Photonic crystals

Martijn de Sterke, Ross McPhedran, Ben Eggleton

2D periodic optical structures

crystalMode
crystalResonator

Photonic crystals rely on coherent scattering of light off large index contrast interfaces (usually material to air) to guide light. The periodicity and arrangement of these interfaces allows Bragg reflection in the media, confining light. The advantage of this form of confinement is that tight, narrow structures with very tight bends compared to total internal reflection as with conventional waveguides. This causes tight confinement of light, allowing for high energy densities - critical for non-linear interactions, as well as allowing for high quality factor cavities.

Materials of choice

Our photonic crystal research focuses on structures with a relatively low refractive index, such as chalcogenide glass (n = 2-3) and diamond (n~2.4). Most other photonic crystal work deals with high-index materials such as silicon (n~3.4)

Chalcogenide glass photonic crystals

Chalcogenide glasses combine a large optical nonlinearity with strong photosensitivity, making them ideal for studying nonlinear photonic effects. Chalcogenide glass photonic crystals are fabricated at the ANU by milling holes in chalcogenide glass films using a focused ion beam. We characterise these structures by measuring transmission and reflection versus incident angle and wavelength.

Diamond photonic crystals

Our diamond research is carried out in collaboration with the Technion in Israel and with the University of Melbourne. NV centers in diamond, a nitrogen defect, form an attractive candidate for use in quantum computing. Photonic crystals may create the required light/defect interactions for this application. We are thus modeling and optimizing photonic crystal cavities in order to obtain high quality resonanances need for this application.

Coupling into structures

We develop methods for coupling light into photonic crystal waveguides and cavities using micro and nano-tapered fibres. Using the resonances in these structures, corresponding to large build-ups of the field intensity, also allows interesting devices based on nonlinear optical phenomena.

Fluid infiltration

By infiltrating holes in a photonic crystal, the refractive index difference at the infiltrated holes can change, changing the band structure of the photonic crystal in the infiltrated region. This can be exploited to change the functionality of a photonic crystal - an example we investigate at CUDOS is fluid induced microcavities. By creating a cavity by fluid infiltration, one can avoid having to tailor the photonic crystal structure on the nanometre scale, but instead infiltrate on the micron scale - a much easier proposition. Fluid cavities also have the advantage of being reconfigurable - one photonic crystal sample can be reused many times and the properties of the cavity tailored to needs.

Modelling nanophotonic structures

nanoZ

We model nanophotonic structures using different methods varying from semianalytic approaches to fully numerical methods.

  • In collaboration with University of Technology, Sydney (UTS) we have developed a suite of methods for photonic crystal calculations in which a photonic crystal is "sliced up” in layers, each of which forms a diffraction grating. Using the well known properties of diffraction gratings we can then find the properties of the entire photonic crystal. This leads to an efficient method of calculation that also provides the physical insight needed to design novel devices, such as a “folded directional coupler” with very narrow resonances.
  • At the other end of the spectrum we use fully numerical methods such as a plane wave method or the Finite Difference Time Domain (FDTD) method, where, we write add-ons to powerful existing commercial software. Examples include a method to calculate efficiently the properties of superprisms, photonic crystal-based devices with dispersive powers that are orders of magnitude larger than of conventional prisms.

