Space-time coupling of the carrier-envelope phase in ultrafast optical pulses

TL;DR

This paper introduces a method for calculating the space-time variation of the carrier-envelope phase (CEP) in ultrafast optical pulses, revealing significant CEP variations in focal regions and enhancing precision in optical applications.

Contribution

The authors develop a novel approach for space-time calculation of CEP, challenging the assumption that CEP is purely a temporal phenomenon and enabling more accurate modeling in complex optical systems.

Findings

Significant CEP variation in focal volumes of focusing elements

Accurate calculation of CEP in spatially defined regions

Implications for improved precision in optical applications

Abstract

The carrier-envelope phase (CEP) plays an increasingly important role in precise frequency comb spectroscopy, all-optical atomic clocks, quantum science and technology, astronomy, space-borne-metrology, and strong-field science. Hitherto, it has been essentially assumed that CEP is strictly a temporal phenomenon. Here we introduce an approach for space-time calculation of the CEP in the spatially defined region of interest. We find a significant variation of CEP in the focal volume of refracting focusing elements and accurately calculate its value. We discuss the implications and importance of this finding. Our method is particularly suitable for application to complex, real-world, optical systems thereby making it especially useful to applications in research labs as well as in the engineering of innovative designs that rely on the CEP.