Figure 1

(a),(b) Atomic force microscopy $5\times 5\mu {\mathrm{m}}^2$ images of the 1PG and 2PG with periods of $760/\sqrt{2}\mathrm{nm}$ and $750/\sqrt{2}\mathrm{nm}$, respectively. Both gratings have been fabricated as $P$ periodic profiles with a modulation amplitude of 25 nm on indium-titanium-oxide (ITO)–coated glass substrates using focused ion beam lithography and covered with a 50 nm thick evaporated Au film. (c),(d) Corresponding IFS recorded in the Fourier plane of a LRM by illuminating the 1PG and 2PG with a laser diode at a wavelength of ${\lambda }_{\mathrm{L}}=785\mathrm{nm}$ (scale bar is $5\mu {\mathrm{m}}^{-1}$) [30]. The leakage radiation is collected using a Nikon objective ($60\times$, numerical aperture $\mathrm{NA}=1.49$). Theoretical band structures have been superposed on the first quadrants, for the air-Au (continuous line) and the Au-ITO (dotted line) interfaces. The modulation depths have been fitted to $\gamma =(0.055,0.020)$ for the 1PG and 2PG, respectively.Reuse & Permissions

Figure 2

(a) Sketch of the whole device, including SG and 1PG. The steering angle ${\theta }_S$ between the group velocity ${\mathbf{v}}_g$ of the excited Bloch wave and the incident wave vector ${\mathbf{k}}_{\mathrm{SP},\mathrm{in}}$ is represented inside the grating. The periodicity of SG is chosen as 760 nm, its dimensions as $100\times 10.6\mu {\mathrm{m}}^2$. The 1PG has a periodicity of $760/\sqrt{2}\mathrm{nm}$ and dimensions of $150\times 32\mu {\mathrm{m}}^2$. (b) Steering angles ${\theta }_S$ measured in the real (filled squares) and the Fourier (empty circles) spaces as a function of the in-plane component $k_x$ of ${\mathbf{k}}_{\mathrm{SP},\mathrm{in}}$. The continuous lines correspond to the steering angles evaluated from theory. Regions of negative refraction are shaded. With a chosen period of the 1PG slightly smaller than $P_{\mathrm{Bragg}}$, the band gap is located slightly off the $k_x=0$ value. (c)–(e) Real space images at $k_x=-0.53$, $+0.05$, $+0.19\mu {\mathrm{m}}^{-1}$. Scale bars correspond to $50\mu \mathrm{m}$.Reuse & Permissions

Figure 3

(a) Theoretical IFS—zoomed-in detail of Fig. 1c, white box—where the steering effect is sketched. The incident SP beam lies on the $k_{\mathrm{SP}}$ dashed circle. At the interface, this beam couples to a Bloch wave of the 1PG defined by conservation of the in-plane component $k_x$ of ${\mathbf{k}}_{\mathrm{SP},\mathrm{in}}$. The Bloch wave lies therefore at the intersection between the IFS and the $k_x$ value. The group velocity ${\mathbf{v}}_g$ of the corresponding Bloch wave is evaluated at this point, and is directed normal to the IFS (red arrow vector). (b) Experimental band-gap region of the IFS of the 1PG, imaged in the Fourier plane of the LRM, by illuminating the SG with a slightly focused ${\lambda }_{\mathrm{L}}=785\mathrm{nm}$ laser beam (removing the filtering slit). The theoretical bands are superposed as red lines. (c) SPR (dashed line) and 1PG (continuous curve) sensor sensitivities evaluated as a function of $n_d$, accounting for the dispersion of Au. The inset illustrates the strongly nonlinear modification of $k_y$ through refractive index changes, when probing the response of the 1PG sensor close to the band gap at $k_x=0$.Reuse & Permissions

Figure 4

(a) Same as Fig. 3b for the 2PG with a period of $750/\sqrt{2}\mathrm{nm}$, smaller than $P_{\mathrm{Bragg}}$. Theoretical IFS are superposed as red curves, with fitted modulation depth $\gamma =0.020$. (b) Same as Fig. 2b for the 2PG.Reuse & Permissions