Final Report Summary - HARMOFIRE (Harmonic Mode-locked Fibre Lasers) The project HARMOFIRE is focused on training activities with a significant effort of fibre lasers development. The key objectives of the project included research-based training in design, fabrication and applications of fibre lasers, development of novel theoretical approaches allowing modelling and stabilization of harmonic mode-locked fibre lasers, fast polarization monitoring and cost-effective stabilisation in fibre lasers. Stabilized mode-locked fibre lasers are important sources for a range of applications such as optical communications, frequency metrology, medical imaging, micro machining and femtochemistry. Mode-locked fibre lasers are cost-efficient, easy to fabricate, have all-fibre design and high output powers. The HARMOFIRE project aims in design, development and optimisation of cost-efficient stable ultra-fast harmonic mode-locked fibre lasers for a range of practical applications that will have a broad positive impact on the European Research Area. HARMOFIRE is focused on theoretical modelling and experimental study of harmonic mode-locked fibre lasers, design and optimization of fibre lasers, polarization control and stabilization of mode-locked fibre lasers with carbon nanotubes saturable absorber. A set of hands-on training activities was performed on design and fabrication of fibre lasers based on carbon nanotubes, fibre splicing, laser dynamics characterization, polarimetry, dispersion measurement, carbon nanotubes and fibre Bragg grating fabrication. Advanced modelling and optimisation of mode-locked fibre lasers was performed using both scalar and vector models. The parameters were chosen close to the experimental system under consideration. The work package was conducted in collaboration with researches from Novosibirsk State University, Moscow Physical Technical Institute and Weierstrass Institute. HARMOFIRE offers novel approaches of monitoring, control and stabilisation of polarization dynamics in fibre lasers. A fast polarimeter with a bandwidth of 500 MHz was developed in collaboration with OFS Labs and Aston University researchers. The novel harmonic mode-locked fibre lasers with carbon nanotubes saturable absorber and highly erbium-doped gain fibre were designed and fabricated. The polarization insensitivity of carbon nanotubes-based saturable absorber extended the possibilities of studying polarization attractors in mode-locked fibre lasers. Polarization dynamics of harmonic mode-locked operation in an erbium-doped fibre laser was performed experimentally. Up to 11th harmonic mode-locking with over 50 dB sidebands suppression ratio was demonstrated in a ring cavity laser with carbon nanotubes saturable absorber. Vector solitons with various polarization dynamics, such as polarization-locked vector solitons, solitons with precessing, switching and chaotic polarization were studied in the harmonic mode-locked fibre lasers for a range of pump power levels. Polarization-locked vector solitons could be obtained for different harmonics and fundamental mode-locking. The novel regime with polarization switching between two orthogonal states of polarization was demonstrated for the grouped solitons. Vector solitons with various polarization attractors were shown at the 11th harmonic, which have a potential application in fibre optic communications, in the context of using multiple polarizations, and in secure communications.The tilted fibre Bragg gratings were implemented into the ring laser cavity to stabilize repetition rate and improve noise performance of the leasers when operating at high harmonics. With the tilted fibre Bragg gratings stable harmonic operation was demonstrated at 19th harmonic with sub-Hz RF linewidth, over 50 dB sidebands suppression ratio (SSR), and pulse repetition rate of 460 MHz. The temporal stability of the mode-locking regime was tested showing stable pulse operation over 16 hours. Stabilized MLFLs will enable increased performance and reduced complexity of optical networks. These results can have potential applications for increased capacity in coherent communications using various polarization-based modulation schemes, such as polarization division multiplexing, polarization switching, and modified coded hybrid subcarrier-amplitude-phase-polarization multiplexing. High flexibility in generation of dynamic polarization states can be also of interest in secure communications, atoms and nanoparticles trapping, and control of magnetization.