Coherent Beam Combining of Three Watt-Level Fiber Amplifiers Using a DSP-Based Stochastic Parallel Gradient Descent Algorithm

We present an experimental study on coherent beam combining of three watt-level fiber amplifiers using a stochas- tic parallel gradient descent （SPGD） algorithm. Phase controlling is performed by running the SPGD algorithm on a digital-signal-processor （DSP） chip with a voltage updating rate of 16500 times per second. Energy encircled in the target pinhole is 2.62 times more than that in an open loop. The combining efficiency is as high as 87%.     

Phase-Locked Fibre Array for Coherent Combination and Atmosphere Aberration Compensation

We report a fibre amplifier array that not only achieves coherent beam combination by compensation of phase noises of fibre amplifier, but also accomplishes correction of atmosphere aberration. It is of master-oscillatormultiple-amplifier （MOPA） configuration, which can be phase-locked by the multidither principle or heterodyne detection principle. First laboratory experiments of atmosphere aberration compensation of a three-element fibre amplifier array are reported. The atmosphere aberration is created by a phase screen in the experiment. The phase changes of the beam, which are introduced by the fibre amplifier and the phase screen, are both detected by the heterodyne detection method. Phase modulators are controlled to compensate for the phase in the three paths. No matter whether there is a phase screen producing atmosphere aberration or not, the dim dynamic interference fringes in the far field turn to a clear and stable pattern, and the peak intensity is maximized. It is indicated that the fibre amplifier array is phase-locked, and coherent combination of the three beams is achieved. It can be used not only to obtain high power fibre laser array but also in laser space communication.     

Realization of an All-Fibre Self-Organization Intra-Cavity Coherent Erbium-Doped Fibre Laser

An intra-cavity coherent coupling Michelson Er-doped fibre （EDF） laser （MCEDFL） is proposed and demonstrated. Characteristics of the MCEDFL are investigated. It is found that the MCEDFL with a polarizer can be coherent combined effectively. By the experiment based on fibre Bragg gratings （FBGs） with different reflectivity, we find that the reflectivity of the FBG play a vital role in improving the performance of the MCEDFL. This outcome adequately shows many favourable features, such as high efficiency, easy operation, and simple all-fibre configuration.     

Enhancing Coherent Combining Efficiency via Choosing Appropriate Lasing Wavelength in a Michelson Compound Cavity Based on Two 3 dB Fibre Loop Mirrors and One Fibre Bragg Grating

Enhancing coherent combining efficiency via choosing appropriate lasing wavelength in a Michelson compound cavity based on two 3 dB fibre loop mirrors and one fibre Bragg grating （FBG） has been experimentally demonstrated. The FBG with 4.5% reflectivity is replaced at the cleaved facet with 4% Fresnel reflection. A high coherent combining efficiency of 93.5% is obtained when the FBG with central wavelength at 1559.845nm is introduced into the cavity, while it is only 90.1% combining efficiency with the FBG at central wavelength 1557.830 nm. In comparison with other reports, the proposed compound-cavity laser has the advantage of needless tuning FBG to obtain the coherent condition, and it is facile to ascertain the seemly wavelength lasing for a Michelson compound cavity.     

Polarization-resolved analysis of the characteristics of a Raman laser made with a polarization maintaining fiber

We derive a simple model describing steady characteristics of Raman fiber lasers made with polarization maintaining fibers. We show both theoretically and experimentally that this kind of laser simply consists of two independent Raman lasers linearly polarized along the fiber birefringence axes. The output power characteristics of the laser are shown not to be influenced by optical Kerr effect. Finally, we use our model to propose answers to questions recently raised about efficiency of Raman lasers made with polarization maintaining fibers.     

Coherent Beam Combination of Eight Watt-Level Polarization-Maintained Fiber Amplifiers

We demonstrate the coherent beam combination of eight Watt-level polarization-maintained fiber amplifiers. The phase control signal of each amplifier is generated by running a stochastic parallel gradient descent algorithm on a digital signal processor （DSP）. The experimental result shows that the whole system in close-loop performs well for long-time observation. Energy encircled in the target pinhole is 6.68 times more than that in open-loop. The combination efficiency is as high as 84.5%.     

