Intense lasers can propagate in air for a distance longer than the Rayleigh length in vacuum, which was found two decades ago. Such a steady propagation in air occurs as a result of the balance of self-focusing and plasma defocusing of the laser light. The intense peak of the femtosecond laser pulse, after Kerr focusing, can slightly ionize (with ionization degree as low as 1%) a small amount of air molecules in its path via multi-photon ionization.

The ionization produced plasma tends to defocus the laser, so that Kerr focusing is dominated again. The focusing- defocusing process is repeated in a continuous manner and the laser pulse can propagate for a long distance until its energy becomes too low.

From such a process one would easily imagine that a laser pulse with a higher energy can propagate a much longer distance in air, provided that the laser intensity keeps around the ionization threshold. However, no physical model has been yet introduced to discuss it.  

Recently, a research team led by State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics of the Chinese Academy of Sciences (CAS), collaborating with Helmholtz Institute Jena, established a simple physical model to deal with the long-pulse lasers propagation in air.  

The model is based on the observation that it is mainly the peak-intensity region of the focused laser pulse that interacts with and ionizes the air molecules.

Starting from the wave equation under the paraxial approximation, the model creatively introduces the dielectric properties of air by taking into account Kerr focusing, multi-photon ionization and dissipative effects. It was then successful to repeat the published experimental results for femtosecond lasers.  

More importantly, the model reveals the relationship between the laser duration and the propagation distance. It was surprisingly found that a high-energy laser pulse with suitable spot radius, suitable intensity, and tens of picosecond duration can propagate tens of kilometers through the atmosphere at relatively low altitudes with a significant amount of energy to spare. 

The results shed lights on various applications, including long-distance diagnostics of the atmosphere, long-distance excitation, guidance of natural/artificial lightning discharge or charged-particle beams, and remote deposition of laser energy, etc.  

The results entitled "Very-long distance propagation of high-energy laser pulse in air" were published in Physics of Plasma.  

This work was supported by the National Natural Science Foundation of China, the National Basic Research Program of China, the Chinese Academy of Sciences President’s International Fellowship Initiative and the Strategic Priority Research Program (B). 

Figure (a) The stretching process from 1 round-trip to 12 round-trips (b) The relationship between the measured and calculated pulse duration and the round-trip (Image by SIOM)