Optics: measuring and testing – By light interference – Using fiber or waveguide interferometer
Reexamination Certificate
2000-03-03
2002-05-28
Turner, Samuel A. (Department: 2877)
Optics: measuring and testing
By light interference
Using fiber or waveguide interferometer
Reexamination Certificate
active
06396586
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to the transmission of signals through a nonlinear medium. More particularly, the present invention relates to an apparatus and method for eliminating the effects of nonlinearities caused by a nonlinear medium, with exemplary application to optical signals and optical transmission media.
BACKGROUND OF THE INVENTION
Fiber optic communication generally involves the transmission of high bit-rate digital data over silica glass fiber by modulating a laser or other optical source. As with any data transmission medium, there are ongoing development efforts to increase the data rate through fiber optic media, as well as to increase the practical transmission distance of single fiber optic spans. Although the development of erbium-doped fiber amplifiers (EDFA) has virtually eliminated fiber attenuation as an obstacle to achieving longer transmission distances, group velocity dispersion and optical fiber nonlinearities continue to represent a barrier to increased transmission capability. Optical fiber nonlinearities begin to manifest themselves as the capabilities of the channel are pushed to their limits through the use of increased signal power, higher bit rates, longer transmission distances, and increased numbers of channels.
Fiber nonlinearities place substantial limits on the capacity of wavelength-division multiplexed (WDM) optical communication systems. As described in Chraplyvy, “Limitations on Lightwave Communications Imposed by Optical-Fiber Nonlinearities,” Journal of Lightwave Technology, Vol.8, No.10, (1990), p1548-1557, the contents of which are hereby incorporated by reference, these limitations include, but are no limited to: limiting the optical power that can be launched into the fiber; limiting the number of channels in WDM optical communications; limiting the amount of dispersion the fiber may have; and limiting the data bit rate. Various methods to reduce the effect of fiber nonlinearities have been proposed, including the use of lower laser power, unequal channel spacing, and other methods. Generally, however, these methods are directed to individual mechanisms by which certain nonlinearities arise, and are not adapted to eliminate all third-order nonlinearities simultaneously.
FIG. 1
shows a block diagram of a generic nonlinear transmission medium
102
having an input signal E and an output signal E′. For optical media, the signals E and E′ are time functions representing the electric field portion of an optical wave at the relevant point along the signal path. Unless otherwise indicated in the present disclosure, the representations E and E′ may be interchanged with the representations E(t) and E′(t). The nonlinear transmission medium
102
, while identified as a fiber optic link in many examples herein, may also be a discrete “point” device such as a semiconductor optical amplifier (SOA), an EDFA amplifier, or generally any optical processing circuit having a nonlinear response characteristic. In such case, the input signal E and transmitted output signal E′ appear very close to each other in space. In summary, the nonlinear transmission medium
102
may have a length that is as long as hundreds of miles or as short as a few nanometers, depending on the specific application.
FIG. 2
shows a timing diagram of an exemplary waveform
202
for E and a corresponding waveform
204
for E′ for the system of FIG.
1
. As represented by
FIG. 2
, the output signal
204
comprises the sum of an attenuated version
206
of E plus an induced nonlinearity
208
. The nonlinear mechanisms in optical media causing the nonlinearities include cross-phase modulation (XPM), stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), optically induced birefringence (OIB), parametric four-wave mixing (FWM), self-phase modulation (SPM), and modulation instability (MI). Although further information on these and other nonlinear mechanisms are described in Agrawal,
Nonlinear Fiber Optics
, Academic Press (2
nd
ed. 1995), the contents of which are hereby incorporated by reference, the preferred embodiments described herein may be advantageously used regardless of the specific nonlinear mechanisms in effect.
When an optical signal E(t) passes through a nonlinear optical medium, the output signal E′(t) may be expressed as:
E
′=&kgr;
1
E
+&kgr;
2
EE
+&kgr;
3
EEE
+&kgr;
4
EEEE
+ . . . {1}
where &kgr;
1
denotes the linear input-output response and &kgr;
2
, &kgr;
3
, &kgr;
4
, etc. are tensors representing nonlinear input-output responses. Local nonlinearities due to the physics of the optical material are responsible for the second order (&kgr;
2
) and third order (&kgr;
3
) nonlinearities, while higher order nonlinearities come into effect only for lengthy optical media which display such higher order effects due to the cascading of the local nonlinearities over an extended distance. As known in the art, for systems where the overall dimension of the optical medium is not excessive or the local nonlinearities are weak, the higher order nonlinear effects are negligible. Also as known in the art, in most optical communication and signal processing systems, the even-order nonlinear effects &kgr;
2
, &kgr;
4
, etc. are not of practical concern, because the wave components generated by these even order nonlinearities are associated with very large frequency shifts which move them far away from the signal band, thereby allowing for removal using conventional filtering techniques at the destination. Therefore, a practical representation of the input-output response includes only the dominant third-order nonlinearity term, as shown in Eq. (2):
E
′=&kgr;
1
E
+&kgr;
3
EEE
{2}
Despite the presence of only a third order nonlinearity in Eq. (2), it is to be appreciated that the preferred embodiments to be described infra are straightforwardly extendible to the cancellation of higher order nonlinearities &kgr;
5
, &kgr;
7
, etc. when they become important. Moreover, the preferred embodiments disclosed herein can also be applied to eliminate even-order nonlinearities &kgr;
2
, &kgr;
4
, etc. where necessary.
In practical optical communication systems using long distance optical fibers with optical amplification by an EDFA amplifier or a semiconductor optical amplifier (SOA), the third order &kgr;
3
-nonlinear effect of Eq. (2) may generate a sizable unwanted term that can significantly distort the input signal E(t). Additionally, in optical amplifiers there is also a cross gain modulation (XGM) effect due to gain saturation in addition to the XPM and FWM effects mentioned supra. In wavelength-division multiplexed (WDM) systems, the unwanted signal &kgr;
3
EEE(t) can lead to serious cross talk and noise level problems. Even in a single wavelength system, the unwanted signal K
3
EEE(t) may significantly distort the desired signal. Thus, in fiber optic communication systems, optical fiber nonlinearities and similar nonlinear effects in optical amplifiers (SOA or EDFA) and other optical signal processing components have become a major factor in limiting system capacity.
Accordingly, it would be desirable to provide an optical fiber transmission system in which nonlinearities induced by the optical fiber medium are eliminated.
It would be further desirable to provide such an optical fiber transmission system that can be physically realized using known, off-the-shelf optical components.
It would be further desirable to eliminate unwanted nonlinear effects in various optical signal processing systems.
It would be still further desirable to provide a method for eliminating the effects of optical transmission system nonlinearities that can be applied to any n
th
-order nonlinearity.
It would be still further desirable to eliminate the effects of multiple nonlinearities of many different orders in a transmission medium.
It would be even further desirable to provide a method for eliminating nonlinear effects t
Wei Haiqing
Xue Xin
Cooper & Dunham LLP
Gazillion Bits Inc.
Turner Samuel A.
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