Polarization selective symmetry breaking in the near-fields of vertical cavity surface emitting lasers

Abstract

We study symmetries in multi-transverse-mode near-fields of circular vertical cavity surface emitting lasers (VCSELs). The 0 • polarized component of the near-field always has circular or high-order rotational symmetry, indicating that all significant optical properties of the laser are isotropic for light of that polarization. In contrast, the simultaneously present 90 • polarized part of the same near-field is always symmetrical only upon reflection. This is evidenced by sequences of near-field images of increasing complexity for increasing pump current. The presence of a preferred direction of the symmetry axis is evidence for a symmetry-breaking anisotropy. We attribute this anisotropy to birefringence, which is induced into any electrically pumped VCSEL by the applied vertical electrical field via the linear electro-optic effect. Thus, the optical index becomes a function of the transverse component of the k-vector of light inside the cavity, which corresponds to an angular dependent index. As the functional dependence on the emission angle is of different strength for orthogonal polarizations, the circular symmetry of the laser is broken only for 90 • polarized light, while the effect on the 0 • polarization is too small to affect the near-field. The highly symmetrical near-field of the unaffected polarization shows remarkable similarities to another physical system of circular symmetry, the static patterns in cellular flames. Our analysis of the symmetry properties of the near-fields has implications for the design of VCSELs as well as for future modelling activities.

Influence of anisotropies on transverse modes in oxide-confined VCSELs

“…As a general feature, the nearfields in orthogonal polarization directions differ qualitatively: the 0 polarized parts of the nearfield in both lasers appear with a high degree of rotational symmetry at all injection currents, while the 90 polarized parts always possess a preferred direction as fixed by the orientation of strongly excited modes with only reflectional symmetry. This phenomenon has been conclusively described in [8] and has been attributed on a phenomenological level to a polarization-selective anisotropic optical guiding due to field-induced birefringence.…”

“…In general, a complicated transverse mode behavior seems to be typical for oxide-confined devices [3]. Consequently, considerable work has been carried out in order to identify the mechanisms that determine the transverse mode formation: interaction of cavity structure and gain medium [4], [5], induced birefringence [6]- [8], and noncircular oxide-windows [9] have been found to play important roles for the VCSELs' emission. However, up to now, a comprehensive analysis taking into account the interaction of all of these mechanisms is still missing due to the complexity of the problem.…”

Picosecond emission dynamics of vertical-cavity surface-emitting lasers: Spatial, spectral, and polarization-resolved characterization

“…The horizontal axis represents the spatial coordinate, the vertical axis is a combination of both spatial and spectral coordinates, with the wavelength increasing from the bottom to top of each snapshot [13], [14]. As a consequence, spatially extended transverse modes that are only slightly separated in wavelength may overlap in this representation.…”

Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell–Bloch laser

“…In the case of lasers, López-Ruiz et al [33] give a bifurcation analysis only in the neighbourhood of the symmetric Takens-Bogdanov point. Krauskopf et al [37,49,11,35] give spectacular and informative bifurcation diagrams away from the Takens-Bogdanov point, for a model that does not, however, involve the Z 2 -symmetry. Rucklidge [13] considers bifurcations only near the Takens-Bogdanov point and with the sign of M T B opposite to ours.…”