Off-Axis Astigmatic Gaussian Beam Combination Beyond the Paraxial Approximation

Taking the off-axis astigmatic Gaussian beam combination as an example, the beam-combination concept is extended to the nonparaxial regime. The closed-form propagation expressions for coherent and incoherent combinations of nonparaxial off-axis astigmatic Gaussian beams with rectangular geometry are derived and illustrated with numerical examples. It is shown that the intensity distributions of the resulting beam depend on the combination scheme and beam parameters in general, and in the paraxial approximation （i.e., for the small f-parameter） our results reduce to the paraxial ones.     

Coherent effects of multiple scattering for scalar and electromagnetic fields: Monte-Carlo simulation and Milne-like solutions

Based on an expansion of the Bethe-Salpeter equation in scattering orders a semi-analytic approach for simulation of coherent phenomena of multiple scattering in random media has been developed. We found that for scalar field the manifestation of these phenomena, observed as temporal field correlation function and coherent backscattering, are universal and well agreed with the results predicted by diffusion approximation. For the electromagnetic field the temporal correlation function and coherent backscattering are noticeably differ from those found for the scalar field, depending strongly on the scattering anisotropy. The obtained numerical results, for the first time to our knowledge, are compared directly with the known generalizations of the Milne solution.     

Matrix-Based Polarization Analysis and Application of Semiconductor Optical Amplifiers

Employing the Mueller matrix method with polar decomposition, we analyse the polarization rotation (PR) effects in semiconductor optical amplifiers (SOAs) and demonstrate that the PR angle is linear to the birefringence dependent gain while the average PR coefficient is about 0.625 for the employed SOA. It is further evident that the current and optical intensity dependent PRs rotate reversely around the same axis. Thus we propose an optical-electric synchronous control scheme to obtain orthogonal polarization states with power-equalization, and implement it by a polarization-sensitive SOA. The polarization duration time is about 10 ns which is applicable to high-speed polarization state generation.     

Focusing of Partially Coherent Vortex Beams by an Aperture Lens

The focusing properties of partially coherent vortex wave fields are studied. Expressions are derived for the intensity distribution and the degree of coherence near the geometrical focus. It is found that the size of coherence vortex dark core in the focal region depends on the topological charges and normalized coherence lengths. It is found that the desired vortex dark core near the geometrical focus can be generated by choosing appropriate values of parameters. The degree of coherence possesses a pair of phase singularities regions in the geometrical focus neighbourhood.     

Coherent presentation of density operator of the harmonic oscillator in thermostat

Based on basis of the coherent states the density matrix of harmonic oscillator in thermostat is obtained. This method is mathematically refined and physically transparent for the interpretation of quantum phenomena in classical language. Such an approach gives an opportunity to easily find the density matrix in the multi-dimensional case.     

Polarization Changes of Partially Coherent Electromagnetic Vortex Beams Propagating in Turbulent Atmosphere

We investigate the polarization change of partially coherent electromagnetic vortex beams propagating in turbulent atmosphere. It is shown that the polarization of the beams will experience changes, and the changes of the polarization are dependent on the spatial coherence, topological charges of the beams, and the degree of polarization of the source plane and the atmospheric turbulence. The results obtained may have applications in space optical communication.     

Coherent recombination of laser beams with interferometrical phase control

A HeNe laser beam is split into four component beams which are subsequently transmitted through four polarization-preserving monomode fibres. At the end of the fibres the emerging beams are coherently recombined in pairs in two steps using inverse beamsplitter cubes. The unavoidable phase differences within each pair of beams, which are caused by temperature and pressure fluctuations in the fibre environment, are detected interferometrically at the fibre ends. Using homodyne techniques, these differences are measured and compensated for by lengthening the optical path in the individual fibres with piezo-electric stretching. With appropriate adjustment of the relative phases the emerging beams can be superimposed onto each other so as to re-form one single coherent beam.     

