Abstract

An effective-index method (EIM) is used to analyze and design photonic crystal fibers (PCFs) for the terahertz radiation. By building an analogy between a conventional optical fiber and a PCF, the EIM solves the effective index of the fiber cladding and the effective modal index of a PCF analytically. The EIM is first validated by comparison with available data in the reference, showing that the role of material dispersion is negligible at higher frequencies. Terahertz PCFs with flattened dispersion are designed based on this method and the scaling property of the Maxwell equations.

© 2006 Optical Society of America

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2006 (1)

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

2005 (2)

2004 (5)

Y. Li, C. Wang, and M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[Crossref]

M. Koshiba and K. Saitoh, "Applicability of classical optical fiber theories to holey fibers," Opt. Lett. 29, 1739-1741 (2004).
[Crossref] [PubMed]

P. H. Siegel, "Terahertz technology in biology and medicine," IEEE Trans. Microwave Theory Technol. 52, 2438-2447 (2004).
[Crossref]

D. Dragoman and M. Dragoman, "Terahertz fields and applications," Prog. Quantum Electron. 28, 1-66 (2004).
[Crossref]

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jpn. J. Appl. Phys. 43, L317-L319 (2004).
[Crossref]

2003 (5)

2002 (4)

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultraflattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002), http://www.opticsexpress.org.
[PubMed]

X.-C. Zhang, "Terahertz wave imaging: horizons and hurdles," Phys. Med. Biol. 47, 3667-3677 (2002).
[Crossref] [PubMed]

H. Park, M. Cho, J. Kim, and H. Han, "Terahertz pulse transmission in plastic photonic crystal fibres," Phys. Med. Biol. 47, 3765-3769 (2002).
[Crossref] [PubMed]

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[Crossref]

2001 (2)

2000 (1)

1998 (1)

C. Winnewisser, F. Lewen, and H. Helm, "Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy," Appl. Phys. A 66, 593-598 (1998).
[Crossref]

1997 (1)

Andres, M. V.

Andres, P.

Birks, T. A.

Bjarklev, A.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[Crossref]

Bjarklev, A. S.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[Crossref]

Broeng, J.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[Crossref]

Brown, T. G.

Chai, L.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Y. Li, C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Appl. Phys. B (to be published) (available online via DOI: 10.1007/ s00340-006-2246-6).
[Crossref]

Chen, Y.

Y. Li, C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Appl. Phys. B (to be published) (available online via DOI: 10.1007/ s00340-006-2246-6).
[Crossref]

Cho, M.

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[Crossref]

H. Park, M. Cho, J. Kim, and H. Han, "Terahertz pulse transmission in plastic photonic crystal fibres," Phys. Med. Biol. 47, 3765-3769 (2002).
[Crossref] [PubMed]

Dragoman, D.

D. Dragoman and M. Dragoman, "Terahertz fields and applications," Prog. Quantum Electron. 28, 1-66 (2004).
[Crossref]

Dragoman, M.

D. Dragoman and M. Dragoman, "Terahertz fields and applications," Prog. Quantum Electron. 28, 1-66 (2004).
[Crossref]

Ferrando, A.

Folkenberg, J. R.

Goto, M.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jpn. J. Appl. Phys. 43, L317-L319 (2004).
[Crossref]

Han, H.

H. Park, M. Cho, J. Kim, and H. Han, "Terahertz pulse transmission in plastic photonic crystal fibres," Phys. Med. Biol. 47, 3765-3769 (2002).
[Crossref] [PubMed]

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[Crossref]

Hansen, K. P.

Hasegawa, T.

Helm, H.

C. Winnewisser, F. Lewen, and H. Helm, "Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy," Appl. Phys. A 66, 593-598 (1998).
[Crossref]

Hu, M.

Y. Li, C. Wang, and M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[Crossref]

Y. Li, C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Appl. Phys. B (to be published) (available online via DOI: 10.1007/ s00340-006-2246-6).
[Crossref]

Kim, J.

H. Park, M. Cho, J. Kim, and H. Han, "Terahertz pulse transmission in plastic photonic crystal fibres," Phys. Med. Biol. 47, 3765-3769 (2002).
[Crossref] [PubMed]

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[Crossref]

Knight, J. C.

Koshiba, M.

Kuhlmey, B.

Lang, L.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Lee, K. S.

Lewen, F.

C. Winnewisser, F. Lewen, and H. Helm, "Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy," Appl. Phys. A 66, 593-598 (1998).
[Crossref]

Li, S.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Li, Y.

Y. Li, C. Wang, and M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[Crossref]

Y. Li, C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Appl. Phys. B (to be published) (available online via DOI: 10.1007/ s00340-006-2246-6).
[Crossref]

Liang, D.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Liu, B.

Y. Li, C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Appl. Phys. B (to be published) (available online via DOI: 10.1007/ s00340-006-2246-6).
[Crossref]

Love, J. D.

A. W. Snyder, and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

McPhedran, R.

Midrio, M.

Miret, J. J.

Mortensen, N. A.

Nielson, M. D.

Ono, S.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jpn. J. Appl. Phys. 43, L317-L319 (2004).
[Crossref]

Park, H.

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[Crossref]

H. Park, M. Cho, J. Kim, and H. Han, "Terahertz pulse transmission in plastic photonic crystal fibres," Phys. Med. Biol. 47, 3765-3769 (2002).
[Crossref] [PubMed]

Park, K. N.

