# Fast and Slow Measurement: Revealing the Shape of a Pulse

07.05.2019

## Two ultrafast pulses, measured together, create a kind of shape-revealing hologram

At mere attoseconds – an attosecond is a billionth of a billionth of a second – the laser pulses in Prof. Nirit Dudovich’s lab are among the fastest ever created. But knowing how fast they are does not tell one exactly how long each pulse is, or how it is shaped. To uncover these properties of attosecond pulses, Dudovich’s group and that of departmental colleague Prof. Dan Oron collaborated with an applied mathematician, Prof. Boaz Nadler, and an advanced attosecond laser lab in Italy.

“Prof. Boaz Nadler, of the Computer Science and Applied Mathematics Department, lived across the way from me in the campus residential neighborhood. I once asked him a question when we were just hanging out with our kids. That question has led to five papers, so far, that we’ve written together with Oron,” says Dudovich, who is in the Weizmann Institute of Science’s Physics of Complex Systems Department. For the current study, which involved applying an innovative algorithm to a long-standing problem in experimental physics, the collaboration with Nadler was a natural choice.

The question of measuring the shape of attosecond pulses has been with attosecond science from its early days. The problem is that they are too fast to be measured by any electronic device. Although the wavelengths that compose the pulse can be measured – these are the colors – the phase of each color cannot be directly resolved. This latter problem has a name – the phase retrieval problem.

The scientists borrowed this concept to demonstrate a 4D, temporal hologram

There are a few methods of circumventing the phase retrieval problem, but they are, in practice, highly challenging. It was Dr. Oren Raz, when he was a PhD student in Dudovich’s group, who had an idea for a new way to approach the problem. The idea was to combine two attosecond laser pulses and measure them together. Combined, these two would act as a hologram. Holography, in physics, is applied to resolve 3D images of spatial objects. In the current work, the scientists borrowed this concept to demonstrate a 4D, temporal hologram. Recording this hologram, together with knowing the interference pattern of the two pulses, enabled the researchers to reconstruct phases of the two light waves. “It is a concept that could, theoretically, be used to measure all sorts of quantum phenomena – for example, to reconstruct the shapes of atomic particles from the interference in their diffraction patterns,” says Dudovich.

Raz, who has recently returned to the Weizmann Institute of Science as a senior scientist, had published this theoretical work while still a student. Advancing from his theoretical prediction to an experimental demonstration was a challenging step: It would take all of the groups – Nadler and the physics groups ‒ working together, several years to accomplish. Dr. Oren Pedatzur in Dudovich’s group and Dr. Ben Leshem in Oron's group worked in collaboration with a group of Italian scientists in the attosecond laser facility in the Politecnico di Milano. The results were published in Nature Photonics and, says Dudovich, they were stunning: “We could measure the shape of these pulses with attosecond accuracy using a direct simple spectral measurement. This could change some ideas in the field, because we showed that you can measure something that is incredibly fast with a detector that is much slower – an entire second or even slower.”

Prof. Nirit Dudovich's research is supported by the Helen and Martin Kimmel Award for Innovative Investigation; the Crown Photonics Center; the Jay Smith and Laura Rapp Laboratory for Research in the Physics of Complex Systems; the Rosa and Emilio Segre Research Award; the Wolfson Family Charitable Trust; the Jacques and Charlotte Wolf Research Fund; and the estate of Raymond Lapon. Prof. Dudovich is the incumbent of the Robin Chemers Neustein Professorial Chair.

Prof. Boaz Nadler is the incumbent of the William Petschek Professorial Chair of Mathematics.

Prof. Dan Oron's research is supported by the Crown Photonics Center; the Wolfson Family Charitable Trust; Dana and Yossie Hollander; the Centre National de la Recherche Scientifique; the European Research Council.

Dr. Oren Raz's research is supported by the Abramson Family Center for Young Scientists; the Barton Award for Young Scientists; and the Harmstieg New Scientist Fund. Dr. Raz is the incumbent of the Shlomo and Michla Tomarin Career Development Chair.