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We investigate linear interference of a plane wave with different localisedwaves using coupled Fokas-Lenells equation(FLE) with four wave mixing (FWM)term. We obtain localised wave solution of the coupled FLE by linearsuperposition of two distinctly independent wave solutions namely plane waveand one soliton solution & plane wave and two soliton solution. We obtainseveral nonlinear profiles depending on the relative phase induced by solitonparameters. We analyse the linear interference profile under four differentconditions on the spatial and temporal phase coefficients of interfering waves.We further investigate the interaction of two soliton solution and a planewave. In this case we notice that asymptotically, two solitons profile may besimilar or different from each other depending on the choices of solitonparameters in the two cases. The results obtained by us might be useful forapplications in soliton control, a fiber amplifier, all optical switching, andoptical computing. Further we believe that the present investigation would beuseful to study the linear interference pattern of other localised waves ofFLE.

Linear interference and systematic soliton shape modulation by engineering plane wave background and soliton parameters