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The propagation properties of a pair of Lissajous singularities with opposite singularity indexes called the Lissajous singularity dipole (LSD) in free space are studied analytically and illustrated numerically. It is shown that the motion, creation, annihilation and change in the degree of polarization of the LSD, and change in the shape of Lissajous figures take place by suitably varying the waist width, off-axis distance or propagation distance. In particular, the creation and shift to infinity of a single Lissajous singularity may appear. A comparison with the free-space propagation of an optical vortex dipole and a C-dipole is also made.

The interaction of the Lissajous singularity and singular Lissajous line in the presence of an astigmatic lens is studied. It is found that the singular Lissajous line is usually unstable, and disappears after passage through the lens. The creation and annihilation of one or two Lissajous singularities may take place by varying the astigmatic coefficient, off-axis parameter, and propagation distance. A comparison with the interaction of the Lissajous singularity and singular Lissajous line in the free-space propagation and in the presence of an ideal lens, and with the vortex–edge dislocation interaction is made. The results are illustrated numerically and interpreted analytically.

A steady thermal model of photonic-bandgap fiber laser (PBFL) is presented. Temperature distribution in PBFL is analyzed by heat transfer equations and numerical finite-element method (FEM) separately. Thermal stress distribution caused by the temperature difference between the inner and outer claddings is calculated. The results show that the thermal stresses in this fiber structure are low less than the critical tensile stress in fused silica.

The temperature distribution and the thermal stress distribution of Bragg fiber laser are analyzed by solving thermal transfer equations. The changes of refractive index derived from the temperature and the thermal stress are discussed separately. Results indicate that the change of index refraction caused by temperature is larger than by thermal stress.

The propagation of Riemann-Silberstein (RS) vortices for Gaussian vortex beams with topological charges m=+1 through a lens is studied. It is shown that if there is an ideal lens, a RS vortex and a circular edge dislocation appear for Gaussian on-axis vortex beams, while only RS vortices take place for Gaussian off-axis vortex beams. In the presence of an astigmatic lens, there exist RS vortices but no edge dislocations for both Gaussian on-axis and off-axis beams. By varying the astigmatic coefficient, the off-axis parameter, and the propagation distance, the motion, creation, and annihilation of vortices may take place, and in the process, the total topological charge of RS vortices remains unchanged.