The accurate calculation of laser energy absorption during femto-or picosecond laser pulse experiments is very important for the description of the formation of periodic surface structures. On a rough material surface, a crack or a step edge, ultrashort laser pulses can excite surface plasmon polaritons (SPP), i.e. surface plasmons coupled to a laser-electromagnetic wave. The interference of such plasmon wave and the incoming pulse leads to a periodic modulation of the deposited laser energy on the surface of the sample. In the present work, within the frames of a Two Temperature Model we propose the analytical form of the source term, which takes into account SPP excited at a step edge of a dielectric-metal interface upon irradiation of an ultrashort laser pulse at normal incidence. The influence of the laser pulse parameters on energy absorption is quantified for the example of gold. This result can be used for nanophotonic applications and for the theoretical investigation of the evolution of electronic and lattice temperatures and, therefore, of the formation of surfaces with predestined properties under controlled conditions. *

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We provide a nonperturbative theory for photoionization of transparent solids. By applying a particular steepest-descent method, we derive analytical expressions for the photoionization rate within the two-band structure model, which consistently account for the selection rules related to the parity of the number of absorbed photons (odd or even). We demonstrate the crucial role of the interference of the transition amplitudes (saddle-points), which in the semi-classical limit, can be interpreted in terms of interfering quantum trajectories. Keldysh's foundational work of laser physics [Sov. Phys. JETP 20, 1307] disregarded this interference, resulting in the violation of selection rules. We provide an improved Keldysh photoionization theory and show its excellent agreement with measurements for the frequency dependence of the two-photon absorption and nonlinear refractive index coefficients in dielectrics.

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