Fifth harmonic generation in a medium with cubic nonlinear response based on cascading third harmonic generation

Laser technology has variety of applications for the laser beam and pulse possessing the range of ultraviolet frequencies. Among them, one can emphasise medicine, and semiconductor processing, and material research and many others. To get the light sources in ultraviolet and deep-ultraviolet ranges of frequencies, the frequency conversion processes are often used. One of these processes is the fifth harmonic generation. As a rule, to achieve this, three crystals, possessing quadratic nonlinear response, is used for sequential frequency up-conversion. This way allows us to obtain the energy up-conversion with high efficiency. But, this scheme requires several nonlinear media, which may be sometimes inconvenient, and more important that the quadratic susceptibility restricts the incident pulse intensity. In this paper we propose a new scheme for the fifth harmonic generation basing on the cascading third harmonic generation. This frequency up-conversion scheme requires only one medium with cubic nonlinear response and can be used directly for the pulses with femtosecond duration. Under the big phase mismatching between fundamental wave and the third harmonic, the fifth-order nonlinear response is induced. As wellknown, its strength is greater than the own fifth-order susceptibility and it is possible to govern its sign. We demonstrate theoretically its feasibility. Using multi-scale approach, we derive the equations which demonstrate a presence of the fifth-order susceptibility. Based on the problem conservation laws we develop the analytical solution in the frame-work of both long pulse duration approximation and plane wave approximation but without using the non-depletion energy approximation for fundamental wave. This solution allows us to estimate the maximal efficiency of the fifth harmonic generation in dependence of both the self- and crossmodulation of waves and the phase mismatching between fundamental wave and wave of fifth harmonic. Under certain condition it is possible to achieve 93% efficiency of the frequency up-conversion. All results obtained using multi-scale approach are confirmed by the computer simulation results based on nonlinear Schro spacing diaeresis dinger equations describing the fifth harmonic generation in a medium with cubic nonlinear response.