Publications

  1. Christelle Monat, Christian Grillet, Matthew Collins, Alex Clark, Jochen Schroeder, Chunle Xiong, Juntao Li, Liam O'Faolain, Thomas F. Krauss, Benjamin J. Eggleton, & David J. Moss,
    "Integrated optical auto-correlator based on third-harmonic generation in a silicon photonic crystal waveguide,"
    Nature Communications 5, Article number: 3246 doi:10.1038/ncomms4246
  2. A. Blanco-Redondo,    C. Husko,    D. Eades,    Y. Zhang,    J. Li, T.F. Krauss    and B.J. Eggleton,
    "Observation of soliton compression in silicon photonic crystals,"
    Nature Communications 5, 3160, doi:10.1038/ncomms4160 (2014)
  3. Yanbing Zhang, Chad Husko, Jochen Schröder, Simon Lefrancois, Isabella H. Rey, Thomas F. Krauss, and Benjamin J. Eggleton,
    "Phase-sensitive amplification in silicon photonic crystal waveguides,"
    Opt. Lett. 39, 363-366 (2014)
  4. Snjezana Tomljenovic-Hanic and C. Martijn de Sterke,
    “Reconfigurable, defectfree, ultrahigh-Q photonic crystal microcavities for sensing,”
    Sensors 13, 3262-3269 (2013)
  5. F. J. Lawrence, C. M. de Sterke, L. C. Botten, R.C. McPhedran, and K. B. Dossou,
    “Modeling photonic crystal interfaces and stacks: impedancebased approaches,”
    Advances in Optics and Photonics 5, 385-455 (2013)
  6. B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke,
     “Absorption enhancing proximity effects in aperiodic nanowire arrays,”
    Optics Express 21, A964-A969 (2013)
  7. C. Xiong, T. D. Vo, M. J. Collins, J. Li, T. F. Krauss, M. J. Steel, A. S. Clark, and B. J. Eggleton,
    "Bidirectional multiplexing of heralded single photons from a silicon chip,"
    Opt. Lett. 38, 5176-5179 (2013)
  8. Joel Carpenter, Chunle Xiong, Matthew J. Collins, Juntao Li, Thomas F. Krauss, Benjamin J. Eggleton, Alex S. Clark, and Jochen Schröder,
    "Mode multiplexed single-photon and classical channels in a few-mode fiber,"
    Opt. Express 21, 28794-28800 (2013)
  9. Chad A. Husko, Alex S. Clark, Matthew J. Collins, Alfredo De Rossi, Sylvain Combrié, Gaëlle Lehoucq, Isabella H. Rey, Thomas F. Krauss, Chunle Xiong & Benjamin J. Eggleton,  
    "Multi-photon absorption limits to heralded single photon sources"
    Sci. Rep. 3, 3087, DOI:10.1038/srep03087 (2013)
  10. Alex S. Clark, Chad Husko, Matthew J. Collins, Gaelle Lehoucq, Stéphane Xavier, Alfredo De Rossi, Sylvain Combrié, Chunle Xiong, and Benjamin J. Eggleton,
    "Heralded single-photon source in a III–V photonic crystal,"
    Opt. Lett. 38, 649-651 (2013)
  11. Chad Husko and Benjamin J. Eggleton, "Energy efficient nonlinear optics in silicon: are slow-light structures more efficient than nanowires?,"
    Opt. Lett. 37, 2991-2993 (2012)
  12. A. Casas Bedoya, P. Domachuk, C. Grillet, C. Monat, E.C. Mägi, E. Li, and B. J. Eggleton,
    "Reconfigurable photonic crystal waveguides created by selective liquid infiltration,"
    Opt. Express 20, 11046-11056 (2012)
  13. C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton,
    "Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,"
    Opt. Express 19, 20681-20690 (2011)
  14. A. Casas Bedoya, S. Mahmoodian, C. Monat, S. Tomljenovic-Hanic, C. Grillet, P. Domachuk, E.C. Mägi, B. J. Eggleton, and R. W. van der Heijden,
    "Liquid crystal dynamics in a photonic crystal cavity created by selective microfluidic infiltration"
    Optics Express 18, 27280-27290 (2010).
