Dmitry V. Vysotsky

Direct numerical simulation of radiation propagation in a multicore fiber

Abstract Modern technology allows for manufacturing of multicore fibers composed of a number of microcores placed on a circle and doped with Nd 3+ ions. 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. 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. The problem of microcore array excitation by injection of a beam into one of them was numerically studied. Results are compared with predictions of simplified coupled-mode theory. For realizable in experiments conditions coupling coefficients are found. Evolution of far-field patterns with fiber length was studied.

Simplified intracavity phase plates for increasing laser-mode discrimination

Recently, a new class of laser resonators was introduced that utilizes diffractive mirrors and an additional intracavity diffractive phase element. High modal discrimination and low fundamental-mode loss were achieved simultaneously by use of sinusoidal and pseudorandom diffractive phase elements. An intracavity phase element consisting of a simple single-step phase modulation is approximated by a Gaussian with a small radius. Explicit expressions are obtained for the modal-discrimination factor as a function of resonator parameters with a Gaussian output mirror. Numerical simulations are performed for a phase element with a step singularity in the phase function, the fundamental mode of this cavity being super-Gaussian. The modal discrimination of the cavity is studied for different radii of the single-step phase modulation, the position of the phase plate, and the cavity Fresnel number. Optimum solutions are found for a plane output mirror with either a striped or a circular shape.

Diffraction Modeling of the Multicore Fiber Amplifier

The 3-D beam propagation method (BPM) and a complementary mode solver for the passive fiber were applied for modeling fiber amplifiers with a hexagonal structure of evanescently coupled cores that have been recently experimentally realized. The modes and modal gains were calculated for 7- and 19-core systems. Diminishing the core index step from Deltan = 2.57 ldr 10-3 to Deltan = 1.27 ldr 10-3 leads to a reduction of the amount of the guided modes from 7 to 3 and from 19 to 10 for the 7- and 19-core structures, respectively. The in-phase mode that has the lowest small-signal gain for the larger index step turns to have the highest small-signal gain at the lower index step. The mechanism lying behind the observed convergence of the wave field in the laser to the in-phase-like mode was analyzed by a study of propagation of a linear combination of two multicore modes. It was found that evolution of the amplified wave field in gain saturation regime can change from dominance of one to another multicore mode at a small variation of the input wave field. The 3-D BPM modeling shows the shortage of modal approach for analyzing the multicore fiber amplifier and indicates the importance of interference between the competing modes, leading to the beatings in saturated gain.

3D modelling of diode laser active cavity

This paper presents a menu-driven computer program developed for numerical simulations of single-mode diode lasers operating well above threshold. The program described here offers additional improvements and increased functionality, allowing us to model a wider class of devices. The software incorporates a subroutine to calculate a set of possible competitor modes using gain and index variations produced by the oscillating mode. These results demonstrated that a single-spatial mode can be maintained to approximately 13.5 times laser threshold. In the absence of thermal effects, it, was found that the experimental data confirms single-spatial mode operation up to at least 12 times threshold, in good agreement with the model.

Round-trip operator technique applied for optical resonators with dispersion elements

The round-trip operator technique is widely used for dispersionless optical resonators beginning from pioneering studies of Fox and Li. The resonator modes are determined as eigenfunctions of the round-trip operator and may be calculated by means of numerical linear algebra. Corresponding complex eigenvalues determine the wavelength shifts relative to reference value and threshold gains. Dispersion elements, for example, Bragg mirrors in a vertical cavity surface emitting laser (VCSEL) cause a dependence of the propagation operator on the wavelength and threshold gain. We can determine the round-trip operator in this case also, but the unknown values of the wavelength and threshold gain enter into the operator in a complicated manner. Trial-and-error method for determination of the wavelength shifts and the threshold gains is possible but it is rather time consuming method. The proposed approximate numerical method for calculation of resonator modes is based on the solution of linear eigenvalue problem for the round-trip operator with reference wavelength and zero attenuation. The wavelength shifts and threshold gains can be calculated by simple formulae using the eigenvalues obtained and the computed effective length of the resonator. Calculations for a cylindrical antiresonant-reflecting optical waveguide (ARROW) VCSEL are performed for verification of the model.

