We demonstrate the utilization of Dammann lenses codified onto a spatial light modulator (SLM) for triggering nonlinear effects. With continuous wave illumination Dammann lenses are binary phase optical elements that generate a set of equal intensity foci. We theoretically calculate the influence of ultrashort pulse illumination on the uniformity of the generated pattern, which is affected by chromatic aberration for pulses with temporal widths lower than 100 fs. The simulations also indicate that acceptable uniformity can be achieved for pulses of several fs by shortening the distance among foci which can be easily modified with the SLM. Multifocal second-harmonic generation (SHG) and on-axis multiple filamentation are produced and actively controlled in β − BaB 2 O 4 (BBO) and fused silica samples, respectively, with an amplified Ti: Sapphire femtosecond laser of 30 fs pulse duration. The study of the non-linear processes [1] that take place during the interaction of light with matter has benefited from the high peak powers achieved with amplified femtosecond (fs) lasers [2]. This opens a huge gate toward the development of many applications in the nonlinear optics field. For instance, second-order parametric processes [3] are efficiently used to tune the central wavelength through SHG or sum/difference-frequency generation, expanding the accessible wavelength range of standard Ti:sapphire laser systems. Third-order processes are also very often exploited to increase the spectral width of fs pulses through optical-Kerr effect (self-phase modulation), or in combination with strongfield ionization and higher order processes (supercontinuum generation [4] and filamentation [5]). The increase of the spectral width by means of the abovementioned nonlinear effects allows subsequent compression of the pulse to a much shorter temporal duration [6]. Most of these processes require the focusing of the laser beam [7] just to reach the high intensities needed to trigger the desired effect. However, under certain circumstances, the spatiotemporal properties of the pulse focusing itself can be exploited to gain control over the nonlinear mechanisms taking place. In this sense, diffractive lenses have been recently employed for SHG [8] or in super continuum generation [9]: the strong chromatic aberration induced by diffraction changes the spectral properties of the pulse.On the other hand, Dammann diffraction gratings are binary phase distributions of alternate 0, π zones for well-defined transient points [10,11]. For continuous wave (CW) illumination, these gratings generate diffraction patterns characterized by a number N of diffracted orders with the same peak intensity. This concept can be easily extended to lenses. The phase of a converging refractive lens can be represented by πr 2
We experimentally demonstrate an extremely compact and programmable pulse shaper composed of a single phase mask encoded into a spatial light modulator. Its principle of operation is similar to the previously theoretically introduced quasi-direct space-to-time pulse shaper [Opt. Express 16, 16993 (2008)], which is based on diffractive optics. The proposed pulse shaper exhibits not only real-time temporal modulation, but also high-efficiency output pulses thanks to an active correction of the wavefront aberrations.
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