Multiphoton absorption with Laguerre-Gaussian beams

Laguerre-Gaussian beams possess a unique transverse mode structure defined by the orbital \(l\) $l$ and radial \(m\) $m$ mode numbers, offering promising potential for controlling nonlinear optical interactions. This comprehensive study aims to elucidate the crucial influence of this transverse mode structure on the nonlinear absorption processes. We first established a rigorous theoretical framework by deriving analytical expressions describing the behavior of the Open Z-scan normalized optical transmittance for an arbitrary nth-order nonlinear process under the weak nonlinearity approximation, accounting for the transmitted optical intensity, power, and their dependency on the beam’s transverse mode profile. In the numerical simulations, we focused on the specific case of second-order ( \(n=2\) $n=2$ ) nonlinear absorption. Subsequently, detailed numerical simulations were employed to systematically analyze the intricate interplay between the \(l\) $l$ and \(m\) $m$ mode indices and their impact on the transmittance characteristics. By precisely varying these indices, we investigated how the observed transmission profiles were affected, revealing distinct behaviors for different Laguerre-Gaussian modes. When only \(m\) $m$ increases, absorption decreases due to the wider transverse energy spread, while varying \(l\) $l$ leads to a non-monotonic trend involving intense lobes. Remarkably, simultaneously increasing both \(l\) $l$ and \(m\) $m$ systematically enhances absorption through constructive interference of the helical and ring-like structures.