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Derive the expression for cutoff wavelength for single mode transmission.

Mumbai University > Electronics and telecommunication > Sem 7 > optical communication and networks

Marks: 10

Years: MAY 2016

1 Answer
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i. Single-mode operation only occurs above a theoretical cutoff wavelength λc given by:

λc=2πan1Vc(2)1/2(1)

ii. Where Vc is the cutoff normalized frequency? Hence λc is the wavelength above which a particular fiber becomes single-mode.

iii. The normalized frequency may be expressed in terms of the numerical aperture NA and the relative refractive index difference Δ respectively, as:

V=2πλa(NA)V=2πλan1(2)1/2(ii)

iv. The normalized frequency is a dimensionless parameter and hence is also sometimes simply called the V number or value of the fiber. Where the core radius a, the relative refractive index difference Δ and the operating wavelength λ.

v. Dividing Eq. 1 by Eq. 2 for the same fiber we obtain the inverse relationship.

λcλ=VVc

vi. Thus for step index fiber where Vc=2.405, the cutoff wavelength is given by

λc=Vλ2.405

vii. An effective cutoff wavelength has been defined by the ITU-T which is obtained from a 2 m length of fiber containing a single 14 cm radius loop.

viii. This definition was produced because the first higher order LP11 mode is strongly affected by fiber length and curvature near cutoff.

ix. Recommended cutoff wavelength values for primary coated fiber range from 1.1 to 1.28 μm for single-mode fiber designed for operation in the 1.3 μm wavelength region in order to avoid modal noise and dispersion problems.

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