Resolving phase information of the optical local density of state with scattering near-field probes

We theoretically discuss the link between the phase measured using a scattering optical scanning near-field microscopy (s-SNOM) and the local density of optical states (LDOS). A remarkable result is that the LDOS information is directly included in the phase of the probe. Therefore by monitoring the spatial variation of the trans-scattering phase, we locally measure the phase modulation associated with the probe and the optical paths. We demonstrate numerically that a technique involving two-phase imaging of a sample with two different sized tips should allow to obtain the image the pLDOS. For this imaging method, numerical comparison with extinction probe measurement shows crucial qualitative and quantitative improvement.

Figure 1

Trans-scattering-type scanning near-field optical microscopy (TS-SNOM). The wave front illustrates the local field being scattered over the tip and propagating to the detector.

Figure 2

Vacuum PPS ${\varphi }_{{\alpha }_{\mathrm{vac}},{\mathbf{e}}_x}$ in the dipolar approximation with radiative correction (DARC), and with Mie calculation, as a function of the probe's radius.

Figure 3

Normalized partial LDOS ${\widehat{\rho }}_{{\mathbf{e}}_x}(\mathbf{r},\omega )$, phase of the dipolar moment ${\varphi }_{p,{\mathbf{e}}_x}$, phase of the local field ${\varphi }_{E_{\mathrm{loc}}}$, and normalized PPS ${\widehat{\varphi }}_{\alpha ,{\mathbf{e}}_x}$ at a variable distance of a 10-nm silver film, with a dielectric probe of 1 nm radius, at $\lambda =400$ nm.

Figure 4

Illustration of the LDOS phase sensitive (LDOS-SP) technique. It is based on the imaging of the trans-scattering phase map with two different tip sizes that is done sequentially and by normalization of the numerical subtraction, we obtain the map of the pLDOS.

Figure 5

PDM for two tip radius, $R=25$ and $1\mathrm{nm}$. In insert, normalized pLDOS, and normalized difference of the PDM between the two tip of radius $R=25$ and 1 nm.

Figure 6

Normalized extinction, normalized pLDOS, and the normalized local intensity for a 1 nm probe radius at a variable distance of a 10-nm silver film, at $\lambda =400$ nm.