Three-dimensional above-threshold analyses of high-index-contrast (HC) photonic-crystal (PC) quantum-cascade-laser arrays (QCLA) structures, for operation at watt-range CW powers in a single spatial mode, have been performed. Threeelement HC-PC structures are formed by alternating active- antiguided and passive-guided regions along with respective metal-electrode spatial profiling. The 3-D numerical code takes into account absorption and edge-radiation losses. Rigrod’s approximation is used for the gain. The specific feature of QCLA is that only the transverse component of the magnetic field sees the gain. Results of above-threshold laser modeling in various approximate versions of laser-cavity description are compared with the results of linear, full-vectorial modeling by using the COMSOL package. Additionally, modal gains for several higher-order optical modes, on a ‘frozen gain background’ produced by the fundamental-mode, are computed by the Arnoldi algorithm. The gain spatial-hole burning effect results in growth of the competing modes’ gain with drive current. Approaching the lasing threshold for a competing higher-order mode sets a limit on the single-mode operation range. The modal structure and stability are studied over a wide range in the variation of the inter-element widths. Numerical analyses predict that the proper choice of construction parameters ensures stable single-mode operation at high drive levels above threshold. The output power from a single- mode operated QCLA at a wavelength of 4.7 μm is predicted to be available at multi-watt levels, although this power may be restricted by thermal effects.
Three-dimensional (3-D) above-threshold analyses have been performed on laterally antiguided laser structures operated
on leaky modes and twin-waveguide structures operated on guided modes for generating watt-range CW powers in a
single, stable spatial mode. The 3-D numerical code takes into account carrier diffusion in the quantum well, thermooptic
effects as well as edge radiation losses. Additionally, higher-order optical modes on a 'frozen background'
provided by the fundamental mode operation are computed by the Arnoldi algorithm. Approaching the threshold for a
competing higher-order mode puts a limit on the range for stable, single-mode operation. The modal structure and
stability for both device types are studied over a wide range of the active core width and widths of the buried waveguides
bordering the low-index device core. The numerical analyses results indicate an essential role of thermal lensing in
transformations of optical-modes shapes and in mode stability loss with the drive current increase. The CW operation in
a stable, single spatial mode to powers as high as 2 W is predicted for 2-mm length lasers operated on leaky modes. The
maximum CW power in single-guided-mode is predicted as high as 2.46 W for 2-mm length and 3.4 W for 3-mm length
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.
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.
We have developed a 3D beam propagation numerical code and applied it to simulations of 7(19)-core of hexagonal
structure fiber amplifier experimentally studied recently. It was shown that the mechanism of phase synchronization of
co-propagating beams is associated with mode filtering by gain spatial structure. The tolerance limits on micro-core
parameter random variations for phase-locking taking place are numerically found for 7-core fiber amplifier with
different random core index sets. It is shown that the smaller core index step stabilizes the phase locking effect. An
original optical mode solver was developed. Spectra of modes and of their gain are studied for 7(19)-core fibers. Gain
self- and cross-saturation effects are examined, and possibilities of core structure tailoring in order to increase singlemode
stability are described.
Along with rapid progress in characteristics of single-fiber lasers much attention is paid these days to the problem of phase locking of multi-core fiber lasers. It is known that only strong-coupled system has a chance to be phase locked despite non-identity of channels. In case of the strong inter-channel coupling the traditional theoretical approach based on expansion over modes of individual cores fails. We have developed 3D diffraction numerical code, and results of its implementation to simulations of 7-core hexagonal fiber structure experimentally studied recently are reported. Detailed analysis of light propagation in this system, where self-organization effect was observed, shows that the dominant mechanism of coherence formation in an array of co-propagating beams is mode spatial filtering produced by the gain assembly. Non-linear resonance refraction exerts a weak influence on appearance of self-organization. The ways to achieve better selection of a single array mode are discussed. For the first time, the tolerance limits on micro-core parameters for keeping phase-locking are numerically found.
