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A theoretical analysis based on mirror symmetry is proposed to analyze and predict the symmetry in intensity, phase and polarization distributions of the tightly focused vector optical field (VOF). We extend the analysis to more cases including more complicated polarization states and weak focusing cases. We further show the symmetric tightly focused fields of the eccentric cylindrical VOF and the redesigned VOF with a radially variant polarization state, which are achieved by redesigning the polarization state of the incident VOF based on the symmetry analysis. We also take the laser fabrication as an example to further show how to apply this symmetry analysis in a specific application area. Such a theoretical analysis can improve the calculation efficiency, provide new insights into the tight focusing process and offer a convenient way to engineer the field distributions in the focal plane, which may have potential applications in areas needing flexibly controllable tightly focused fields, such as laser fabrication, optical trapping, and optical storage.

We introduce the concept of multifractal into vector optical fields (VOFs). We propose, design and generate new fractal VOFs–multifractal VOFs (MF-VOFs), in which multifractal structure and VOF act as the lattice and the base, respectively. We generate two kinds of MF-VOFs experimentally and explore their focusing behaviors. We also investigate the self-healing and information recovering abilities of MF-VOFs, comparing with those of single-fractal VOFs (SF-VOFs) when their lattices are composed of the same hierarchy of fractal geometries. The results show that MF-VOFs have better self-healing and information recovering abilities than that of traditional SF-VOFs, meaning that MF-VOFs have better ability to resist the information loss during the focusing and imaging processes. These properties may find potential applications in information transmission, optical communication, and so on.

Polarization singularities have topological properties, because they can maintain their features invariably during propagation. The topological property can be destroyed by shifting the polarization singularities away from the central axis, and this destruction originates from the space separation of spin angular momentum components. We find that paired centrosymmetric off-axis polarization singularities can recover the topological property in the Fourier plane (reciprocal space), which belongs to the pseudo-topological property. We reveal that the pseudo-topological property is related to the invisible redistribution of both spin and orbital angular momentum states. We experimentally generate a series of Julia fractal vector optical fields with the pseudo-topological property. They may have potential applications in optical encryption and quantum information.

Curved filament with large bent angle and controllable propagation behavior has always been great expectation and challenge due to its novelty and complexity. The unique properties of curved filaments make it possible to achieve many applications in micro-fabrication, spectroscopy and meteorology. Here we realize experimentally and theoretically control on helical filaments induced by twisted beams in CS

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

Curved filament with large bent angle and controllable propagation behavior has always been great expectation and challenge due to its novelty and complexity. The unique properties of curved filaments make it possible to achieve many applications in micro-fabrication, spectroscopy and meteorology. Here we realize experimentally and theoretically control on helical filaments induced by twisted beams in CS2. The results show that helical filaments exhibit a robust pattern and high rotation rate. Specific intensity pattern of the twisted beam confines the filaments in fixed relative position and the azimuthal energy flux drives the rotating of the filamentation pattern. In addition, we demonstrated that the global orbital angular momentum (OAM) of twisted beams is still conservative to be zero, but local OAMs exhibit distinct variation during nonlinear propagation. Our idea has its significance which realizes the construction of helical filaments with flexibility and controllability and then facilitates to push the development of related researches.

We present an inverse method to engineer uniform-intensity focal fields with arbitrary shape. Amplitude, phase, and polarization states, as adjustable parameters, are used to seek the desired focal fields in the non-iterative computational procedure. Our method can be applied to the cases with low and moderate numerical aperture (NA), in which case the feasibility and validity of our approach have been demonstrated in theory, simulation and experiment, respectively. For the case of higher NA, simulated results based on the Richards-Wolf diffraction integral are shown. We also made some discussions on the experiments with the higher NA. Our method should have wide applications in optical micro machining, optical trapping and so on.

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

We present a generalized Poincar\'e sphere (G sphere) and generalized Stokes parameters (G parameters), as a geometric representation, which unifies the descriptors of a variety of vector fields. Unlike the standard Poincar\'e sphere, the radial dimension in the G sphere is not used to describe the partially polarized field. The G sphere is constructed by extending the basic Jones vector basis to the general vector basis with the continuously changeable ellipticity (spin angular momentum, SAM) and the higher dimensional orbital angular momentum (OAM). The north and south poles of different spherical shell in the G sphere represent the pair of different orthogonal vector basis with different ellipticity (SAM) and the opposite OAM. The higher-order Poincar\'e spheres are just the two special spherical shells of the G sphere. We present a quite flexible scheme, which can generate all the vector fields described in the G sphere. The salient properties of this representation are able to treat the complicated geometric phase of arbitrary vector fields in the future.

We numerically and experimentally explored generation and regulation of subwavelength multiple focal spots produced by tight focusing patterned vector optical fields (PVOFs). We presented a modified Richard-Wolf diffraction integration method suitable for the tight focusing of the PVOFs. By tailoring the spatial geometry and the polarization distributions of the PVOFs, simulations show that the diverse spatial configurations of subwavelength multiple focal spots can be achieved. To verify our idea, we experimentally generated the theoretically calculated examples of femtosecond PVOFs, then tightly focused them on the surface of the crystalline silicon wafers, and finally characterized the morphologies of modified surfaces. The SEM (scanning electronic microscopy) images confirmed that the experimental results are in good agreement with the simulations. Based on the diverse controlling degrees of freedom of PVOFs, the resultant subwavelength focal fields are flexible and powerful in parallel processing, optical manipulation and so on.

We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

We present, design and generate a new kind of vector optical fields with linear polarization distributions modeling to electric and magnetic field lines. The geometric configurations of "electric charges" and "magnetic charges" can engineer the spatial structure and symmetry of polarizations of vector optical field, providing additional degrees of freedom assisting in controlling the field symmetry at the focus and allowing engineering of the field distribution at the focus to the specific applications.

We have fabricated the complicated two-dimensional subwave-length microstructures induced by the femtosecond vector light fields on silicon. The fabricated microstructures have the interval between two ripples in microstructures to be around 670-690 nm and the depth of the grooves to be about 300 nm when the pulse fluence of 0.26 J/cm2 is slightly higher than the ablated threshold of 0.2 J/cm2 for silicon under the irradiation of 100 pulses. The ripples are always perpendicular to the direction of the locally linear polarization. The designable spatial structure of polarization of the femtosecond vector light field can be used to manipulate the fabricated microstructure.

A theoretical model is established to study the self-similar pulses in nonlinear polarization evolution (NPE) mode-locked fiber lasers. The propagation of pulse in single mode fibers and gain fibers are described by coupled Ginzburg- Landau equation (GLE). Two wave plates and a polarizer are considered to realize the NPE mechanism in simulation. This model describes the laser completely and provides some useful pulses' information. In our simulation the laser generates high quality self-similar pulses output. The region of steady self-similar pulses operation is found. The polarization states of different parts across the pulse are simulated along the laser cavity. It is found that polarization states across the pulse are modulated from elliptical to almost circular before the pulse passing through the polarizer.

The authors have presented in this paper the fabrication and characterization of double line written type waveguides in c-cut periodically poled potassium titanyl phosphate crystals. The waveguides were fabricated by using a femtosecond laser, and were utilized for second harmonic generation at 1064 nm. Our experiments have shown that single mode propagation was observed at optimal waveguide width of 14.5 microm. And a conversion efficiency of 39.6% can be achieved.