Long Wave–Short Wave Resonance in Nonlinear Negative Refractive Index Media

We show that long wave–short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.

Figure 1

Depiction of LWSW resonance on a dispersion diagram $\omega$ vs $k$ based on Eq. (3) with $\Omega <{\omega }_0<{\omega }_b<{\omega }_a$. The parallel lines show the matching of the group and phase velocities on the negative and lower branches, respectively.

Figure 2

Contour plot of the normalized phase mismatch ($c_0\Delta k$) with ${\omega }_s$ and ${\omega }_3$ normalized to ${\omega }_a$. The lower curve with $\Delta k=0$ is the curve satisfying Eq. (4). The characteristic frequencies are $\Omega =0.3{\omega }_a$, ${\omega }_0=0.4{\omega }_a$, and ${\omega }_b=0.9{\omega }_a$.