coupler as a function of the gain asymmetry is shown in fig2 the fraction of the total energy in the cross state i e coupled from one waveguide into the other is plotted as a function of distance along the coupler for various values of the gain asymmetry at a single half beat length at the operating wavelength for zero mean differential gain coefficient there is strong modulation of the cross state transmission fraction provided by a non zero mean differential gain coefficient but insufficient to be of use however a three half beat length device again at the operating wavelength for zero mean differential gain coefficient shows total modulation as the gain is increased in one arm which changes the mean differential gain coefficient the fraction of energy in the cross state reduces and indeed can go to zero in fig3 there is shown the cross state switching fraction as a function of the differential mean gain coefficient u03b4 u03b3 for a three half beat length device the curve does not depend on the mean gain but does depend on the device length the asymmetry in fig3 is not particularly surprising given the asymmetric gain provided by the waveguides of the device one can obtain a simple expression for the switching point by comparing the phase shift in the b field for the symmetric and asymmetric cases full switching occurs in a 2n 1 beat length coupler when equ6 referring now to fig1 an optical switch comprises a four port linear coupler configured as dual core silica optical fibre with waveguiding cores 4 and 6 each core being doped with erbium ions to form fibre amplifiers the waveguide defined by core 4 has optical ports 8 and 10 one at each end similarly the waveguide defined.