An electromagnetic wave (EMW) interacting with the moving singularity of the charged particle flux undergoes the reflection and absorption as well as frequency change due to Doppler effect and nonlinearity. The singularity corresponding to a caustic in plasma flow with inhomogeneous velocity can arise during the breaking of the finite amplitude Langmuir waves due to nonlinear effects. A systematic analysis of the wave-breaking regimes and caustics formation is presented and the EMW reflection coefficients are calculated.