Optical Waveguide Gratings and Slow Light

Enbang Li, Martijn de Sterke, Benjamin Eggleton

Optical Grating Writing

Many of the nonlinear materials exploited in CUDOS exhibit a degree of photosensitivity, allowing the modification of the refractive index using lasers. By interfering light in complex ways, detailed resonant structures can be created in waveguides and fibres, which underpin many of the experimental programs in CUDOS. We have established a facility to produce complex grating structures in optical fibres at 1 µm as well as 1.5 µm. These have been used as filters and complex dispersion compensators for nonlinear experiments as well as specialized long gratings for gap soliton studies. In addition, value added grating based devices have been demonstrated, including the variable bandwidth dispersionless filter for reconfigurable networks. More recently, we have demonstrated strong gratings in chlacogenide waveguides. The high nonlinearity and high refractive index modulation achievable in this material (dn/n=1%) open up the possibility of fully integrated waveguide components, such as photonic switches or optical regenerators on a chip.


Figure 1. A Sagnac based interefometer was used to write a Bragg resonance into a chalcogenide waveguide with FWHM ~10nm.


Figure 2. Apodised fibre Moire grating 120mm - Index modulation made visible via sidescan spectroscopy

Slow light in optical gratings

Even though the phase velocity of light is more or less fixed, the group velocity can vary widely. The group velocity (dw/dk) determines the time it takes an optical pulse to travel through an optical waveguide is. In dispersive media like gratings and photonic crystals the group velocity can become much less than the phase velocity c/n, so the transit time of the pulse in the waveguide stretches proportionally. If the range of frequencies over which this dispersive behaviour exists encompasses the spectrum of the pulse and the group velocity is constant, then the pulse will be slowed with minimal distortion in its shape – hence the term "slow light". Slow light is of fundamental interest and may also be useful in applications such as optical delay lines and ultra-low threshold optical devices.

The ability to control the group velocity of light, the velocity at which the energy travels, has important applications in all-optical network routers and other devices where buffereing is required. In these applications it is important that the light can be delayed in time by a tunable amount longer than the pulse length. Currently this is done electronically, but electronics will not be able to deal with the short pulses used in the next generation of networks.

Slow Gap Solitons

In applying grating based slow light to the problem of optical bufferes, one of the problems faced is that group velocity in general is not constant and so pulse distortion occurs. To address this, we have developed a slow-light approach based on the excitation of temporal gap solitons (Fig 1.), which are intense pulses that can propagate inside the bandgap of a nonlinear periodic structure. Pulses are reflected at low incident intensities, but are transmitted at intensities above a certain threshold, with the transmitted pulse travelling at low group velocity. Unlike linear systems, slow light by exciting gap solitons is not limited by the delay-bandwidth trade-off imposed by the Kramers-Kroning relation.

Slow light

Fig. 3 Experimental setup for demonstrating temporal gap solitors within a fiber Bragg grating. Grating resonance can be tuned by moving one stage.

An apodized fibre Bragg grating is used as the medium to observe such behaviour. Experiments show a nonlinear transmission of the device, which is characteristic of gap soliton formation (Fig. 2). Pulse measurement reveals that the transmitted pulse is delayed by as much as 1.6 ns, corresponding to a group velocity of 0.23 c/n (Fig. 3). Results also show that one can achieve some tunability in the delay by controlling the incident intensity.

Slow Light

Fig. 4 Observation of nonlinear transmission for different offsets of the grating bandgap.

Slow Light

Fig. 5 Measured behaviour of the slow light progation for different pulse powers. (red dotted line is when the resonance is detuned from the pulse while the blue solid line is when the pulse is slowed by the resonance)


