Nonlinearity Management in Optics: Experiment, Theory, and Simulation

We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show that wave collapse can be prevented. We corroborate these experimental results with numerical simulations of the ($2+1$)-dimensional focusing cubic nonlinear Schrödinger equation with piecewise constant coefficients and a theoretical analysis of this setting using a moment method.

Figure 1

Experimental setup. $\mathrm{ND}=\mathrm{\text{neutral density filters}}$, $\mathrm{NLM}=\mathrm{\text{nonlinear medium}}$, and $\mathrm{L}1–\mathrm{L}3=\mathrm{\text{lenses}}$.

Figure 2

Dynamics for power $P=5.9P_c$. (Top) Beam FWHM (in $\mu \mathrm{m}$) as a function of propagation distance (in mm) for air, the layered medium, and glass. The respective experimental results are denoted by ⋄, ○, and × (the solid curves are visual guides). The FWHM computed from Eq. (1) is shown by the thin dash-dotted curve, and simulations incorporating time propagation are shown by the thick dashed curve. (Bottom right) Spatial dependence of the field in Eq. (1). (Bottom left) The (normalized) experimentally measured beam energy for glass and the layered medium as a function of the number of glass slides.

Figure 3

Comparison of NM for different powers. The top left panel shows the experimental results for $P=2.3P_c$ (pluses), $P=3.9P_c$ (stars), $P=4.9P_c$ (triangles), and $P=5.9P_c$ (circles). We plot the FWHM as a function of the propagation distance $z$. The individual cases of $2.3P_c$ (top right), $3.9P_c$ (bottom left), and $4.9P_c$ (bottom right) are compared with the PDE diagnostic (see text), shown by the dash-dotted curves, and the ODE results (thick dashed curves).

Figure 4

NM for different layered media. (Top) Numerical results for $P=5.9P_c$ with 1 mm glass-1 mm air slide layers (thinnest dash-dotted curve), with 1 mm glass-1.5 mm air layers (intermediate thickness dash-dotted curve), and with 1 mm glass-2 mm air layers (thickest dash-dotted curve). (Bottom) Corresponding solid curves with increasing thicknesses and symbol sizes representing the experimental results for the respective cases.