Abstract

In a long period grating (LPG) made on a silica-based single material photonic crystal fibre (PCF), the effect of material dispersion on the resonance wavelength of the LPG is negligible. The resonance wavelength, the period and length of the LPG, and the diameter and pitch of the air-hole lattice of the PCF are found to obey a scaling law that is derived from the scaling property of the Maxwell’s Equations. Simulations show that the resonance wavelength has a non-monotonic dependence on the grating period and, for a particular grating period, there could exist multiple resonance wavelengths and hence multiple transmission dips due to phase matching between the fundamental core mode and a cladding mode simultaneously at multiple wavelengths.

©2004 Optical Society of America

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References

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2004 (2)

2003 (7)

2002 (1)

2000 (2)

1999 (1)

1997 (1)

Turan Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[Crossref]

Birks, T.A.

Bjarklev, Anders

Burdge, G.L.

Chong, Joo-Hin

Diez, A.

Dybendal Nielsen, Martin

Eggleton, B.J.

Erdogan, Turan

Turan Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[Crossref]

Folkenberg, J.R.

Folkenberg, Jakob Riis

Guo, S.

Guobin, R.

Hansen, K.P.

Joannopoulos, J.D.

J.D. Joannopoulos, R.D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light, (New York, Princeton university press, 1995).

Kakarantzas, G.

Kerbage, C.

Kim, Jin C.

Knight, Jonathan C.

Jonathan C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[Crossref] [PubMed]

Lee, Byeong H.

Lee, Kyung S.

Lim, Jong H.

Lu, Chao

Mangan, B.J.

Marcuse, Dietrich

Dietrich Marcuse, Theory of dielectric optical waveguides, (New York: Academic press, 1974).

Meade, R.D.

J.D. Joannopoulos, R.D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light, (New York, Princeton university press, 1995).

Miyake, Yoshihiro

Morishita, Katsumi

Mortensen, N. A.

Nielsen, M. D.

Ramachandran, S

S Ramachandran, “Novel photonic devices in few-mode fibres,” IEE Proc. Circuits Syst. 150, 473–479, (2003).
[Crossref]

Rao, M.K.

Reeves, W.H.

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Russell, P.St. J.

Russell, P.St.J.

Shum, Ping

Shuqin, L.

Spalter, S.

Strasser, T.A.

Vienne, guillaume

Weijun, L.

Westbrook, P. S.

Westbrook, P.S.

White, C.A.

Windeler, R. S.

Windeler, R.S.

Winn, J. N.

J.D. Joannopoulos, R.D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light, (New York, Princeton university press, 1995).

Zhi, W.

Zhu, Yinian

IEE Proc. Circuits Syst. (1)

S Ramachandran, “Novel photonic devices in few-mode fibres,” IEE Proc. Circuits Syst. 150, 473–479, (2003).
[Crossref]

J. Lightwave Technol. (3)

Nature (1)

Jonathan C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (7)

Science (1)

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Other (2)

Dietrich Marcuse, Theory of dielectric optical waveguides, (New York: Academic press, 1974).

J.D. Joannopoulos, R.D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light, (New York, Princeton university press, 1995).

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Figures (5)

Fig.1 .
Fig.1 . CF with a triangular lattice of air-holes in a silica base. The definition of pitch Λ and hole diameter d are shown in the figure.
Fig. 2.
Fig. 2. Wavelength dependent beat lengths between the fundamental LP01 mode and a few HOMs of a conventional silica-based step index fiber with core radius of 4.5µm and relative index difference of 0.3%. λc of LP11, LP21, LP02 and LP31 are plotted as vertical lines.
Fig.3 .
Fig.3 . Normalized beat length between LP01 and LP02 modes as a function of the normalized wavelength for the PCF shown in Fig.1. ‘o’ and ‘+’ are obtained by FEM method and others are obtained by the super cell method.
Fig. 4.
Fig. 4. The electric field intensity profile of the core mode LP01 (left panel) and the cladding mode LP02 (right panel) at wavelength 1.55µm. The PCF parameters are: Λ=3µm and f=0.2.
Fig. 5.
Fig. 5. (a) Beat length between modes LP01 and LP02 as a function of wavelength for a PCF with Λ=3µm and f=0.2. (b) Transmission spectra of three LPGs inscribed in the PCF with Λ=3µm and f=0.2. There are two resonance transmission dips for each of the LPGs.

Equations (8)

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Λ g = L B = λ ( n co n cl ) ,
τ = τ m + τ w , β = β m + β w , n eff = n effm + n effw ,
Λ g = L B = λ ( n co , w n cl , w ) .
e ( M Λ , r , f , λ ) = e ( Λ , r M , f , λ M ) .
n eff ( M Λ , f , λ ) = n eff ( Λ , f , λ M ) .
Λ g ( M Λ , f , λ ) M Λ = Λ g ( Λ , f , λ M ) Λ .
K co , cl = 2 π n 1 δ n mod λ n co n cl grating area dxdy e co , t ( x , y ) · e cl , t ( x , y ) dxdy e co , t ( x , y ) 2 · dxdy e cl , t ( x , y ) 2 ,
K co , cl ( M Λ , f , λ ) = K co , cl ( Λ , f , λ M ) M .

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