Directional Local Density of States of Classical and Quantum Propagating Surface Plasmons

We theoretically and experimentally introduce the concept of the local density of states (LDOS) associated with propagative surface plasmons (PSPs) launched along a structured thin gold film (a concept we call PSP LDOS). The alternative method couples a near-field optical microscope, in either the classical or the quantum regime of excitation, to a far-field leakage-radiation microscope. This method allows for selecting and collecting a very narrow portion of the directional SP wave vectors, thereby offering sufficient resolution to probe the collimation efficiency of a SP beam for a source near the focal point of a Bragg parabolic reflector. We are able to build and image the PSP LDOS in a fully integrated quantum SP launcher by depositing a diamond nanocrystal hosting nitrogen-vacancy centers at the focal point of the mirror. Our demonstration of the PSP LDOS with quantized SPs offers alternative prospects in the field of quantum plasmonics.

Figure 1

Principle of the experiment. (a) Either a classical-aperture NSOM tip (not shown here) or an active NV-based NSOM tip excites SPs on a 50-nm-thick gold film evaporated on a glass substrate. Leakage radiation of the emitted SPs in the Fourier plane in a given direction (1) or (2) is collected with a high-numerical-aperture (NA) microscope objective. (b) Image of the direct plane of the structured gold film in transmission under global illumination. Five confocal parabolic slits, each of 150 nm width, are milled by a FIB. Most SPs emitted by a dipole located at the focus point (the green double arrow) are reflected in the same direction by the parabolas’ induced dipoles (the yellow double arrow), giving a collimated SP beam.

Figure 2

LRM images [recorded, respectively, in the (a) Fourier and (b) direct planes] with a classical NSOM tip facing the gold film at the focus of the parabolas. The inset in (a) is an enlargement of the simulation for the Fourier-plane zone collected by fiber 1. The inset in (b) is a LRM image obtained with the same NSOM tip along the plain metal film (500 nm is the scale bar for the inset). In (a) NA stands for numerical aperture. In (b), a double white arrow indicates the dipole orientation. The closest parabola to the focus point $F$ is represented by a white dashed curve.

Figure 3

(a),(b) Experimental partial PSP LDOS of the parabolic structures with an aperture NSOM tip in the classical regime for the collections in regions 1 and 2 of Fig. 2, respectively. The white arrow on the top-right corner indicates the collection direction. (Insets) Simulated partial PSP LDOS, scale bar 200 nm. The closest parabola to the focus point is represented by the white dashed curve. (c),(d) Experimental partial PSP LDOS obtained in the direct plane after $\mathbf{k}$ filtering with a collection fiber of 200 and $50\mu \mathrm{m}$ diameter, respectively. The bottom insets in (c) and (d) show a $\mathbf{k}$-filtered direct-plane image, with the corresponding collection area, taking into account the X100 magnification of the optical setup. White circle in inset (c), $2\mu \mathrm{m}$ diameter; black circle in inset (d), 500 nm diameter. The top inset in (c) is a simulation of the total PSP LDOS.

Figure 4

(a) Unfiltered direct plane NSOM and (b),(c) partial PSP-LDOS images of discretized slits forming a parabolic Bragg mirror that includes a nanometric defect near the focus point. The right arrow in the top-right corner in (b),(c) indicates the collection direction. [Inset in (b)] Enlargement of the focus point, scale bar 500 nm. (d) Simulation of PSP-LDOS images (c) with the nanohole only.

Figure 5

Deposition of the ND at the focus point of confocal parabolas. (a) NSOM image with the tip retracted (500 nm), with a ND hosting 17 NV centers. The parabolas are the same as they were previously, but with an additional $4\text{−}\mu \mathrm{m}$-long slit milled through the focus point. (Inset) The ND is deposited on the slit. Scale bar, $2\mu \mathrm{m}$. (b) Fourier-plane image when the deposited ND is excited. (c) Experimental quantum partial SP LDOS of the parabolas without an additional slit with the NV-based tip. (d) Scan on the structure with the deposited ND while collecting the Fourier plane in the area marked by the white circle in (b). (e) $g^{(2)}(\tau )$ functions of the ND (top chart) above glass and (bottom chart) after a dropoff in gold.