Detection and characterization of attenuated multimode waveguiding in ${\mathrm{SiO}}_2$ slabs using photoemission electron microscopy

Multimode waveguiding in the visible and near-ultraviolet spectral regime is observed and characterized in thermally grown ${\mathrm{SiO}}_2$ layers on silicon using photoemission electron microscopy (PEEM). Comparison with finite-element-method simulations allows identifying order and character of the attenuated modes. Real-time investigations on mode propagation support these findings and give additional evidence for the existence of radiative modes. Finally, the presented experimental results illustrate how a defined deposition of gold nanoparticles can substantially enhance the sensitivity of the PEEM technique to electromagnetic field modes supported by thin dielectric and insulating layers.

Figure 1

(a) Schematic of the sample geometry; relevant dimensions are indicated. (b) SEM image of a sample showing the intersection of four segments; individual gold nanoparticles appear as bright spots. (c) TPEEM image of four segments recorded at illumination with the Hg discharge lamp ($h\nu =4.9\mathrm{eV}$). (d) TPEEM image of four segments recorded at illumination with the fourth harmonic laser light ($h\nu =5.9\mathrm{eV}$, laser incident from the left); dashed lines indicate the borders of the individual segments, which were determined by comparison with TPEEM data recorded with the Hg discharge lamp. Note the different scale bars in (b) and (c) and (d), respectively.

Figure 2

(a) PE intensity profile across segment A in Fig. 1; (b) FFT spectra of the PE intensity profiles across the different segments labeled A–D in Fig. 1; the black symbols are FEM results for effective indices of the slab waveguide modes. “Diff” denotes the diffracted, quasicylindrical mode, whereas “TMX” indicates the transverse magnetic waveguide mode of order X.

Figure 3

(a) 2PPEEM image of the sample illuminated with 400-nm laser light; the sample is illuminated with the laser light incident from the left. (b) FFT spectra of 2PPE intensity profiles across the four segments in Fig. 2 for different excitation wavelengths; black and colored triangles mark effective mode indices obtained from the FEM simulations. $n_{\mathrm{eff}}=1$ (black triangles) indicates the incident laser mode which is diffracted at the coupling edge (quasicylindrical mode). Red, green, blue, and purple triangles mark the position of the TM8, TM7, TM6, and TM5 waveguide modes supported by the ${\mathrm{SiO}}_2$ slab, respectively.

Figure 4

(a) Mode dispersion diagram compiled from the results of the FEM calculations; the solid black and gray lines represent the light line in vacuum and ${\mathrm{SiO}}_2$, respectively. Colored dashed lines represent TM waveguide modes. (b) Calculated magnetic field amplitude of the TM7 mode for excitation with 400-nm light and a slab thickness of 1.5 $\mu m$.

Figure 5

(a) ITR-2PPEEM intensity profiles of segment D at different time delays recorded within one optical cycle of the excitation laser; the time delays correspond to incremental phase delays of $\approx \pi /2$; blue arrows mark the position of interference maxima, starting positions of the maxima are marked with gray lines; (b) delay-distance diagram of segment D generated from the ITR-2PPEEM scan; the red arrow marks the slope of the interference maxima associated with the phase propagation of the TM7 mode. Green arrows mark beating nodes arising from the superposition of the TM7 mode and propagating lower-order modes.

Figure 6

(a) ITR-2PPEEM intensity profiles of segment A at time delays within one optical cycle of the excitation laser pulse; blue and red arrows mark the position of interference maxima, gray lines additionally mark the interference maxima in the first panel. (b) Delay-distance diagram of segment A generated from the ITR-2PPEEM scan; the inset shows a closeup of the region marked by the white box. The red line in the inset marks the negative slope $\frac{d\tau }{dx}$ of the interference maxima associated with a radiative mode of the ${\mathrm{SiO}}_2$ slab. Blue lines mark for comparison the positive slope $\frac{d\tau }{dx}$ of interference maxima associated with the dominating nonradiative mode.

Figure 7

(a) 2PPEEM image of a sample which was not covered with gold nanoparticles (NP); the image was recorded with 400-nm laser light. (b) FFT power spectral density of the 2PPE intensity profile of segments A and B in (a) in comparison to corresponding data from a nanoparticle covered surface and the results of the FEM simulations.