Abstract
The aim of this chapter is to introduce the general concept of photonic crystals. The chapter will start by guiding the reader to an understanding of photonic crystals and explain their basic characteristics, and indicate methods of fabrication and potential applications. The purpose of the chapter is not to give an exhaustive presentation of the wide field of photonic crystals, but to establish a fundamental understanding of the concepts, terminology and theoretical tools that is required for conducting research in photonic crystal waveguides. Readers interested in general aspects of photonic crystals are pointed to the introductory book by Joannopoulos et al, [2.1], or the more recent book by Johnson et al. [2.2]. We may also recommend one of the very good web-sites [2.12], where relevant papers such as e.g., [2.90-2.91] may be found.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Joannopoulos, I. Winn, and R. Meade, “Photonic Crystals: Molding the Flow of Light”, Princeton University Press, 1995. ISBN:0-691-03744-2
S. G. Johnson, and J. Joannopoulos, “Photonic Crystals: The Road from Theory to Practice”, Kluwer Academic Publishers, 2002. ISBN: 0-7923-7609-9.
J. Joannopoulos, P. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature, vol. 386, pp. 143-149, March 1997.
E. Yablonovitch, “Photonic band-gap structures”, Journal of the Optical Society of America B, vol. 10, pp. 283-295, Feb. 1993.
C. Soukoulis, ed., “Photonic band gaps and localization”, Proceedings of the NATO advanced research workshop, Heraklion 1992, vol. 308 of NATO ASI series. Series B, Physics, Dordrecht: Kluwer, 1993.
E. Burstein and C. Weisbuch, eds., “Confined electrons and photons New physics and applications”, Proceedings of a NATO Advanced Study Institute, Erice 1993, vol. 340 of NATO ASI series. Series B, Physics, New York, N.Y. : Plenum Press, 1995.
C. Soukoulis, ed., “Photonic band gap materials”, Proceedings of the NATO advanced study institute, Elounda 1995, vol. 315 of NATO ASI series. Series E, Applied sciences, Dordrecht: Kluwer, 1996.
J. Rarity and C. Weisbuch, eds., “Microcavities and photonic band gaps Physics and applications”, NATO ASI series. Vol. 324, Series E, Applied sciences, Dordrecht: Kluwer, 1996.
C. M. Bowden, J. P. Dowling, and H. O. Everitt (Editors), “Development and Applications of Materials Exhibiting Photonic Band Gaps”, Journal of the Optical Society of America B, vol. 10, Feb. 1993, special issue.
[2.10] Special issue on: “Photonic Crystals and Photonic Microstructures”, Vol. 145, IEE Proceedings - Optoelectronics, Dec. 1998.
[2.11] J. Dowling, H. Everitt, and E. Yablonovitch, “Photonic & sonic band-gap bibliography”, http://home. earthlink. net/jpdowling/pbgbib. html.
[2.12] Y.Vlasov, “The ultimate collection of photonic band gap research links”, http://www.pbglink. com.
S. Ramo, J. Whinnery, and T.Van Duzer, “Fields and waves in communications electronics”, Wiley, 1994
G. Agrawal, “Fiber-optic communications systems”, Wiley Inter science, seconded., 1997.
E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics”, Physical Review Letters, Vol.58, pp.2059-62, May 1987.
S.John, “Strong localization of photons in certain disordered dielectric superlattices”, Physical Review Letters, Vol. 58, no. 23, pp. 2486-9, 1987.
D. Chigrin, A. Lavrinenko, D. Yarotsky, and S. Gaponenko, “Observation of total omni-directional reflection from a one-dimensional dielectric lattice”, Appl. Phys. A, vol. 68, pp. 25-28, 1999.
Y. Fink, J. Winn, S. Fan, C. Chen, J. Michel, J. Joannopoulos, and E. Thomas, “A dielectric omnidirectional reflector”, Science, vol. 282, pp. 1679-1682, Nov. 1999.
T. Søndergaard, J. Broeng, A. Bjarklev, K. Dridi, and S. Barkou, “Suppression of spontaneous emission for a two-dimensional honeycomb photonic band gap structure estimated using a new effective-index model”, IEEE Journal of Quantum Electronics, vol. 34, pp. 2308-2313, Dec. 1998.
