Abstract

We have investigated optical properties of an optical fiber having a six-fold symmetric quasiperiodic array of air holes in cladding, a six-fold symmetric photonic quasicrystal fiber. The photonic quasicrystal fiber exhibits larger cutoff ratio for endlessly single mode operation than that of a triangular photonic crystal fiber having six-fold symmetry and almost zero ultra-flattened chromatic dispersion, 0±0.05 ps/km/nm, in the range of wavelength from 1490 to 1680 nm. The dispersion value is much less than those of the proposed dispersion flattened PCFs.

© 2007 Optical Society of America

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  1. 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]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).
  3. J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003).
    [CrossRef] [PubMed]
  4. P. Russell, "Appl. Phys.: Photonic Crystal Fibers," Science 299, 358-362 (2003).
    [CrossRef] [PubMed]
  5. T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  6. M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
    [CrossRef] [PubMed]
  7. B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
    [CrossRef] [PubMed]
  8. Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
    [CrossRef]
  9. C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
    [CrossRef]
  10. K. Nozaki and T. Baba, "Quasiperiodic potonic crystal microcavity lasers," Appl. Phys. Lett. 84, 4875-4877 (2004).
    [CrossRef]
  11. S. K. Kim, J. H. Lee, S. H. Kim, I. K. Hwang, and Y. H. Lee, "Photonic quasicrystal single-cell cavity mode," Appl. Phys. Lett. 86, 031101 (2005).
    [CrossRef]
  12. P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
    [CrossRef]
  13. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003).
    [CrossRef] [PubMed]
  14. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  15. F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A. Cucinotta, and S. Selleri, " Single-mode regime of square-lattice photonic crystal fibers," J. Opt. Soc. Am. A 22, 1655-1661 (2005).
    [CrossRef]
  16. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrës "Nearly zero ultraflattened dispersion in photonic crystal fibers," Opt. Lett. 25, 790-792 (2000).
    [CrossRef]
  17. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002).
    [PubMed]
  18. F. Poletti, V. Finazzi, T. M. Morno, N. G. R. Broderick, V. Tse, and D. J. Richardson, " Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005).
    [CrossRef] [PubMed]
  19. F. Fogil, L. Saccomandi, and P. Bassi, "Full vectorial BPM modeling of index-guding photonic crystal fibers and couplers," Opt. Express 10, 54-59 (2002).
  20. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2000).
  21. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic band gap guidance in optical fiber," Science 282, 1476-1478 (1998).
    [CrossRef] [PubMed]

2006

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
[CrossRef]

2005

2004

K. Nozaki and T. Baba, "Quasiperiodic potonic crystal microcavity lasers," Appl. Phys. Lett. 84, 4875-4877 (2004).
[CrossRef]

2003

J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

P. Russell, "Appl. Phys.: Photonic Crystal Fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003).
[CrossRef] [PubMed]

2002

2000

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrës "Nearly zero ultraflattened dispersion in photonic crystal fibers," Opt. Lett. 25, 790-792 (2000).
[CrossRef]

M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

1999

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

1998

Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic band gap guidance in optical fiber," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

1997

1995

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]

1990

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Andrës, P.

Atkin, D. M.

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]

Baba, T.

K. Nozaki and T. Baba, "Quasiperiodic potonic crystal microcavity lasers," Appl. Phys. Lett. 84, 4875-4877 (2004).
[CrossRef]

Ban, S.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Bartal, G.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

Bassi, P.

Baumberg, J. J.

M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic band gap guidance in optical fiber," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

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]

Bottacini, M.

Broderick, N. G. R.

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic band gap guidance in optical fiber," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Burani, N.

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
[CrossRef]

Chariton, M. D. B.

M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

Cheng, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Christoet, D. N.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

Cucinotta, A.

Ferrando, A.

Finazzi, V.

Fogil, F.

Folkenberg, J. R.

Foroni, M.

Freedman, B.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

Fuochi, M.

Hansen, K. P.

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Hwang, I. K.

S. K. Kim, J. H. Lee, S. H. Kim, I. K. Hwang, and Y. H. Lee, "Photonic quasicrystal single-cell cavity mode," Appl. Phys. Lett. 86, 031101 (2005).
[CrossRef]

Jin, C.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Kim, S. H.

S. K. Kim, J. H. Lee, S. H. Kim, I. K. Hwang, and Y. H. Lee, "Photonic quasicrystal single-cell cavity mode," Appl. Phys. Lett. 86, 031101 (2005).
[CrossRef]

Kim, S. K.