  15. Bill Corcoran, Christelle Monat, Dominik Pudo, Benjamin J. Eggleton, Thomas F. Krauss, David J. Moss, Liam O'Faolain, Mark Pelusi, and Thomas P. White
    "Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide"
    Optics Letters, Vol. 35, Issue 7, pp. 1073-1075 (2010)
  16. B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss,
    "Optical signal processing on a silicon chip at 640Gb/s using slow-light,"
    Opt. Express 18, 7770-7781 (2010)
  17. Christelle Monat, Christian Grillet, Bill Corcoran, David J. Moss, Benjamin J. Eggleton, Thomas P. White, Thomas F. Krauss
    "Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics"
    Opt. Express 18, 7, 2010
  18. Christelle Monat, Bill Corcoran, Dominik Pudo, Majid Ebnali-Heidari, Christian Grillet, Mark D. Pelusi, David J. Moss, Benjamin J. Eggleton, Thomas P. White, Liam O'Faolain, Thomas F. Krauss
    "Slow Light Enhanced Nonlinear Optics in Silicon Photonic Crystal Waveguides"
    J. Sel. Top. Quantum Electron., 16, 1, 2010
  19. Michael W. Lee, Christian Grillet, Snjezana Tomljenovic-Hanic, Eric C. Mägi, David J. Moss, Benjamin J. Eggleton, Xin Gai, Steve Madden, Duk-Yong Choi, Douglas A. P. Bulla, and Barry Luther-Davies,
    "Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,"
    Optics Letters, Vol. 34, Iss. 23, pp. 3671–3673 (2009).
  20. C. Martijn de Sterke, K.B. Dossou, T.P. White, L.C. Botten, and R.C. McPhedran,
    "Efficient coupling into slow light photonic crystal waveguide without transition region: role of evanescent modes,"
    Optics Express 17, 17338-17343 (2009)
  21. A. Joushaghani, R. Iyer, J.K.S. Poon, J.S. Aitchison, C.M. de Sterke, J. Wan, and M.M. Dignam,
    "Quasi-Bloch oscillations in curved coupled optical waveguides,"
    Phys. Rev. Lett 103, 143903:1-4 (2009)
  22. Felix J. Lawrence, Lindsay C. Botten, Kokou B. Dossou, C. Martijn de Sterke, and R. C. McPhedran,
    "Impedance of square and triangular lattice photonic crystals"
    Phys. Rev. A 80, 023826 (2009), DOI:10.1103/PhysRevA.80.023826
  23. S. Mahmoodian, C. G. Poulton, K. B. Dossou, R. C. McPhedran, L. C. Botten, and C. M. de Sterke,
    "Modes of shallow photonic crystal waveguides: semi-analytic treatment"
    Optics Express, 17, 22 (2009)
  24. Boris T. Kuhlmey, Stéphane Coen, and Sahand Mahmoodian,
    "Coated photonic bandgap fibres for low-index sensing applications: cutoff analysis"
    Optics Express, Vol. 17, Issue 18, pp. 16306-16321 (2009)
  25. K. B. Dossou, C. G. Poulton, L. C. Botten, S. Mahmoodian, R. C. McPhedranand C. Martijn de Sterke
    "Modes of symmetric composite defects in two-dimensional photonic crystals"
    Phys. Rev. A 80, 013826 (2009)
  26. M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K Moravvej-Farshi,
    "A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration,"
    Opt. Express 17, 18340-18353 (2009)
  27. D. Pudo, B. Corcoran, C. Monat, M. Pelusi, D.J. Moss, B.J. Eggleton, T.P. White, L. O'Faolain, T.F. Krauss
    "Investigation of slow light enhanced nonlinear transmission for all-optical regeneration in silicon photonic crystal waveguides at 10 Gbit/s"
    Photonics and Nanostructures: Fundementals and Applications, doi:10.1016/j.photonics.2009.08.002, (2009)
  28. Snjezana Tomljenovic-Hanic, Adel Rahmani, M. J. Steel, and C. Martijn de Sterke
    "Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors"
    Optics Express Vol. 17, No. 17, pp. 14552–14557 (2009).
