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.
Highlights
Helical beams are optical beams characterized by a transversal phase distribution with an additional helical phase term l θ
We simulate the optical system using the spectrum of plane-waves method [27] for propagation between spiral phase plate (SPP) and mode converter (MC), while using ray tracing for propagation between the front face of MC and rear face of the lens, for evaluation of wavefront aberrations, and for optimization of aspherical shapes of MC interfaces
We briefly describe the methods used for simulations in the first subsection, while we give the expression for all aspherical surfaces, including both lenses and MC for both variations, in the second subsection, and we present and discuss the results regarding the focal spot in the third subsection
Summary
Helical beams are optical beams characterized by a transversal phase distribution with an additional helical phase term l θ. Polarization state may change with the azimuthal angle around the discontinuity, whereby the resulted beam is called a cylindrical vector beam [1]. Structured light and especially helical beams and cylindrical vector beams are deemed suitable for applications like optical trapping and particle manipulation [2,3,4], stimulated emission depletion (STED) microscopy [5,6], laser micromachining [7], or charged particle acceleration in plasma [8]. Cylindrical vector beams can be produced by selection of radial polarization from a circularly polarized beam using a conical window cut at Brewster angle [9], using microstructured birefringent plates, known as spatially variant polarization converters [10] or liquid crystal modulators [11].
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