J. P. Gordon

Theory of the soliton self-frequency shift.

Raman effects cause a continuous downshift of the mean frequency of pulses propagating in optical fibers. For solitons in silica fibers, the effect varies roughly with the inverse fourth power of the pulse width. At 1.5-microm wavelength in a fiber with 15 psec/nm/km time-of-flight dispersion, a soliton of 250-fsec duration is predicted to shift by its own spectral width after about l00m of propagation. The theory agrees well with recent measurements.

Random walk of coherently amplified solitons in optical fiber transmission.

In an optical-communications system using soliton pulse transmission, periodic amplification is needed to maintain the energy of the solitons. We show that amplifier noise causes a solitons group velocity to undergo a random-walk process. The resultant timing errors at the receiver limit the systems product of length times bit rate, in one example, to about 24 000 GHz-km.

Negative dispersion using pairs of prisms.

We show that pairs of prisms can have negative group-velocity dispersion in the absence of any negative material dispersion. A prism arrangement is described that limits losses to Brewster-surface reflections, avoids transverse displacement of the temporally dispersed rays, permits continuous adjustment of the dispersion through zero, and yields a transmitted beam collinear with the incident beam.

Phase noise in photonic communications systems using linear amplifiers

Spontaneous emission noise limits the capacity and range of photonic communications systems that use linear optical amplifiers. We consider here the question of phase detection in such systems. Amplitude-to-phase-noise conversion occurs owing to the nonlinear Kerr effect in the transmission fiber, resulting in optimal phase noise performance when the nonlinear phase shift of the system is approximately 1 rad. Error-free state-of-the-art systems that use phase detection at multigigabit rates are thereby limited to a range of a few thousand kilometers.

Polarization multiplexing with solitons

It is shown both analytically and with numerical simulation, and confirmed experimentally in transmission over distances up to approximately 10000 km, that solitons maintain a high degree of polarization over an ultra-long distance transmission system consisting of birefringent dispersion-shifted fiber segments and erbium amplifiers. Based on that fact, the authors propose a polarization/time division multiplexing technique which should allow the single-wavelength bit-rate capacity of an ultra-long distance soliton transmission system to be doubled with little or no significant increase in bit error rate. >

Interaction forces among solitons in optical fibers

The propagation of light pulses as solitons in optical fibers may form the basis of a viable means of communication. We show here from the general two-soliton function that solitons in fibers exert forces on their neighbors that decrease exponentially with the distance between them and depend sinusoidally on their relative phase. These forces account for the displacements suffered by solitons during collisions, and their effects must be taken into account in system design.

The sliding-frequency guiding filter: an improved form of soliton jitter control

By gradually translating the peak frequency of guiding filters along its length, we create a fibertransmission line that is substantially opaque to noise while remaining transparent to solitons. This trick allows the use of stronger filters, and hence greater jitter reduction, without incurring the usual penalty of exponentially rising noise from the excess gain required to overcome filterloss.

Generation of optical pulses as short as 27 femtoseconds directly from a laser balancing self-phase modulation, group-velocity dispersion, saturable absorption, and saturable gain

We describe an ultrasbort-pulse laser that, under specific operating conditions, balances the mechanisms of conventional passive mode locking and solitonlike pulse shaping in a single resonator to generate optical pulses that are to our knowledge the shortest yet emitted directly from a laser, 27 fsec.

Dispersive perturbations of solitons of the nonlinear Schrödinger equation

A useful analysis of dispersive (radiative) perturbations of solitons of the nonlinear Schrodinger equation is developed. With reference to the propagation of optical solitons in glass fibers, the analysis is used to treat the collision of a low-intensity wave packet with a soliton, the radiation field created by the local perturbation of a soliton, and finally that created by a spatially periodic perturbation of the parameters of the fiber, or equivalently by a periodic variation in gain and loss that averages to zero. Perturbations whose wavelength is short compared with the soliton period produce exponentially small radiation fields as a result of the need for phase matching.

Effects of fiber nonlinearities and amplifier spacing on ultra-long distance transmission

It is shown that it should be possible to send error-free signals at a 2.5-Gb rate (or higher) over distances of at least 9000 km using an amplitude shift keying (ASK) soliton modulation system. To accomplish this, the amplifiers must be kept close enough that their power gain is less than 10 dB. (It is noted that timing jitter and other noise effects measured in recent soliton transmission experiments carried out at low D and with amplifier spacing of 25 km are in close accord with predictions of this work). Frequency division multiplexing of several channels over the same fiber should also be possible, as solitons of different frequencies interact very weakly, provided the distance over which they pass through one another is large compared to the amplifier spacing. >