Menyuk first derived the nonlinear pulse propagation equation in a single-mode optical fiber (SMF) under weak birefringence.
His equation concerns the nonlinear interaction (cross-phase modulation and coherent energy exchange) between the two orthogonal polarization components of the vector soliton.
Researchers have obtained both analytical and numerical solutions of this equation under weak, moderate and even strong birefringence.
[6] The following pictures show that, when the fiber birefringence is taken into consideration, a single nonlinear Schrödinger equation (NLSE) fails to describe the soliton dynamics but instead two coupled NLSEs are required.
Numeric simulations also confirmed that the formation of the new type of spectral sidebands was caused by the FWM between the two polarization components.
[12] Vector dark bright solitons have been reported in incoherently coupled spatial DBVSs in a self-defocusing medium and matter-wave DBVS in two-species condensates with repulsive scattering interactions,[13][14][15] but never verified in the field of optical fiber.
Using a birefringent cavity fiber laser, an induced vector soliton may be formed due to the cross-coupling between the two orthogonal polarization components.
It is unknown whether or not a phase-locked gain-guided vector soliton could be formed in a fiber laser: either the polarization-rotating or the phase-locked dissipative vector soliton can be formed in a fiber laser with large net normal cavity group velocity dispersion.
[17] Recently, multiwavelength dissipative soliton in an all normal dispersion fiber laser passively mode-locked with a SESAM has been generated.
It is found that depending on the cavity birefringence, stable single-, dual- and triple-wavelength dissipative soliton can be formed in the laser.
But for vector solitons, the polarization state can be rotating arbitrarily but still locked to the cavity round-trip time or an integer multiple thereof.
For example, SESAMs require complex and costly clean-room-based fabrication systems such as Metal-Organic Chemical Vapor Deposition (MOCVD) or Molecular Beam Epitaxy (MBE), and an additional substrate removal process is needed in some cases; high-energy heavy-ion implantation is required to introduce defect sites in order to reduce the device recovery time (typically a few nanoseconds) to the picosecond regime required for short-pulse laser mode-locking applications; since the SESAM is a reflective device, its use is restricted to only certain types of linear cavity topologies.
Furthermore, the presence of bundled and entangled SWNTs, catalyst particles, and the formation of bubbles cause high nonsaturable losses in the cavity, despite the fact that the polymer host can circumvent some of these problems to some extent and afford ease of device integration.
In addition, under large energy ultrashort pulses multi-photon effect induced oxidation occurs, which degrades the long term stability of the absorber.
It is potentially possible to use graphene or graphene-polymer composite to make a wideband saturable absorber for laser mode locking.
Indeed, with an erbium-doped fiber laser we self-started mode locking and stable soliton pulse emission with high energy have been achieved.
[25] Furthermore, atomic layer graphene possesses wavelength-insensitive ultrafast saturable absorption, which can be exploited as a "full-band" mode locker.