  1. Andrea Blanco-Redondo, Imanol Andonegui, Matthew J. Collins, Gal Harari, Yaakov Lumer, Mikael C. Rechtsman, Benjamin J. Eggleton, and Mordechai Segev,
    "Topological Optical Waveguiding in Silicon and the Transition between Topological and Trivial Defect States",
    Phys. Rev. Lett. 116, 163901, doi: http://dx.doi.org/10.1103/PhysRevLett.116.163901 (2016)
  2. Andrea Blanco-Redondo, de Sterke C. Martijn, J.E. Sipe, Thomas F. Krauss, Benjamin J. Eggleton & Chad Husko,
    "Pure-quartic solitons,"
    Nat. Commun. 7:10427 doi: 10.1038/ncomms10427 (2016)
  3. Yanbing Zhang, Chad Husko, Simon Lefrancois, Isabella H. Rey, Thomas F. Krauss, Jochen Schröder, and Benjamin J. Eggleton,
    "Cross-phase modulation-induced spectral broadening in silicon waveguides,"
    Opt. Express 24, 443-451 (2016), doi: 10.1364/OE.24.000443
  4. Andrea Blanco-Redondo, Daniel Eades, Juntao Li, Simon Lefrancois, Thomas F. Krauss, Benjamin J. Eggleton, and Chad Husko,
    "Controlling free-carrier temporal effects in silicon by dispersion engineering,"
    Optica 1, 299-306 (2014)
  5. Yanbing Zhang, Jochen Schröder, Chad Husko, Simon Lefrancois, Duk-Yong Choi, Steve Madden, Barry Luther-Davies, and Benjamin J. Eggleton,
    "Pump-degenerate phase-sensitive amplification in chalcogenide waveguides,"
    J. Opt. Soc. Am. B 31, 780-787 (2014)
  6. 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)
  7. 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)
  8. S. V. Afshar, T. M. Monro, and C. M. de Sterke,
    “Understanding the contribution of mode area and slow light to the effective Kerr nonlinearity of waveguides,”
    Optics Express 21, 18558-18571 (2013)
  9. Eilenberger, F., Kabakova, I.V., de Sterke, C.M., Eggleton, B.J. & Pertsch, T.,
    "Cavity Optical Pulse Extraction: ultra-short pulse generation as seeded Hawking radiation,"
    Sci. Rep. 3, 2607; DOI:10.1038/srep02607 (2013)
  10. L. E. Zou, I. V. Kabakova, E. C. Mägi, E. Li, C. Florea, I. D. Aggarwal, B. Shaw, J. S. Sanghera, and B. J. Eggleton, "Efficient inscription of Bragg gratings in As2S3 fibers using near bandgap light,"
    Opt. Lett. 38, 3850-3853 (2013)
  11. 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)
  12. Irina V. Kabakova, Liner Zou, George A. Brawley, Catalin Florea, Ishwar D. Aggarwal, Jasbinder S. Sanghera, Eric C. Mägi, Enbang Li, and Benjamin J. Eggleton,
    "Dynamics of photoinduced refractive index changes in As2S3 fibers,"
    Appl. Opt. 51, 7333-7338 (2012)
  13. 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)
  14. Shu-Wei Huang, Giovanni Cirmi, Jeffrey Moses, Kyung-Han Hong, Siddharth Bhardwaj, Jonathan R Birge, Li-Jin Chen, Irina V Kabakova, Enbang Li, Benjamin J Eggleton, Giulio Cerullo and Franz X Kärtner,
    "Optical waveform synthesizer and its application to high-harmonic generation,"
    Journal of Physics B: Atomic, Molecular and Optical Physics 45 074009 (2012)
  15. Ravi Pant, Adam Byrnes, Christopher G. Poulton, Enbang Li, Duk-Yong Choi, Steve Madden, Barry Luther-Davies, and Benjamin J. Eggleton,
    "Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,"
    Opt. Lett. 37, 969-971 (2012)
  16. 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)
  17. Irina V. Kabakova, Dan Grobnic, Stephen Mihailov, Eric C. Mägi, C. Martijn de Sterke, and Benjamin J. Eggleton,
    "Bragg grating-based optical switching in a bismuth-oxide fiber with strong χ(3)-nonlinearity,"
    Opt. Express 19, 5868-5873 (2011)
  18. Michael W. Lee, Christian Grillet, Christelle Monat, Eric Mägi, Snjezana Tomljenovic-Hanic, Xin Gai, Steve Madden, Duk-Yong Choi, Douglas Bulla, Barry Luther-Davies, Benjamin J. Eggleton,
