Nickolai N. Elkin

Reconstruction of field distributions of an active multicore fiber in multimode fibers

Multimode interference is fairly known from the 1D case of slab waveguides. We present for the first time to our knowledge the reconstruction of the 2D radial symmetric structure of a multicore fiber laser in a multimode fiber. In the concept of multicore fiber, rare earth-doped single mode waveguides (micro cores) are placed on a ring inside a big pump core. The situation of injecting radiation from N incoherent emitting sources into a multimode waveguide is described analytically. Experimental and numerical results for various multimode diameters and fiber lengths dealing with the reconstruction of the injected near-field pattern and the corresponding far-field patterns are presented. We propose that the reconstructed field could be re-injected into the multicore fiber-laser in order to introduce parallel coupling of all emitters. Additionally, using the multimode fiber as a passive element, without re-injection, the on-axis intensity of the multicore laser radiation is significantly increased by a single pass through a multimode fiber with a certain length. This effect takes place without any loss of energy.

Modal characteristics of 2D antiguided VCSEL arrays

Cold-cavity modal behavior of a 2-D (4x4 square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array is studied by the means of an effective-index model and fiber-mode approximation. The calculations show that the 2-D array can operate under a resonant condition, provided that a resonance in both of the 1-D directions is satisfied. Although out-of-phase and adjacent modes will compete with the in-phase mode around its resonant position, our simulation shows that, with the introduction of inter-element loss, the in-phase mode can be favored to lase for a wide range of inter-element width, s, around its resonant position. The effective-index model is shown to be in qualitative agreement with a more comprehensive (exact) 3-D beam-propagation-based simulation, which takes into account the actual layered structure. The 2-D antiguides are constructed from shifting the cavity resonance between the element and inter-element regions and fabricated by chemically selective etching and two-step MOCVD growth. While both diffraction-limited resonant in-phase and out-of-phase modes are observed from top-emitting arrays, a 2-D bottom-emitting structure is adopted to improve heat removal. Preliminary results of 40 mW pulsed and 10 mW CW powers have been obtained from the junction up and down arrays respectively.

Modeling and observations of modal structure in antiguided VCSEL array

Modal behavior of a 2-D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied by 3-D bi-directional beam propagation method. Above threshold operation of leaky modes was simulated using multiple iterations. Besides, a method based on functions of Krylov’s subspace, was developed to find a number of array optical modes in a VCSEL array with gain and index distributions established by the oscillating mode. In calculations, both Fourier and space variable descriptions of beam propagation were combined. The FFT technique was used for calculations of the Fourier image and the original. Conditions are found for favorable lasing of the in-phase mode providing high laser beam quality. Experimentally realized 5x5 laser array was studied numerically. The 2-D antiguided array results from shifting the cavity resonance between the element and inter-element regions and is fabricated by selective chemical etching and two-step metalorganic chemical vapor deposition (MOCVD) growth. In-phase and out-of-phase array mode operation is observed from top-emitting rectangular arrays as large as 400 elements, depending on the inter-element width, in good agreement with theory.

Stability of phase-locked lasing in a two-coupled-unstable-resonator system

We describe the performance of two lasers with homogeneously saturated gain, coupled through a central hole in a common mirror of symmetric unstable resonators. A new iterative procedure is proposed based on combining the Fox-Li and Prony methods. The suggested procedure allow us to calculate several resonator modes and find a stable phase-locked operating region for various sizes of coupling hole and small-signal gain values. Far-field patterns from combined lasers are computed for various operating regimes.

Mathematical simulation of composite optical systems loaded with active medium

A set of programs to simulate a diffractive optics in various laser systems is developed. The codes are based on the efficient and general diffractive propagation computer program that employs FFT (FHT) techniques and the scheme of splitting the diffractive and gain-refractive steps of calculation. The codes include a new method of iterative calculation for the optical resonators loaded with active medium. This method solves the problem of the calculations convergency in a case of several equal-loss modes and allows one to find the single modes stability limits. The method is proposed to calculate continuous multimode lasing when neglecting a transverse-mode beating. The results of numerical simulation of several laser systems are reported: (1) the slave laser under the injection of an external signal (injection locked laser, 2-D code); (2) three-mirror resonators with active medium (3-D code); (3) two optically coupled lasers having unstable resonators (3-D code); (4) 1-D laser array in the Talbot cavity (self-imaging resonator 2-D code). Most suitable parameters of pointed optical schemes to achieve high efficiency and high beam quality can be found by using mathematical simulation.

