Distortion of Femtosecond Laser Pulses in Lenses and Lens Systems

Phase and polarization changes of pulsed Gaussian beams during focusing and propagation

“…Consider a beam consisting of several monochromatic components and that we are interested in the effect of their superposition in the vicinity of focus. Due to the chromatic aberration of the focusing element [75,76,130,[147][148][149], or because the different radii of the wave fronts, the focusing of each harmonic wave would be treated in a different coordinate system with different positions of the origin O. This is due to the wavelength dependence of the wave front radius R = R(ω), which is measured from plane of the exit pupil, which has a fixed place.…”

“…The other problem is that different parts of the beam traverse different extent in the material, as lenses have a spatially varying thickness. One effect of the different amounts of dispersive material is the propagation-time difference (PTD) of rays [75]. This causes pulse broadening, especially in the focal region [147].…”

“…However, the effect of PTD -which is caused in fact by the chromatic aberration [147] -was examined originally with fully illuminated lenses and using ultraviolet wavelengths, which enhance this unwanted phenomenon [75,147]. Most femtosecond lasers operate in the infrared regime, not the whole cross-section of the lens is used, and the focusing is loose compared to that considered in the cited articles [75,147].…”

“…To fulfill this condition, lenses are often avoided for focusing few-cycle pulses, because of their long-known distorting effects, especially the ones increasing pulse duration [75,147]. The first issue with lenses is that -as being refractive optics -the light passes through their material, which -due to dispersion -increases their temporal duration (see Section 2.2.1).…”

“…The effect of focusing on laser pulses, that is, how the carefully shaped wave packets change while they propagate from the focusing element to the focal point has been examined for decades, and the focusing attosecond pulses has also been the subject of studies recently [73,74]. The material of the lens [75], the aberrations of the focusing systems [76], or the Gouy phase shift [77] -this latter being a general property of beams -can affect the spatiotemporal evolution of the electric field in the focal region [78]. The result of these changes -primarily affecting the phase properties -has been directly shown, for example, in attosecond pulse production [79], or in optical coherence tomography [80].…”