## 6 All-dielectric-DBR GaN-based VCSELs Using an Atomically Smooth Monolithic Curved Mirror  
As discussed in Section 4, one approach to overcoming potential problems associated with all-dielectric DBR VCSELs is to introduce lateral optical confinement, which allows the use of relatively long cavities (greater than 10 \(\upmu\)m) with no diffraction loss. There have been a few studies on this topic regarding GaN-VCSELs. [PERSON] et al. simulated the effect of lateral optical confinement by step-like lateral structures on the internal losses of GaN-VCSELs [27]. In addition, [PERSON] et al. experimentally demonstrated one of those structures and found that the multi-lateral-mode of the device provided evidence for lateral optical guiding [21]. [PERSON] et al. reported improved slope efficiency in the case of a device incorporating a mesa structure [22], which confirmed the effect of lateral optical confinement of the cavity. However, those step-like lateral structures also induced scattering losses. For this reason, the authors of the present review proposed a GaN-VCSEL having a cavity with a graded lateral structure instead of a mesa structure. Resonators cladded with curved and plane mirrors are known to form stable cavities without diffraction and scattering losses, in association with the generation of a beam waist on the plane mirror [28]. Thus, the introduction of curved mirrors on one side of the VCSEL may allow for longer cavities that would help to relax the strict processing requirements during polishing that have prevented GaN-VCSELs from being mass produced. The first experimental result based on this concept was reported following work with GaN-VCSELs by [PERSON] et al. [29], who investigated the optical pumping of devices having 50-\(\upmu\)m-long cavities with plane and curved end mirrors. InGaN quantum wells were grown epitaxially on the (0001) plane of a sapphire template (t = 50 \(\upmu\)m) to fabricate these devices and a monolithic curved mirror was generated on the (000-1) plane of the template using ball-up resin patterns as sacrificial masks during the reactive ion etching of the sapphire. However, this study only demonstrated laser operation in conjunction with optical pumping. The author's group investigated lasing as a result of current injection into VCSELs with a similar structure, in which InGaN wells were grown epitaxially on (0001) GaN substrates and a curved mirror was fabricated on (000-1) GaN rather than on sapphire substrates (see Figure 6) [16]. These devices were fabricated by growing three InGaN/GaN MQWs via MOCVD, a p-GaN layer doped with Mg (approximately 1 \(\times\) 10\({}^{19}\) cm\({}^{-3}\)) and a contact layer doped with Mg (approximately 1 \(\times\) 10\({}^{20}\) cm\({}^{-3}\)), to a total thickness of 105 nm, on a (0001) GaN substrate. A 20-nm-thick ITO layer and a p-side DBR with 11.5 Ta\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) bilayers were deposited on the contact layer. A hole was etched next to the aperture, reaching the n-GaN layer and two Ti/Pt/Au electrodes were deposited so that they made contact with the ITO layer and the exposed n-GaN, respectively, to form a current path. A circular current injection region was electrically confined by boron implantation, leaving a current aperture with a diameter of 3 \(\upmu\)m that was in contact with the ITO and one Ti/Pt/Au electrode to form an emitter. The remaining processing steps during fabrication of the curved mirror were similar to those used in [PERSON] research. That is, ball-up resin patterns were employed as sacrificial masks during reactive ion etching of the GaN substrate. Figure 7a,b show laser confocal microscopy images of a lenslet fabricated on the (000-1) plane of a GaN substrate fabricated through these procedures. The top and bird's-eye views in Figure 7a both demonstrate the smooth droplet shape that was formed. In the cross-sectional analysis (Figure 7b), an ideal parabolic curve has been overlaid on the experimentally determined cross-sections.