Theoretical Investigation of The Dynamical and Static Characteristics of Vertical-Cavity Surface-Emitting Lasers Incorporating Two-Dimensional Photonic Crystals

Abstract

In this work we present a spatial and dynamical model of a semiconductor vertical-cavity surface-emitting laser (VCSEL) incorporating a spatial built-in optical waveguide created by the defect in a two-dimensional photonic crystal (PC). The PC is created by an array of air-holes etched in to the VCSEL. Results of investigations of power versus current and dynamical characteristics of a conventional proton-implanted VCSEL and VCSELs incorporating PC defect waveguides operating with effective index and photonic band-gap guidances are presented and discussed. Results show that the VCSELs with incorporated PCs between laser mirrors provide a dramatic decrease of the power of the fundamental laser mode. Application of multiple-defect photonic bandgap (PBG) waveguides provides an additional dominance of the fundamental mode, and thus, the PC creates high-power but single-mode radiation of VCSELs which is impossible in conventional VCSELs.

Theoretical investigation of static and dynamic characteristics of vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals

“…Although it is shown with the holes through the active region it is probable that the gain region itself would not have the PC within it. This structure has been applied to theoretical investigations of the PC-VCSELs before (Song et al 2002;Ivanov et al 2007Ivanov et al , 2009a and renewed interest as fabrication of this type of structures is being investigated by several groups (Matsubara et al 2008;Ivanov et al 2009b). PC-VCSEL of type (III) shown in Fig.…”

“…The WM used in this work is based on the model published works (Yu 1998;Ivanov et al 2007Ivanov et al , 2009a and it can describe PC-VCSELs type (II) and (III).…”

“…Two optical models of the PC-VCSEL were used in the work: the SLM and WM. They both use numerically solved scalar Helmholtz equations as described in (Ivanov et al 2007;. It is assumed that the cavity of the VCSEL supports only one longitudinal mode, but multiple transverse optical modes.…”

“…It was shown that such partial current differentiation is possible in proton-implanted PC-VCSELs with the PC-defect diameter ranging from 3 to 9 µm (Leisher et al 2007). However, it was also found that both oxide and implant confinements still control transverse optical modes and compete with the PC confinement in PC-VCSELs (Leisher et al 2007;Ivanov et al 2007Ivanov et al , 2009a). The oxide confinement control relies on higher refractive index contrast than proton implant and it makes the fabrication of the single-mode oxide-confined PC-VCSELs more challenging.…”

“…To our best knowledge, there is no dynamical model of PC-VCSELs including interactions between (i) the modal fields spatially-controlled by the PCs with (ii) the evolving spatial carrier distribution and also including (iii) the optical losses introduced by the holes of the PC. We have made some initial modelling of PC-VCSELs to consider the single mode output power and dynamical behaviour of the PC-VCSEL (Ivanov et al 2007) and this approach is extended and made more complete here.…”