Abstract

We propose one-dimensional photonic bandgap (PB) dielectric structures to be used at grazing incidence in order to obtain an extended bandgap exhibiting considerably reduced reflection loss and dispersion compared to similar structures used at a normal incidence of light. The well-known quarter-wave condition is applied for the design in this specific case, resulting in resonance-free reflection bands without drops in reflection versus wavelength function and a monotonous variation of the group delay dispersion versus wavelength function, which are important issues in femtosecond pulse laser applications. Based on these results we extend our studies to two-dimensional PB structures and provide guidelines to the design of leaking mode-free hollow-core Bragg PB fibers providing anomalous dispersion over most of the bandgap.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Macleod, “Thin-Film Optical Filters,” 3rd ed. (Taylor and Francis, 2001).
    [CrossRef]
  2. F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comm. Phys. (London) 1, 81-85 (1976).
  3. E. J. Mayer, J. Möbius, A. Euteneuer, W. W. Rühle, and R. Szip?cs, “Ultrabroadband chirped mirrors for femtosecond lasers,” Opt. Lett. 22, 528-530 (1997).
    [CrossRef] [PubMed]
  4. I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5 fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009-1011 (1997).
    [CrossRef] [PubMed]
  5. K. Ferencz and R. Szip?cs, “Recent development of laser optical coatings in Hungary,” Opt. Eng. 32, 2525-2538 (1993).
    [CrossRef]
  6. A. Stingl, C. Spielmann, F. Krausz, and R. Szip?cs, “Generation of 11 fs pulses from a Ti:sapphire laser without the use of prisms,” Opt. Lett. 19, 204-206 (1994).
    [CrossRef] [PubMed]
  7. P. St. J. Russell, “Photonic crystal fibers,” J. Lightwave Technol. 24, 4729-4749 (2006).
    [CrossRef]
  8. G. Bouwmans, F. Luan, J. Knight, P. St. J. Russell, L. Farr, B. Mangan, and H. Sabert, “Properties of a hollow-core photonic bandgap fiber at 850 nm wavelength,” Opt. Express 11, 1613-1620 (2003).
    [CrossRef] [PubMed]
  9. G. Vienne, Y. Xu, C. Jakobsen, H. J. Deyerl, J. Jensen, T. Sorensen, T. Hansen, Y. Huang, M. Terrel, R. Lee, N. Mortensen, J. Broeng, H. Simonsen, A. Bjarklev, and A. Yariv, “Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports,” Opt. Express 12, 3500-3508(2004).
    [CrossRef] [PubMed]
  10. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196-1201 (1978).
    [CrossRef]
  11. M. Foroni, D. Passaro, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. Bjarklev, “Confinement loss spectral behavior in hollow-core Bragg fibers,” Opt. Lett. 32, 3164-3166 (2007).
    [CrossRef] [PubMed]
  12. K. Saitoh, N. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12, 394-400 (2004).
    [CrossRef] [PubMed]
  13. J. Hebling, E. J. Mayer, J. Kuhl, and R. Szip?cs, “Chirped-mirror dispersion-compensated optical parametric oscillator,” Opt. Lett. 20, 919-921 (1995).
    [CrossRef] [PubMed]
  14. Z. Bor, B. Rácz, G. Szabó, and Z. G. Horváth, “Two-dimensional halo laser performance,” Phys. Lett. A 80, 153-155 (1980).
    [CrossRef]
  15. Z. Várallyay, J. Fekete, and R. Szip?cs, “Higher-order mode photonic bandgap fibers with reversed dispersion slope,” in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2008), paper JWA8.

2008 (1)

Z. Várallyay, J. Fekete, and R. Szip?cs, “Higher-order mode photonic bandgap fibers with reversed dispersion slope,” in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2008), paper JWA8.

2007 (1)

2006 (1)

2004 (2)

2003 (1)

2001 (1)

H. A. Macleod, “Thin-Film Optical Filters,” 3rd ed. (Taylor and Francis, 2001).
[CrossRef]

1997 (2)

1995 (1)

1994 (1)

1993 (1)

K. Ferencz and R. Szip?cs, “Recent development of laser optical coatings in Hungary,” Opt. Eng. 32, 2525-2538 (1993).
[CrossRef]

1980 (1)

Z. Bor, B. Rácz, G. Szabó, and Z. G. Horváth, “Two-dimensional halo laser performance,” Phys. Lett. A 80, 153-155 (1980).
[CrossRef]

1978 (1)

1976 (1)

F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comm. Phys. (London) 1, 81-85 (1976).

Bjarklev, A.

Bor, Z.

Z. Bor, B. Rácz, G. Szabó, and Z. G. Horváth, “Two-dimensional halo laser performance,” Phys. Lett. A 80, 153-155 (1980).
[CrossRef]

Bouwmans, G.

Broeng, J.

Cucinotta, A.

Deyerl, H. J.

Euteneuer, A.

Farr, L.

Fekete, J.

Z. Várallyay, J. Fekete, and R. Szip?cs, “Higher-order mode photonic bandgap fibers with reversed dispersion slope,” in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2008), paper JWA8.

Ferencz, K.

K. Ferencz and R. Szip?cs, “Recent development of laser optical coatings in Hungary,” Opt. Eng. 32, 2525-2538 (1993).
[CrossRef]

Foroni, M.

