Solitons

M. SUMATHIProfessor and HeadDepartment of ECE

Dhirajlal Gandhi College of TechnologySalem

SOLITONS

CONTENTS

- Overview

Solitons – General definition

- Recorded by John Scott Russell in the

Scottish canals

- They are special kind of waves that can

propagate undistorted over long distance

and remain unaffected after collision with

each other

Optical Solitons

- In optical communication solitons are very

narrow, high intensity optical pulses that

retain their shape as they propagate due to

the interaction of

Group Velocity Dispersion (GVD) and

Self Phase Modulation (SPM)

Solitons- Principle

- Group Velocity Dispersion (GVD) causes pulse to broaden as they

propagate along the fiber

- Self Phase Modulation (SPM) is a non linear effect resulting from

Kerr nonlinearity, which causes frequency chirping

- If relative effects of GVD and SPM are controlled rightly, and the

right pulse shape chosen, compression due to SPM can compensate

the pulse broadening due to GVD, thus maintaining the shape of the

pulse

SPM

Effect of SPM on frequency

Gaussian Pulse Chirped Gaussian Pulse

Effect of SPM

Effect of SPM on frequency

Effect of GVD

Effect of GVD on a frequency chirped pulse

- Different frequency components of a pulse travel at slightly

different speeds along the fiber because of GVD

GVD parameter, β2 = (-1/Vg2) dVg / dω

i. when β2 < 0 (Anomalous region), dVg / dω is positive

- Therefore as frequency increases, velocity increases

- Leading edge is red shifted and travels slower, trailing edge travels

faster

- Hence, when narrow high intensity pulse travels in a medium with

negative GVD parameter, due to the effects of SPM and GVD the

pulse shape is retained

Effect of GVD

ii. when β2 > 0 (Normal region), dVg / dω is negative

- Therefore as frequency increases, velocity decreases

- Leading edge travels faster and trailing edge travels slower

- Hence, the pulse broadens further

Soliton pulse shape

Hyperbolic Secant function used for soliton pulses

Queries ???

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