Chapter 1. Introduction
1.2 VCSEL – vertical cavity surface emitting laser
Vertical-cavity surface-emitting lasers (VCSELs) are made by sandwiching a light emitting layer between two highly reflective mirrors. The light emitting layer is generally composed in multi-quantum layer for high gain efficiency and the high reflective mirror can be dielectric multilayered or distributed Bragg reflectors (DBRs).
The transverse confinement of optical field and electrical current is important for designing VCSELs. Generally, there are three types to confine the transverse optical field: gain guiding, index guiding, or antiguiding mechanisms. In Fig. 1.1, gain guiding is generally achieved by ion implantation into the DBR to control the flow of the injection current into the active layer [12,13]. However the configuration of ion-implanted region can not well define the diffusion of carrier concentration along the transverse direction of the active layer. Additionally, it is hard to apply the ion implantation to the active region for well defining the current distribution because it
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will increase the optical absorption loss of the VCSEL. Thus, at high power operation, the VCSEL with ion implantation can be excited high-order transverse modes due to the thermal lensing because of the non-well defined transverse confinement of the active layer. The other problem is the electrical resistivity of the DBR, which may increase the heat generation inside the laser cavity. The only benefit of this structure is planer configuration, which improves the simplification in fabrication process so the low production cost could achieve.
Compared to the gain-guided VCSELs, index-guided VCSELs have better transverse confinement of optical field. The index-guided VCSELs are implemented by inserting a material which has a low refractive index then the semiconductor of active layer to confine the optical field of transverse mode. This structure is similar to the waveguide of a fiber. Several types of index-guided VCSELs are implemented such as airposted, etched mesa and oxide aperture. These types have different mechanisms to confine the optical field and injection current as well as different production costs in fabrication process. The airposted VCSELs [14] as shown in Figure 1.2, the edge of active layer is direct contact with the outside air. The large difference in refractive index between the semiconductor material and the air provide very robust transverse confinement on optical field. But the roughness of the sidewall and the aperture-like structure from the active layer to the downside DBR increase the scattering and diffraction loss respectively. According to the research of waveguide, the larger the difference of refractive index between the materials of core and cladding layer the stronger confinement of optical field in the core, but conversely, the mode number will increase. Thus the single-mode operation is not stable in airposted VCSELs, especially at high injection current. Another type of index-guide VCSELs called oxide aperture VCSEL (Fig. 1.3) are now the most popular and promising devices for several applications such as short range communication, optical disk
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readout head, laser printing, and sensor application [15-17]. For the confinement of optical field, effective refractive index between the oxide aperture and the surrounding semiconductor material can be controlled though the thickness of the oxide aperture and the location relative to the active layer. Additionally, the insulation of silicon oxide of oxide aperture forces the injection current though the aperture, which enhance the wall-plug efficiency [18]. As a result, the oxide aperture VCSELs have advantages on the well define of transverse lasing modes, extremely low threshold current [19], and low cost and high yield production of the oxidization procedure.
For analogously studying the direction emission from a transverse mode of a microcavity by VCSEL, we have to confirm the relation between the transverse mode of a microcavity and the transverse optical filed of VCSELs. The electric field of optical beams obeys the wave equation
(
∇ −2µ ε
0 ∂2∂t2)
Ε(
x y z t, , :)
=0 . According
to the waveguide theory, the electric fields with a predominantly z direction of propagation can be approximated as Ε
(
x y z t, , :)
= Ε( )
x y e, i k z( z −ωt), where kz is the wave vector along z-direction and ω is the angular frequency [20]. Although VCSELs have highly symmetric structure, the existence of anisotropy can break the degeneracy of transverse modes in two orthogonal polarizations, resulting in a split in oscillation frequency. Therefore, total electric field includes the two polarized states can be expressed as frequency in i -polaried state. After separating the z component in the wave equation, we are left with a two-dimensional Helmholtz equation in the two polarized states
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( ) ( )
coordinates. Since the electric field in VCSELs experience total reflection on the lateral walls, transverse optical field at the boundary of cavity can be approximated as( )
, , 0i x y x y∈ℑ
Ε = with i x= or y . Obviously, transverse electric fields of VCSELs are thoroughly equivalent to eigenfunctions of 2D Schrödinger equation with infinity potential well of the same geometry. In other words, the transverse optical fields
( )
,i x y
Ε of VCSELs can be used to analogously investigate the wave functions
( )
x y,y
in two-dimensional (2D) quantum billiard. In our previous works [21], we have confirmed this important theoretical prediction by experiment.6
Fig. 1.1 Schematic diagram of a gain-guided VCSEL with ion implantation regions to confine the injection current as the effective active transverse region [13, Fig. 1.9].
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Fig. 1.2 Schematic diagram of airposted VCSEL (index-guided structure) [14, Fig. 1.].
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Fig. 1.3 Schematic diagram of an index-guided VCSEL with oxide aperture [17, Fig.
6.].
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