S. K. Kim, J. H. Lee, S. H. Kim, I. K. Hwang, and Y. H. Lee, "Photonic quasicrystal single-cell cavity mode," Appl. Phys. Lett. 86, 031101 (2005).
[CrossRef]

Knight, J. C.

Kuo, H. -C.

P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
[CrossRef]

Lee, J. H.

S. K. Kim, J. H. Lee, S. H. Kim, I. K. Hwang, and Y. H. Lee, "Photonic quasicrystal single-cell cavity mode," Appl. Phys. Lett. 86, 031101 (2005).
[CrossRef]

Lee, P. -T.

P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
[CrossRef]

Lee, Y. H.

S. K. Kim, J. H. Lee, S. H. Kim, I. K. Hwang, and Y. H. Lee, "Photonic quasicrystal single-cell cavity mode," Appl. Phys. Lett. 86, 031101 (2005).
[CrossRef]

Li, Z.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Lifshitz, R.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
[CrossRef]

Lu, T. -C.

P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
[CrossRef]

Lu, T. -Q.

P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
[CrossRef]

Man, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Miret, J. J.

Morno, T. M.

Mortensen, N. A.

Netti, M. C.

M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

Nielsen, M. D.

Nozaki, K.

K. Nozaki and T. Baba, "Quasiperiodic potonic crystal microcavity lasers," Appl. Phys. Lett. 84, 4875-4877 (2004).
[CrossRef]

Parker, G. J.

M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

Poletti, F.

Poli, F.

Reeves, W. H.

Richardson, D. J.

Roberts, P. J.

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002).
[PubMed]

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]

Rosa, L.

Russell, P.

P. Russell, "Appl. Phys.: Photonic Crystal Fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Russell, P. St. J.

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002).
[PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic band gap guidance in optical fiber," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

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]

Saccomandi, L.

Segev, M.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

Selleri, S.

Shepherd, T. J.

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]

Silvestre, E.

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Sun, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Tsai, F. -M.

P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
[CrossRef]

Tse, V.

Zhang, D.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Zoorob, M. E.

M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

K. Nozaki and T. Baba, "Quasiperiodic potonic crystal microcavity lasers," Appl. Phys. Lett. 84, 4875-4877 (2004).
[CrossRef]

S. K. Kim, J. H. Lee, S. H. Kim, I. K. Hwang, and Y. H. Lee, "Photonic quasicrystal single-cell cavity mode," Appl. Phys. Lett. 86, 031101 (2005).
[CrossRef]

P. -T. Lee, T. -Q. Lu, F. -M. Tsai, T. -C. Lu, and H. -C. Kuo, "Whispering gallery mode of modified octagonal quasiperiodic photonic crystal single-defect microcavity and its side-mode reduction," Appl. Phys. Lett. 88, 201104 (2006).
[CrossRef]

Electron. Lett.

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]

J. Opt. Soc. Am. A

Nature

M. E. Zoorob, M. D. B. Chariton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, and D. N. Christoet, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
[CrossRef]

Science

P. Russell, "Appl. Phys.: Photonic Crystal Fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic band gap guidance in optical fiber," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic cross section of a six-fold symmetric photonic quasicrystal fiber and elementary units of the quasicrystal (dotted lines). Black circles denote air holes. a is the distance between neighboring air holes and d is the diameter of air holes.

Fig. 2.
Fig. 2.

V parameters of the six-fold symmetric PQF, VPQF , for various d/a. The values of d/a are inserted as insets and assigned to different colors. VPQF is normalized to π. The dashed line denotes the cutoff value below which a single mode is allowed and circles denote the cutoff wavelength of the second-order mode.

Fig. 3.
Fig. 3.

Dispersion behavior of the six-fold symmetric PQF for d /a=0.31 and a = 2.41 μm in the range of wavelength from 1.0 to 1.9 μm. D(λ), D g(λ), and -D m(λ) are denoted by red line, blue line, and black line, respectively.

Fig. 4.
Fig. 4.

Dispersion of the six-fold symmetric PQF (red line) and a triangular lattice PCF (blue line) in the range from 1.3 to 1.8 μm for d/a = 0.31 and a = 2.41 μm. The gray region denotes the almost zero ultra-flattened dispersion (0 ± 0.05 ps nm-1 km-1) in the range from 1.49 to 1.68 μm. The detailed dispersion behavior is shown in the inset.

Equations (2)

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V PQF ( λ cutoff ) = π
D ( λ ) D g ( λ ) + D m ( λ ) = λ c d 2 n g ( λ ) 2 λ c d 2 n m ( λ ) 2 ,

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