  29. Christian Karnutsch, Cameron L. C. Smith, Alexandra Graham, Snjezana Tomljenovic-Hanic, Ross McPhedran, Benjamin J. Eggleton, Liam O'Faolain, Thomas F. Krauss, Sanshui Xiao, and N. Asger Mortensen
    "Temperature stabilization of optofluidic photonic crystal cavities"
    Appl. Phys. Lett. 94, 231114 (2009), DOI:10.1063/1.3152998
  30. Felix J. Lawrence, Lindsay C. Botten, Kokou B. Dossou, and C. Martijn de Sterke
    "Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition"
    Appl. Phys. Lett. 93, 121114, 2008
  31. S. Mahmoodian, R. C. McPhedran, and C. Martijn de Sterke K. B. Dossou, C. G. Poulton, and L. C. Botten
    "Single and coupled degenerate defect modes in two-dimensional photonic crystal band gaps"
    Physical Review A, 79, 013814, 2009
  32. C. Grillet, C. Monat, C.L. Smith, M.W. Lee, S. Tomljenovic-Hanic, C. Karnutsch, B.J. Eggleton
    "Reconfigurable photonic crystal circuits"
    Laser & Photonics Reviews, Published Online: 16 Mar 2009.
  33. S. Tomljenovic-Hanic, A.D. Greentree, C.M. de Sterke, and S. Prawer
    “Flexible design of ultrahigh-Q cavities in diamond-based photonic crystal slabs,”
    Optics Express 17, 6465-6475 (2009).
  34. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain & T. F. Krauss
    "Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides "
    Nature Photonics, doi:10.1038/nphoton.2009.28 (2009)
  35. Christelle Monat, Bill Corcoran, Majid Ebnali-Heidari, Christian Grillet, Benjamin J. Eggleton, Thomas P. White, Liam O'Faolain, and Thomas F. Krauss, "Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,"
    Opt. Express 17, 2944-2953 (2009)
  36. M. Ebnali-Heidari, C. Grillet, C. Monat, and B. J. Eggleton,
    "Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,"
    Opt. Express 17, 1628-1635 (2009)
  37. U. Bog, C. L. Smith, M. W. Lee, S. Tomljenovic-Hanic, C. Grillet, C. Monat, L. O'Faolain, C. Karnutsch, T. F. Krauss, R. C. McPhedran, and B. J. Eggleton
    "High-Q microfluidic cavities in silicon-based two-dimensional photonic crystal structures,"
    Opt. Lett. 33, 2206-2208 (2008)
  38. C. L. Smith, U. Bog, S. Tomljenovic-Hanic, M. W. Lee, D. K. Wu, L. O'Faolain, C. Monat, C. Grillet, T. F. Krauss, C. Karnutsch, R. C. McPhedran, and B. J. Eggleton
    "Reconfigurable microfluidic photonic crystal slab cavities"
    Opt. Express 16, 15887-15896 (2008)
  39. M. W. Lee, C. Grillet, C. G. Poulton, C. Monat, C. L. Smith, E. Mägi, D. Freeman, S. Madden, B. Luther-Davies, and B. J. Eggleton
    "Characterizing photonic crystal waveguides with an expanded k-space evanescent coupling technique,"
    Opt. Express 16, 13800-13808 (2008)
  40. S. Campbell, L.C. Botten, C. Martijn de Sterke, R.C. McPhedran
    "Fresnel formulation for multi-element lamellar diffraction gratings in conical mountings"
    Waves in Random and Complex Media, 17 (4), 455-475 (2007)
  41. Andrei Faraon, Dirk Englund, Douglas Bulla, Barry Luther-Davies, Benjamin J. Eggleton, Nick Stoltz, Pierre Petroff, and Jelena Vuckovic
    "Local tuning of photonic crystal cavities using chalcogenide glasses"
    Appl. Phys. Lett. 92, 043123 (2008)
  42. S. Tomljenovic-Hanic, C.M. de Sterke, M.J. Steel, B.J. Eggleton, Y. Tanaka and S. Noda
    "High-Q cavities in multilayer photonic crystal slab"
    Optics Express 15, 17248-17253 (2007).
  43. Darren Freeman, Christian Grillet, Michael W. Lee, Cameron L.C. Smith, Yinlan Ruan, Andrei Rode, Maryla Krolikowska, Snjezana Tomljenovic-Hanic, C. Martijn de Sterke, Michael J. Steel, Barry Luther-Davies, Steve Madden, David J. Moss, Yong-Hee Lee and Benjamin J. Eggleton
