Superlens in the Time Domain

It has been predicted theoretically and demonstrated experimentally that a planar slab supporting surface plasmons or surface phonon polaritons can behave as a super lens. However, the resolution is limited by the losses of the slab. In this Letter, we point out that the resolution limit imposed by losses can be overcome by using time-dependent illumination.

Figure 1

Dispersion relation of a surface phonon polariton at the SiC-air interface displaying the real part of $\omega$ versus the real part of $K$. Green (dashed) curve: the wave vector is chosen to be complex, there is an upper bound for $K$. Blue (solid) curve: the circular frequency is chosen to be complex, there is no upper bound for $K$.

Figure 2

Scheme of the planar lens with thickness $h$. The image is located at $z=z_0+2h$.

Figure 3

Transmission factor as a function of the wave vector for three different frequencies. An ideal superlens is characterized by a transmission factor $\tilde{t}(K,\omega )=1$ at the optimum frequency. In the presence of losses, we obtain the best behavior at $\omega =Re({\omega }_{\mathrm{sw}})$.

Figure 4

Incident field $H(-t)\exp (-i{\omega }_{\mathrm{sw}}^{\prime }t)$ used to excite the system mode with complex frequency.

Figure 5

Normalized profile of the intensity at the image location. A 60% reduction of the width of the pulse is observed at $t=16\mathrm{ps}$. The amplitudes have been normalized in order to compare the widths.

Figure 6

Spatial frequency filter $\Pi (K,t)$ at different times. It is seen that the bandwidth increases. This filter depends on the choice of the incident field.