Harmonic

Quantum mechanics

Gaussian

Linguistics

Voltage

High harmonic generation

Philosophy

Computational physics

Optical vortex

Economics

Harmonics

Classical mechanics

Laguerre polynomials

Riemann zeta function

Laser

Physics

Total angular momentum quantum number

Divergence (linguistics)

Mathematics

Optics

Quantum electrodynamics

Angular momentum coupling

Angular momentum

Harmonic number

Mathematical analysis

Momentum (technical analysis)

Finance

Order (exchange)

Physical review. A/Physical review, A

We report on a method to generate extreme ultraviolet vortices from high-order harmonic generation with two-color counter-rotating Laguerre-Gaussian ($\text{LG}$) beams that carry a well-defined orbital angular momentum (OAM). Our calculations show that the OAM of each harmonic can be directly controlled by the OAM of the incident $\text{LG}$ modes. Furthermore, we show how the incoming $\text{LG}$ modes have to be tailored, in order to generate every possible value of OAM in the emitted harmonics. In addition, we analyze the emitted harmonics with respect to their divergence and find that it decreases with the harmonic order and increases with the OAM of the emitted harmonic.

Tailored orbital angular momentum in high-order harmonic generation with bicircular Laguerre-Gaussian beams