# Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics

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## Abstract

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## 1. Introduction

## 2. Experimental Section

#### 2.1. Principle

#### 2.2. Experimental Considerations

## 3. Results

#### 3.1. Spatio-Temporal Dynamics of Raman Fibre Lasers

#### 3.2. Spatio-Temporal Dynamics of Partially Mode Locked Fibre Lasers

## 4. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Principle of spatio-temporal dynamics—(

**a**) Intensity dynamics $I\left(t\right)$ (simulated) depicting evolution over multiple round trips; (

**b**) The autocorrelation $K\left(\tau \right)$ of the intensity dynamics $I\left(t\right)$. The periodic interval between the peaks gives the round trip time ${\tau}_{RT}$; (

**c**) The spatio-temporal dynamics, describing evolution of the pulse features. Horizontal co-ordinate—temporal, vertical co-ordinate—spatial.

**Figure 2.**Spatio-temporal dynamics of Raman fibre lasers—Typical quasi-continuous wave intensity dynamics of a Raman fibre laser over (

**a**) long and (

**b**) short time scales; (

**c**) The corresponding spatio-temporal dynamics. The color scale indicates normalized intensity.

**Figure 3.**Spatio-temporal regimes of the Raman fibre laser—Spatio-temporal dynamics of a Raman fibre laser operating in the normal dispersion regimes, at different pump powers ${P}_{p}$; (

**a**) ${P}_{p}$ = 1.5 W; (

**b**) ${P}_{p}$ = 2.0 W; (

**c**) ${P}_{p}$ = 3.0 W; and (

**d**) ${P}_{p}$ = 3.25 W.

**Figure 4.**Polarized rogue waves in the Raman fibre laser—(

**a**) Experimentally measured polarization resolved intensity dynamics of the Raman fibre laser, and (

**b**,

**c**) corresponding polarization resolved spatio-temporal dynamics ((

**b**)—blue curve, (

**c**)—red curve), revealing the existence of linearly polarized rogue waves.

**Figure 5.**Spatio-temporal dynamics of a partially mode locked fibre laser regime—(

**a**,

**b**) Typical intensity dynamics observed at different time instants; and (

**c**) the spatio-temporal dynamics of the operational regime.

**Figure 6.**Spatio-temporal diversity of the partially mode locked regimes—Different spatio-temporal regimes with varying characteristics accessed via tuning of the polarization controllers. The panels give examples of regimes exhibiting (

**a**) stationary characteristics over evolution co-ordinate T; (

**b**) periodicity over evolution co-ordinate T; (

**c**) interactions between the pulse and the background; and (

**d**) highly chaotic, turbulent generation.

**Figure 7.**Cross-correlation based analysis for revealing the constituents of radiation—(

**a**) Spatio-temporal dynamics $I(t,T)$ of the background region between the pulses for the regime of Figure 5c; (

**b**) Cross correlation of intensity dynamics, $\kappa {(\tau ,{T}_{2})}_{{T}_{1}}=\left(\right)open="\langle "\; close="\rangle ">I(t,{T}_{1})I(t+\tau ,{T}_{2})$. Here ${T}_{1}$ is chosen to be the 500th round trip of Figure 7(

**a**); (

**c**) Close up of cross correlation matrix $\kappa {(\tau ,{T}_{2})}_{{T}_{1}}$. The peak progressively shifting with ${T}_{2}$ indicates the possible existence of coherent features moving with a distinct velocity; and (

**d**) the spatio-temporal dynamics of the background corresponding to its rest frame, revealing the existence of dark solitons.

**Figure 8.**Pulse-background interactions—Spatio-temporal dynamics showing the interaction of the background dark solitons and the pulse. (

**a**) Faster moving dark solitons meet the slow moving pulse; (

**b**) Trapped dark solitons at the pulse-background interface.

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**MDPI and ACS Style**

Sugavanam, S.; Tarasov, N.; Churkin, D.V.
Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics. *Appl. Sci.* **2016**, *6*, 65.
https://doi.org/10.3390/app6030065

**AMA Style**

Sugavanam S, Tarasov N, Churkin DV.
Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics. *Applied Sciences*. 2016; 6(3):65.
https://doi.org/10.3390/app6030065

**Chicago/Turabian Style**

Sugavanam, Srikanth, Nikita Tarasov, and Dmitry V. Churkin.
2016. "Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics" *Applied Sciences* 6, no. 3: 65.
https://doi.org/10.3390/app6030065