In this paper, Two Dimensional (2D) Photonic Crystal (PhC) based 3-input all optical NOR, NAND and XNOR gates is proposed and designed. The proposed device is formed by the combination of line defects and square cavity. The performance of the device is analyzed using 2D Finite Difference Time Domain (FDTD) method. The band gap analysis is done by Plane Wave Expansion (PWE) method. The device has the lattice constant and refractive index of 616 nm and 3.46, respectively. The dimension of the proposed structure is about 12.5 µm*12 µm which is highly compact and suitable for photonic integrated circuits (PIC).

Stokes phase is the phase difference between orthogonal component states in the decomposition of any polarization state. Phase singularities in the Stokes phase distribution are Stokes singularities of an inhomogeneous polarization distribution. Under circular decomposition, Stokes phase distribution $$(\phi _{12})$$ ( ϕ 12 ) represents polarization azimuth $$(\gamma )$$ ( γ ) distribution and the singularities present in it are polarization singularities. Therefore, the charge of the Stokes vortices depicted as Stokes index $$\sigma _{12}$$ σ 12 is an important parameter associated with the polarization singularity. The Hybrid order Poincaré sphere (HyOPS)/Higher order Poincaré sphere (HOPS) beams, all having same Stokes index, contain a Stokes singularity at the center of the beam as these beams are constructed by vortex superposition. These beams, being superposition of orthogonal orbital angular momentum (OAM) states in orthogonal spin angular momentum (SAM) states can offer great multiplexing capabilities in communication. In this article, we identify these degenerate Stokes index states and discuss the ways and means of lifting this degeneracy. Otherwise, there are limitations on intensity based detection techniques, where demultiplexing or segregation of different HOPS/HyOPS beams is warranted. The method adduced here uses the diffraction of these beams through an equilateral triangular aperture in combination with polarization transformation as a probe to lift the Stokes index/Stokes phase degeneracy. Successively, the novelty of the detection scheme is discussed in the context of beams with alike polarization distributions where even the technique of Stokes polarimetry fails to predict the OAM and SAM content of the beam.

In this article we show that diffraction segregates the polarization singularities according to their handedness. Polarization singularities are superpositions of left and right handed circular polarization vortex states. In the superposition, the component states possess different orbital angular momenta depending on the type of the singularity. A fork grating that can generate different orbital angular momentum (OAM) states in different diffraction orders is shown to segregate right and left handed polarization singularities. A V-point polarization singularity that corresponds to one combination of OAM states incident on the fork grating is found to diffract in such a way that the same OAM combination does not occur in all the nonzero diffraction orders. As a result, each of the diffraction orders will have different polarization singularities. This OAM transfer by the fork grating segregates the right and left handed polarization singularities thereby, making the diffraction helicity dependent.

In this paper, we report the morphological transformations of vector-field singularities (V-points) under symmetric and asymmetric perturbation using a diamond-shaped diffracting aperture. The number of null intensity points in the diffraction pattern depicts the magnitude of the polarization singularity index. Also, under symmetric perturbation, a higher-order V-point singularity disintegrates into | η | number of unit-index singularities following the index conservation rule. Asymmetric perturbations, realized by laterally shifting the aperture, lead to the formation of pairs of generic elliptic-field singularities (C-points) that are more fundamental and stable. In this process, the helicity and polarization singularity index are both conserved. This may find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams [Phys. Rev. Lett. 109, 183903 (2012)PRLTAO0031-900710.1103/PhysRevLett.105.053904].

The superposition of spin and orbital angular momentum states of light generates polarization singularities. By perturbing and disintegrating their component orbital angular momentum (OAM) states, the polarization singularity indices can be determined. The spatially varying polarization distribution of these beams possesses information about the helical wavefront structures of the component OAM states, although they have plane wavefronts. The polarization singular beam (PSB) is focused using a tilted lens, and the intensity distribution at a predicted position in the direction of propagation is used to determine the component OAM content in the beam. Astigmatism introduced by the tilt of the lens modulates the vortex beam to introduce intensity nulls in the propagated beam. We demonstrate by simulations and experiments the index determination of the V points and C points using a tilted lens. This method is effective in the index determination of V points and C points formed by the superposition of component scalar vortices having opposite-sign topological charges. The degeneracy of C points with the same Stokes indices can be lifted through this technique.