# Polarization Properties of Laser Solitons

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## Abstract

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## 1. Introduction

## 2. Materials and Method

- ${I}_{x}$: Horizontally polarized component of the intensity.
- ${I}_{y}$: Vertically polarized component of the intensity
- ${I}_{45}$: Intensity component diagonally polarized.

- ${I}_{circ}$: Circular component of the emission. In this case, a QWP is used in addition to the linear polarizer. including the ${S}_{3}$ factor associated with this component, the Stokes parameters are calculated from the following set of equations:$$\begin{array}{cc}\hfill {S}_{0}& ={I}_{x}+{I}_{y}\hfill \end{array}$$$$\begin{array}{cc}\hfill {S}_{1}& =\frac{({I}_{x}-{I}_{y})}{{S}_{0}}\hfill \end{array}$$$$\begin{array}{cc}\hfill {S}_{2}& =\frac{2\xb7{I}_{45}}{{S}_{0}}-1\hfill \end{array}$$$$\begin{array}{cc}\hfill {S}_{3}& =\frac{2\xb7{I}_{circ}}{{S}_{0}}-1\hfill \end{array}$$$$FP=\sqrt[]{{S}_{1}^{2}+{S}_{2}^{2}+{S}_{3}^{2}}$$

## 3. Results

#### 3.1. Single Soliton Case. The Cavity Soliton

#### 3.2. The Ring-Shaped Structure. The Optical Vortex Beam

## 4. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Experimental setup: A volume Bragg grating (VBG) provides frequency-selective feedback to a vertical-cavity surface-emitting laser (VCSEL). BS: beam sampler, CCD: charge-coupled device camera, PD: photo-detector, LP: linear polarizer, QWP: quarter-wave plate, HWP: half-wave plate. The upper arm is used to measure the spatially resolved Stokes parameter at high magnification (CCD1), the lower monitors power (PD) and near (CCD3) and far field (CCD2) distributions of potentially the whole laser.

**Figure 2.**Typical L–I characteristic curve obtained by monitoring the output power of the VCSEL. The black dots account for regular spaced samples taken when the current is rising (continuous line); the constant value of the power measured is due to the absence of any output apart from the spontaneous emission. Once the system switches on, a complicated structure is formed (zone III); as we lower the injection current (dotted line), this structure changes and simplifies as can be seen in the second upper image (zone II) corresponding to the vortex beam. The last picture shows the single soliton (Zone I).

**Figure 3.**The left column depicts the intensity profile and dimensions of the single soliton. The right column accounts for the shape of the ring distribution; in this case, the distance between peaks is about ten microns. The intensity pattern resembles the shape of an optical vortex, including the phase singularity at the center.

**Figure 4.**Results obtained for the single soliton showing the existence of two orthogonal directions clearly represented by streamlines with constant orientation.

**Figure 5.**Results obtained for the frequency spectrum (

**left**), and the I-L diagram for a cycle centered in the zone where the change in the soliton polarization orientation happens (

**right**) using a linear polarizer with different orientations as the analyzer.

**Figure 6.**Total intensity ${S}_{0}$ for the vortex case showing two-peak structure in the left and three-peak structure in the right part of the figure. The polarization streamline representation for the two orthogonal polarization orientations that appear in the vortex beam reaches values very close to those of the single soliton.

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**MDPI and ACS Style**

Rodriguez, P.; Jimenez, J.; Guillet, T.; Ackemann, T.
Polarization Properties of Laser Solitons. *Appl. Sci.* **2017**, *7*, 442.
https://doi.org/10.3390/app7050442

**AMA Style**

Rodriguez P, Jimenez J, Guillet T, Ackemann T.
Polarization Properties of Laser Solitons. *Applied Sciences*. 2017; 7(5):442.
https://doi.org/10.3390/app7050442

**Chicago/Turabian Style**

Rodriguez, Pedro, Jesus Jimenez, Thierry Guillet, and Thorsten Ackemann.
2017. "Polarization Properties of Laser Solitons" *Applied Sciences* 7, no. 5: 442.
https://doi.org/10.3390/app7050442