Optical pulse propagation

Details Optical pulse propagation Optical pulse propagation

1998-06-01

2002-12-24

Negash, Kinfe-Michael (Department: 2633)

Optical: systems and elements

Deflection using a moving element

Using a periodically moving element

C359S199200, C359S199200

Reexamination Certificate

active

06498669

ABSTRACT:

This invention relates to optical pulse propagation.
BACKGROUND OF THE INVENTION
Group velocity dispersion (GVD) is the main phenomenon restricting the maximum useable bit rate of optical fibre transmission systems. When a short pulse propagates down the fibre, different spectral components of the pulse travel with different velocities (due to GVD) which results in pulse broadening.
Considering a spectral region in which “blue” (shorter wavelength) components propagate faster then “red” (longer wavelength) ones (and such a situation occurs for wavelengths longer than 1300 nm in conventional non-dispersion-shifted single mode fibres) then the leading edge of the pulse contains the shorter-wavelength spectral components while longer ones are found on the tailing edge of the pulse. In other words, the instantaneous frequency varies across the pulse and the pulse becomes “chirped”.
Pulse broadening &Dgr;&tgr; can be expressed in the form
&Dgr;&tgr;=Dz&dgr;&lgr;,
where D is the chromatic dispersion in ps
m·km, z is the length of the fibre and &dgr;&lgr; is the spectral width of the pulse. It is this pulse broadening effect which limits the maximum pulse repetition frequency in a transmission system.
One acknowledged way of minimizing or reducing the pulse broadening is the use of dispersion-shifted fibres with parameter D close to zero. Another way to reach high bit-rates is to compensate for group velocity dispersion (instead of attempting to minimize it) using the nonlinear properties of the glass from which the fibre is made (usually doped silica).
It is known that the refractive index of silica glass can be expressed as a combination of linear and nonlinear components. The latter can be written in the form
n
n1
=n
2
I,
where n
2
is the so-called nonlinear refractive index (which in silica glass is equal to 2.6·10
−16
cm
2
/W) and I is the intensity of the light. The nonlinear part of the refractive index causes a phase change
&phgr;
n1
=kn
2
Iz=2&tgr;n
2
Iz/&lgr;,
(where &lgr; is the wavelength) and if the light intensity I depends on time (as found in a pulse of light) then the refractive index nonlinearity results in a variation of the instantaneous frequency across the pulse. Indeed, the pulse phase can be written in the form
&phgr;=&ohgr;
0
t−&phgr;
1
−&phgr;
n1
=&ohgr;
0
t−knz−kn
2
I(t)z,
where &ohgr;
0
is the pulse central frequency and &phgr;
1
is a linear phase shift. The first derivative of the pulse phase is the pulse instantaneous frequency
d&phgr;/dt=&ohgr;=&ohgr;
0
−kn
2
z dI(t)/dt.
Thus the refractive index nonlinearity results in a pulse chirp with opposite sign to the dispersion-induced chirp (assuming fibre dispersion in the region longer than 1300 nm to be positive). A physical interpretation is that the fibre nonlinearity causes the red components of the pulse spectrum to travel faster than the blue ones and this effect can be used to compensate dispersion-induced pulse broadening.
It is clear that in order to cancel dispersion broadening of the pulse using refractive index non-linearity one needs a certain pulse intensity for a given pulse width &tgr;
c
and dispersion. Such pulses with dispersion broadening balanced by nonlinear compression are called solitons. Their intensity corresponds to the intensity of the so-called fundamental soliton I
s
and can be written in the form
I
S
=0.322&lgr;
3
D/(4&pgr;
2
&tgr;
2
c
)
Thus the lower the dispersion and the broader the pulse the less intensity one needs to compensate for dispersion-induced broadening.
Solitons have a number of interesting properties, but the most important (for practical applications) soliton properties are listed below. These will be referred to later as properties #1 to #7.
1. A soliton is a bandwidth-limited pulse with time-bandwidth product &tgr;&Dgr;&ngr;=0.315, where &Dgr;&ngr;=c&dgr;&lgr;/&lgr;
2
is the soliton's spectral bandwidth.
2. The soliton's phase is constant across the pulse.
3. The soliton's temporal shape is sech
2
t (where t is time).
4. The soliton's intensity and pulse width are related to each other, namely
P&tgr;
2
=Const·D.
(typically P=10 mW for &tgr;=5 ps and D=1 ps
m·km)
5. After some distance of propagation a non-sech
2
t pulse evolves into a soliton (sech
2
t) pulse and a non-soliton component.
6. A soliton accompanied by spurious radiation transforms into another soliton with modified parameters (central frequency, intensity, pulse width) and a nonsoliton component.
7. Two solitons closely situated in time interact with each other through overlapping optical fields. To avoid soliton interactions the separation time between solitons should exceed five times their pulsewidths.
When a soliton propagates down a fibre with loss then its intensity becomes less and, in accordance with soliton property #4, it becomes broader. When the soliton becomes broader it begins to interact with adjacent pulses which is not acceptable for transmission systems.
Another serious problem is associated with soliton property #5. During propagation in a lossy fibre the soliton remains an essentially nonlinear pulse for some distance which results in narrowing of its spectral bandwidth, but after that distance its intensity is insufficient for the compressive effect of the non-linear refractive index to adequately balance the fibre dispersion and the soliton experiences only temporal broadening without any significant changes in spectral bandwidth. This means that the original bandwidth-limited pulse becomes a chirped one. The longer the distance the soliton propagates the more it differs from the ideal sech
2
t-shape and therefore the bigger the fraction of non-soliton component in the propagating pulse. After amplification this non-soliton component is shed by the soliton according to soliton property #5. Physically the non-soliton component is a dispersive pulse which may propagate faster or slower than the soliton and can interact with the main pulse changing its parameters and even destroying it. The strength of this nonlinear coupling depends on the intensity of the non-soliton component and hence the more the soliton shape differs from the “ideal soliton” the stronger the non-soliton component affect the propagation of the main pulse.
The situation becomes much worse when a soliton propagates in a transmission system which normally comprises a chain of fibre links and optical amplifiers. At each stage the soliton emits the non-soliton component, and after several amplification stages the level of non-soliton component becomes so high that nonlinear coupling between the two fields causes the soliton to break-up.
Thus interaction between soliton pulses and the accompanying non-soliton component results in soliton instability. One previously proposed way of reducing this effect is to keep the amplifier spacing much shorter than the soliton dispersion length z
d
, which is approximately equal to &tgr;
2
/D. Doing so reduces the amount of the radiated non-soliton component at the expense of shortening the required amplifier spacing. The latter is expensive and is thus commercially undesirable.
For example, in standard telecom fibres with group velocity dispersion around 17 ps
m·km the dispersion length is of the order of 0.5 km for 5 ps pulses and 40 km for 50 ps pulses and normally the amplifier spacing should be less than this distance. An improvement is obtained in dispersion-shifted fibre with typical dispersion 1 ps
m·km, in which case the dispersion length and hence the appropriate amplifier spacing can be as long as 7 km for 5 ps pulses and 700 km for 50 ps pulses. Thus, practically speaking, the effect of soliton instability not only imposes a limitation on the pulsewidth and amplifier spacing but also dictates the use of dispersion-shifted fibres in soliton transmission systems.
There is another serious problem associated with soliton property #6. At each amplifier some small amount of ba

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