Interference pattern formation from an array of coherent laser beams

Abstract

We present numerical analysis of interferometric patterns formed by multiple sources. Multiple beams can be achieved either from a synchronized laser array or by splitting a coherent light source. We assume Gaussian form for each beam, and all the beams are combined at the near field. The condition for achieving periodic structures with the feature size significantly smaller than λ/4 is obtained. Multiple beam interference has the potential of achieving smaller feature size, less power requirement, and more flexibility than the conventional two-beam interferometric lithography method.

The Rahman-Nat diffraction on a thin laser-induced grating of the refractive index in semiconductors

“…Up o recent years, to form laser-induced surface structures in solids, interference of two or more laser beams has been used [4][5][6][7][8][9][10]. In practice, a system of the interference beams can be formed by both one source with a light divider and a proper system of mirrors or slits and by a bunch (a grating) of the identical lasers [13].…”

“…Let us consider a condensed matter (semiconductor), an outer surface of which is irradiated by two coherent light beams (CLBs) with an equal frequency that satisfies the inequality, g       (  is the carrier average energy and ε g is the bandgap of this semiconductor). These CLBs, as known [2][3][4][5][6][7][8][9][10], form an interference pattern on a condensed matter surface an interference pattern (Fig. 1).…”

“…The special interest is caused by the laser-induced spatially periodic surface structures. As a rule, they are created at interference of a few laser beams on solid surface [2][3][4][5][6][7][8][9][10]. This technology has already found practical application, in particular, during melting metals [6], and making printing plates [11].…”

Space-invariant multiple-beam achromatic EUV interference lithography

“…Alternatively three or more mutually coherent beams can be used simultaneously for the same purpose [4,6]. However, if four or more beams are used then special attention must be paid to satisfy proper phase relationships between the beams [6][7][8]. This can be readily controlled in diffraction grating based IL by controlling the relative phases of the gratings on the mask [7].…”

“…Three, four, six and eightbeam interference patterns were proposed and recorded in photoresist films with this technique [7,8]. However, even with proper control of the phases of the beams, the interference pattern depends on the distance from the mask (z-direction) if the beams do not all originate from gratings with the same period.…”