T. Krauss, R. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths”, Nature, vol. 383, pp. 699-702, 24 Oct. 1996.
M. Plihal and A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Physical Review B, vol. 44, pp. 8565-8571, Oct. 1991.
S. McCall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices”, Physical Review Letters, vol. 67, pp. 2017-2020, Oct. 1991.
R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, “Existence of a photonic band gap in two dimensions”, Applied Physics Letters, vol. 61, pp. 495-497, July 1992.
P. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices”, Physical Review B, vol. 46, pp. 4969-4972, Aug. 1992.
A. Maradudin and A. McGurn, “Photonic band structure of a truncated, two-dimensional, periodic dielectric medium”, Journal of the Optical Society of America B, vol. 10, pp. 307- 313, Feb. 1993.
J. Gerard, A. Izrael, J. Marzin, R. Padjen, and F. Ladan, “Photonic bandgap of two- dimensional dielectric crystals”, Solid-State Electronics, vol. 37, pp. 1341-1344, April-June 1994.
H.- B. Lin, R. Tonucci, and A. Campillo, “Observation of two-dimensional photonic band behavior in the visible”, Applied Physics Letters, vol. 68, pp. 2927-2929, May 1996.
C. Anderson and K. Giapis, “Larger two-dimensional photonic band gaps”, Physical Review Letters, Vol. 77, pp. 2949-2952, Sept. 1996.
A. Rosenberg, R. Tonucci, H.-B. Lin, and A. Campillo, “Near-infrared two-dimensional photonic band-gap materials”, Optics Letters, Vol. 21, pp. 830-832, June 1996.
K. Inoue, M. Wada, K. Sakoda, M. Hayashi, T. Fukushima, and A. Yamanaka, “Near-infrared photonic band gap of two-dimensional triangular air-rod lattices as revealed by transmittance measurement”, Physical Review B, Vol. 53, pp. 1010-1013, Jan. 1996.
V. Kuzmiak, A. A. Maradudin, and A. R. McGurn, “Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal”, Physical Review - Section B - Condensed Matter, Vol. 55, pp. 4298-4311, Feb. 1997.
V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation”, Physical Review - Section B - Condensed Matter, Vol. 55, pp.7427-7444, Mar. 1997.
D. Labilloy, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals”, Applied Physics Letters, Vol. 71, pp. 738-740, Aug. 1997.
D. Cassagne, C. Jouanin, and D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure”, Applied Physics Letters, Vol. 70, pp. 289-291, Ian. 1997.
A. Barra, D. Cassagne, and C. Jouanin, “Existence of two-dimensional absolute photonic band gaps in the visible”, Applied Physics Letters, Vol. 72, pp. 627-629, Feb. 1998.
M. Charlton and G. Parker, “Nanofabrication of advanced waveguide structures incorporating a visible photonic band gap”, J. Micromech. Microeng., Vol. 8, pp. 172-176, Jun. 1998.
J. Nielsen, T. Sondergaard, S. Barkou, A. Bjarklev, J. Broeng, and M. Nielsen, “The two-dimensional Kagome structure, a new fundamental hexagonal photonic crystal configuration”, IEE Electronics Letters, Vol. 35, pp. 1736-1737, Sept. 1999.
T. Birks, P. Roberts, P. Russell, D. Atkin, and T. Shepherd, “Full 2-d photonic bandgaps in silica/air structures”, IEE Electronics Letters, Vol. 31, pp. 1941-1943, Oct. 1995.
J. Broeng, S. Barkou, A. Bjarklev, J. Knight, T. Birks, and P. Russell, “Highly increased photonic band gaps in silica/air structures”, Optics Communications, Vol. 156, pp. 240-244, Nov. 1998.
A. Maradudin and A. McGurn, “Out of plane propagation of electromagnetic waves in a two-dimensional periodic dielectric medium”, Journal of Modern Optics, Vol. 41, pp. 275- 284, Feb. 1994.
