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

Marks: 10

Years: MAY 2014

Pulse broadening within a single mode is called as intramodal dispersion or chromatic dispersion.

$\Rightarrow $ The two main causes of intramodal dispersion are as follows:

a. Waveguide dispersion:

$\Rightarrow $ It occurs because a single mode fiber confines only about 80% of the optical power to the core.

$\Rightarrow $ Dispersion thus arises since the 20% light propagating in the cladding travels faster than light confined to the core.

b. Material dispersion:

$\Rightarrow $ It is the pulse spreading due to the dispersive properties of material.

$\Rightarrow $ It arises from variation of refractive index of the core material as a function of wavelength.

$\Rightarrow $ Material dispersion is a property of glass as a material and will always exist irrespective of the structure of the fiber.

$\Rightarrow $ It occurs when the phase velocity of the plane wave propagation in the dielectric medium varies non-linearly with wavelength and a material is said to exhibit a material dispersion, when the second differential of the Refractive index w.r.t wavelength is not zero.

i.e. $\dfrac {d^2 n}{dλ^2} ≠ 0$

$\Rightarrow $ The pulse spread due to material dispersion may be obtained by considering the group delay $τ_g$ in the optical fiber which is the reciprocal of group velocity $v_g.$

The group delay is given by

$τ_g= \dfrac {dβ}{dω} = \dfrac 1c (n_1- \dfrac {λdn_1}{dλ} --------------- (1) $

where $n_1$ is the refractive index of the core material

ω is the angular frequency

$\beta$ is the propagation constant

The pulse delay $τ_m$ due to material dispersion in a fiber of length L is

$τ_m = \dfrac LC (n_1-λ \dfrac {dn_1}{dλ} ----------------- (2)$

For a source with rms spectral width $σ_λ$ & mean wavelength λ, the rms pulse broadening due to material dispersion σ_m may be obtained from the expansion of equation (2) in a Taylor series about λ.

$σ_m = σ_λ \dfrac {dτ_m}{dλ} + σ_λ \dfrac {d^2 τ_m}{dλ^2} + . . . . . . ------------ (3)$

As the 1st term in eq.(3) usually dominate for the source operating over 0.8-0.9μm wavelength range.

$σ_m = σ_λ \dfrac {dτ_m}{d_λ} ----------------- (4)$

Hence the pulse Spread may be evaluated by considering the dependence of $τ_m$ on λ.

From eq.(2)

$\dfrac {dτ_m}{dλ} = L \dfrac λC [\dfrac {dn_1}{dλ} - \dfrac {d^2 n_1}{dλ^2} - \dfrac {dn_1}{dλ}] \\ = -L \dfrac λC \dfrac {d^2 n_1}{dλ^2} ----------- (5)$

Substitute eqn (5) in eqn (4)

The rms pulse broadening due to material dispersion is given by

$σ_m = \dfrac {σ_λ L}C │λ \dfrac {d^2 n_1}{dλ^2 }│ ---------- (6)$

The material dispersion for optical fiber is sometimes quoted as the $│λ^2 (d^2 n_1/ dλ^2)│$

or $│d^2 n_1/dλ^2│$

However it may be given in terms of material dispersion parameter M given as:

$M =\dfrac 1L \dfrac {dτ_m}{dλ} = \dfrac λC│\dfrac {d^2 n_1}{dλ^2} │$

Total pulse spreading caused by material dispersion is given by $∆t_{mat}$ (P.S)

Where∆λ is the spectral width of light source

L is the fiber length

$∆t_{mat} (P.S) = M∙L (∆λ)$