12.10 Principles of Solitons
495
12.10 Principles of Solitons
As Chap. 3 describes, group velocity dispersion (GVD) causes most pulses to broaden
in time as they propagate through an optical fiber. However, a particular pulse shape
known as a soliton takes advantage of nonlinear effects in silica, particularly selfphase modulation (SPM) resulting from the Kerr nonlinearity, to overcome the pulsebroadening effects of GVD [16–20].
The term “soliton” refers to special kinds of waves that can propagate undistorted
over long distances and remain unaffected after collisions with each other. John
Scott Russell made the first recorded observation of a soliton in 1838, when he saw a
peculiar type of wave generated by boats in narrow Scottish canals [16]. The resulting
water wave was of great height and traveled rapidly and undiminished over a long
distance. After passing through slower waves of lesser height, the waves emerged
from the interaction undistorted, with their identities unchanged.
In an optical communication system, solitons are very narrow, high-intensity
optical pulses that retain their shape through the interaction of balancing pulse dispersion with the nonlinear properties of an optical fiber. If the relative effects of SPM and
GVD are controlled just right, and the appropriate pulse shape is chosen, the pulse
compression resulting from SPM can exactly offset the pulse broadening effect of
GVD. Depending on the particular shape chosen, the pulse either does not change
its shape as it propagates, or it undergoes periodically repeating changes in shape.
The pulses that do not change in shape are called fundamental solitons, and those
that undergo periodic shape changes are called higher-order solitons. In either case,
attenuation in the fiber will eventually decrease the soliton energy. Because this
weakens the nonlinear interaction needed to counteract GVD, periodically spaced
optical amplifiers are required in a soliton link to restore the pulse energy.
12.10.1 Structures of Soliton Pulses
No optical pulse is completely monochromatic, because it excites a spectrum of
frequencies. For example, as Eq. (10.1) shows, if an optical source emits power in
a wavelength band λ, its spectral spread is v. This is important, because in an
actual fiber a pulse is affected by both the GVD and the Kerr nonlinearity. This is
particularly significant for high-intensity optical excitations. Because the medium is
dispersive, the pulse width will spread in time with increasing distance along the fiber
owing to GVD. In addition, when a high-intensity optical pulse is coupled to a fiber,
the optical power modulates the refractive index seen by the optical excitation. This
induces phase fluctuations in the propagating wave, thereby producing a chirping
effect in the pulse, as shown in Fig. 12.8. The result is that the front of the pulse (at
smaller times) has lower frequencies and the back of the pulse (at later times) has
higher frequencies than the carrier frequency.
495
12.10 Principles of Solitons
As Chap. 3 describes, group velocity dispersion (GVD) causes most pulses to broaden
in time as they propagate through an optical fiber. However, a particular pulse shape
known as a soliton takes advantage of nonlinear effects in silica, particularly selfphase modulation (SPM) resulting from the Kerr nonlinearity, to overcome the pulsebroadening effects of GVD [16–20].
The term “soliton” refers to special kinds of waves that can propagate undistorted
over long distances and remain unaffected after collisions with each other. John
Scott Russell made the first recorded observation of a soliton in 1838, when he saw a
peculiar type of wave generated by boats in narrow Scottish canals [16]. The resulting
water wave was of great height and traveled rapidly and undiminished over a long
distance. After passing through slower waves of lesser height, the waves emerged
from the interaction undistorted, with their identities unchanged.
In an optical communication system, solitons are very narrow, high-intensity
optical pulses that retain their shape through the interaction of balancing pulse dispersion with the nonlinear properties of an optical fiber. If the relative effects of SPM and
GVD are controlled just right, and the appropriate pulse shape is chosen, the pulse
compression resulting from SPM can exactly offset the pulse broadening effect of
GVD. Depending on the particular shape chosen, the pulse either does not change
its shape as it propagates, or it undergoes periodically repeating changes in shape.
The pulses that do not change in shape are called fundamental solitons, and those
that undergo periodic shape changes are called higher-order solitons. In either case,
attenuation in the fiber will eventually decrease the soliton energy. Because this
weakens the nonlinear interaction needed to counteract GVD, periodically spaced
optical amplifiers are required in a soliton link to restore the pulse energy.
12.10.1 Structures of Soliton Pulses
No optical pulse is completely monochromatic, because it excites a spectrum of
frequencies. For example, as Eq. (10.1) shows, if an optical source emits power in
a wavelength band λ, its spectral spread is v. This is important, because in an
actual fiber a pulse is affected by both the GVD and the Kerr nonlinearity. This is
particularly significant for high-intensity optical excitations. Because the medium is
dispersive, the pulse width will spread in time with increasing distance along the fiber
owing to GVD. In addition, when a high-intensity optical pulse is coupled to a fiber,
the optical power modulates the refractive index seen by the optical excitation. This
induces phase fluctuations in the propagating wave, thereby producing a chirping
effect in the pulse, as shown in Fig. 12.8. The result is that the front of the pulse (at
smaller times) has lower frequencies and the back of the pulse (at later times) has
higher frequencies than the carrier frequency.