Abstract

The properties and applications of laser modes with helical (vortex) phase front have attracted a great deal of attention at present (see, e.g., [1] and references therein). The Laguerre-Gaussian vortex nm-mode has the form: $E_L(r,\phi ;z)=E_0\times \left(w_0/w\right){\rho }^m{L}_n^m\left(2{\rho }^2\right)\exp \left[+im\phi -(1-i\zeta ){\rho }^2-i(2n+m+1)\mathrm{arctg}\zeta \right]$, where $\rho =r/w,\zeta =2z/\left(k{w}_0^2\right),L_n^m$ is the Laguerre polynomial, w= w₀[1+ζ²]^1/2, w₀is the value of win the mode waist, mis the vortex charge. At m>0 these modes have the phase discontinuity at the center.

© 1998 IEEE