Exactness of simplified scalar optical approaches in modelling a threshold operation of possible nitride vertical‐cavity surface‐emitting diode lasers

Abstract

Modern small‐size vertical‐cavity surface‐emitting diode lasers (VCSELs) require principally fully vectorial optical modelling because their cavity sizes are of the order of the wavelength of emitted radiation. However, much simpler scalar approaches are often surprisingly exact even beyond the limits of their confirmed validity. Therefore, in the present paper, reasonable limits of an application of simplified scalar optical approaches (instead of more exact but also much more involved and time‐consuming rigorous vectorial ones) are determined to model threshold operation of possible nitride VCSELs equipped with tunnel junctions with the aid of a comparison of results of the scalar effective frequency method with those obtained using the fully vectorial three‐dimensional plane wave admittance method. Both these optical methods have been found to give usually quite close results for the fundamental transverse mode. Larger discrepancies between the results of both approaches have been found for first‐order transverse modes (and even larger are expected for higher‐order ones) and for larger (or very small) active regions. Some structural modifications of nitride VCSELs, which may enable their low‐threshold single‐fundamental‐mode room‐temperature continuous‐wave operation, are proposed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analysis of structurally sensitive loss in GaN-based VCSEL cavities and its effect on modal discrimination

“…where k = nk 0 = nω c 0 was used, where n is the (real part of) the refractive index of the material inz = 0, and γ = −2n ′′ ω c 0 , where n ′′ is the imaginary part of the refractive index. Evidently, the last term in (12) is responsible for the standing wave effect, depending on the phase relation ∆ϕ between the counterpropagating fields. In a material without gain/loss, n ′′ = 0, so the power flux can then be viewed as being composed of independent contributions from the right and left propagating field.…”

“…The scalar method is almost identical with our 2D method, and is based on the effective index or effective frequency method [14], which assumes a moderate refractive index contrast so that the optical field is separable in the spatial coordinates in such a way that the wave equation can be reduced to a pair of almost one-dimensional equations. It is shown in [12,13] that the simplified scalar method and the rigorous vectorial method agree remarkably well in cases where diffraction losses are negligible. The vectorial method is very similar to our 3D method in the consideration of the structure and the cavity field.…”

“…A similar dual-method approach is taken in [12,13] where the optical modeling of GaNbased VCSEL cavities is discussed in detail and a strongly simplified scalar approach is compared with a vectorial method. The scalar method is almost identical with our 2D method, and is based on the effective index or effective frequency method [14], which assumes a moderate refractive index contrast so that the optical field is separable in the spatial coordinates in such a way that the wave equation can be reduced to a pair of almost one-dimensional equations.…”

Numerical Self-Consistent Analysis of VCSELs

“…The latter is directly associated with a radial profile of the threshold current density injected into the VCSEL active region (Figure 7), becoming in these double intracavity contacted VCSELs more and more nonuniform with increasing active-region radius r A [25,26]. Therefore, for larger r A it is found that higher-order transverse modes become the lowest-threshold modes, which limits the desired Guassian mode operation to relatively small active region diameter.…”

“…The structure and parameters used in the simulations are described in [26]. Our self-consistent simulation model is used to determine possible room-temperature CW performance characteristics of GaN-based VCSELs.…”