Optical: systems and elements – Deflection using a moving element – Using a periodically moving element
Reexamination Certificate
1999-05-20
2003-06-24
Pascal, Leslie (Department: 2633)
Optical: systems and elements
Deflection using a moving element
Using a periodically moving element
C359S199200, C359S199200, C359S199200, C359S199200, C359S199200, C359S199200, C359S199200, C359S199200, C359S199200, C359S199200
Reexamination Certificate
active
06583905
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates generally to an apparatus and method for reducing the non-linear distortion of pulses in a high-power optical communication system, and specifically to an apparatus and method for reducing the distortion produced by the interaction between Self Phase Modulation (SPM) and Group Velocity Dispersion (GVD) in an optical system operating at a high power level.
DISCUSSION OF THE BACKGROUND
The availability of optical amplifiers with increasing output power capacity has expanded the possibilities for high-power optical communication systems. Before the availability of high-power optical amplifiers, optical transmission systems typically employed relatively low power optical sources for initiating signals within a fiber optic system, and relied on a series of repeaters or amplifiers to regenerate or boost the optical signal along its path. High-power optical amplifiers, on the other hand, permit a reduction in the number of repeaters or amplifiers required along a fiber optic link.
Optical signals traveling in a fiber optic system at high power levels, however, are subject to distortions not evident at lower power levels. In conventional low power systems, a single-mode optical fiber behaves as a lossy, dispersive, linear medium. An optical pulse at a low power level attenuates as it passes along the fiber, and becomes symmetrically broadened due to first-order Group Velocity Dispersion (GVD) if the fiber is sufficiently long, e.g. over 600 km. At transmission rates that approach 100 Gb/s, second-order GVD causes the data pulse to spread asymmetrically as well. Nonetheless, typical optical communication at low power levels results in an overall linear response along a standard transmission fiber.
For high-bit rate systems that have an input power in excess of, for example, 5 mW, a single-mode optical fiber begins to exhibit non-linear distortion characteristics caused by Self Phase Modulation (SPM). As an optical pulse propagates in a transmission fiber at high power levels, SPM generates new frequency components that develop a positive frequency chirp. Interaction between SPM and GVD produces non-linear distortion for an optical pulse that is governed by several parameters. These include the optical peak power level launched into the fiber, the sign and the amount of the dispersion of the transmission fiber, and the dispersion map of the total link (i.e. how the signal accumulates dispersion along the link).
Various publications, including Agrawal,
Nonlinear Fiber Optics
, Academic Press, 2nd. ed. (1989), describe theoretically the amount of positive chirp produced by SPM on a Gaussian pulse. The power of such a pulse conforms to the following relationship:
P
(
t
)
=
P
0
exp
[
-
(
T
T
0
)
2
m
]
(
1
)
where P
0
is the pulse peak power and T
0
is the pulse half-width at 1/e-intensity point. As is readily known in the art, the value m corresponds to the order of the Gaussian pulse. When m=1, the pulse is Gaussian. A larger value of m represents a super-Gaussian pulse, i.e. a sharper Gaussian pulse having shorter rise and fall times. With very high values of m, such as where m>>1, the pulse approaches the shape of a square pulse. With respect to SPM-induced chirp, Agrawal defines it mathematically as follows:
δ
ω
(
T
)
=
2
m
z
eff
T
0
L
NL
(
T
T
0
)
2
m
-
1
exp
[
-
(
T
T
0
)
2
m
]
(
2
)
where m changes with the shape of the pulse, the effective fiber length z
eff
is defined as z
eff
=[1−exp(&agr;z)]/&agr;, z being the fiber length, the nonlinear length is defined as L
NL
=1/(&ggr;P
0
) and &ggr; is the fiber nonlinearity coefficient. The maximum spectral broadening of the pulse is given by:
δ
ω
max
=
2
m
Φ
max
T
0
(
1
-
1
2
m
)
1
-
1
/
2
m
exp
[
-
(
1
-
1
2
m
)
]
(
3
)
where &phgr;
max
=&ggr;P
0
z
eff
. Likewise, GVD causes a chirp on an optical pulse in high-power systems. Agrawal defines the GVD chirp as follows:
δ
ω
=
2
sgn
(
β
2
)
(
z
/
L
D
)
1
+
(
z
/
L
D
)
2
T
T
0
2
(
4
)
where L
D
=T
0
2
/|&bgr;
2
| is the dispersion length for the pulse and &bgr;
2
the group velocity dispersion parameter.
