The Modal Decomposition Method For The Optical Fibers Based On The Phase Space Optics Theorem

Over the past two decades,the fiber lasers have been widely applied in diversity areas such as industry and defense,etc due to the output powers of which have shown a exponential increase rate.This unprecedented increase in the output power of fiber lasers also make the nonlinear effect become more remarkable,which has become one of the main obstacles preventing the output power further rise.Employing the large-mode-area(LMA)fiber is the most effective way to mitigate the nonlinear effect.When the LMA fiber is operated at high average power level,it could induce the complex mode competition,mode coupling,and even the mode instability(MI)which will dramatically degrade the beam quality.The modal decomposition(MD)technique is demonstrated to decompose the total field propagating in an optical fiber into sum of individual transverse modes,which helps to suppress the higher-order mode(HOM)and has become an indispensable diagnostic tools for the development of high power fiber lasers.In order to overcome the limitations of existing MD techniques,in this dissertation,we proposed several novel MD method based on the phase space optics(PSO)theorem.The PSO possesses several unique properties that are very suited to be employed in MD.The MD approaches proposed in this dissertation can be classified into methods which only can be applied for fully-coherent modal field and those which can be applied for the modal field with arbitrary degree of coherence.The former includes the scale-invariant and rotation-invariant optical correlation method and the MD method using the fractional Fourier transform(Fr FT)system.The latter is based on the Wigner distribution function(WDF)which is one of the representative phase space representations of optical field provided by the PSO.We also proposed two four-dimensional(4D)WDF measurement methods due to the reason that there are no effective ways to reconstruct it.The details of above-mentioned works is as follows:We extend the existing correlation filter method by incorporating the optical Mellin transform(MT)into the conventional matched filter.This extended ability allows the decomposition of modal fields without any restriction regarding their scale parameter.The input modal fields are transformed into Mellin space by the optical MT.And the matched filter is also formed from the basis modes of the Mellin transformed version.Since the MT is scale invariant,the matched filter will perform the scale-invariant filtering in Mellin space and the correlation answer will be independent to the input scale.The validity and reliability of the proposed technique are demonstrated through numerical simulation.The results show that even the scale difference between the input beams and the basis modes is up to a factor of 2,this approach can still give the promising results.The existing phase retrieval algorithm based on the Fr FT power spectra is extended to account for the effect of optical vortex.This extended capability can then be employed to reconstruct the phase of modal field to high fidelity in a non-iterative and noninterferometric manner.Combining the reconstructed phase with the measured near-field intensity,the modal field could be obtained and based upon which the complete MD(involving modal weights and phases)is performed.The validity and reliability of the method are demonstrated through several numerical examples including the noisy signals with different signal-to-noise ratio levels.A novel MD scheme employing the WDF is introduced,which allows the decomposition of modal fields without any restrictions regarding their degree of coherence.A novel measurement method for the 4D WDF using the non-redundant array(NRA)is also proposed.The code of the NRA is generated by Singer sets.Based on the reconstructed WDF,the modal coefficients as well as the mutual modal degree of coherence will be determined unambiguously.The validity and reliability of the proposed approach are illustrated with several reperesentative numerical examples.The results show that this new ability can process the modal contents of partially coherent fiber beams properly.A novel reconstruction approach for the 4D WDF based on the 2D parity sorter is also proposed.The validity and reliability of the proposed approach are also illustrated with several representative numerical examples.The results show that this new ability can process the modal contents of partially coherent fiber laser beams properly too.Compared to the reconstruction method using the coded aperture technique,although the experimental realization of the current method is a little bit more complex,it is more suitable for the low signal-to-noise situation.And these two 4D WDF reconstrucation techniques can become reciprocal complementation.