    "Photosensitive and thermal nonlinear effects in chalcogenide photonic crystal cavities,"
    Opt. Express 18, 26695-26703 (2010)
  19. Irina V. Kabakova, C. Martijn de Sterke, and Benjamin J. Eggleton,
    "Bistable switching and reshaping of optical pulses in a Bragg grating cavity,"
    J. Opt. Soc. Am. B 27, 2648-2653 (2010)
  20. Irina V. Kabakova, Therese Walsh, C. Martijn de Sterke, and Benjamin J. Eggleton,
    "Performance of field-enhanced optical switching in fiber Bragg gratings,"
    J. Opt. Soc. Am. B 27, 1343-1351 (2010)
  21. Falk Eilenberger, C. Martijn de Sterke, and Benjamin J. Eggleton,
    "Soliton mediated optical quantization in the transmission of one-dimensional photonic crystals,"
    Opt. Express 18, 12708-12718 (2010)
  22. 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)
  23. 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)
  24. 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
  25. 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
  26. Movchan, N.V., McPhedran, R.C., Movchan, A.B., and Poulton, C.G.
    "Wave scattering by platonic grating stacks"
    Proceedings of the Royal Society A, 465, 3383-3400 (2009).
  27. McPhedran, R.C., Chen, P.Y., Bonod, N. and Popov, E.
    "Gratings and their quasistatic equivalents for high optical absorptance"
    Phys. Rev. A, 79, 053850 (2009)
  28. 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)
  29. 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)
  30. Baker, N.J.; Roelens, M.A.F.; Madden, S.; Luther-Davies, B.; De Sterke, C.M.; Eggleton, B.J.
    "Pulse train generation by soliton fission in highly nonlinear chalcogenide (As2S3) waveguide Bragg grating,"
    Electronics Letters , vol.45, no.15, pp.799-800, July 16 2009
  31. J. Moses, S.-W. Huang, K.-H. Hong, O. D. Mücke, E. L. Falcão-Filho, A. Benedick, F. Ö. Ilday, A. Dergachev, J. A. Bolger, B. J. Eggleton, and F. X. Kärtner,
    "Highly stable ultrabroadband mid-IR optical parametric chirped-pulse amplifier optimized for superfluorescence suppression,"
    Opt. Lett. 34, 1639-1641 (2009)
  32. 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)
  33. Irina V. Kabakova, Bill Corcoran, Jeremy A. Bolger, Martijn de Sterke, and Benjamin J. Eggleton,
    "All-optical self-switching in optimized phase-shifted fiber Bragg grating,"
    Opt. Express 17, 5083-5088 (2009)
  34. 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)
  35. 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)
  36. B. T. Kuhlmey, F. Luan, L. Fu, D. Yeom, B. J. Eggleton, A. Wang, and J. C. Knight,
    "Experimental reconstruction of bands in solid core photonic bandgap fibres using acoustic gratings,"
    Opt. Express 16, 13845-13856 (2008)
  37. H. C. Nguyen, D. Yeom, E. C. Mägi, B. T. Kuhlmey, C. M. de Sterke, and B. J. Eggleton
    "Nonlinear switching using long-period gratings in As2Se3 chalcogenide fiber"
    J. Opt. Soc. Am. B 25, 1393-1401 (2008)
  38. Brawley, G.A.; Taeed, V.G.; Bolger, J.A.; Sanghera, J.S.; Aggarwal, I.; Eggleton, B.J.,
    "Strong photoinduced Bragg gratings in arsenic selenide optical fibre using transverse holographic method,"
    Electronics Letters, vol.44, no.14, pp.846-847, July 3 2008
  39. Tsoy, EN; de Sterke, CM
    "Oscillations of the soliton parameters in nonlinear interference phenomena"
    PHYSICS LETTERS A, 372, 11, 1856-1861, 2008
  40. H. C. Nguyen, D. I. Yeom, E. C. Mägi, L. B. Fu, B. T. Kuhlmey, C. M. de Sterke, and B. J. Eggleton
    "Nonlinear long-period gratings in As2Se3 chalcogenide fiber for all-optical switching,"
    Appl. Phys. Lett. 92, 101127 (2008).
  41. Mok, J.T.; Ibsen, M.; Martijn De Sterke, C.; Eggleton, B.J.,
