Modulational Instability in a Layered Kerr Medium: Theory and Experiment

We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of alternating glass-air layers, is the piecewise-constant nature of the material properties, which allows a theoretical linear stability analysis leading to a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between theoretical, numerical, and experimental diagnostics of the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, there are multiple instability regions rather than just one as in a uniform medium.

Figure 1

Experimental setup. BS1 and BS2 are beam splitters, DL is a variable delay line, M1 and M2 are mirrors, NLM is the layered nonlinear medium, and L1 and L2 are lenses.

Figure 2

Comparison of experimental (top), numerical (middle), and analytical (bottom) results for the 1 mm glass—2.1 mm air configuration as a function of the dimensionless wave number $k$. For the diagnostics $R$ and $|G|$ (defined in the text), values larger than 1 correspond to MI.

Figure 3

Experimental normalized 1D intensity patterns (top) and Fourier spectra (middle) and numerical Fourier spectra (bottom) at the end of propagation ($z=16.5\mathrm{mm}$) of the layered structure with six 1 mm glass slides, each pair of which sandwiches 2.1 mm of air. We depict the wave numbers $k=0.0042$ (first instability band; left panels) and $k=0.017$ (second band; right panels). The dashed (solid) curves are for high (low) intensity $I_{\mathrm{P}1}$ ($I_{\mathrm{P}2}$).

Figure 4

Same as Fig. 2 but for the 1 mm glass—3.1 mm air configuration. Here there is a third MI band.