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Optics Letters

Bandwidth limits due to mutual pulse interaction in optical soliton communication systems

Dan Anderson, M. Lisak

Published Mar 1, 1986• 111 citations
Publisher

Abstract

Mutual interaction between soliton pulses may severely limit the maximum bit rate of a soliton-based optical communication system. We present explicit analytical results for soliton separation as a function of propagation distance in the presence of mutual pulse interaction. In particular, we find that soliton coalescence can be avoided by proper phase shifting of consecutive pulses and that a phase shift of π/2 minimizes the initial mutual interaction.

DOI
10.1364/ol.11.000174

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Mutual interaction between soliton pulses may severely limit the maximum bit rate of a soliton-based optical communication system. We present explicit analytical results for soliton separation as a function of propagation distance in the presence of mutual pulse interaction. In particular, we find that soliton coalescence can be avoided by proper phase shifting of consecutive pulses and that a phase shift of π/2 minimizes the initial mutual interaction.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2
Classical optical solitons propagate in optical fibers without temporal or spectral distortion as a result of a balance between phase shifts due to group velocity dispersion and those due to nonlinear self-phase modulation. This balance is achieved by the proper choice of pulse shape and duration for a given pulse energy. The quantum fluctuations associated with a coherent soliton do not undergo stationary propagation, however, and a number of effects are predicted, including the evolution of vacuum noise associated with the input coherent pulse into squeezed fluctuations and the temporal spreading of the soliton pulse because of dispersion acting on quantum fluctuations of the pulse frequency.
One of the key issues when dealing with slow light is the inevitable effect of dispersion, the result of which is to broaden a pulse upon propagation. Moreover, the dispersion tends to increase when the group velocity, the speed at which the pulse propagates, decreases. To see this, we note that if we write the group velocity vg ≡ c/ng, where ng is the group index, then we find that ng = n+ωdn/dω. Since for the materials we are interested in, the refractive index does not vary strongly in magnitude, and slow light is obtained when the derivative dn/dω is large and positive. However, as the variations in the magnitude of n itself are limited, the large derivative can only be maintained over a narrow bandwidth ∝ (dn/dω)−1. Therefore, a large delay implies a narrow bandwidth, and hence a limited pulse width. Here we discuss how to avoid this limit by using nonlinear effects in the form of gap solitons. Though this argument is quite simple, it can be made rigorous using the Kramers-Kronig relations. In this way it can be shown that the achievable delay in a linear, two-port device is subject to a limitation of the product of the delay and the bandwidth (Lenz et al., 2001).
The simultaneous propagation of two optical pulses through a nonlinear dispersive medium composed of a resonant three-level system is investigated. By choosing a soliton of area 4 pi and order N=2 at the pump frequency, together with a weaker pulse with a sech profile at the signal frequency, we show that the pump soliton breaks up into a pair of solitary waves which are cloned to the signal frequency. Due to a combination of coherent population trapping and nonlinear dispersive effects, the pair interacts in a repulsive fashion so that the taller wave travels faster than the shorter one.
We study the interaction between an intense soliton and a weak control pulse in optical media with a zero-nonlinearity wavelength (ZNW). By means of numerical simulations, we show that the soliton’s wavelength and group delay can be modified by a proper choice of parameters of the control pulse, such as its power, frequency, and initial delay. Most remarkably, we demonstrate either the suppression of the soliton’s Raman-Induced Frequency Shift (RIFS) or the enhancement of this effect and explain it by temporal analogies of reflection and transmission. Finally, we propose an all-optical switching scheme based on time and frequency windows.