Abstract

A radially- or azimuthally-polarized mode is one of the axially-polarized modes, changing its local polarization state as a function of the azimuthal angle. It can be expressed by a superposition of the left-circularly polarized (LCP; s = +1: spin angular momentum (SAM) of light) l = −1 optical vortex and the right-circularly polarized (RCP; s=−1) l =+1 optical vortex. Here, the term optical vortex simply refers to a Laguerre-Gaussian mode with a zero-radial index. l is an orbital angular momentum (OAM) of light per photon in $\overline{h}$ units which causes the phase ramp around the phase singular point [1]. In a beam propagating along the optic axis of a uniaxial crystal, the crystal anisotropy induces its SAM conversion between s=+1 and s= −1 states under the conservation of total angular momentum s + l. Thus, a uniaxial crystal is used for high-power generation of s= −1, l =2 optical vortex pulses from Gaussian beam pulses (s=+1, l =0) [2], or enables us to separate radially- or azimuthally-polarized pulses from s=±1, l =∓1 optical vortex pulses [3]. This method using a uniaxial crystal is suited for high power pulse generation because the threshold value is higher than those in other methods using a spiral plate [3], a spatial light modulator (SLM) [4] or a photonic-crystal axially-symmetric polarizer/waveplate [5]. However, earlier studies [2,3] avoid nonlinear effects by inputting a diverging beam into a uniaxial crystal and hence the nonlinear effects, such as Kerr or four-wave-mixing effects between radially- and azimuthally-polarized modes, have not been well investigated. In the present paper, we experimentally investigate optical-vortex pulse propagation in a uniaxial crystal through nonlinear converting between radially- and azimuthally-polarized pulses.

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