P. Roberts, T. Birks, P. Russell, T. Shepherd, and D. Atkin, “Two-dimensional photonic band-gap structures as quasi-metals”, Optics Letters, Vol. 21, pp. 507-509, April 1996.
X. Feng and Y. Arakawa, “Off-plane angle dependence of photonic band gap in a two-dimensional photonic crystal”, IEEE Journal of Quantum Electronics, Vol. 32, pp. 535-542, Mar. 1996.
A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides”, Physical Review Letters, Vol. 77, pp. 3787-3790, act. 1996.
R. Ziolkowski, “FDTD modelling of photonic nanometer-sized power splitters and switches”, Integrated Photonics Research, Vol. 4 of Technical Digest Series, p. IThA2, OSA, March 30-Aprill 1998.
S. Fan, P. Villeneuve, J. Joannopoulos, and H. Hails, “Channel drop tunneling through localized states”, Physical Review Letters, Vol. 80, pp. 960-963, Feb. 1998.
O. Painter, R. Lee, A. Scherer, A. Yariv, P. O'Brien, J. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser”, Science, Vol. 284, pp. 1819-1821, June 1999.
P. Russell, J. Pottage, J. Broeng, D. Mogilevtsev, and P. Philips, “Leak-free bound modes in photonic crystal films”, CLEO’99: Conference on Lasers and Electro-Optics, p. CWF65, May 1999.
S. Johnson, S. Fan, P. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs”, Physical Review B, Vol. 60, pp. 5751-5758, Aug. 1999.
O. Martin, C. Girard, D. Smith, and S. Schultz, “Generalized field propagator for arbitrary finite-size photonic band gap structures”, Phys. Rev. Lett., Vol. 82, pp. 315-318, Jan. 1999.
S. Lin and G. Arjavalingam, “hotonic bound states in two-dimensional photonic crystals probed by coherent-microwave transient spectroscopy,” Journal of the Optical Society of America B, vol. 11, pp. 2124-7, Oct. 1994.
E. Yablonovitch, T. Gmitter, and K. Leung, “hotonic band structure: the face-centered-cubic case employing nonspherical atoms”, Physical Review Letters, Vol. 67, pp. 2295-2298, Oct. 1991.
E. Ozbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas, and K.-M. Ho, “Mromachined millimeter-wave photonic band-gap crystals” Applied Physics Letters, Vol. 64, pp. 2059- 2061, April 1994.
E. Brown, C. Parker, and E. Yablonovitch, “adiation properties of a planar antenna on a photonic-crystal substrate”, Journal of the Optical Society of America B, Vol. 10, pp. 404-407, Feb. 1993.
S. Cheng, R. Biswas, E. Ozbay, S. McCalmont, G. Tilttle, and K-M. Ho, “ptimized dipole antennas on photonic band gap crystals” Applied Physics Letters, Vol. 67, pp. 3399-3401, Dec. 1995.
L. Jasper and G. Tran, “hotonic band gap (pbg) technology for antennas” SPIE, vol 7,Iulyl996.
M. Kesler, J. Maloney, B. Shirley, and G. Smith, “Antenna design with the use of photonic band-gap materials as all-dielectric planar reflectors”, Microwave and Optical Technology Letters, Vol. II, pp. 169-174, March 1996.
Y. Qian, R. Coccioli, D. Sievenpiper, V. Radisic, E. Yablonovitch, and T. Itoh, “A mirostrip patch antenna using novel photonic band-gap structures” MICROWAVE J Vol. 42, p. 66, Jan. 1999.
U. Gruning and V. Lehmann, “wo-dimensional infrared photonic crystal based on macroporous silicon” Thin Solid Films, Vol. 276, no. 151, 1996.
J. Knight, T. Birks, P. Russell, and D. Atkin, “All-silica mode optical fiber with photonic crystal cladding”, Optics Letters, Vol. 21, pp. 1547-1549, Oct. 1996.
S. Rowson, A. Chelnokov, and J.-M. Lourtioz, “acroporous silicon photonic crystals at 1.55 micrometers” IEE Electronics Letters, Vol. 35, No. 9, pp. 753-755, Apr. 1999.