Coherent and incoherent polarization encoding of electromagnetic fields

We study a method generating certain distributions of the degree and state of polarization of a light field across a transverse beam cross-section. We use the introduced polarization encoding scheme to study the distribution of polarization ellipses in a cross-section of a beam generated by superposing two encoded beams, the effects of coherence relation between the input beams on this distribution were theoretically analyzed and illustrated by contour plots of the parameters representing polarization ellipses.     

Coherence properties of the radiation from X-ray free electron laser

We present a comprehensive analysis of coherence properties of the radiation from X-ray free electron laser (XFEL). We consider practically important case when XFEL is optimized for maximum gain. Such an optimization allows to reduce significantly parameter space. Application of similarity techniques to the results of numerical simulations allows to present all output characteristics of the optimized XFEL as functions of the only parameter, ratio of the emittance to the radiation wavelength, . Our studies show that optimum performance of the XFEL in terms of transverse coherence is achieved at the value of the parameter of about unity. At smaller values of the degree of transverse coherence is reduced due to strong influence of poor longitudinal coherence on a transverse one. At large values of the emittance the degree of transverse coherence degrades due to poor mode selection. Comparative analysis of existing XFEL projects, European XFEL, LCLS, and SCSS is presented as well.     

Coherent thermal emission by microstructured waveguides

Following Greffet et al. [Coherent emission of light by thermal sources. Nature 2002;416:61-4], we study in this article, the possibility to engineer thermal coherent sources with waveguides. The idea is to rule a grating on a waveguide made of a slice of germanium deposited on a participating media such as glass. The guided waves, thermally excited are coupled to the far field by the grating and increase the system emissivity in certain directions and wavelengths. We numerically compute the diffraction of a plane wave by the grating by a rigorous coupled waves algorithm (RCWA). The reflected, transmitted and absorbed energy calculated allows to obtain the system emissivity by means of the Kirchhoff law.     

Modeling and optimizing of high-concentration erbium-doped fiber amplifiers with consideration of ion-clusters

Starting from the modeling of isolated ions and ion-clusters, a closed form rate and power evolution equations for high-concentration erbium-doped fiber amplifiers are constructed. Based on the equations, the effects of the fraction of ion-clusters in total ions and the number of ions per cluster on the performance of high-concentration erbium-doped fiber amplifiers are analyzed numerically. The results show that the presence of the ion-clusters deteriorates amplifier performance, such as the signal power, signal gain, the threshold pump power for zero gain, saturated signal gain, and the maximum gain efficiency, etc. The optimum fiber length or other parameters should be modified with the ion-clusters being taken into account for the amplifiers to achieve a better performance.     

Tunable, μs-pulsed ytterbium fiber laser system with a linewidth below 2.7 GHz

We report on a widely tunable, pulsed laser system with narrow spectral linewidth based on a continuous wave ytterbium fiber oscillator, a pulse shaper and a power amplifier stage. The system is tunable from 1055 nm to 1085 nm and provides a maximum pulse energy of 155 μJ with a pulse duration of 1-5 μs. The linewidth is less than 2.7 GHz over the whole tuning range.     

Switchable Multi-Wavelength Erbium-Doped Fiber Lasers based on a Mach-Zehnder Interferometer Using a Twin-Core Fiber

A switchable multi-wavelength erbium-doped fiber ring laser based on a compact in-fiber Mach-Zehnder interferometer comb filter at room temperature is presented. The comb filter is formed by splicing a section of twin-core fiber between two single mode fibers. By adjusting the states of the polarization controller appropriately, the laser can be made to operate in stable single-, dual- and three-wavelength lasing states. The operation principle is based on spectral hole burning induced by the saturated effect and polarization hole burning.     

Numerical Simulation for Coherent and Partially Coherent Beam Propagation through Atmospheric Turbulence

Propagation properties of coherent and partially coherent beams in atmospheric turbulence are investigated respectively by using numerical simulation It is found that a partially coherent beam has a spreading larger than a coherent beam. However, from the point view of relative beam spreading and intensity scintillation, a partially coherent beam is less affected than the corresponding coherent beam, which may be the most important virtue of partially coherent beams that could be utilized to improve the performance of laser engineering. The beam wandering is almost independent of the degree of the source coherence. More aperture averaging occurs when beam becomes more coherent.