Laser Beam Shape

The **Gaussian beam** is one of the most used laserbeam in free space optical communication, due to its properties to focus light. The electric field $E$ of a Gaussian beam is a Gaussian function according to the following equation:
\begin{align}
E(r, z) = E_0 \; \frac{w_0}{w(z)} \cdot e^{-\left(\frac{r}{w(z)}\right)^2} \cdot e^{i k \frac{r^2}{2R(z)}} \cdot e^{i (k z -\eta(z)) } \space \space [4]
\end{align}
where

A** Bessel beam** is also used in this webdemo. It has the special property of being non-diffracting.

It is important to mention that the Bessel beam is just a therotical beam and thus**not realizable**.

The amplitude $E$ of the electric field of a Bessel beam is a Bessel function according to the following equation: \begin{align} E(r,z) = E_0 \; \cdot \exp(-i k_z z)\cdot \mathrm{J_0}\left(k_r r\right) \space\space [5] \end{align} where $\mathrm{J_0}$ is the 0th Bessel function, $k_r$ and $k_z$ are the radial and longitudinal component of the wavenumber $k$, respectively.

- $z$ is the propagation axis
- $r$ is the distance from the propagation axis
- $w(z) = w_0 \sqrt{1+ \left(\frac{z}{z_R}\right)^2}$ is the waist radius
- $z_R = \frac{\pi w^2_0}{\lambda}$ describes the Rayleigh length
- $\theta_{div} = \frac{\Theta}{2} = \tan^{-1}\left(\frac{w(z)}{z}\right) \stackrel{z \gg z_R}{\approx} \tan^{-1}\left(\frac{\lambda}{\pi w_0}\right)$ is the divergence angle
- $R(z) = z\left(1+\left(\frac{z_R}{z}\right)^2\right)$ is the radius of curvature of the beam's wavefronts
- $\eta (z) = \tan^{-1}\left(\frac{z}{z_R}\right)$ is the Gouy phase

A

It is important to mention that the Bessel beam is just a therotical beam and thus

The amplitude $E$ of the electric field of a Bessel beam is a Bessel function according to the following equation: \begin{align} E(r,z) = E_0 \; \cdot \exp(-i k_z z)\cdot \mathrm{J_0}\left(k_r r\right) \space\space [5] \end{align} where $\mathrm{J_0}$ is the 0th Bessel function, $k_r$ and $k_z$ are the radial and longitudinal component of the wavenumber $k$, respectively.