Mumbai University > Electronics Engineering > Sem7 > Optical Fiber Communication

Marks: 10M

Year: May2014, Dec2012

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

• The two main causes of intramodal dispersion are as follows:

  a. Waveguide dispersion:

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

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

  b. Material dispersion:

  • It is the pulse spreading due to the dispersive properties of material.

  • It arises from variation of refractive index of the core material as a function of wavelength.

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

  • 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. $ \frac{d^2 n}{dλ^2} ≠ 0$

• 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

  $τ_g= dβ/dω = 1/c (n_1-(λdn_1)/dλ) ------ (1)$

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

  $\omega$ 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

$$τ_m = \frac{L}{C} \big(n_1-λ \frac{(dn_1)}{dλ}\big) ------ (2)$$

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.

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

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

$$σ_m = σ_λ (dτ_m)/d_λ ---- (4)$$

Hence the pulse Spread may be evaluated by considering the dependence of $τ_m$ on λ. From eq.(2)

$$\frac{dτ_m}{dλ} = \frac{L λ}C \big[\frac{dn_1}{dλ} - \frac{d^2 n_1}{dλ^2} - \frac{dn_1}{dλ}\big]$$

$$= -L\frac{λ}C \frac{d^2 n_1}{dλ^2}------(5)$$

Substitute eqn(5) in eqn(4)

The rms pulse broadening due to material dispersion is given by

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

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:

$$M = \frac{1}{L} \frac{dτ_m}{dλ} = \frac{λ}C│\frac{d^2 n_1}{dλ^2} │$$

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

$$\boxed{∆t_{mat} (P.S) = M.L (∆λ)}$$