Quema, A.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jpn. J. Appl. Phys. 43, L317-L319 (2004).
[Crossref]

Reeves, W. H.

Renversez, G.

Roberts, P. J.

Russell, P.

P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[Crossref] [PubMed]

Russell, P. St. J.

Saitoh, K.

Sarukura, N.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jpn. J. Appl. Phys. 43, L317-L319 (2004).
[Crossref]

Sasaoka, E.

Siegel, P. H.

P. H. Siegel, "Terahertz technology in biology and medicine," IEEE Trans. Microwave Theory Technol. 52, 2438-2447 (2004).
[Crossref]

Silvestre, E.

Singh, M. P.

Snyder, A. W.

A. W. Snyder, and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Someda, C. G.

Takahashi, H.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jpn. J. Appl. Phys. 43, L317-L319 (2004).
[Crossref]

Tian, Z.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Wang, C.

Y. Li, C. Wang, and M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[Crossref]

Y. Li, C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Appl. Phys. B (to be published) (available online via DOI: 10.1007/ s00340-006-2246-6).
[Crossref]

Wang, Q.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Winnewisser, C.

C. Winnewisser, F. Lewen, and H. Helm, "Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy," Appl. Phys. A 66, 593-598 (1998).
[Crossref]

Xing, Q.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Zhang, N.

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

Zhang, X.-C.

X.-C. Zhang, "Terahertz wave imaging: horizons and hurdles," Phys. Med. Biol. 47, 3667-3677 (2002).
[Crossref] [PubMed]

Zhu, Z.

Appl. Phys. A (1)

C. Winnewisser, F. Lewen, and H. Helm, "Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy," Appl. Phys. A 66, 593-598 (1998).
[Crossref]

Appl. Phys. B (1)

Y. Li, C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Appl. Phys. B (to be published) (available online via DOI: 10.1007/ s00340-006-2246-6).
[Crossref]

Appl. Phys. Lett. (2)

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[Crossref]

Q. Xing, S. Li, Z. Tian, D. Liang, N. Zhang, L. Lang, L. Chai, and Q. Wang, "Enhanced zero-order transmission of terahertz radiation pulses through very deep metallic gratings with subwavelength slits," Appl. Phys. Lett. 89, 041107 (2006).
[Crossref]

IEEE Trans. Microwave Theory Technol. (1)

P. H. Siegel, "Terahertz technology in biology and medicine," IEEE Trans. Microwave Theory Technol. 52, 2438-2447 (2004).
[Crossref]

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jpn. J. Appl. Phys. 43, L317-L319 (2004).
[Crossref]

Nature (1)

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

Opt. Commun. (1)

Y. Li, C. Wang, and M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Phys. Med. Biol. (2)

X.-C. Zhang, "Terahertz wave imaging: horizons and hurdles," Phys. Med. Biol. 47, 3667-3677 (2002).
[Crossref] [PubMed]

H. Park, M. Cho, J. Kim, and H. Han, "Terahertz pulse transmission in plastic photonic crystal fibres," Phys. Med. Biol. 47, 3765-3769 (2002).
[Crossref] [PubMed]

Prog. Quantum Electron. (1)

D. Dragoman and M. Dragoman, "Terahertz fields and applications," Prog. Quantum Electron. 28, 1-66 (2004).
[Crossref]

Science (1)

P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[Crossref] [PubMed]

Other (2)

A. W. Snyder, and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

(Color online) Schematic of the principle of the effective-index method:a photonic crystal fiber with an air-hole diameter D and an air-hole pitch Λ as shown in the left is approximated as a step-index fiber in the right with an effective cladding index n eff and an effective core diameter D eff = 2 ρ .

Fig. 2
Fig. 2

(Color online) Comparison of the effective modal index and group index obtained by EIM with those from Ref. [5]. Fiber parameters are air-hole pitch Λ = 500 μm and air-hole size D = 400 μm .

Fig. 3
Fig. 3

(Color online) Dispersion parameter of the TPCF of Fig. 2.

Fig. 4
Fig. 4

(Color online) Influence of the scale on the dispersion for TPCFs with D / Λ = 0.8 .

Fig. 5
Fig. 5

(Color online) Influence of the air-hole size D on the dispersion for a TPCF with Λ = 500 μm .

Fig. 6
Fig. 6

(Color online) TPCFs with flattened dispersion, Λ = 700 μm .

Equations (7)

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

V eff = k ρ n core 2 n eff 2 = 2 π λ ρ n core 2 n eff 2 ,
p 1 ( u a ) = 1 2 { [ 1 + ( n air n mat ) 2 ] } i 1 ( w a )
1 2 { [ 1 ( n air n mat ) 2 ] 2 i 1 2 ( w a ) + T } 1 / 2 .
i 1 ( w a ) = I 1 ( w a ) w a I 1 ( w a ) ,
T = 4 [ ( 1 u a ) 2 + ( 1 w a ) 2 ] [ ( 1 u a ) 2 + ( n air n mat ) 2 ( 1 w a ) 2 ] ,
p 1 ( u a ) = P 1 ( u a ) u a P 1 ( u a ) ,
D ( λ ; M ) = 1 M D ( λ M ) .

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