Super-resolved optical lithography with phase controlled source

Recently, we have demonstrated that second-order subwavelength interference could be realized in an optical lithography scheme with an effective entangled source [P. Hong and G. Zhang, Phys. Rev. A 88, 043838 (2013)]. In this paper, by considering the correlation function in both the source plane and observation plane, we show how the coherence property of such a source is controlled via introduction of random-phase correlation, which finally affects the two-photon interference effect observed in the far-field plane. Furthermore, by introducing different but similar random-phase correlations, we generalize the phase controlled source with particular high-order coherence properties to obtain higher-order subwavelength interference, i.e., high-order super-resolved optical lithography. These results show the importance of phase control in generating a light field with particular high-order coherence properties.

Figure 1

A typical far-field diffraction scheme of an object, i.e., projection scheme of optical lithography. Here correlation measurement is employed in the far-field plane to measure the high-order coherence diffraction pattern.

Figure 2

Single- and two-photon interference of pure phase objects in different conditions. (a) Cubic phase structure of a pure phase object with aperture function $A\left(x_0\right)=rect(x_0/R)e^{-i\pi {(2x_0/R)}^3}$. (b) and (c) First-order coherence of the pure phase objects with aperture function $A\left(x_0\right)$ and $A^2\left(x_0\right)$ illuminated by coherent light, respectively. (d) and (e) Two-photon interference of pure phase object with an effective aperture function $A^2\left(x_0\right)$ based on the phase controlled source under opposite and synchronous scanning modes, respectively. (f) Synchronous position two-photon interference of pure phase object with an effective aperture function $A\left(x_0\right)$ based on the phase controlled source.