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We present theoretically and generate experimentally a vector optical field with parabolic symmetry of linear polarization. We extend the study to the modified parabolic-symmetry vector fields. We explore their tightly focusing behaviors, in particular, a modified parabolic-symmetry vector field can be tightly focused into a high-performance subwavelength sharp line. [ABSTRACT FROM AUTHOR]

We propose a convenient approach for managing orbital angular momentum (OAM) of second-harmonic photons generated by a quadratic nonlinear interaction under noncolinear type-I phase matching condition. Since the OAMs of two fundamental photons can be flexibly controlled by using computer-generated holograms, we were able to realize arbitrary combination of both OAMs and experimentally confirm the OAM conservation selection rule l2?, = l'? + l"? in general cases. In particular, our approach could be used to generate the secondharmonic photon states with fractional and odd-order OAMs. [ABSTRACT FROM AUTHOR]

We propose an approach for the optical encryption of ghost images reconstructed from the spatially correlated classical two-beam pairs. This approach has the capability of encrypting ghost images by flexibly manipulating the position correlation of a pair of "signal" and "idler" beams. We experimentally demonstrate that the perfect ghost image can be extracted by decrypting the encrypted information of an object, in particular, our approach under eavesdropping has a higher security for encryption compared with previous approaches. [ABSTRACT FROM AUTHOR]

The Heisenberg uncertainty principle suggests that it is impossible to determine the trajectory of a quantum particle in the same way as a classical particle. However, we may still yield insight into novel behavior of photons based on the average photon trajectories (APTs). Here we explore the APTs of optical fields carrying spin angular momentum (SAM) and orbital angular momentum (OAM) under the paraxial condition. We define the helicity and differential helicity for unveiling the three-dimensional spiral structures of the APTs of optical fields carrying the SAM and/or the OAM. We clarify the novel behaviors of the APTs caused by the SAM and OAM as well as the SAM-OAM coupling. The APT concept is also very helpful for profoundly understanding trapped particle motion and has the potential to elucidate other physical systems. Due to the presence of the helical path caused by the SAM and/or the OAM, the actual traveling distance of the photons might be much longer than the geometric distance. [ABSTRACT FROM AUTHOR]

We theoretically and experimentally explore the redistribution of polarization states and orbital angular momentum (OAM) in the output plane, induced by the symmetry breaking in the spatial frequency domain. When the vector fields are obstructed by sector-shaped filters in the spatial frequency domain, the local polarization states in the output plane undergo an abrupt transition from linear to circular polarization. The results reveal the polarization-dependent splitting and the appearance of a series of opposite OAMs in the output plane. We also find the self-healing effect of the vector fields broken in the spatial frequency domain and further explore its potential application. If the vector optical fields are used for information transferring or for imaging, even if the optical field carrying the information or image is partially blocked, the complete information or image can still be obtained, implying that which may increase the robustness of the information transferring and the imaging. [ABSTRACT FROM AUTHOR]