Scaling the abruptly autofocusing beam

Abruptly autofocusing beams (AAF) have been intensively investigated since their debut in 2010. Thanks to their abruptly focusing properties, AAF beams have great potentials in diverse applications. One of the demonstrated applications is the multiphoton polymerization in multiple scales. On the otherside, more and more novel efficient shaping techniques are demanded for material processing particularly in the nano-/micro-scale. In this scale, the precise control of the optical focus is quite critical for fabricating finer structures of higher qualities. Despite of the possibility of shaping AAF beams either in Fourier-space or in direct-space, more shaping schemes were proposed and implemented in the Fourier space. And scaling the AAF beams in the direct space have remained the most significant challenge.

Researchers led by Professor Chen Xie at Tianjin University in China in collaboration with Professor Francois Courvoisier at Université de Bourgogne-Franche-Comté in France developed a smart scaling technique to manipulate the geometry of the AAF beams in the direct space, including the peak intensity, the focal size and its axial location. In their studies, the analytical, numerical simulations and experimental results were all taken into consideration and agreements inbetween the three results come up with a more convincing conclusion. To better understand this technique, they first modelize their AAF beams based on the caustic theory. This model could present a quite intuitive picture in terms of the curved trajectories forming the AAF geometries. With the help of this physical model, a shaping scheme is proposed by introducing a scaling factor directly in the radial phase of a self-accelerating AAF beams. Besides, they also build a numerical model based on the real physical parameters in their experimental setup to beter design this complex structured beams. The authors’ work is published in the Optics Express, one of the renowned journals from the Optical Society of America.

Their analytical results predict exactly the same scaling trend confirmed by experimental and simulated results, revealing the effects of their scaling factors on the profiles of the AAF beams. With the factor multiplied to the raidal phase of an AAF beam, the radial size of its focus would be linearly-scaled with a linearly-shifted axial location. Besides, with the dependence of peak intensity on the scaling factor revealed in their analytical study, they also demonstrated the possibility of keeping the peak intensity of the beams on a constant level while varying scaling factors. This could be very interesting to many applications such as material processing and particle manipulation.

The study is considered one of the most notable studies in terms of shaping AAF beams. Even if their analytical results were deduced under paraxial approximation, good agreement are also demonstrated in the non-paraxial experiments. Besides, their analytical results on the scaling characteristic are applied not only to AAF beams, but also to any cylindrically symmetric structured beam. The technique can also reduce the cost and complexity of scaling AAF beams as less lens are required in the direct-space scheme comparing with those in the Fourier space. The simplicity and workability of the advanced technology make it very reliable and hence will benifit many potential applications.