Harmonic generation in multiresonant plasma films

We investigate second- and third-harmonic generation in a slab of material that displays plasma resonances at the pump and its harmonic frequencies. Near-zero refractive indices and local field enhancement can deplete the pump for kW/cm${}^2$ incident powers, without resorting to other resonant photonic mechanisms. We show that low-threshold, highly efficient nonlinear processes are possible in the presence of losses and phase mismatch in structures that are 10${}^4$ times shorter than typical nonlinear crystals, for relatively low irradiance values.

Figure 1

(a) Field intensity map as a function of normalized slab thickness and incident angle; the enhancement approaches 8000 as $d\to 0$ (not shown); (inset) sketch of the system under investigation: a TM-polarized pump with electric field ${\mathbf{E}}_{\omega }$ and wave vector ${\mathbf{k}}_{\omega }$ impinges on a slab of thickness $d$ at an angle ${\vartheta }_i$. (b) Total normalized conversion efficiency vs slab thickness; we assume ${\chi }_{}^{\left(2\right)}=1\mathrm{pm}/\mathrm{V}$ and ${\vartheta }_i=1.8^{\circ }$.

Figure 2

(a) Normalized SH conversion efficiency ($I_{2\omega }/I_{\omega }^2$) on a logarithmic color scale for a bulk medium 2 μm long calculated using Eq. (6), assuming normal incidence and ${\chi }_{}^{\left(2\right)}=1\mathrm{pm}/\mathrm{V}$; blue, square markers indicate the phase-matching condition; black, circle markers indicate wave-vector mismatch conditions. (b) Total (forward plus backward) normalized SH conversion efficiency ($I_{2\omega }/I_{\omega }^2$) on a logarithmic color scale for a slab $d=2\mu \mathrm{m}$ thick, calculated by means of full-wave simulations (CW analysis) assuming ${\chi }_{}^{\left(2\right)}=1\mathrm{pm}/\mathrm{V}$ and ${\vartheta }_i=1.8^{\circ }$; purple, square markers indicate the phase-matching condition; white, cross markers indicate wave-vector mismatch conditions; red and green dashed lines indicate Fabry-Pérot resonances for ${\lambda }_{\omega }$ and ${\lambda }_{2\omega }$, respectively.

Figure 3

(a) SH conversion efficiency vs input irradiance for a 1-μm-thick film and incident angle ${\vartheta }_i=1.8^{\circ }$ for lossless CW (blue, solid curve), lossy CW (red, solid curve), $\tau =2$ ps (red, dotted curve), and τ = 6 ps (red, dashed curve) pulses for lossy film. (b) Same as (a) for THG.