Two-dimensional photonic lattices with a low-index defect have been studied. Simulations demonstrate that this type of structure has potential for realizing single-spatial mode operation from a relatively large emitting aperture, making it ideal for fiber coupling applications. A 2-D finite difference model is used to calculate the radiation loss of the modes in various low-index defect based two-dimensional photonic lattices. The simulation results are also compared to the results from a comprehensive the 3-D bi-directional beam propagation model. These calculations have been used to guide mask design and the experimental realization of the defect VCSEL devices.
There is an increasing need for single-spatial-mode, edge-emitting semiconductor lasers with reliable cw output power of around 1 W for applications such as pumps for rare-earth-doped fiber amplifiers and free-space communications. The design of respective devices is still a challenging task for experimenters, and software can assist very much in doing analyses of potentially perspective designs. We have developed a 3D numerical code supplied with a user-friendly interface for active diode-laser structures, taking into account light diffraction and carrier diffusion. The Watt-Ampere characteristics are calculated by changing the drive current density in the equation for the carrier-number density. To evaluate a single-mode stability limit, a procedure is developed to calculate 3-5 higher order optical modes on a 'frozen background': gain, carrier-induced index variation, as produced by the operated mode at a fixed drive level. Modal gains of these modes are compared to the calculated threshold gains for each mode. Because of non-uniform gain saturation by the operated mode, modal gains for higher-order modes increase with drive current due to beneficial overlap of their fields with the gain. When one of the higher-order modes approaches its threshold, this puts an upper limit for stable single-mode operation. A graphical interface allows for viewing near- and far-field patterns of any mode in the form of 3D surfaces or contour-plots. Scanning of profiles of mode intensity in an arbitrary cross section in the output plane and in far-field zone is available, too. Results of analyses of a number of published designs are reported.
Single-mode high-power emission from a single VCSEL can be achieved by means of mode control in an external resonator. A problem arises how to analyse interference between wave field coming from external resonator to VCSEL structure. Analytical approach is formulated allowing for simplified description of the system. Numerical approach is based on 3-D bi-directional beam propagation method. Modal content and discrimination of higher-order modes in passive resonator are examined. Besides, above threshold operation of optical modes is simulated using multiple iterations. A method based on functions of Krylov's subspace, is developed to find a number of optical modes in a VCSEL with gain and index distributions established by the oscillating mode. In calculations, both Fourier and space variable descriptions of beam propagation are combined. This approach allows us to evaluate critical conditions for single-mode operation.
Resonance periodical structures were found to have the one uniformly distributed mode. The difference between this mode gain and all the others modes gain is independent from the number of channels, while it is smaller, than the obtained critical value.
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.
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.
Multiple images formation after propagation of periodical wave field over a fraction of Talbot distance (Zr) was received explicitly. The phase-locking of multi core fiber laser radiation was achieved experimentally by usage sector mirror placed at a distance of Zr/8.
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.
The multicore fiber laser (MCFL), containing several single mode microcores on the circle inside the pump core, is a promising compact high brightness laser source. The problem is to synchronize the radiation of microcores having different propagation constant values at a given radiation frequency. We present a theory of phase-locking of MCFL with a mirror spaced at fraction of Talbot distance. The collective mode selection appears to occur due to spatial filtering at fractional Talbon distance in combination with radiation frequency selection from the spectral gain range. Good agreement is found between the theory and experiment.
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.
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.
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.
Recently, a new class of laser resonators was introduced by one of the authors that utilizes diffractive mirrors and an additional intracavity diffractive phase element. High modal discrimination and low fundamental mode loss were achieved simultaneously using sinusoidal and pseudo-random diffractive phase elements.In this paper, an analytical approach is developed to study a simplified diffractive mirror resonator for producing Gaussian-shaped beams. Explicit expressions are obtained for the fundamental mode loss and modal discrimination by assuming a Gaussian-shaped reflectivity for the output mirror. An intracavity phase element consisting of a simple single-step phase modulation was approximated by a Gaussian with small radius. Explicit expressions are obtained for the modal discrimination factor as a function of resonator parameters with a Gaussian output are obtained for the modal discrimination factor as a function of resonator parameters with a Gaussian output mirror. Analytical results demonstrate that simple single- step phase elements can enhance cavity performance. Numerical simulations were performed for a phase element with a step singularity in the phase function. This element was found to increase the modal discrimination of the cavity, while simplifying element fabrication and cavity alignment.