    "Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,"
    Electronics Letters , vol.43, no.25, pp.1418-1419, Dec. 6 2007
  42. Thomas Grujic, Hong C. Nguyen, Michael R.E. Lamont, C. Martijn de Sterke and Benjamin J. Eggleton
    "All-optical regeneration based on a nonlinear long period grating"
    Optics Communications, Available online 26 November 2007.
  43. Eduard N. Tsoy and C. Martijn de Sterke
    "Theoretical analysis of the self-frequency shift near zero-dispersion points: Soliton spectral tunneling"
    Phys. Rev. A 76, 043804 (2007).
  44. J. A. Bolger, F. Luan, D. -I. Yeom, E. N. Tsoy, C. M. de Sterke, and B. J. Eggleton
    "Tunable enhancement of a soliton spectrum using an acoustic long-period grating,"
    Opt. Express 15, 13457-13462 (2007)
  45. D. -Y. Choi, S. Madden, A. Rode, R. Wang, B. Luther-Davies, N. J. Baker,
    and B. J. Eggleton, "Integrated shadow mask for sampled Bragg gratings in
    chalcogenide (As2S3) planar waveguides," Opt. Express 15, 7708-7712 (2007)
  46. D. -I. Yeom, J. A. Bolger, G. D. Marshall, D. R. Austin, B. T. Kuhlmey, M.
    J. Withford, C. Martijn de Sterke, and B. J. Eggleton, "Tunable spectral
    enhancement of fiber supercontinuum," Opt. Lett. 32, 1644-1646 (2007)
  47. K. Finsterbusch, N. J. Baker, V. G. Ta'eed, B. J. Eggleton, D. -Y. Choi, S.
    Madden, and B. Luther-Davies, "Higher-order mode grating devices in As2S3
    chalcogenide glass rib waveguides," J. Opt. Soc. Am. B 24, 1283-1290 (2007)
  48. J.A. Bolger, I.C.M. Littler and B.J. Eggleton
    Optimisation of superimposed chirped fibre Bragg gratings for the generation of ultra-high speed optical pulse bursts
    Optics Communications, Volume 271, Issue 2, 15 March 2007, Pages 524-531
  49. Joe T. Mok, C. Martijn de Sterke, Ian C. M. Littler and Benjamin J. Eggleton
    Dispersionless slow light using gap solitons
    Nature Physics, Published online: 22 October 2006
  50. Finsterbusch, K.; Baker, N.; Ta'eed, V.G.; Eggleton, B.J.; Choi, D.; Madden, S.; Luther-Davis, B.,
    Long-period gratings in chalcogenide (As2S3) rib waveguides
    Electronics Letters , vol.42, no.19pp. 1094- 1095, Sept. 2006
  51. N. J. Baker, H. W. Lee, I. C. Littler, C. M. de Sterke, B. J. Eggleton, D.-Y. Choi, S. Madden, and B. Luther-Davies
    Sampled Bragg gratings in chalcogenide (As2S3) rib-waveguides
    Opt. Express 14, 9451-9459 (2006)
  52. I.C. M. Littler, L. B. Fu, E. C. Mägi, D. Pudo, and B. J. Eggleton
    Widely tunable, acousto-optic resonances in Chalcogenide As2Se3 fiber
    Opt. Express 14, 8088-8095 (2006)
  53. Ian C.M. Littler, Martin Rochette and Benjamin J. Eggleton
    Impact of chromatic dispersion and group delay ripple on self-phase modulation based optical regenerators
    Optics Communications, Volume 265, Issue 1, 1 September 2006, Pages 95-99.
  54. Ian C.M. Littler, Libin Fu, Michael Lee and Benjamin J. Eggleton
    Investigation of single harmonic group delay ripple on picosecond pulses using FROG: Tailoring pulse bursts
    Optics Communications, Volume 265, Issue 1, 1 September 2006, Pages 147-152.
  55. M. Shokooh-Saremi, V. G. Ta'eed, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies
    High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer
    J. Opt. Soc. Am. B 23, 1323-1331 (2006)
  56. Ian C. M. Littler, Tom Grujic, and Benjamin J. Eggleton
    Photothermal effects in fiber Bragg gratings
    Appl. Opt. 45, 4679-4685 (2006)
  57. P. Steinvurzel, E. D. Moore, E. C. Mägi, and B. J. Eggleton
    Tuning properties of long period gratings in photonic bandgap fibers
    Opt. Lett. 31, 2103-2105 (2006)
  58. Magne, J. Bolger, J. Rochette, M. LaRochelle, S. Chen, L.R. Eggleton, B.J. Azana, J