Influence of non-linear index on coherent passive beam combining of fiber lasers

Coherent laser beam combining is potentially attractive way to increase the output beam brightness beyond the limits imposed on single-mode lasers by technological problems. Passive phase locking does not need complex external management. A specific feature of fiber amplifiers and lasers is that they possess optical path differences of many wavelengths magnitude. Cold-cavity theory of coherent laser beam combining predicts in this case rather low efficiency of beam combining even for an array of 8 lasers. Experiments, in contrast, demonstrated in such systems that high degree of phasing takes place for up to 20 lasers in an array. Possible explanation of this discrepancy may be associated with a number of factors. These factors are: gain saturation, intensity-dependent index, laser wavelength self-adjustment within the gain bandwidth. Besides, high degree of phase-locking can be established in self-sustained pulse periodic or spiky regime. Our approach takes injection controlled laser as a base unit of an ensemble. Beams from the neighboring lasers are injected into the reference laser in the array. Then a relationship between reference laser characteristics and whole wave field parameters can be found. As an example, fiber laser array with global coupling is numerically simulated with laser wavelength scanned within the gain bandwidth. Non-linear index is found to improve essentially passive phasing efficiency independent of the non-linearity sign.

Theory of spatial mode competition in a fiber amplifier

A theory is developed of monochromatic wave field amplification in a waveguide array based on expansion of the wave field in terms of guided array modes. The equations for the expansion coefficients include cross-modal gain, which completely changes the behavior of the amplified wave field. Analysis of the two-mode amplification reveals unusual features in its characteristics. Instead of unlimited growth of both modes for incoherent fields, one of the modes grows with no limit and suppresses the lower-power mode. Effects associated with the cross-modal gain are illustrated analytically on a system of two thin parallel planar waveguides. Conditions are found where the mode with lower gain can become the dominant one at the output of the amplifier.

Comprehensive Analysis of Mode Competition in High-Power CW-Operating Diode Lasers of the Antiresonant Reflecting Optical Waveguide (ARROW) Type

Three-dimensional above-threshold analyses have been performed on laterally antiguided laser structures of the antiresonant-reflecting-optical-waveguide (ARROW) and simplified (S)-ARROW types, of relatively large core width (10 μm), for generating watt-range continuous wave (CW) powers in a single, stable spatial mode. The 3-D numerical code takes into account carrier diffusion in the quantum wells, thermo-optic effects as well as edge radiation losses. The behavior of both device types is studied over a wide range in the variation of the width of the high-index regions s bordering the low-index device core. The results of the analyses indicate that thermal lensing plays an essential role in optical-mode competition. Best results (i.e., single-mode CW powers in excess of 1.5 W) are obtained when s corresponds to a lateral resonant condition. When s corresponds to one full lateral wave, both ARROW and S-ARROW devices reach CW single-mode powers of 1.7 W. When s corresponds to about one half lateral wave, both ARROW and S-ARROW devices display isolated regions of modal instability followed by CW operation in a stable, single spatial mode to powers as high as 2.0 W.

Coherent combination of fiber amplifiers with arbitrary optical phase differences

Coherent laser beam combining potentially provides an opportunity to achieve extremely high brightness of the output beam, permitting high on-target power density. All passive phasing techniques are limited by existence of optical path differences of individual fiber amplifiers. Cold-cavity theory predicts fast decrease in efficiency of coherent fiber laser beam combining with number of lasers. Experiments demonstrated in such systems that high degree of phasing takes place for laser array of up to 16 lasers. Origins of this illusory contradiction will be analyzed in the paper. Effects of laser wavelength self-adjustment and non-linearity of gain will be discussed.

Antiresonant reflecting optical waveguide-type vertical-cavity surface emitting lasers: comparison of full-vector finite-difference time-domain and 3-D bidirectional beam propagation methods

The cold-cavity modal characteristics of an antiresonant optical waveguide-type cylindrical vertical-cavity surface-emitting laser (VCSEL) are investigated through numerical simulations using a three-dimensional (3-D) bidirectional beam propagation method (BD-BPM) and a full-vector axisymmetric finite-difference time-domain (FDTD) method. Good agreement between the BPM- and FDTD-computed radial mode profiles as well as the mode-dependent radiation losses is obtained. The results of this paper establish the accuracy of the BD-BPM technique for simulating this class of devices and confirm effective-index method predictions that antiresonance conditions for cylindrical geometry devices (i.e., VCSELs) differ from those of planar geometry devices (i.e., edge emitters).