Abstract The Keldysh photoionization theory is a conceptual cornerstone and a universal framework for the description of a broad class of fundamental effects in light–matter interaction. Here, we provide an overview of the Keldysh theory as a significant milestone in the development of modern optical physics and offer a historical perspective on the fundamental role of this theory, from the early pioneering work on quantum tunneling to the latest breakthroughs in laser optics, attosecond technologies, and ultrafast optics of high-intensity laser pulses.Abstract The Keldysh photoionization theory is a conceptual cornerstone and a universal framework for the description of a broad class of fundamental effects in light–matter interaction. Here, we provide an overview of the Keldysh theory as a significant milestone in the development of modern optical physics and offer a historical perspective on the fundamental role of this theory, from the early pioneering work on quantum tunneling to the latest breakthroughs in laser optics, attosecond technologies, and ultrafast optics of high-intensity laser pulses.

Physics-UspekhiAug 31, 201745 citations

Complete Keldysh theory and its limiting cases

Howard R. Reiss

An investigation of the foundations of strong-field theories of the Keldysh type is undertaken. It is found first that the Volkov solution, upon which the Keldysh approximation depends, exists unambiguously only in the relativistic case. Accordingly, a fully relativistic theory of atomic photoionization is formulated from first principles. A strong-field approximation (SFA) is expressed, based only on the proposition that the photoionizing field dominates the atomic potential in the final state. The nonrelativistic limit of the SFA gives exactly one of the known Keldysh-type theories, but the original Keldysh theory itself is found to neglect some fraction of the strong-field effects. It is shown on a variety of grounds that ${\mathbf{A}}^{2}$ terms must be fully retained in Keldysh-type theories. Important in this matter are the proper application of asymptotic conditions, the interchangeability of A\ensuremath{\cdot}p and ${\mathbf{A}}^{2}$ terms, and the consistent reduction to the nonrelativistic limit.An investigation of the foundations of strong-field theories of the Keldysh type is undertaken. It is found first that the Volkov solution, upon which the Keldysh approximation depends, exists unambiguously only in the relativistic case. Accordingly, a fully relativistic theory of atomic photoionization is formulated from first principles. A strong-field approximation (SFA) is expressed, based only on the proposition that the photoionizing field dominates the atomic potential in the final state. The nonrelativistic limit of the SFA gives exactly one of the known Keldysh-type theories, but the original Keldysh theory itself is found to neglect some fraction of the strong-field effects. It is shown on a variety of grounds that ${\mathbf{A}}^{2}$ terms must be fully retained in Keldysh-type theories. Important in this matter are the proper application of asymptotic conditions, the interchangeability of A\ensuremath{\cdot}p and ${\mathbf{A}}^{2}$ terms, and the consistent reduction to the nonrelativistic limit.

Physical Review AAug 1, 1990160 citations

{\mathbf{A}}^{2}

terms must be fully retained in Keldysh-type theories. Important in this matter are the proper application of asymptotic conditions, the interchangeability of A\ensuremath{\cdot}p and

{\mathbf{A}}^{2}

terms, and the consistent reduction to the nonrelativistic limit.