    Generation of a 4$times$100 GHz Pulse-Train From a Single-Wavelength 10-GHz Mode-Locked Laser Using Superimposed Fiber Bragg Gratings and Nonlinear Conversion
    Lightwave Technology, Journal of, May 2006 Volume: 24, Issue: 5
  59. D. Pudo, E. C. Mägi, and B. J. Eggleton
    Long-period gratings in chalcogenide fibers
    Opt. Express 14, 3763-3766 (2006)
  60. J. T. Mok, C. M. de Sterke, and B. J. Eggleton
    Delay-tunable gap-soliton-based slow-light system
    Opt. Express 14, 11987-11996 (2006)
  61. N. J. Baker, H. W. Lee, I. C. Littler, C. M. de Sterke, B. J. Eggleton, D.-Y. Choi, S. Madden, and B. Luther-Davies
    Sampled Bragg gratings in chalcogenide (As2S3) rib-waveguides
    Opt. Express 14, 9451-9459 (2006)
  62. M. Sumetsky and B.J. Eggleton
    Fiber Bragg gratings for dispersion compensation in optical communication systems
    Journal of Optical and Fiber Communications Reports, Volume 2, Issue 3, Sep 2005, Pages 256 - 278
  63. Joe T. Mok, Ian C. M. Littler, Eduard Tsoy, Benjamin J. Eggleton
    Soliton compression and pulse-train generation by use of microchip Q-switched pulses in Bragg gratings,
    Optics Letters, Volume 30, Issue 18, 2457-2459 September 2005.
  64. Shokooh-Saremi, M.; Ta'eed, V.G.; Littler, I.C.M.; Moss, D.J.; Eggleton, B.J.; Ruan, Y.; Luther-Davies, B.
    Ultra-strong, well-apodised Bragg gratings in chalcogenide rib waveguides
    Electronics Letters Volume 41, Issue 13, 23 Jun 2005 Page(s):21 - 22.
  65. M. Rochette, I.C.M. Littler, R.W. McKerracher, B.J. Eggleton
    A Dispersionless and Bandwidth-Adjustable FBG Filter for Reconfigurable 2R-Regeneration
    Photonics Technology Letters, IEEE Volume 17, Issue 8, Aug. 2005 Page(s):1680 - 1682
  66. I.C. M. Littler, Libin Fu, B. J. Eggleton
    Effect of group delay ripple on picosecond pulse compression schemes
    Applied Optics, Vol. 44 Issue 22 Page 4702 (August 2005).
  67. Fu LB, Marshall GD, Bolger JA, Steinvurzel P, Magi EC, Withford MJ, Eggleton BJ
    Femtosecond laser writing Bragg gratings in pure silica photonic crystal fibres
    ELECTRONICS LETTERS 41 (11): 638-640 MAY 26 2005.
  68. Steinvurzel P, MacHarrie RA, Baldwin KW, Van Hise CW, Eggleton BJ, Rogers JA
    Optimization of distributed resistive metal film heaters in thermally tunable dispersion compensators for high-bit-rate communication systems
    Applied Optics, 44 (14), 2782-2791 (2005)
  69. Ian C.M. Littler, Martin Rochette & Benjamin Eggleton
    Adjustable bandwidth dispersionless bandpass FBG optical filter
    Optics Express 13, 3397-3407, (2005).
  70. Jong H. Chow, Benjamin S. Sheard, David E. McClelland, Malcolm B. Gray and Ian C. M. Littler
    Photothermal effects in passive fiber Bragg grating resonators
    Optics Letters, 30, 708-710, (2005)
  71. C. Martijn de Sterke and Benjamin J. Eggleton
    Spectral Talbot effect: interpretation via band diagrams
    Optics Communications, 248(1-3), 117-121 (2005)
  72. Lobo AE, Besley JA, de Sterke CM
    Gain-flattening filter design using rotationally symmetric crossed gratings
    Journal of Lightwave Technology 21 (9): 2084-2088 SEP 2003
  73. Sumetsky M, Litchinitser NM, Westbrook PS, et al.
    High-performance 40 Gbit/s fibre Bragg grating tunable dispersion compensator fabricated using group delay ripple correction technique
    Electronics Letters 39 (16): 1196-1198 AUG 7 2003.
  74. Libin Fu, Ian C.M. Littler, Joe T. Mok & Benjamin Eggleton
    Matched photonic bandgap fibre and fibre Bragg grating dispersion for all in-fibre stretch pulse amplification
    Electronics Letters 41, 306-307 (2005).
  75. Mok JT, Eggleton BJ, Photonics
    Expect more delays
    Nature 433 (7028), 811-812 (2005)