The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems

<table>Bifurcation diagram of the total cavity energy of the reconstructed field <svg height="7.9499998" id="M236" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.2749996 7.9499998" width="9.2749996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D462"></use></g>
</svg> as a function of <svg height="12.175" id="M237" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 16.125 12.175" width="16.125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D454"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.738,11.762)"><use xlink:href="#x30"></use></g>
</svg>. Here the bottom branch (blue) represents the single-pulse solution, and the top branch (red) represents the double-pulse solution. The middle branch (green) denotes the extrema of the energy of the periodic solution.</table>

International Journal of Optics

fig9

Figure 9

Figure 9: The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems 