## 6 All-dielectric-DBR GaN-based VCSELs Using an Atomically Smooth Monolithic Curved Mirror
An atomic force microscopy (AFM) image of the top of the lenslet is shown in Figure 7c. The root mean square roughness of this surface was determined to be 0.2 nm, which is comparable to the value reported for a plane mirror that allowed lasing from a GaN-VCSEL in a prior study [30]. This image also clearly shows atomic steps at the top of the lenslet (inset to Figure 7c), indicating the minimal roughness of this surface. Figure 7d presents a transmission electron microscopy (TEM) image of the cross-section of the curved mirror in this device. Each DBR layer is seen to bend smoothly across the top of the lenslet formed on the GaN, forming a perfect curved mirror. Figure 6: Schematic of a GaN-VCSEL having a curved mirror [16]. Figure 7: (**a**) Laser scanning confocal microscope images and (**b**) cross-sectional profiles of lenslets fabricated on the (000-1) plane of GaN wafers. In (**b**), multiple profiles acquired from specimens having different diameters are overlaid, while the red dashed line is an ideal parabolic curve fitted to one of the plots. (**c**) AFM image of the top of a lenslet fabricated on the (000-1) plane of a GaN substrate. The inset is a high-resolution image of a 1 μm \(\times\) 1 μm area that shows atomic steps on the surface. (**d**) Cross-sectional TEM image of the curved mirror of the device used for an optical pumping test. Figure 8 shows the current-voltage (I-V) and current-optical output (I-L) curves for the GaN-VCSEL device. The I-L curve exhibits a clear threshold at an injected current of 0.25 mA (J\({}_{\text{th}}\) = 3.5 kA/cm\({}^{2}\) for a current aperture diameter of 3 \(\upmu\)m) during CW injection. Figure 9 provides the emission spectrum for the device above the threshold current, which exhibits a dominant peak at a wavelength of 445.3 nm. The width of this spectrum is equivalent to the resolution limit of the analyzer (0.1 nm). The emission spectrum contains multiple peaks and the primary peaks are spaced at intervals of 1.27 nm, as indicated by the filled triangles. This interval corresponds to the mode spacing calculated for a cavity length of 27 \(\upmu\)m when using \(n\) = 2.45, \(\lambda\) = 445.3 nm and _dn/d\(\lambda\)_ = \(-\)0.001 [16]. This result demonstrates that the lasing occurred with multi-longitudinal modes. The dimensional parameters for this device were determined to be L = 27 \(\upmu\)m using scanning electron microscopy (data not shown) and R = 29.1 \(\upmu\)m using confocal laser microscopy. According to classic Gaussian optics theory [16], this cavity had an associated resonant mode with a beam waist (4\(\sigma\)) of 1.3 \(\upmu\)m on the planar mirror. This value is smaller than the current injection diameter of 3 \(\upmu\)m.  
The research described above confirmed the appearance of a near field image and the beam waist matched the theoretically predicted shape, demonstrating that the resonant mode was confined in the  
Figure 8: I-V and I-L curves obtained from a GaN-VCSEL with a 3 \(\upmu\)m aperture at room temperature in response to continuous current injection. The inset shows an enlarged view of the data around the threshold current. Figure 9: Emission spectrum generated by a GaN-VCSEL with a threshold current of 0.25 mA in response to a current injection of 0.30 mA. lateral direction, as predicted by Gaussian optics. Because a small aperture of 1 to 2 \(\upmu\)m in conjunction with a cavity longer than 20 \(\upmu\)m should result in a large diffraction loss (up to approximately 100%) per round trip (see Figure 2a), the previously discussed small threshold current strongly suggests the occurrence of lateral optical confinement in this type of GaN-based VCSEL.