l[w_, w0_,  g_]  =  
      Exp[I ArcTan[g w/(w0^2  -  w^2)] ] / 
        Sqrt[(w0^2  -  w^2)^2  +  g^2 w^2]

Plot[Abs[l[w, 1000,  100]], {w,  800,  1200}]

Plot[Arg[l[w, 1000,  100]], {w,  800,  1200}, 
      PlotRange -> All]