  The topology of the surface electronic states is detected with photoemission.
We explain the photoemission from the topological surface state . This is done
by identifying the effective coupling between surface electrons-photons and
vacuum electrons. The effective electron photon coupling is given by $e\tau^2$
where $\tau$ is the dimensionless tunneling amplitude of the zero mode surface
states to tunnel into the vacuum. We compute the polarization and intensity of
the emitted photoelectrons. We introduce a model which takes in account the
Dirac Hamiltonian for the surface electron to photons coupling and the
tunneling of the zero mode into the vacuum.
  Within the Green's function formalism we obtain exact results for the emitted
Photoelectrons to second order in the laser field. The number of the emitted
photoelectrons is sensitive to the laser coherent state intensity, the
polarization is sensitive to the surface topology of the electronic states and
the incoming photon polarization. The calculation is performed for the helical,
Zeeman and warping case allowing to study spin textures.