    "Chalcogenide Glass Photonic Crystals: Photonics and Nanostructures - Fundamentals and Applications"
    In Press - Available online (Science Direct) 19 November 2007.
  44. Cameron L. C. Smith, Darran K. C. Wu, Michael W. Lee, Christelle Monat, Snjezana Tomljenovic-Hanic, Christian Grillet, Benjamin J. Eggleton, Darren Freeman, Yinlan Ruan, Steve Madden, Barry Luther-Davies, Harald Giessen and Yong-Hee Lee
    "Microfluidic photonic crystal double heterostructures,"
    Applied Physics Letters, Volume 91, Issue 12, 121103, 17 September 2007
  45. C. Smith, C. Grillet, S. Tomljenovic-Hanic, E.C. Magi, D. Moss, B.J. Eggleton, D. Freeman, S. Madden and B. Luther-Davies
    "Characterisation of chalcogenide 2D photonic crystal waveguides and nanocavities using silica fibre nanowires"
    Physica B: Condensed Matter, Volume 394, Issue 2
  46. Kuhlmey BT, McPhedran RC
    Photonic crystal fibres with resonant coatings
    PHYSICA B-CONDENSED MATTER 394 (2): 155-158 MAY 15 2007
  47. Asatryan AA, Botten LC, Nicorovici NA, et al.
    Tailoring the enhanced frequency shift in two-dimensional photonic clusters
    PHYSICA B-CONDENSED MATTER 394 (2): 213-216 MAY 15 2007
  48. Dossou KB, Botten LC, Wilcox S, et al.
    Exact modelling of generalised defect modes in photonic crystal structures
    PHYSICA B-CONDENSED MATTER 394 (2): 330-334 MAY 15 2007
  49. Dossou KB, McPhedran RC, Botten LC, et al.
    Gap-edge asymptotics of defect modes in two-dimensional photonic crystals
    OPTICS EXPRESS 15 (8): 4753-4762 APR 16 2007
  50. M. W. Lee, C. Grillet, C. L. C. Smith, D. J. Moss, B. J. Eggleton, D. Freeman, B. Luther-Davies, S. Madden, A. Rode, Y. Ruan, and Y. -h. Lee
    Photosensitive post tuning of chalcogenide photonic crystal waveguides
    Opt. Express 15, 1277-1285 (2007)
  51. S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke and D. J. Moss
    High-Q cavities in photosensitive photonic crystals
    Optics Letters, 32, pp 542-544 (2007).
  52. S. Tomljenovic-Hanic, C. M. de Sterke, and M. J. Steel
    Design of high-Q cavities in photonic crystal slab heterostructures by air-holes infiltration
    Opt. Express 14, 12451-12456 (2006)
  53. C. Martijn de Sterke, T.P. White, L.C. Botten, and R.C. McPhedran
    Low interface reflection of rod-type photonic crystals: a bottom up approach
    in Photonic Crystal Materials and Devices IV, edited by A. Adibi, S.-Y. Lin, and A. Scherer,
    Proceedings of SPIE Vol. 6128 (SPIE, Bellingham, 2006), 61281B:1-13.
  54. K. Dossou, L.C. Botten, Shigang Chen, J. Brnovic, R.C. McPhedran, and C. Martijn de Sterke
    Efficient couplers for photonic crystal waveguides
    Optics Communications 265, 207-219 (2006)
  55. L.C. Botten, T.P. White, C. Martijn de Sterke, and R.C. McPhedran,
    Very low reflection, wide-angle coupling into rod-type photonic crystals
    Phys. Rev. E 74, 026603:1-10 (2006)
  56. L. C. Botten, R. C. McPhedran, C. M. de Sterke, N. A. Nicorovici, A. A. Asatryan, G. H. Smith, T. N. Langtry, T. P. White, D. P. Fussell, and B. T. Kuhlmey
    From Multipole Methods to Photonic Crystal Device Modelling
    Chapter 2 of "Electromagnetic Theory and Applications for Photonic Crystals," Ed. K. Yasumoto (CRC Press Inc., 2006, ISBN 0849336775), pp. 47-122.
  57. S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke and J. Salzman:
    Diamond based photonic crystal microcavities
