Abstract

In this paper we investigate Bragg fibres and compare calculations on the exact fibre structures with calculations based on band diagrams and a simplified model involving multilayers. We show how the number of layers and the core size affect the wavelengths guided, the loss and the effective singlemodedness. An approximate relation between the real and imaginary parts of the effective mode indices is derived. The general design considered has a TE mode as the least lossy mode providing effectively single polarisation non-degenerate mode guidance.

© 2002 Optical Society of America

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References

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  9. F. Brechet, P. Roy, J. Marcou and D. Pagnoux, �??Singlemode propagation into depressed-core-index photonicbandgap fibre designed for zero-dispersion propagation at short wavelengths,�?? Electron. Lett. 36, 514, (2000).
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  10. A. Argyros, and I. Bassett, �??Counting Modes in Optical Fibres with Leaky Modes,�?? in Symposium on Optical Fiber Measurements SOFM 2002, (National Institute of Standards and Technology, Colorado, 2002)
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Electron. Lett. (1)

F. Brechet, P. Roy, J. Marcou and D. Pagnoux, �??Singlemode propagation into depressed-core-index photonicbandgap fibre designed for zero-dispersion propagation at short wavelengths,�?? Electron. Lett. 36, 514, (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (5)

Science (1)

S.D. Hart et al., �??External Reflection from Omnidirectional Dielectric Mirror Fibers,�?? Science 296, 510, (2002).
[CrossRef] [PubMed]

Other (4)

K. Sakoda, Optical Properties of Photonic Crystals, Chapter 2 (Springer, Berlin, 2001).

A. Argyros, and I. Bassett, �??Counting Modes in Optical Fibres with Leaky Modes,�?? in Symposium on Optical Fiber Measurements SOFM 2002, (National Institute of Standards and Technology, Colorado, 2002)

W.C. Chew, Waves and fields in inhomogeneous media, Chapter 3 (Van Nostrand Reinhold, New York, 1990).

M. Born and E. Wolf, Principles of Optics, Chapter 1.6 (Pergamon Press, Oxford, 1980).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram showing the refractive index profile of the Bragg fibre design investigated, with the various parameters and values thereof indicated. The parameters r co; and the number of layers N are treated as variables in this work.

Fig. 2.
Fig. 2.

(a) Re{neff} vs wavelength for various values of r co as indicated, with n co = 1.0, n 1 = 1.49, n 2 = 1.17, d 1 = 0.2133 μm, d 2 = 0.346 μm and N= 32. (b) Loss = 40πIm{n eff}/(ln(10)λ) vs wavelength for the same. (c) Absolute value of the change in Re{n eff}when N is decreased from 32 to 26. (d) Ratio of the loss at N = 26 to N = 32. Some of the data values used to plot the curves are shown in (c) as circles.

Fig. 3.
Fig. 3.

Plot of Re{n eff} against wavelength [same parameters as Fig. 2(a)] as calculated using Eq. (2) (solid lines) and from calculations on the fibre structure (points). The lowest loss points are indicated in red. The case where the fibre behaves like an antiguide (r co = 1.3278 μm, TE02 mode) and Eq. (2) is inapplicable is indicated in blue.

Fig. 4.
Fig. 4.

(a) Band diagram (TE polarisation) for the alternating layers used in the fibre designs, defined by {n 1 = 1.49, n 2 = 1.17, d 1 = 0.2133 μm, d 2 = 0.346 μm}. The axes are in dimensionless units of frequency ω and propagation constant ω = n eff k, a = d 1 + d 2 is the periodicity. White represents band-gap regions and the position of the modes (from Fig. 2 plus additional ones as in the text) is indicated by coloured curves. The “lowest loss” curve is shown in black. The TE02 mode for r co = 1.3278 μm is the left-most mode and is entirely outside the band-gap. (b) A contour plot of loss (blue represents low loss) superimposed on the band diagram to show that the loss of a mode can be inferred from its position relative to the band-gap and the light line. (c) Band diagram for TM polarisation.

Fig. 5.
Fig. 5.

Comparison between the results for Im{n eff} from direct calculations and Eq. (5) for various modes (TE01 and TE02 modes for r co = 1.5278, 1.8278, 2.0278, 2.3278 and 2.5278 μm and TE01 for r co = 1.3278 μm with N = 26 and 32, remaining parameters as in Fig. 1). The comparison is made around the lowest loss wavelength for each mode. As expected from the assumptions made, the agreement increases with decreasing Im{n eff}.

Equations (5)

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E r ϕ z J 1 ( κr ) e i ( n eff kz ωt ) φ ̂ ,
n eff , TE 0 i = 1 j 1 , i 2 k 2 r co 2 .
k r co = 2 π r co λ < j 1 , i ,
2 π r co j 1,2 < λ ,
Im { n eff } = ln ( r ) 2 k r co tan θ i = ln ( r ) 2 j 1 , i tan θ i sec θ i .

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