Modelling of NOLM Demultiplexers Employing Optical Soliton Control Pulse

An optical soliton pulse may be used as a control signal in non-linear optical loop mirror demultiplexers in order to reduce timing-jitter noise and cross-talk. A mathematical model for calculating the width of the soliton switching window and optimizing critical parameters such as walk-off time and pulse width has been presented, and its accuracy is verified by solving the nonlinear Schrodinger equation. Key word: Semiconductor laser amplifier, optical switching, soliton, optical time division demultiplexer, optical loop mirrors. 1INTRODUCTION The non-linear optical loop mirror (NOLM) demultiplexer is a promising configuration for achieving all-optical time division demultiplexing because of its high operating speed [1]. Channel demultiplexing is realised by the phase difference between the clockwise (CW) and counter-clockwise (CCW) signal pulses propagating within the fibre loop, see Figure 1. In ultra-high speed systems, there are two major problems: 1) difficulty in achieving complete switching of the signal pulses; and 2) timing jitter between the copropagating control and signal pulses. The latter is reduced to a certain extent by introduction of walk-off time Tw between the control and signal pulses. This results in a square switching window shape, with a width of TwL, where L is the fibre loop length, rather than bell shape, thus enabling improved switching and consequently better tolerance to timing jitter [2]. A 100% switching is difficult to achieve because of the control pulse experiencing a soliton compression effect due to interaction between the fibre dispersion and self phase modulation (SPM) [4]. This will result in an increased control signal peak power which in turn leads to an asymmetrical switching window with an increasing phase shift towards the end of the switching profile. Maximum switching may be achieved by employing optical soliton as a signal or control pulse, since the fundamental properties of the soliton are uniform phase over the entire pulse and constant pulse shape over the entire propagation length. Here, we investigate the later option, and show that the problem of pulse deformation during propagation within the loop is solved, thus resulting in a much improved switching window with high transmittance and reduced timing jitter effects. 2THEORY To study the output transmittance of the NOLM demultiplexer it is best to consider the combined impact of the following effects: 1) cross phase modulation (XPM), 2) propagation of optical soliton pulse within the fibre loop; and 3i) walk-off time between the control and signal pulses. The switching window is created by the phase difference between the CW and CCW signals. The phase of the signal pulse copropagating with the control pulse is substantially changed by the XPM effect. With the inclusion of walk-off time, the phase change can be represented by ∆φ = − ⋅ ∫ 2 0 γ P T T x dx w L ( ) (1) where γ is the non-linear coefficient, P is the optical power profile, and Tw = the walk-off time per unit length. The control pulse has to meet the following soliton conditions in order to propagate undisortedly along a lossless fibre [6]: 1the propagation equation of a fundamental soliton wave u i ( , ) sec ( ) exp ( / ) ξ τ τ ξ = h 2 2the peak power P T o o =| |/ β γ 2 2 where u is the normalised amplitude, τ = T/To and ξ = z/LD, z is the travelling distance, LD is the dispersion length = To/| β2 |, T FWHM o ≈ 1763 . is the pulse width of the optical soliton control pulse, and β2 is the first order dispersion coefficient. The control pulse walks through the signal pulse due to difference in the group velocity, and with the phase change of the signal depending on the value of the total walk-off time, the time varying optical power profile in Eq. (1) can be replaced by the pulse average power over the duration of total walk-off time. The maximum average power of the control pulse, resulting in XPM, is given as