Fig. 1. The working principle of far-field super-resolution imaging based on nonlinearly excited evanescent waves. (a) Schematic of the far-field super-resolution imaging process with localized evanescent-wave illumination excited by the FWM process at the interface. The zoomed inset shows that the FWM process takes place on nonlinear medium’s interface. (b) Mechanism illustrated in Fourier space. NA and $k_{\mathrm{3,0}}$ represent numerical aperture and the free-space wavenumber of the FWM signal beam, respectively. $\mathrm{NA}\times k_{\mathrm{3,0}}$ determines the cutoff frequency of the imaging system; correspondingly, the blue-circled area represents the system’s passband. Striped-shadow regions represent evanescent fields, which carry sub-wavelength details of the imaging target. In the current experiment, we introduce evanescent wave vector ${\mathbf{k}}_{3,\mathrm{eva}}$ along $k_x$ as illumination light, which can map evanescent fields into propagating ones and extend the accessible region of the target’s spectrum on dimension $k_x$.

Fig. 2. Demonstration of wave vector control in surface FWM and local excitation of evanescent waves. (a) Illustration of the FWM process takes place at the interface and the partial-phase-matching condition. (b), (c) Fourier space images of reflected pump/probe beams ${\lambda }_1$, ${\lambda }_2$, and signal beam ${\lambda }_3$ taken by EMCCD, characterizing incident angles, and output angle, respectively. (d) Dependence of FWM output angle ${\theta }_3$ on probe incident angle ${\theta }_2$ under different pump angles ${\theta }_1$. (e) Numerical simulation result of FWM signal field distribution, which is the case of an evanescent wave with a large transverse wave vector ${\mathbf{k}}_{3,\mathrm{eva}}$ localized at the top film of SOI. The inset shows the signal’s amplitude variation along with the interface, where the scale bar represents the wavelength of FWM.

Fig. 3. Demonstration of super-resolution imaging using FWM evanescent-wave illumination. Fourier space representation of (a) the probe beam at 780 nm with normal illumination, (b) FWM signal at 403 nm with ${\mathbf{k}}_{3,\mathrm{eva}}$ illumination, and (c) the complete imaging method (d)–(f). Simulated images of a pair of 90-nm-wide slits spaced 50 nm apart, corresponding to cases of (a)–(c). (g)–(i) Experimental results. Scale bar: 500 nm. (j) Scanning electron microscopy image of the two-slit target. (k) Inverse-intensity cross-section comparison of probe beam normal illumination image and proposed super-resolution method.

Fig. 4. Super-resolved nano-slit grating and evanescent wave excitation on the grating. (a) and (b) Simulated images of a slit array with 110-nm slit width and 400-nm period by probe beam illumination and our super-resolution method, respectively. (c) and (d) Experimental results. Scale bar: $1\mu \mathrm{m}$. (e) Cross-section comparison of the two cases, showing a great improvement in resolution by our method. (f) Experimental demonstration of the modified partial-phase-matching condition mixed with grating modes when ${\theta }_2=41\mathrm{deg}$, solid lines are the theoretical prediction calculated from Eq. (4), and insets show typical $k$-space images used to estimate the signal’s output angles. (g) Partial-phase-matching condition mixed with grating modes $-G$, making the FWM signal become propagating waves. (h) Partial-phase-matching condition mixed with $G$, resulting in a further increment of $k_{3,\mathrm{eva}}$.