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 (original) (raw)
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Journal of Lightwave Technology, 2000
Modal characteristics of antiresonant reflecting optical waveguide (ARROW) vertical-cavity surface-emitting lasers (VCSELs) are studied under high current injection. It is found that the influence of carrier spatial hole burning increases the radiation loss margin of ARROW at low injection current, while the thermal lensing effect significantly reduces radiation loss margin of ARROW at high injection current. Hence, the excitation of multiple-transverse modes in VCSELs is inevitable under high injection current even if the dimensions of the ARROW have been optimized to maximum radiation loss margin. Therefore, it is proposed to modify the refractive index profile of the ARROW to compensate against the influence of thermal lensing in VCSELs. It can be shown that the radiation loss margin of the modified ARROW can remain unchanged under the influence of thermal lensing if the dimensions and refractive index profile of the ARROW are properly designed. Hence, stable single-mode operation can be obtained in ARROW VCSELs at high injection current.
Two-Dimensional Antiguided Vertical Cavity Surface Emitting Laser Arrays With Reflecting Boundary
IEEE Journal of Selected Topics in Quantum Electronics, 2000
Strong coupling between elements in 2-D resonant antiguided vertical cavity surface emitting laser (VCSEL) arrays results in a good ability to select the in-phase array mode. This ability can be enhanced by proper tailoring of the gain/loss spatial distributions and elimination of lateral radiation loss. To evaluate quantitatively an impact of these means on single-mode stability, numerical simulations are performed for the resonant antiguided VCSEL arrays. A bidirectional beam propagation method was implemented for solving the wave equation in a 3-D scalar diffraction approximation to describe the VCSEL array with reflecting outer boundaries. This structure is composed of distributed Bragg reflectors, active layer, and a thin absorption spacer separated from the active layer. Openings in the top metal electrode pattern the output facet. The above threshold oscillating wave field distribution was calculated. The transverse gain and index distributions were calculated in each quantum well by the 2-D carrier diffusion equation. Stability of single-mode operation against the lasing onset of higher order modes was studied numerically. A parabolic temperature profile was used to imitate thermal focusing. The maximum output power 90 mW for a 5 × 5 array and up to 350 mW for a 10 × 10 array is predicted in the single-mode regime.
Numerical simulations of 2-D vertical cavity surface emitting laser arrays
Proceedings of LFNM 2002. 4th International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE Cat. No.02EX549)
Modal behavior of a 2D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied by the 3D bidirectional beam propagation method. Above-threshold operation of leaky modes was simulated using multiple iterations. In addition, a method based on functions of Krylov's subspace was developed to find the 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. Analysis of an effective-index approximation is made, and explicit expressions are derived for the effective index and blue shift of the laser frequency. Conditions are found for favorable lasing of the in-phase mode providing high laser beam quality. The 2D antiguided array results from shifting the cavity resonance between the element and interelement 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 interelement width, in good agreement with theory. The experimentally realized set of laser arrays of variable size was studied numerically.
Modeling of and Experimentation on Vertical Cavity Surface Emitting Laser Arrays
Modal behavior of a 2D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied by the 3D bidirectional beam propagation method. Above-threshold operation of leaky modes was simulated using multiple iterations. In addition, a method based on functions of Krylov's subspace was developed to find the 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. Analysis of an effective-index approximation is made, and explicit expressions are derived for the effective index and blue shift of the laser frequency. Conditions are found for favorable lasing of the in-phase mode providing high laser beam quality. The 2D antiguided array results from shifting the cavity resonance between the element and interelement 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 interelement width, in good agreement with theory. The experimentally realized set of laser arrays of variable size was studied numerically.
IEEE Journal of Selected Topics in Quantum Electronics, 2000
We have investigated the modal behavior of twodimensional (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 × 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.
Journal of The Optical Society of America B-optical Physics, 2003
Traditionally, one can calculate the update coefficients of the finite-difference time-domain algorithm at material interfaces by averaging the material properties of both sides, which leads to numerical inaccuracies of the reflection depending on the grid resolution. We propose a novel method to calculate the update coefficients such that the algorithm exactly fulfills the boundary conditions at a frequency of optimization, which allows a significant increase in grid spacing while limiting the numerical error. Using the proposed method, we reduced the computational expenses for the full-wave simulation of vertical-cavity surface-emitting lasers such that large structures can be treated without the need to exploit rotational symmetry. The method is demonstrated with the help of several examples.
Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement
Optics Communications, 2005
Two extensions of weighted index method are presented in order to calculate the splitting of degeneracy for non-circular vertical-cavity surface-emitting lasers. Both of them automatically satisfy which transverse optical modes split, and give a reliable approximation for the resonant frequencies, threshold gains and confinement factors. The intuitive effective radius method traces back the splitting for different effective aperture radii which are defined according to the transverse intensity distributions. The hybrid analytical axial and numerical lateral method is more precise from a _mathematical point of view, and provides the mode patterns as well as the optical data.
Theory and Modeling of Lasing Modes in Vertical Cavity Surface Emitting Lasers
VLSI Design, 1998
The problem of obtaining the lasing modes and corresponding threshold conditions for vertical cavity surface emitting lasers (VCSELs) is formulated as a frequency-dependent eigenvalue problem in required gain amplitudes and corresponding fields. Both index and gain guiding are treated on an equal footing. The complex gain eigenvalues define necessary but not sufficient conditions for lasing. The actual lasing frequencies and modes that the VCSEL can support are then determined by matching the gain necessary for the optical system in both magnitude and phase to the gain available from the laser's electronic system. Examples are provided.
Single-mode performance analysis for vertical-cavity surface-emitting lasers
Journal of Computational Electronics, 2007
In this work, the simulation of the single-mode stability in vertical-cavity surface-emitting lasers (VCSELs) is presented using a microscopic electro-opto-thermal model. Experimental data for oxide-confined VCSELs emitting at 850 nm with different contact metal designs are also available. It is shown that detailed models for the optical losses in the cavity consisting of outcoupling and absorption are required in order to explain the experiments. The role of cavity losses and spatial hole burning in the nonlinear electro-opto-thermal simulation framework is discussed in a quantitative manner.