*“An exact mathematical solution reveals how to tilt a laser pulse and move intensity peaks at faster than the speed of light, or even backwards*

*A breakthrough in the mathematical solution for manipulating pulses of light clarifies the physics of ‘tilted’ laser pulses, and shows how they can be used to produce exotic effects1. The solution, developed by researchers from A*STAR and the Massachusetts Institute of Technology (MIT), could advance applications such as terahertz lasers, X-ray generation and ultrafast electron imaging.*

*Pulsed lasers are commonly used in industrial and research applications to deliver precision doses of high-intensity laser energy, which for example can prevent the target from being damaged while still heating or exciting it to a certain energy state. Some of the latest techniques use ultrashort pulses which last just a few femtoseconds — one quadrillionth of a second — to excite atoms and molecules and observe how they respond.*

*One of the methods used to enhance the interaction between a laser pulse and the target atom or molecule is to tilt the wavefront of the pulse so that the energy delivery becomes slightly spread over time and in space, like the angle on the blade of a snow-plow. This effect can also be used to match pulses from different sources, which at such ultrashort pulse-lengths can be extremely challenging. Until now, the mathematics used to calculate the parameters and behavior of tilted laser pulses have only been approximations, with limited insight into the physics involved.*

*“It is interesting to study very short tilted-pulse-front pulses not only because of the new physics they contain, but also because such pulses can allow us to achieve target intensities with much lower energies, which could translate to cost savings,” says Liang Jie Wong from A*STAR’s Singapore Institute of Manufacturing Technology (SIMTech). “However, it is notoriously challenging to obtain exact analytical solutions for realistic pulses.”*

*Wong and collaborator, Ido Kaminer, from MIT and the Technion, Israel, originally set out to develop exact mathematical solutions for a new type of laser pulse called a needle pulse, but ended up with something much bigger.*

*“This result was mostly serendipity,” says Wong. “We simply played around with possible mathematical expressions that could solve the equations exactly.”*

*The new mathematical solution not only describes tilted pulses with exact physical precision (see image), allowing for rigorous study for optimization of existing applications, but also reveals that a beam of tilted-pulse-front pulses can be tailored for some exotic physics.*

*“We can create wave packets with intensity peaks that can propagate at faster or slower than the speed of light, and even backwards,” says Wong.*

*The A*STAR-affiliated researchers contributing to this research are from SIMTech.”*