Quantum-interferometric optical lithography: Towards arbitrary two-dimensional patterns

Optical lithography is a widely used printing method. In this process, light is used to etch a substrate. The exposed or unexposed areas on the substrate then define the pattern. In particular, the microchip industry uses lithography to produce smaller and smaller processors. However, classical optical lithography can only achieve a resolution comparable to the wave length of the light used @1–3#. It therefore minimizes the scale of the patterns. To create smaller patterns we need to venture beyond this classical boundary @4#. In Ref. @5# we introduced a procedure called quantum lithography that offers an increase in resolution beyond the diffraction limit. This process allows us to write closely spaced lines in one dimension. However, for practical purposes ~e.g., optical surface etching! we need to create more complicated patterns in both one and two dimensions. Here, we study how quantum lithography can be extended to create these patterns. This paper is organized as follows: first, for completeness, we present a derivation of the Rayleigh diffraction limit. Then, in Sec. II we reiterate the method introduced in Ref. @5#. Then, in Sec. III we give a generalized version of the states used in this procedure. We show how we can tailor arbitrary one-dimensional patterns with these states. In Sec. IV we show how four-mode entangled states lead to patterns in two dimensions. Sec. V addresses the physical implementation of quantum lithography.