A. Naka et al., “In-line Amplifier Transmission Distance Determined by Self-Phase Modulation and Group-Velocity Dispersion, ”
Journal of Lightwave Technology
, Vol. 12, No. 2, pp. 280-287 (February 1994) numerically analyze the propagation of intensity-modulated signal in an optical fiber, taking self-phase modulation, group-velocity dispersion, and 2nd-order group-velocity dispersion into account. Transmission distances yelding a prescribed eye-opening penalty are shown to relate to three characteristic lengths: the dispersion length, the 2nd-order dispersion length, and the nonlinear length.
U.S. Pat. No. 5,539,563 (Park) disclose a system and method for simultaneously compensating for chromatic dispersion and self phase modulation in optical fibers. At least one dispersion compensating (DCF) fiber is utilized to compensate for chromatic dispersion of an externally modulated signal carried by at least one single-mode, standard fiber optical cable. The signal power launched in the DCF fiber is controlled such that precise compensation for the SPM effect in the standard fiber can be achieved.
Other references also discuss the impact of SPM and GVD on optical communications with respect to pulse compression devices and techniques. Peter et al., “Compression of Pulses Spectrally Broadened by Self-Phase Modulation Using a Fiber-Grating: A Theoretical Study of the Compression Efficiency,”
Optics Communications
, Vol. 112, pp. 59-66 (Nov. 1, 1994), discusses a theoretical analysis of the potential for using short-fiber gratings with constant grating period for the compression of optical pulses spectrally broadened by SPM. For fiber gratings with constant grating period, this paper confirms through theory and simulations that the maximum achievable pulse compression factor is practically independent of the grating parameters and is typically on the order of two.
Stern et al., “Self-Phase Modulation and Dispersion in High Data Rate Fiber-Optic Transmission Systems, ”
Journal of Lightwave Technology
, Vol. 8, No. 7, pp. 1009-16, (July 1990), describes the limitations caused by the interaction of first and second-order GVD and intensity-dependent SPM. The paper investigates the theoretical transmission limits imposed by these effects for a range of wavelengths around the zero dispersion wavelength &lgr;
0
for fibers in which polarization dispersion is negligible. The paper finds that operating at wavelengths longer than &lgr;
0
improves the transmission distance for data rates greater than 50 Gb/s due to the cancellation of first-order dispersion by SPM. Above 100 Gb/s, higher order dispersion limits the transmission distance even at wavelengths equal to or longer than &lgr;
0
. The paper concludes that linear dispersion compensation using a grating-telescope combination can significantly improve system performance for wavelengths where first order dispersion dominates.
These references, however, focus on the performance of relatively smooth Gaussian pulses in optical systems.
Applicant has observed that modulated optical pulses in a link having less than 600 km of optical fiber do not face pulse overlap due to GVD pulse spreading as considered by the literature for very long distances, even at relatively high bit rates of 2.5 Gb/s. Applicant has further identified that the amount of frequency chirping depends heavily on the shape of the pulses, in particular the pulse edges, which in turn depend on the type of transmission equipment used. Moreover, Applicant has discovered that modulated optical pulses from many conventional SDH and SONET-based transmitters are quite different from smooth Gaussian pulses consi
Bonato Gainluca
Macchi Mauro
Ottolenghi Paolo
Cisco Photonics Italy S.r.L.
Pascal Leslie
Phan Hanh
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