    Optics Express 14, 3556-3562 (2006)
  58. C. Grillet, C. Smith, D. Freeman, S. Madden, B. Luther-Davies, E. Magi, D. Moss, and B. Eggleton
    Efficient coupling to chalcogenide glass photonic crystal waveguides via silica optical fiber nanowires
    Opt. Express 14, 1070-1078 (2006)
  59. S. Tomljenovic-Hanic, C. M. de Sterke and M. J. Steel
    Packing density of conventional waveguides and photonic crystal waveguides
    Optics Communications, Vol. 259, 142-148 (2006)
  60. C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton
    Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes
    Opt. Express 14, 369-376 (2006)
  61. L. C. Botten, R. A. Hansen, and C. M. de Sterke
    Supermodes in multiple coupled photonic crystal waveguides
    Opt. Express 14, 387-396 (2006)
  62. D.P. Fussell, M.M. Dignam, M.J. Steel, C. Martijn de Sterke, and R.C. McPhedran
    Spontaneous emission and photon dynamics in coupled microcavities
    Phys. Rev. A 74, 043806:1-12 (2006)
  63. S. J. Myers, D. P. Fussell, J. M. Dawes, E. Mägi, R. C. McPhedran, B. J. Eggleton, and C. M. de Sterke
    Manipulation of spontaneous emission in a tapered photonic crystal fibre
    Opt. Express 14, 12439-12444 (2006)
  64. M.M. Dignam, D.P. Fussell, M.J. Steel, C. Martijn de Sterke, and R.C. McPhedran
    Spontaneous emission suppression via quantum path interference in coupled-microcavities
    Phys. Rev. Lett. 96, 103902:1-4 (2006).
  65. A.A. Asatryan, L.C. Botten, N.A. Nicorovici, R.C. McPhedran, and C. Martijn de Sterke
    Frequency shift of sources embedded in finite two-dimensional photonic clusters
    Waves in Random and Complex Media 16, 151165 (2006).
  66. White TP, de Sterke CM, McPhedran RC and Botten LC
    Highly-efficient Wide-angle Transmission into Uniform Rod-type Photonic Crstals
    Applied Physics Letters, 87 111107-1-3 (2005)
  67. M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton
    Analytic properties of photonic crystal superprism parameters
    Phys. Rev. E 71, 056608 (2005)
  68. Wilcox S, Botten LC, de Sterke CM, Kuhlmey BT, McPhedran RC, Fussell DP, Tomljenovic-Hanic S
    Long wavelength behavior of the fundamental mode in microstructured optical fibers
    Optics Express 13 (6): 1978-1984 Mar 21 2005
  69. S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C. Martijn de Sterke
    Exact modelling of defect modes in photonic crystals
    Phys. Rev. E 71 056606:1-11 (2005)
  70. A. Asatryan, L.C. Botten, M.A. Byrne, T.N. Langtry, N. Nicorovici, R.C. McPhedran, C.M.de Sterke, and P.A Robinson
    Conductance of photons in disordered photonic crystals
    Phys. Rev. E 71 36623:1-8 (2005)
  71. D.P. Fussell, R.C.McPhedran, and C.M. de Sterke
    Decay rate and level shift in a circular dielectric waveguide
    Phys. Rev. A 71, 013815 (2005)(15 pp.).
  72. D.P. Fussell, R.C. McPhedran, and C.M. de Sterke
    Two-dimensional Treatment of the decay Rate and Level Shift in Photonic Crystals
    Phys. Rev. E, 72, 046605 (2005) (14 pp).
  73. R.C.McPhedran, L.C. Botten, J. McOrist., A.A. Asatryan., C.M. de Sterke, and N.A. Nicorovici
    Density of states functions for photonic crystals
    Physical Review E, 69,016609 (16 pp.)(2004).
  74. D.P. Fussell, R.C. McPhedran, and C.M. de Sterke
    Three-dimensional Green's Tensor, local Density of States and Spontaneous Emission in Finite Two-dimensional Photonic Crystals Composed of Cylinders,
    Phys. Rev. E 70, 066608 (2004) (19 pp.)