Hansen, T.

Hebling, J.

Horváth, Z. G.

Z. Bor, B. Rácz, G. Szabó, and Z. G. Horváth, “Two-dimensional halo laser performance,” Phys. Lett. A 80, 153-155 (1980).
[CrossRef]

Huang, Y.

Jakobsen, C.

Jensen, J.

Jung, I. D.

Kärtner, F. X.

Keller, U.

Knight, J.

Koshiba, M.

Krausz, F.

Kuhl, J.

Laegsgaard, J.

Lee, R.

Luan, F.

Macleod, H. A.

H. A. Macleod, “Thin-Film Optical Filters,” 3rd ed. (Taylor and Francis, 2001).
[CrossRef]

Mangan, B.

Marom, E.

Matuschek, N.

Mayer, E. J.

Mezei, F.

F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comm. Phys. (London) 1, 81-85 (1976).

Möbius, J.

Morier-Genoud, F.

Mortensen, N.

Passaro, D.

Poli, F.

Rácz, B.

Z. Bor, B. Rácz, G. Szabó, and Z. G. Horváth, “Two-dimensional halo laser performance,” Phys. Lett. A 80, 153-155 (1980).
[CrossRef]

Rühle, W. W.

Russell, P. St. J.

Sabert, H.

Saitoh, K.

Scheuer, V.

Selleri, S.

Simonsen, H.

Sorensen, T.

Spielmann, C.

Stingl, A.

Sutter, D. H.

Szabó, G.

Z. Bor, B. Rácz, G. Szabó, and Z. G. Horváth, “Two-dimensional halo laser performance,” Phys. Lett. A 80, 153-155 (1980).
[CrossRef]

Szipocs, R.

Terrel, M.

Tilsch, M.

Tschudi, T.

Várallyay, Z.

Z. Várallyay, J. Fekete, and R. Szip?cs, “Higher-order mode photonic bandgap fibers with reversed dispersion slope,” in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2008), paper JWA8.

Vienne, G.

Xu, Y.

Yariv, A.

Yeh, P.

Zhang, G.

Comm. Phys. (London) (1)

F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comm. Phys. (London) 1, 81-85 (1976).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

K. Ferencz and R. Szip?cs, “Recent development of laser optical coatings in Hungary,” Opt. Eng. 32, 2525-2538 (1993).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Phys. Lett. A (1)

Z. Bor, B. Rácz, G. Szabó, and Z. G. Horváth, “Two-dimensional halo laser performance,” Phys. Lett. A 80, 153-155 (1980).
[CrossRef]

Other (2)

Z. Várallyay, J. Fekete, and R. Szip?cs, “Higher-order mode photonic bandgap fibers with reversed dispersion slope,” in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2008), paper JWA8.

H. A. Macleod, “Thin-Film Optical Filters,” 3rd ed. (Taylor and Francis, 2001).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Reflectivity and group delay as a function of wavelength for (a) a periodic ML structure designed for normal incidence, (b) a chirped ML structure designed for normal incidence, and (c) a periodic ML structure designed for grazing incidence, S polarization. GDD versus wavelength functions are shown in the insets.

Fig. 2
Fig. 2

(a) Computed physical thickness of the low index layer ( PT L ) as a function of the layer index ( n L ) when meeting the λ / 4 condition at an angle of incidence Θ 0 = 86 ° and computed bandwidth ( Δ ω ) of the bandgap as a function of n L when n H = 1.45 (P polarized light). (b) Computed modification factor of the OT of different refractive index layers as a function of the incident angle.

Fig. 3
Fig. 3

(a) Refractive index profile of the 1D equivalent of the fiber and (b) cross section of the HC Bragg PBF used in our FEM simulations.

Fig. 4
Fig. 4

(a) One-dimensional computation results for transmission of the ML structure (corresponding to the loss of the fiber) as a function of wavelength for structures of the following designs: n L = 1.00 and PT L = 3.58 μm ideal structure without silica struts (black dashed curve), n L = 1.02 and PT L = 3.58 μm leaking modes (blue dotted curve), n L = 1.02 and PT L = 1.18 μm corrected λ / 4 structure (red solid curve), n L i = 1.006 , 1.005, and 1.004 and PT L i = 1.92 , 2.05, and 2.16 μm , respectively, iterated chirped structure (green solid curve). (b) Corresponding FEM results including the homogenized iterated chirped structure with n eff , i values instead of the silica struts (light blue narrow dash–dotted curve). Points in the graph marked with circles refer to different mode-field distributions shown in Fig. 5.

Fig. 5
Fig. 5

Mode distributions of (a) the fundamental mode [corresponding to Point 1 in Fig. 4b], (b) the leaking mode [corresponding to Point 2 in Fig. 4b], and (c) the surface mode [corresponding to Point 3 in Fig. 4b, green curve].

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Θ 0 = arcsin ( ( n eff ) ) .
PT i = λ 0 4 1 n i cos ( Θ i ) ,
sin 2 α i = sin 2 α 0 + 2 ( n i 1 ) n i .
PT i = λ 0 4 1 n i 1 cos 2 Θ 0 + 2 SFF i · ( n s 1 ) ,

Metrics