 67, 046608-1-8 (2003). [CrossRef]
  7. K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, �??Hollow multilayer photonic bandgap fibers for NIR applications,�?? Opt. Express 12, 1510-1517 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1510">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1510</a> . [CrossRef] [PubMed]
  8. S. Wong, V. Kitaev, and G.A. Ozin, �??Colloidal Crystal Films: Advances in Universality and Perfection,�?? J. Amer. Chem. Soc. 125, 15589-15598 (2003). [CrossRef]
  9. H. Giesche, �??Synthesis of monodispersed silica powders II. Controlled growth reaction and continuous production process,�?? J. Eur. Ceramic Soc. 14, 205-214 (1994). [CrossRef]
  10. J. Li, L. E. Ladan, P. R. Herman, V. Kitaev, and G. A. Ozin, �??Colloidal photonic crystal mirrors for high-resolving- power Fabry-Perots,�?? in Technical Digest of Conference on Lasers and Electro-Optics (CLEO), CTuDD2 (San Francisco, CA, May 16-24, 2004).
  11. H. C. Nguyen, P. Domachuk, B. J. Eggleton, M. J. Steel, M. Straub, M. Gu, and M. Sumetsky, �??New slant on photonic crystal fibers, �?? Opt. Express 12, 1528-1539 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1528">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1528</a>. [CrossRef] [PubMed]
  12. A. Blanco, E. Chomski, S. Grabchak, M Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, �??Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,�?? Nature 405, 437-440 (2000). [CrossRef] [PubMed]
  13. Y. A. Vlasov, X. Bo, J. C. Sturn, D. J. Norris, �??On-chip natural assembly of silicon photonic bandgap crystals,�?? Nature 414, 289-293 (2001). [CrossRef] [PubMed]
  14. J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, �??Photonic crystals: putting a new twist on light,�?? Nature 386, 143-149 (1997) [CrossRef]
  15. E. �?zbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, �??Micromachined millimeter-wave photonic band-gap crystals,�?? Appl. Phys. Lett. 64, 2059-2061 (1994). [CrossRef]
  16. 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]
  17. J. G. Fleming, S. Y. Lin, I. EI-Kady, R. Biswas, and K. M. Ho, �??All-metallic three-dimensional photonic crystals with a large infrared bandgap,�?? Nature 417, 52-55 (2002). [CrossRef] [PubMed]
  18. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, �??Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,�?? Science 289, 604-606 (2000). [CrossRef] [PubMed]
  19. S. G. Johnson and J. D. Joannopoulos, �??Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,�?? Appl. Phys. Lett. 77, 3490-3492 (2000). [CrossRef]
  20. Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, E. L. Thomas, �??Guiding optical light in air using an all-dielectric structure,�?? J. Lightwave Technol. 17, 2039-2041 (1999).

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