Vera N. Troshchieva

Near-diffraction-limited coherent emission from large aperture antiguided vertical-cavity surface-emitting laser arrays

We demonstrate that in-phase mode operation with a near-diffraction-limited beam can be realized in large aperture (up to 100 elements) antiguided vertical-cavity surface-emitting laser (VCSEL) arrays. A selective etching process with two-step metalorganic chemical vapor deposition is used for fabrication of the antiguided VCSEL array structures. Modal discrimination is enhanced by intentionally choosing a GaAs cap thickness so as to introduce suitable loss to array interelement regions. Far field patterns indicate in-phase mode operation from both triangular and rectangular geometry antiguided VCSEL arrays, which is in good agreement with theory.

Modeling, fabrication, and characterization of large aperture two-dimensional antiguided vertical-cavity surface-emitting laser arrays

We have investigated the modal behavior of two-dimensional (up to 400 elements) active-photonic-lattice-based antiguided vertical-cavity surface-emitting laser (VCSEL) arrays by both modeling and device characterization. A two-dimensional (2-D) model based on the effective index method has been constructed to analyze 2-D resonance and calculate array mode frequencies in rectangular geometry arrays. A more comprehensive three-dimensional bi-directional beam propagation code has also been developed to theoretically describe 2-D antiguided arrays with the VCSEL structure in the primary wave propagation direction. Gain spatial hole burning (GSHB) effects above laser threshold are applied to find conditions favorable for in-phase mode lasing and high intermodal discrimination. Three rectangular geometry array structures based on different interelement loss mechanisms have been designed and fabricated. Both far-field and spectral characterization were conducted on the devices to make detailed comparison with theoretical results. We found that introducing higher loss within the interelement region can allow the in-phase mode to exhibit the lowest threshold gain for a wide range of interelement widths around the in-phase resonance condition. A detailed spectral study of 5/spl times/5 arrays with the highest interelement loss design has demonstrated suppression of competing guided array modes and higher order leaky array modes at drive currents up to 10 times threshold.

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.

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.

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.

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).

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.

Paradoxical features of monochromatic light amplification in multicore fibers

It is numerically revealed and properly interpreted a phenomenon of predominant amplification of an optical mode with lower modal gain in 7-core fiber laser. Mode beating is a key factor responsible for this effect.