A Method to Generate Vector Beams with Adjustable Amplitude in the Focal Plane

Abstract

We design and investigate an original optical component made of a c-cut uniaxial crystal and an optical system to generate cylindrical vector beams with an adjustable polarization state. The original optical component has a specific, nearly conical shape which allows it to operate like a broadband wave retarder with the fast axis oriented radially with respect to the optical axis. We show via numerical simulations, using the Debye–Wolf diffraction integral, that the focal spot changes depending on the polarization state, thus enabling the control of the focal shape. Non-symmetrical shapes can be created although the optical system and incoming beam are circularly symmetric. We explained, using Jones matrix formalism, that this phenomenon is connected with the Gouy phase difference acquired by certain modes composing the beam due to propagation to the focal plane. We present our conclusions in the context of two potential applications, namely, stimulated emission depletion (STED) microscopy and laser micromachining. The optical system can potentially be used for STED microscopy for better control of the point-spread function of the microscope and to decrease the unwanted light emitted from the surroundings of the focal point. We give an analytical expression for the shape of the original component using the aspherical lens formula for the two versions of the component: one for each potential application.

Analysis of Hybrid Vector Beams Generated with a Detuned Q-Plate

“…This simple case was analyzed in the far field in [30] and we include it here to compare with the next cases. According to Equation (12) the output is…”

“…This input state was obtained by illuminating with LCP a static q-plate of q = 1 (Thorlabs WPV10L-633) inserted in the PSG. According to Equation (12) this input RCP vortex beam now provides an output beam given by V out = 1 √ 2…”

“…While these systems offer great flexibility because they can be reprogrammed with arbitrary functions, they are bulky and introduce losses caused by the SLM pixelated structure. Other recent approaches use patterned polarizers [9], patterned retarders (q-plates) combined with polarization rotation devices [10], metasurfaces that encode a spiral geometric phase [11] or uniaxial crystals with special shapes [12]. Initial works made use of pure geometric phase elements where the retardance was adjusted to create different types of pure and hybrid vector beams [13].…”

Superposition of vortex beams generated by polarization conversion in uniaxial crystals

“…One of the most intriguing phenomena that have been observed for the linearly polarized Laguerre–Gauss beam incident on the optical system is the breaking of the circular symmetry as the beam propagates to the lens’s focal plane. This behaviour is theoretically explained in one of our previous work 31 as well as in Quiceno-Moreno et al 21 to be caused by the Gouy phase shift associated with the propagation of Laguerre–Gauss modes to the focal plane of a lens.…”

“…Loussert et al 30 have demonstrated that 100% efficiency can be achieved using a single piece of uniaxial material illuminated by a nearly conical superposition of plane-waves. In addition, a collimated input beam on an optical system consisting of an SPP and a uniaxial crystal with a special shape has been theoretically proven to generate HVBs 31 . Using uniaxial crystals to generate VVBs and HVBs may have some advantages over the other methods, for instance, the possibility to achieve conversion without losses and also to use high power fs pulsed beams.…”