S. Lin, J. Fleming, D. Hetherington, B. Smith, R. Biswas, K. Ho, M. Sigalas, W. Zubrzycki, S. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths”, Nature, Vol. 394, pp. 251-253, July 1998.
A. A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “arbon structures with three-dimensional periodicity at optical wavelengths” Science, Vol. 5390, pp. 897-901, Oct. 1998.
S. Kawakami, “abrication of submicrometere 3d periodic structures composed of Si/Si02”, IEE Electronics Letters, Vol. 33, p. 1260, 1997.
J. Fleming and S. Lin, “ree-dimensional photonic crystal with a stop band from 1.35 to 1.95mu m”, Optics Letters, Vol. 24, pp. 49-51, Jan. 1999.
P R. Fan, S. Villeneuve, and J. D. Joannopoulos, “Toretical investigation of fabrication-related disorder on the properties of photonic crystals”, J. Appl. Phys., Vol. 78, p. 1415, 1995.
A. Chutinan and S. Noda, “Effects of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal”, J. Opt. Soc. Am. B, Vol. 16, pp. 240-244, Feb. 1999.
A.Yariv, “Propagation, modulation and oscillation in optical dielectric waveguides”, Saunders Clooege Publishing, 1991.
P. Villeneuve, S. Fan, J. Joannopoulos, K.-Y. Lim, G. Petrich, L. Kolodziejski, and R. Reif, “Air idge microcavities”, Applied Physics Letters, Vol. 67, pp. 167-169, July 1995.
A. Yariv, “Quantum Electronics”, Wiley, 1988.
R. Coccioli, M. Boroditsky, K. Kim, Y. Rahmat-Samii, and E. Yablonovitch, “Smallest possible electromagnetic mode volume in a dielectric cavity”, lEE proc. -Optoelectron., Vol. 145 , Dec. 1998.
B. D'Urso, 0. Painter, J. O'Brien, T. Tombrello, A. Yariv, and A. Scherer, “Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavities”, J. Opt. Soc. Am. B, Vol. 15, pp. 1155-1159, Mar. 1998.
M. Boroditsky and E. Coccioli, R. Yablonovitch, “Analysis of photonic crystals for light emitting diodes using the finite difference time domain technique”, SPIE-Int. Soc. Opt. Eng., Vol. 3283, pp. 184-190, 1998.
H. Hirayama, T. Hamano, and Y. Aoyagi, “Novel spontaneous emission control using 3-dimensional photonic bandgap crystal cavity”, Mat. Sci. Eng. B-Solid, vol. 51, pp. 99-102, Feb. 1998.
K. Yoshino, S. Tatsuhara, Y. Kawagishi, M. Ozaki, A. Zakhidov, and Z. Vardeny, “Amplified spontaneous emission and lasing in conducting polymers and fluorescent dyes in opals as photonic crystals”, Appl. Phys. Lett., Vol. 74, pp. 2590-2592, May 1998.
K. Yoshino, S. Lee, S. Tatsuhara, Y. Kawagishi, M. Ozaki, and A. Zakhidov, “Observation of inhibited spontaneous emission and stimulated emission of rhodamine 6G in polymer replica of synthetic opal”, Appl Phys. Lett., Vol. 73, pp. 3506-3508, Dec. 1998.
C. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdre, T. Krauss, R. De la Rue, and C. Weisbuch, “Near-infrared micro cavities confined by two-dimensional photonic bandgap crystals”, IEE Electronics Letters, Vol. 35, pp. 228-230, Feb. 1999.
R. Lee, 0. Painter, B. D'Urso, A. Scherer, and A. Yariv, “Measurement of spontaneous emission from a two-dimensional photonic band gap defined micro cavity at near-infrared wavelengths”, Appl Phys. Lett, Vol. 74, pp. 1522-1524, Mar. 1999.
T. Søndergaard, J. Broeng, and A. Bjarklev, “Suppression of spontaneous emission for two-dimensional GaAs photonic crystal mirocavities”, CLEO'99: Conference on Lasers and Electro Optics, p. 525, May 1999. Paper JFA2.
H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries”, Journal of Applied Physics, Vol. 79, pp. 7483-7492, May 1996.
