Shape and polarization distribution of non-circular conical diffraction beams from conjugate cascades.

Peculiar non-circularly shaped vector type beams can be obtained naturally by the conical diffraction phenomenon if specific manipulations in wavevector space are performed between optically biaxial crystals arranged in a cascade. We analyze in detail this situation by focusing on the general shapes and the polarization distribution. Both are shown to be correlated to the values of structure parameters introduced in this work. These control parameters depend on the conical diffraction cone aperture angle, on the crystal lengths, and on the magnification values due to x- and y-oriented cylindrical lenses placed between the crystals and coupling common conjugate planes. The local polarization is found to be always linear with the exception of regions where structures composing the pattern intersect or overlap, where elliptical or circular polarization can occur. The way in which the obtained patterns depend on the orientation of individual crystal samples around the common optical axis and on an eventual polarization filtering at various stages of the cascade is discussed as well. Theoretical and experimental findings agree well, as verified for the case of a cascade of two crystals.

Non-circularly shaped conical diffraction.

Waves with tailored shape and vectorial non-homogeneous polarization are of much interest due to the many prospects for relevant applications in the classical and quantum domains. Such vector beams can be generated naturally via conical diffraction in optically biaxial crystals. The recent strongly revived attention to this phenomenon is motivated by modern applications such as optical trapping, polarimetry or super-resolution imaging, partly enabled by new configurations increasing the beam complexity, like those with several crystals in cascade. However, up to now all beams generated by conical diffraction conserve at their sharpest plane the underlying circular shape connected with the planar section of light cones. Here we show that a proper manipulation in wave-vector space within a conical diffraction cascade produces vector beams with highly peculiar non-circular forms, leading to an interesting and reconfigurable platform for easily shaping all structured wave properties, increasing complexity and information content. The experimental observations are confirmed by numerical integration of a paraxial model incorporating the effects of the wave-vector space manipulation.