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• In this work, we investigate the in- and out-of-plane shifts of the PSHE based on a full-wave theory, revealing that they have the same physical mechanism. • The in- and out-of-plane displacements of the PSHE are determined by momentum-dependent Pancharatnam-Berry (PB) phase, where the in-plane wavevector k x -dependent phase gradient determines the in-plane shift, and the transverse wavevector k y -dependent phase gradient dictates the out-of-plane shift. • We discover that the intrinsic OAM (IOAM) and extrinsic OAM (EOAM) carried by incident off-axis vortex beams can respectively convert into the EOAM and IOAM of abnormal modes in the transmitted beam. • The OAM generated during the spin-reversal process, together with the OAM carried by the incident beam, collectively determines the in- and out-of-plane displacements. • When off-axis vortex beams are incident, the competition between the IOAM and EOAM is more complex than in those without OAM. Our study unifies in- and out-of-plane shifts into a single theoretical framework, which offers an alternative perspective on the spin–orbit interaction of light. The photonic spin-Hall effect (PSHE) is a result of the interaction of spin and orbital angular momentum (OAM). However, previous research on the PSHE has primarily focused on out-of-plane (transverse) shifts. In fact, it encompasses both out-of-plane shifts and relatively weaker in-plane shifts, and the latter of which plays a crucial role in controlling the direction of spin separation. Here, we investigate the in- and out-of-plane shifts of the PSHE based on a full-wave theory, revealing that they have the same physical mechanism. The in- and out-of-plane displacements of the PSHE are determined by a momentum-dependent Pancharatnam-Berry (PB) phase, where the in-plane wavevector k x -dependent phase gradient determines the in-plane shift, and the transverse wavevector k y -dependent phase gradient dictates the out-of-plane shift. We discover that the intrinsic OAM (IOAM) and extrinsic OAM (EOAM) carried by incident off-axis vortex beams can respectively convert into the EOAM and IOAM of abnormal modes in the transmitted beam. The OAM generated during the spin-reversal process, together with the OAM carried by the incident beam, collectively determines the in- and out-of-plane displacements. When off-axis vortex beams are incident, the competition between the IOAM and EOAM is more complex than in those without OAM. Our study unifies in- and out-of-plane shifts into a single theoretical framework, which offers an alternative perspective on the spin–orbit interaction of light. [ABSTRACT FROM AUTHOR]

• The existence regions and dynamics of both QSSP and DPQS have been revealed. • The QSSP can carry more energy than that of DPQS pulse. • The stability of DPQS is limited by excessive pulse pedestal. Recently, both quartic self-similar pulses (QSSPs) and dissipative pure-quartic-solitons (DPQSs) pulses have been theoretically demonstrated in mode-locked fiber laser with pure positive fourth-order dispersion (FOD). Here, we investigate the existence regions and dynamics of those two soliton pulses by numerically solving the cubic-quintic Ginzburg-Landau equation. We find the positive FOD fiber laser tends to emit QSSPs in the presence of high nonlinear gain, while it is apt to generate DPQS pulses in the case of low nonlinear gain. An unstable pulse region separates the QSSP region from the DPQS region. The characteristics of QSSP and DPQS pulses are dependent on the nonlinear gain and FOD. The QSSP can carry more energy than that of DPQS pulse, because the DPQS pulse with large energy could be unstable due to the excessive pulse pedestal. Our results are not only useful for understanding the dynamics of the DPQS pulse and QSSP in the cubic-quintic Ginzburg-Landau equation with pure FOD, but also provide a guideline for generating high-energy pulses from the positive FOD fiber laser. [ABSTRACT FROM AUTHOR]