S.-Y. Lin, E. Chow, V. Hietala, P. Villeneuve, and J. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal”, Science, Vol. 282, pp. 274-276, Oct. 1998.
O. Hanazumi, Y. Ohtera, T. Sato, and S. Kawakami, “Propagation of light beams along line defects formed in a-Si/Si02 three-dimensional photonic crystals: Fabrication and observation”, Applied Physics Letters, Vol. 74, No.6, pp. 777-779, 1999.
S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals”, Optics Communcations, Vol. 161, No.4-6, pp. 171-176, 1999.
S. Lin, V. Hietala, L. Wang, and E. Jones, “Highly dispersive photonic band-gap prism”, Optics Letters, Vol. 21, pp. 1771-1773, 1996.
H. Kosaka, T. Kawashima, T. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals”, Phys. Rev. B, Vol. 58, pp. 10096-10099, 1998.
J. Mathews, and R. Walker, “Mathematical methods of physics”, Addison-Wesley, Redwood City, California, 1964.
C.Kittel, “Solid state physics”, John Wiley & Sons, New York, 1986.
S. I. Bozhevolnyi, J. Erland, K. Leosson K, et al. “Waveguiding in surface plasmon polariton band gap structures”, Phys. Rev. Lett., Vol. 86, No.14, pp. 3008-3011, Apr. 2001.
S. G. Romanov, T. Maka, C. M. S. Torres, “Suppression of spontaneous emission in incomplete opaline photonic crystal”, J. Appl. Phys., Vol. 91, No. 11, pp. 9426-9428, Jun. 2002.
H. Notomi, A. Shinya, K. Yamada, “Singlemode transmission within photonic bandgap of width-varied single-line-defect photonic crystal waveguides on SOI substrates”, IEE Electronics Letters, Vol. 37, No.5, pp. 293-295, Mar 2001.
T. Søndergaard, A. Bjarklev, M. Kristensen, J.Erland østergaard, and J.Broeng, “Designing finite-height two-dimensional photonic crystal waveguides”, Appl. Phys. Lett., Vol. 77, No. 6, pp. 785-787, Aug. 2000.
Sakoda K, Sasada M, Fukushima T, Yamanaka A, Kawai N, Inoue K, “Detailed analysis of transmission spectra and Bragg-reflection spectra of a two-dimensional photonic crystal with a lattice constant of 1.15 microns”, J. Opt. Soc. Am. B, Vol. 16, No.3, pp. 361-365, Mar. 1999.
C. S. Kee, J. E. Kim, H. Y. Park, K. J. Chang, H. Lim, “Essential role of impedance in the formation of acoustic band gaps” J. Appl. Phys., Vol. 87, No.4, pp. 1593-1596, Feb. 2000.
P. Villeneuve, and M. Piche, “Photonic bandgaps: What is the best numerical representation of periodic structures?,” Journal of Modern Optics, vol. 41, pp. 241-256, Feb. 1994.
R. Meade, A. Rappe, K. Brommer, and J. Joannopoulos, “Nature of the photonic band gap: some insights from a field analysis,” Journal of the Optical Society of America B, vol. 10, pp. 328-332, Feb. 1993.
R. Meade, A. Rappe, K. Brommer, J. Joannopoulos, and 0. Alerhand, “Accurate theoretical analysis of photonic band-gap materials”, Physical Review B, vol. 48, pp. 8434-8437, Sept. 1993.
H. Söziüer, J. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method”, Physical Review B, vol. 45, pp. 13962-13972, June 1992.
M. Teter, M. Payne, and D. Allan, “Solution of Schrödinger's equation for large systems,” Physical Review B, 1989.
D. Aspnes, “Local-field effects and effective- medium theory: A microscopic perspective,” Am.]. Phys., vol. 50, pp. 704-709, Aug. 1981.
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bjarklev, A., Broeng, J., Bjarklev, A.S. (2003). Fundamentals of Photonic Crystal Waveguides. In: Photonic Crystal Fibres. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0475-7_2
Download citation
DOI: https://doi.org/10.1007/978-1-4615-0475-7_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5095-8
Online ISBN: 978-1-4615-0475-7
eBook Packages: Springer Book Archive