Experimental phase-space-based optical amplification of scar modes

Wave billiards which are chaotic in the geometrical limit are known to support nongeneric spatially localized modes called scar modes. The interaction of the scar modes with gain has been recently investigated in optics in microcavity lasers and vertical-cavity surface-emitting lasers. Exploiting the localization properties of scar modes in their wave-analogous phase-space representation, we report experimental results of scar mode selection by gain in a doped D-shaped optical fiber.

Figure 1

Experimental setup for the amplification of scar modes in the double clad ytterbium-doped fiber amplifier. L${}_1$, lens (15-mm working distance); L${}_2$, lens (10-mm working distance); L${}_3$, lens (2.5-cm focal length $f$); DM, dichroic mirror ($T=90$$\%$ @ 1064 nm, $R=90$$\%$ @ 978 nm); P${}_1$, P${}_2$, 3D positioning supports; F${}_1$, bandpass filter (3 nm @ 1064 nm); BC, beam collimator; BE, beam expander; M, mirror. Right inset, transverse cross section of the D-shaped fiber amplifier with the off-center doped area (circle) and the 2-PO along the $x$ axis. The polymer cladding is not represented.

Figure 2

Far-field intensity observations [panels (a) and (c)] and their transverse horizontal cut at ${\kappa }_y=0$ [panels (b) and (d)] for the unpumped and pumped configurations, respectively, for ${\kappa }_p=7$. Far-field-intensity pattern and transverse horizontal cut superimposed for the pumped configuration with ${\kappa }_p=6$ (e). Horizontal cut of the far-field intensity of a calculated scar mode (f).

Figure 3

Field intensity of specific modes and their respective Husimi representations. For a generic speckle mode, panels (a) and (b); for a scar mode along the 2-PO, panels (c) and (d); and for the mode with ${\kappa }_{\mathit{NS}}$, panels (e) and (f).

Figure 4

Intensity spectrum at the input of the fiber amplifier (dashed line) and after amplification at the output of the fiber (gray line) associated with a Gaussian signal launched into the fiber with ${\kappa }_{\mathit{NS}}$.