Twisted-Light–Ion Interaction: The Role of Longitudinal Fields

Abstract

The propagation of light beams is well described using the paraxial approximation, where field components along the propagation direction are usually neglected. For strongly inhomogeneous or shaped light fields, however, this approximation may fail, leading to intriguing variations of the light-matter interaction. This is the case of twisted light having opposite orbital and spin angular momenta. We compare experimental data for the excitation of a quadrupole transition in a single trapped 40 Ca + ion by Schmiegelow et al, Nat. Comm. 7, 12998 (2016), with a complete model where longitudinal components of the electric field are taken into account. Our model matches the experimental data and excludes by 11 standard deviations the approximation of complete transverse field. This demonstrates the importance of all field components in the interaction of twisted light with matter.The full vector character of the electromagnetic field is responsible for a variety of basic physical processes, such as those occurring in near-field optics and the propagation of focused beams close to the diffraction limit [1,2]. Moreover, electromagnetic fields with components in all possible directions play a special role in applied science. For example, the sub-diffraction-limited focusing of radially polarized beams producing strong longitudinal fields [3] can be used to improve material processing [4,5]. Also, longitudinal fields have seen application in Raman spectroscopy [6], optical tweezers [7], and have been used to observe circular dichroism in non-chiral nanostructures [8].Light carrying orbital angular momentum, known also as twisted light (TL) or optical vortices, has introduced us to a new realm of structured light [9][10][11][12][13]. An unusual property of TL has to do with the relative orientation of the photon's angular momenta. When the orbital and spin angular momenta are antiparallel to each other, longitudinal field components become important. As a result, the light-matter interaction is different for parallel or anti-parallel momenta beams. This has been suggested in several theoretical articles dealing with tightly-focused TL [14,15] and TL-related beams [16][17][18][19][20]. Longitudinal fields in structured beams promise new applications, such as the control of the spin state of electrons or impurities in quantum dots [14,21], and the excitation of intersubband [22] transitions in quantum wells [23].For propagating fields that are not tightly focused the complexity of the full vector model can be reduced, still retaining an excellent description of the physics under consideration. In the paraxial approximation [24] one assumes that the transverse profile changes slowly along the propagation direction, here z. To lowest order in the ratio of wavelength to beam waist the electric and magnetic fields have no longitudinal component [25,26]. Although very common, such a strong assumption is not always correct. Theory shows that Laguerre-Gaussian (LG) beams, the paradigmatic paraxial TL, has a nonnegligible longitudin...

An intuitive approach to structuring the three electric field components of light

“…In particular any integration curve joining the two points yields the same result 8 . In fluid dynamics, the stream function characterizes the flow velocity quite intuitively, as already suggested by its name.…”

“…These definitions do not involve the longitudinal component E z , which is why they are termed transverse. From equations (8) and (9), the well-known fact that any nonzero linearly or circularly polarized field necessarily gives rise to a longitudinal electric field component becomes immediately clear; in these cases V is nonzero and has a nontrivial spatial dependence, and hence equation (5) gives rise to a nonzero E z . Throughout this paper, we will refer to these transverse polarization states when we mention linear and circular polarization.…”

“…x y f f 7 We follow the common terminology which labels magnetic fields of stationary currents as magnetostatic, even though time inversion symmetry is violated. 8 We consider a simply connected region.…”

“…Taking the longitudinal electric field component properly into account leads to a range of novel physical phenomena, such as a significant decrease of the focal spot size [4,5], the realization of so-called 'needle beams' [6] and Möbius strips in the polarization of light [7]. In the context of light-matter interaction, taking into account the effect of the longitudinal electric field component can be crucial [8], and it may even dominate over the transverse components [9].…”

Chiroptical interactions between twisted light and chiral media

“…This interplay between SAM and OAM is an interesting facet of the work, and gives rise to questions about its physical interpretation. The issue may be explained through a spin-orbit interaction approach [27][28][29] , and could potentially lead to further interesting applications. 30 Another issue which requires future work involves looking at the E2E2 and M1E2 terms which appear to suggest the possibility of a chiroptical response even with achiral media 21,15 : this is a prospect that chiral sensitivity might arise solely from the total angular momentum possessed by the radiation components of the system, exhibiting.…”