Four-wave Interference Research Articles

Wave propagation in metamaterials mimicking the topology of a cosmic string

We study the interference and diffraction of light when it propagates through a metamaterial medium mimicking the spacetime of a cosmic string—a topological defect with curvature singularity. The phenomenon may look like a gravitational analogue of the Aharonov–Bohm effect, since the light propagates in a region where the Riemann tensor vanishes, being nonetheless affected by the non-zero curvature confined to the string core. We carry out the full-wave numerical simulation of the metamaterial medium and give the analytical interpretation of the results by use of the asymptotic theory of diffraction, which turns out to be in excellent agreement. In particular, we show that the main features of wave propagation in a medium with conical singularity can be explained by four-wave interference involving two geometrical optics and two diffracted waves.

Four-wave interference and perfect blaze

The recently calculated high diffraction efficiencies for TE- and TM-polarized light (perfect blaze) for echelette gratings are explained by four-wave interference, which is formed as a double periodical pattern in the cross section of the grating plane. The blazed grating profile should match this interference pattern for a single reference light wavelength. The recently published data are the special case of a general design. The prognoses of the model are connected with large grating constants in comparison with the light wavelength, where short grating constants need comparison with numerical methods.

Dislocation lines in the swallowtail diffraction catastrophe

The three-dimensional distribution of amplitude and phase represented by the swallowtail catastrophe diffraction integral is based on a network of null lines for amplitude (wave dislocations or optical vortices), where the phase is singular. In the tail region there is four-wave interference, which results in an approximately repeating pattern of amplitude based on the monoclinic space group C 2/ m and also an approximately repeating pattern of wave dislocations based on the black–white monoclinic space group C 2/ m ′. Helical dislocations spring from the plane of symmetry and gradually straighten out to be parallel to the two riblines of the caustic; eventually they become the straight dislocations of the Pearcey pattern for the cusp catastrophe. In the front region, where there are zero or two points of stationary phase, each dark Airy fringe surface associated with the fold surface condenses into a single dislocation in the plane of symmetry.

Formation of two-dimensional periodic nanostructures on fused quartz, polyimide, and polycrystalline diamond by pulsed four-wave interference laser modification

Atomic force microscopy is used to examine the topography of submicron periodic structures formed on the surfaces of synthetic polycrystalline diamond and polyimide films. The films are deposited on fused quartz substrates by four-wave interference modification using a pulsed 308-nm UV XeCl excimer laser. It is demonstrated that a two-dimensional periodic relief with a submicron period can be formed on the diamond surface directly by laser evaporation in the absence of a photoresist. Depending on the exposure, two mechanisms of polyimide film modification are observed. At exposures less than 100 mJ/cm2, the relief is formed due to swelling at the positions of interference maxima. At exposures greater than 100 mJ/cm2, holes are formed in the films. A periodic relief on the fused quartz surface is formed by using a UV photoresist exposed to pulsed interference laser radiation and subsequent Ar ion etching.