# Generating Bessel-Gaussian Beams with Controlled Axial Intensity Distribution

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling

_{00}mode formed by laser resonators of a stable configuration corresponds to a Gaussian beam with a radially symmetric field distribution [30]:

## 3. Experimental Implementation of the Bessel-Gaussian Beam

#### 3.1. Experimental Setup

^{x}magnification was placed in front of a sCMOS camera CS2100M-USB (Thorlabs, Newton, NJ, USA) on the optical axis.

#### 3.2. Results and Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schemes for the formation of a zero-order Bessel beam with a quasi-rectangular dependence of axial intensity: (

**a**) the Bessel zone starts right after the axicon; (

**b**) the Bessel zone is moved away from the axicon. $2{h}_{w}$—waist diameter of the Gaussian beam, $2{\mathsf{\alpha}}_{0}$—apex angle axicon, $n$—refractive index axicon, ${z}_{AP}$—analysis plane after the axicon, ${z}_{B}$—length of the Bessel zone, D—clear aperture of the binary mask, d—diameter of the inner aperture of the mask, ${\mathsf{\tau}}_{A}$—amplitude transmittance.

**Figure 2.**Axial intensity distributions of a Bessel beam and the gradient from the longitudinal coordinate ${z}_{\mathrm{AP}}$ for various parameters of the mask before the axicon: (

**a**) without binary mask, $d=0$ mm, $D\to \infty $; (

**b**) with binary mask, $d=4$ mm, $D\to \infty $; (

**c**) with binary mask, $d=0,D=7$ mm; (

**d**) with binary mask, $d=4,D=7$ mm.

**Figure 3.**Axial intensity distributions of a zero-order Bessel beam and gradient from the longitudinal coordinate ${z}_{\mathrm{AP}}$ for various parameters of the binary mask in front of the axicon: (

**a**) without binary mask, $d=0$ mm, $D\to \infty $; (

**b**) with binary mask, $d=4$ mm, $D\to \infty $; (

**c**) with binary mask, $d=0,D=7$ mm; (

**d**) with binary mask, $d=4,D=7$ mm.

**Figure 4.**Cross sections of field intensity: (

**a**) without binary mask, $d=0$ mm, $D\to \infty $; (

**b**) with binary mask, $d=4$ mm, $D\to \infty $, Z

_{ap}= 240 mm; (

**c**) with binary mask, $d=0,D=7$ mm, Z

_{ap}= 360 mm; (

**d**) with binary mask, $d=4,D=7$ mm, Z

_{ap}= 240 mm; (

**e**) with binary mask, $d=4,D=7$ mm, Z

_{ap}= 360 mm.

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**MDPI and ACS Style**

Stsepuro, N.; Nosov, P.; Galkin, M.; Krasin, G.; Kovalev, M.; Kudryashov, S.
Generating Bessel-Gaussian Beams with Controlled Axial Intensity Distribution. *Appl. Sci.* **2020**, *10*, 7911.
https://doi.org/10.3390/app10217911

**AMA Style**

Stsepuro N, Nosov P, Galkin M, Krasin G, Kovalev M, Kudryashov S.
Generating Bessel-Gaussian Beams with Controlled Axial Intensity Distribution. *Applied Sciences*. 2020; 10(21):7911.
https://doi.org/10.3390/app10217911

**Chicago/Turabian Style**

Stsepuro, Nikita, Pavel Nosov, Maxim Galkin, George Krasin, Michael Kovalev, and Sergey Kudryashov.
2020. "Generating Bessel-Gaussian Beams with Controlled Axial Intensity Distribution" *Applied Sciences* 10, no. 21: 7911.
https://doi.org/10.3390/app10217911