**2. Theoretical formulation of OAM and its comparison with plane wave**

The set of nondiffractive Bessel beams solutions is based on the free-space differential Helmholtz equation, and their intensity profile has phase singularity with null amplitude at the center. The scalar form of Bessel beam skewing and propagating along the Z-axis in the cylindrical coordinates ð Þ *ρ*, *ϕ*, *z* is given by [63]:

$$E\left(\overrightarrow{r},t\right) = E\_o I\_l\left(k\_\rho \rho\right) e^{j\left(k\_x x - \alpha t \pm l\phi\right)}\tag{1}$$

$$H(\overrightarrow{r},t) = H\_o I\_l(k\_\rho \rho) e^{j(k\_x x - \alpha t \pm l\phi)}\tag{2}$$

where *Eo* and *Ho* stand for amplitude; *Jl* is the *l*th order Bessel function of the first kind, *k<sup>ρ</sup>* and *kz* are the corresponding radial and longitudinal wave vectors satisfying the equation *k* ¼ 2*π=λ* ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *k*2 *<sup>ρ</sup>* <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> *z* q . The detailed derivation of the vector form of the Bessel beam is illustrated below.
