Figure 1

(a) Schematic of the system under study. A cylindrical silicon tip with a diameter of 125 nm is placed at height $z_{\mathrm{tip}}$ and lateral position ${\mathbf{r}}_{\parallel }$ above a photonic crystal slab. Reduction of diameters for 3 pores (shaded red) and shift of two of them yields a cavity resonance at $\lambda =1500\mathrm{nm}$ with a $Q$ factor of 13 000. (b) Intensity distribution $|{\mathbf{E}}_0{|}^2$ of the unperturbed mode in a plane 30 nm above the slab. The black circles outline the air pores (red circles for tuned pores), whereas the white dots mark the original pore locations in the hexagonal lattice. (c) Calculated resonance frequency shift induced by the tip placed 30 nm above the slab, as a function of its lateral position. (d) The inverse $Q$ corresponding to (c). The unperturbed cavity has $1/Q=7.5\times {10}^{-5}$. (e) Contribution of the $z$ component $|E_{z,0}{|}^2$ to the unperturbed field intensity, integrated over the extent of the tip above the slab. Field intensities in (b) and (e) are normalized to the maximum total field intensity $|{\mathbf{E}}_0{|}^2$.Reuse & Permissions

Figure 2

Relative frequency shift (solid symbols, left hand axis) and inverse $Q$ (open symbols, right hand axis) as a function of the distance $z_{\mathrm{tip}}$ between the surface of the photonic crystal and a Si tip of 125 nm diameter aligned with the central defect. The gray area indicates the extent of the membrane. For $z_{\mathrm{tip}}<0$ the tip extends into the defect. The dashed line indicates $z_{\mathrm{tip}}=30\mathrm{nm}$ corresponding to the data in Fig. 1. The black curve (scaled) shows the unperturbed mode profile $|{\mathbf{E}}_0{|}^2$. The horizontal line indicates $1/Q$ in absence of the tip.Reuse & Permissions

Figure 3

Relative frequency shift (solid symbols, left hand axis) and inverse $Q$ (open symbols, right hand axis) as a function of the effective polarizability per length ${\alpha }_{\mathrm{eff}}/d=3({ϵ}_{\mathrm{p}}-1)/({ϵ}_{\mathrm{p}}+2)\pi r_{\mathrm{p}}^2$, for cylindrical tips positioned 30 nm above the central defect in Fig. 1. Symbol shapes indicate various tip materials (Si, ${\mathrm{TiO}}_2$, ${\mathrm{ZrO}}_2$, polystyrene, and ${\mathrm{SiO}}_2$ in order of decreasing ${ϵ}_{\mathrm{p}}$ as indicated). The frequency shift is proportional to ${\alpha }_{\mathrm{eff}}$ (solid curve). The loss $1/Q$ can be fitted (dashed curve) with the sum of the loss without the tip (horizontal dashed line) and a contribution proportional to ${\alpha }_{\mathrm{eff}}^2$.Reuse & Permissions