Multicore fiber laser phase-locking by virtue of fractional Talbot effect

Multicore fiber (MCF) can absorb pump radiation at small length giving opportunity to construct compact fiber laser. Phase-locking of generation in different microcores improves the output radiation beam quality. We have developed simple analytical description of multiple imaging of periodical field distribution propagating in space -- fractional Talbot effect, and have shown that this effect allows phase-locking MCF ever in the case of large variation of microcore parameters. The reason is all of the microcores to be equally coupled each with other: the global (parallel) coupling. Partial phase-locking has been demonstrated in experiment with fiber laser, consisting from 18-cores MCF and ¼-th Talbot length annular waveguide.

Modeling of phase-locking of slab-lasers with hybrid resonators

RF CO2 slab lasers with waveguide-unstable resonators demonstrated last years to be an effective tool for many applications. Increase of the total power using technique of phase locking of lasers can be achieved without deterioration of beam quality. Till now, no attempt was made to develop such technique for slab-laser arrays. Authors propose to arrange optical coupling between individual resonators using beams diffracting over the edge of convex mirror in asymmetric unstable resonator. 3-dimensional diffraction code was applied taking into account refractive index gradients and gain saturation effects in combination with diffraction and waveguiding effects in a whole optical tract including the coupling channel. In-phase and out-of-phase mode competition was studied in dependence on parameters of resonators and active medium, assuming the lasers were identical. Key parameters for phase locking are defined: optical coupling channel length and position of the resonator optical axis relative to the nearest edge of the convex mirror. The numerical simulations evaluate tolerances for the length of optical coupling channel. A range of the key parameters providing in-phase mode stable operation at high above threshold conditions is found for a particular laser construction. An option to generalize optical coupling method to N-slab-laser array is discussed.

Simple way for in-phase mode selection in lasers with annular gain region

Properties of laser cavity composed of two plane segmented mirrors placed at half-Talbot distance are considered theoretically in application to gas laser with annular active medium. Discrimination of in-phase mode against other supermodes is demonstrated. For saturable gain model, a critical small gain is found for which the in-phase mode become unstable.

Experimental and numerical investigation of field propagation in multicore fibers

Multicore fiber-lasers are designed to build high-power short length fiber-lasers. In our case the active single- mode cores (micro cores) are placed on a ring inside a big pump core. The micro cores are placed together very closely so that evanescent coupling between adjacent micro cores should be provided. To understand the coupling behavior in a multicore fiber in order to phase-lock all the micro cores we measured experimentally the coupling constant between the micro cores. Simultaneously we calculated the evolution of an injected field in a multicore fiber. In the experiment and in the simulations 38 micro cores with a diameter of approximately 6.9 micrometers are placed on a ring with a diameter of 115 micrometers . The distance between adjacent cores is about 2.6 micrometers . The measured coupling constant of 2cexp equals 0.82 mm-1 is in good agreement with the value 2cth equals 0.83 mm-1. Furthermore the phase evolution in each micro core was evaluated.

Numerical diffraction modeling of light propagation in multicore fiber

Modern technology allows for manufacturing of multicore fibers composed of a number of microcores placed on a circle and doped with Nd3+ ions. The construction is attractive because of effective absorption of diode laser pump radiation. High-power conditions are easily achievable, and phase coupling between microcore lasers looks very promising for receiving high-brightness radiation from compact fiber lasers. To understand in detail coupling between microcores and evaluate an opportunity to achieve phase-locked operation of the array, a mathematical code describing light propagation in this composed fiber was developed. A numerical code performs direct integration of scalar wave equation in paraxial approximation. Refractive index profile corresponds to N index-guiding microcores. The composite fiber was embedded into square region imitating fiber cladding with lower index. The wave equation was solved using a splitting technique for diffraction/refraction processes on every propagation step. Calculations on the diffraction step were made with help of 2D FFT technique on Cartesian mesh. Numerical accuracy was checked by special tests. Results on simulations of microcore array excitation by injection of a beam into one of microcores will be reported. For realizable in experiments conditions coupling lengths are found. Evolution of far-field patterns for different fiber lengths was studied.