Nonlinear conversion between ultrashort radially- and azimuthally-polarized pulses in an anisotropic media

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 h units which causes the phase ramp around the phase singular point. 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), or enables us to separate radially- or azimuthally-polarized pulses froms = ±1, l = =±1 optical vortex pulses. 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, a spatial light modulator (SLM) or a photonic-crystal axially-symmetric polarizer/waveplate. However, earlier studies 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.