Abstract

Random nonuniformities in the photonic crystal lattice are shown to reduce the coupling length and the coupling efficiency of two-core photonic crystal fibers. These coupling properties are extremely sensitive to imperfections when the air holes are large; variations in the lattice of less than 1% are sufficient to cause essentially independent core propagation due to a drastic reduction in the efficiency of the core coupling. The observed sensitivity of two-core fibers to lattice imperfections is explained through a comparison with coupled mode theory.

© 2005 Optical Society of America

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References

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J. Opt. Soc. Am. B

Opt. Commun.

D. Chremmos, G. Kakarantzas and N. K. Uzunoglu, "Modeling of a highly nonlinear chalcogenide dual-core photonic crystal fiber coupler," Opt. Commun. 251, 339-345 (2005).
[CrossRef]

Opt. Express

Other

CUDOS MOF UTILITIES Software ©Commonwealth of Australia 2004. All rights reserved. <a href= "http://www.physics.usyd.edu.au/cudos/mofsoftware/">http://www.physics.usyd.edu.au/cudos/mofsoftware/</a>.

A. Snyder and J. Love, Optical Waveguide Theory (Kluwer, London, 1983).

C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).

A. Barybin and V. Dmitriev, Modern Electrodynamics and Coupled-Mode Theory: Application to Guided-Wave Optics (Rinton Press, 2002).

S. L. Chuang, Physics of Optoelectronic Devices (Wiley-Interscience, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

The x-polarized modes (Ex is much larger than Ey) of the fundamental mode group for a perfect lattice two-core PCF with d/Λ=0.90 and Λ=2.5μm. (a) and (b) display the PCF cross-section and the real x-componenet of the electric field; the white circles are air holes. (c) and (d) show the profile of the field along y=0; (a) and (c) are a symmetric mode, while (b) and (d) are antisymmetric.

Fig. 2.
Fig. 2.

The normalized power in each core is plotted versus the propagation distance. The coupling efficiency changes from (a) 1 to (b) 0.20 when a random variation of 2.2% in the air hole size is introduced, Λ = 2.5 μm and d/Λ = 0.58.

Fig. 3.
Fig. 3.

The average coupling efficiency (a) and the average coupling length, normalized to the value for a perfectly uniform structure, (b) are plotted vs. d/Λ for a percentage variation of 1% (solid line) and 4% (dashed line), Λ = 2.5 μm. The lines have been added to facilitate the eye.

Fig. 4.
Fig. 4.

The coupling efficiency vs. the x polarization coupling length for Λ = 2.5 μm and d/Λ = 0.58, 0.70, 0.75, 0.80, 0.85 and 0.90 from upper left to lower right. Note that the axis scaling differs for each plot.

Fig. 5.
Fig. 5.

Kab, as computed from a perfect structure, (dashed lines) and ∆β, calculated from the birefringence induced from variations in the lattice of a single core PCF, (solid lines) are plotted versus the normalized wavelength. ∆β is the average value for 20 structures with variations of 1% in the air hole separation.

Fig. 6.
Fig. 6.

A cross-sectional view of the z-component of the real part of the Poynting vector for two of the modes from the highest index mode group of a two-core PCF with Λ = 2.5 m and d/Λ = 0.90 and nonuniformities of 0.67% appears in (a) and (b), while (c) and (d) show the profile along the line where y = 0. Similar behavior is observed for the two other modes in the group.

Fig. 7.
Fig. 7.

The ratio of power in the left core to that in the right core for a mode that is predominantly left is shown as a function of the normalized air hole size, d/Λ, for a percentage variation of 1% (solid line) and 4% (dashed line), Λ = 2.5 μm. The lines have been added to facilitate the eye. The value for a perfect two-core fiber is 1.

Tables (2)

Tables Icon

Table 1. The slopes of linear fits to the log-log data of Fig. 4.

Tables Icon

Table 2. The fit parameter, or the coefficient of a quadratic fit to the data in Fig. 4, is listed according to the relative air hole size. Kab is calculated from the fit parameter according to Eq. (8). The final columns compare the coupling length as calculated from the fit using CMT with the value determined directly from the perfect structure.

Equations (11)

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E ( x , y , z ) = j a j e j ( x , y ) exp ( i β j z ) ,
a j = 1 2 N j E ( x , y , 0 ) × h j * ( x , y ) z ̂ dxdy ,
1 2 e j ( x , y ) × h j * ( x , y ) z ̂ dxdy = 1 2 e ( x , y ) × h j * ( x , y ) z ̂ dxdy = N j
P core ( z ) = 1 2 Re core area E ( x , y , z ) × H * ( x , y , z ) z ̂ dxdy ,
E ( x , y , z ) = a ( z ) e a ( x , y ) + b ( z ) e b ( x , y )
H ( x , y , z ) = a ( z ) h a ( x , y ) + b ( z ) h b ( x , y )
d d z a ( z ) = i β a a ( z ) + i K ab b ( z )
d d z b ( z ) = i K ba a ( z ) + i β b b ( z ) ,
p b ( z ) = b ( z ) 2 = K ab ψ 2 sin 2 ψ z ,
where : ψ = ( β b β a ) 2 4 + K a b K b a ,
Efficiency = 4 K a b 2 π 2 L c 2

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