Subdiffraction Light Focusing on a Grating Substrate

We describe a way to generate subdiffraction light spots that can be moved over a surface without resorting to near-field manipulation, nonlinear effects, or negative index materials. We use a periodically patterned substrate that converted efficiently, through scattering, the impinging propagative waves into evanescent ones. Then we optimize the wave front of the incident propagative beam so that the grating-scattered evanescent waves interfere constructively at the focal point. Numerical simulations show that focus spots as small as one-sixth of a wavelength can be obtained at any point on the substrate. One foreseen application is high resolution surface imaging.

Figure 1

(a) Geometry of the grating substrate. Side view (top) and top view (bottom): A slab of ${\mathrm{Ta}}_2{\mathrm{O}}_5$ ($n_b=2.1$) is pierced by an hexagonal array of holes of period $d=0.26\lambda$ filled with silicon ($n_a=3.72+i0.012$), sandwiched between two layers of silicon and deposited on a glass prism ($n_s=1.5$). Radius of the holes: $r=0.13\lambda$; layer thicknesses: $d_1=0.09\lambda$, $d_2=0.07\lambda$, and $d_3=0.18\lambda$, $\lambda =700\mathrm{nm}$. (b) Principle of the phase conjugation focusing method (see text).

Figure 2

Light focusing on a homogeneous prism covered by a silicon layer. (a) Geometry. (b) Intensity map obtained at $z=0\mathrm{nm}$ when the substrate is illuminated with 24 $p$-polarized plane waves, with polar angle equal to ${\theta }_0=64°$ and azimuthal angles $\varphi =q\pi /12$, where $q=1,\dots ,24$.

Figure 3

Light focusing on the grating substrate depicted in Fig. 1 using an incident beam specified with the phase conjugation method described in Fig. 2. (a) Intensity at $z=0$. (b) Intensity at $z=\lambda /2$.

Figure 4

(a) As in Fig. 3a except that the focus spot is located at an equidistance between two holes. (b) As in (a) except that the complex amplitudes of the 24 incident plane waves are perturbed by a random Gaussian noise on both the real and the imaginary parts.