Michael J. Noble

Comparison of optical VCSEL models on the simulation of oxide-confined devices

We compare the results of different optical vertical-cavity surface-emitting laser models on the position-dependent effects of thin oxide apertures. Both scalar and vectorial models as well as hybrid models are considered. Physical quantities that are compared are resonance wavelength, threshold material gain, and modal stability. For large device diameters and low-order modes, the agreement between the different models is quite good. Larger differences occur when considering smaller devices and higher order modes. It is also observed that the spread in the resonance wavelengths is smaller than that for the threshold material gain.

Analysis of microcavity VCSEL lasing modes using a full-vector weighted index method

Presents a semi-analytic full-vector method for calculating the spatial profile, optical confinement factor resonant frequency, absorption loss, and mirror loss of lasing modes in cylindrically symmetric microcavity vertical-cavity surface-emitting lasers (VCSELs). It can be shown that this method gives the best separable approximation for the electric and magnetic vector potentials. Our technique can model the entire VCSEL structure and can treat complex media. We apply the method to etched-post and oxide-apertured VCSELs designed for 980-nm emission and find a blueshift in cavity resonance as the cavity radius shrinks. We also find a minimum optical cavity radius below which radially bound lasing modes cannot be supported. This radius depends on the device geometry and lies between 0.5 and 1 /spl mu/m for the devices studied. Once this model is augmented to include diffraction losses-the dominant loss mechanism for conventional small aperture lasers-it will provide a complete picture of lasing eigenmodes in microcavity VCSELs.

Effects of native oxides and optical confinement on microactivity VCSEL spontaneous emission

Threshold currents in small-aperture VCSELs are likely to be dominated by diffraction losses. We have developed a semianalytic technique to estimate the lasing mode energies, field profiles and cavity losses--including absorption, mirror, and diffraction losses--in oxide-apertured VCSELs. By coupling these modes to the full, nonparabolic electronic bandstructure, and by solving the resulting multimode related rate equations, we can model the light versus current characteristics of microcavity VCSELs. We apply our model to a low-threshold VCSEL structure and calculate threshold currents of 30 - 40 (mu) A, in qualitative agreement with experiments. We estimate spontaneous emission factors (beta) as large as 1.7 X 10-2 for a 1.5 micrometers radius device.

Calculation of microcavity VCSEL field modes using a doubly iterative weighted index method

We generalize the weighted index method for analysis of modal structure in various devices, including vertical cavity surface emitting lasers. Our model uses a doubly iterative process to calculate the bound modes for any dielectric device with an azimuthally symmetric geometry. In order to calculate the modes we assume a separable form for the electric and magnetic vector potentials. The scalar wave equation is then solved for the axial components of electric and magnetic vector potentials. Assuming a functional form of Az equals F((rho) )G(z) and Fz equals P((rho) )Q(z) we form coupled differential equations between F((rho) ) and G(z). These equations are then iteratively solved using the coupled boundary conditions for Az and Fz. Convergence by tracking the change in the eigenfrequency for the radial and axial eigenvalue equations. Our method allows rapid calculation, compared to an analogous finite element approach, and will handle any azimuthally-symmetric geometry with piecewise-constant indices of refraction. This model is particularly well suited to the calculation of bound modes in microcavity and oxidized structures where field confinement effects can be very important. The model can also, in principle, be adapted to obtain radiative modes, and should provide a valuable tool to analyze field behavior and quantum optics effects in microcavity devices.

Semi-analytic calculation of diffraction losses and threshold currents in microcavity VCSELs

We present a new semi-analytic technique for estimating the diffraction loss and threshold gain of oxide apertured microcavity VCSELs. Apart from a few geometric simplifications, our calculation is based on a rigorous first-principles analysis of the modal fields. By combining the threshold gain with the electronic bandstructure and optical matrix elements, we calculate the threshold currents of microcavity VCSELs and obtain good agreement with experiments.

Calculation of VCSEL lasing mode threshold gain with the weighted index method

We present an extension of the weighted index method (WIM) for calculation of VCSEL lasing mode threshold gain. The WIM is a modal technique which gives the best separable solution for the VCSEL modes in a variational sense. The approach for inclusion of threshold gain in the WIM is a generalization of the classic Fabry-Perot round-trip amplitude and phase conditions.

Measurement of resonant-mode blueshifts in quantum-dot vertical-cavity surface-emitting lasers

We experimentally investigate the modal properties of vertical cavity surface emitting lasers with vertically coupled quantum dot active regions. Etched air-post structures with aluminum-gallium-oxide apertures and aluminum-oxide distributed Bragg reflectors are electrically-pumped below the lasing threshold. The wavelengths of the resonant cavity modes are revealed by room temperature electroluminescence measurements. In concert with our earlier theoretical predictions, we find that the resonant cavity modes blueshift as the radius of the oxide aperture decreases.

Optical optimization of microcavity VCSELs

We present a full vector, finite element analysis of oxide apertured VCSELs, focusing on the optical properties required for low threshold design. We examine several versions of an 870 nm oxide DBR, oxide aperture VCSEL design to gain insight into the physical processes determining diffractive loss. Our results suggest the diffraction may be modeled as a coupling loss to the parasitic mode continuum. In this approach, the loss is determined from two competing factors: (1) the lasing mode penetration into the radial cladding region, and (2) the relative alignment of the eignenmode and parasitic mode wavevectors. We also find the characteristic blueshift resulting from the transverse optical confinement.

Analysis of three dimensionally confined microcavity surface emitting lasers using vector finite elements

This new finite element method model is expected to be valuable for the design of microcavity devices. It can be used to optimize optical mode control by examining changes of size, shape, number, and location of native oxide layers. It may also be combined with semiconductor gain calculations to determine the higher-order mode suppression level for various microcavity surface emitting laser designs. Finally, it may be used to analyze VCSEL lasing and spontaneous emission near-field structure. This information is of considerable importance in the design of optical interconnect and communication systems.