Lasing at the band edges of plasmonic lattices

We report room-temperature lasing in two-dimensional diffractive lattices of silver and gold plasmon particle arrays embedded in a dye-doped polymer that acts both as waveguide and gain medium. As compared to conventional dielectric distributed feedback (DFB) lasers, a central question is how the underlying band structure from which lasing emerges is modified by both the much stronger scattering and the disadvantageous loss of metal. We use spectrally resolved back-focal plane imaging to measure the wavelength and angle dependence of emission below and above threshold, thereby mapping the band structure. We find that, for silver particles, the band structure is strongly modified compared to dielectric reference DFB lasers since the strong scattering gives large stop gaps. In contrast, gold particles scatter weakly and absorb strongly, so that thresholds are higher, but the band structure is not strongly modified. The experimental findings are supported by finite element and Fourier modal method calculations of the single-particle scattering strength and lattice extinction.

Figure 1

(a) Schematic of the setup. We illuminate the sample with laser light ($\lambda =532$ nm) from the glass side. We measure the fluorescence using the CCD and spectrometer. Right after the laser there are two lenses (1 and 2) that constitute a telescope to increase the beam diameter. After reflection off a mirror, there is an epilens (3) followed by a filter cube (4) that contains the dichroic mirror and a long pass filter, allowing only fluorescent red light on the detector side. On the right side of the filter cube there is a flippable Fourier lens ($f=200$ mm) (5) followed by a tube lens ($f=200$ mm) (6). The objective is mounted in a specially designed microscope mount (7). Not shown in the image are the AOM, together with a polarizer just in front of the telescope, to tune the laser power. In (b), we show a schematic of the objective with the sample. In (c), a scanning electron micrograph of one of the fabricated particle arrays is shown.

Figure 2

(a) Plot of emission spectra for different pump powers measured by imaging a Ag particle array (pitch 380 nm, particle diameter 100 nm) onto the spectrometer slit measured upon excitation with a single pump pulse. A clear threshold behavior can be seen from the sharp peak occurring for pump powers above 59 nJ. Panel (b) threshold curve, plotting the area under the lasing peak versus pump pulse energy. The inset shows two spectra just above and just below threshold.

Figure 3

Fourier images below the lasing threshold for a pitch of (a) 360, (b) 370, (c) 380, and (d) 400 nm. The color map ranges are [223, 1196], resp., [102, 739], [128, 941], and [319, 1948]. The reported wave vector axes are normalized to $\omega /c$.

Figure 4

Fourier images just above the lasing threshold for a pitch of (a) 360, (b) 370, (c) 380, and (d) 400 nm. The color map ranges are the same as in Fig. 3. Note the appearance of the narrow feature in the center of all images, which shows the onset of lasing emission. The reported wave vector axes are normalized to $\omega /c$.

Figure 5

Fourier spectra for four different pitches, just below threshold (a)–(d) and just above threshold (e)–(h), and a schematic of a general band diagram (i). Measurements are for a pitch of 360 nm [(a) and (e)], 370 nm [(b) and (f)], 380 nm [(c) and (g)], and 400 nm [(d) and (h)]. The maximum values of the color bar are set at 230, 200, 200, and 250 counts, respectively, in (a)–(d). Above threshold, the maximum values of the color bar are 230, 250, 200, and 300 counts, respectively [panels (e)–(h)]. All color bars start at 0. Note the lasing emission that appears as a narrow feature at $k_{\parallel }=0$ (the horizontal lines across the diagram, surrounding the lasing peak, are CCD blooming artifacts). For clarity, we have indicated the lower and upper stop band edges for second-order diffraction by white arrows in panel (f). Lasing occurs at the lower edge.

Figure 6

In (a) the relative size of the stop gap is plotted for Ag (blue dots), Au (red triangles), and ${\mathrm{TiO}}_2$ (green squares) together with literature values of van Beijnum [39] (black), Turnbull [49] (purple), and Noda [58] (red). In addition, fluorescence in the $\omega$, $k_y$ plane is plotted for Au (b), Ag (c), and ${\mathrm{TiO}}_2$ (d) for a pitch of 370 nm. The maximum values of the color bar are 550, resp., 250 and 300 counts in panels (b)–(e), with color bars starting at 0. The plots are made just above the lasing threshold, meaning pump powers differ from panel to panel. The pump powers are 944 nJ (Au), 99.5 nJ (Ag), and 38 nJ (${\mathrm{TiO}}_2$), respectively. The notably larger pump power for Au results in a much higher background fluorescence level as is visible for a frequency range centered at the the Rh6G emission peak in (b).

Figure 7

Extinction cross sections for Ag, Au, and ${\mathrm{TiO}}_2$ as a function of $\omega$ obtained using comsol. The $z$ axis is defined as the axis parallel to the symmetry axis of the particle disks. In plot (a) the plane wave is incident along the $z$ axis and in plot (b) the plane wave is incident from the side of the particle, with polarization in the plane of the particle. For clarity, the curves for ${\mathrm{TiO}}_2$ are scaled by a factor 10 as indicated.

Figure 8

Extinction as a function of ${\mathrm{k}}_{\parallel }$ and $\omega$ for gold (a) and silver (b). Evident for both diagrams are (1) the high-extinction region for lower $\omega$, corresponding to the single-particle resonance, and (2) the generic folded band diagram features (lines and parabolas). For silver, a clear stop gap is visible at the $\Gamma$ point (${\mathbf{k}}_{\parallel }=0$) that is not apparent in the diagram for gold. The inset shows a zoom-in of this region, highlighting the intricate anticrossing with the two parabolic bands.