## 4 Conclusions  
In conclusion, we have demonstrated a blue GaN-based VCSEL featuring a SiO\({}_{2}\)-buried LOC structure, in which the reflectivity can be tuned by varying the AlInN/GaN DBR. Without the LOC structure, a conventional GaN-based VCSEL exhibits an extremely high transverse radiation loss, shown by internal loss measurements. The internal loss was significantly reduced by introducing the SiO\({}_{2}\)-buried LOC configuration. This decrease in the internal loss, combined with an adjustment of the  
Figure 9: **(a)** I-L characteristics of the 5\(\uplambda\)- and 10\(\uplambda\)-cavity VCSELs with 5.5-\(\upmu\)m aperture under CW operation at 20 \({}^{\circ}\)C. **(b)** Full width at half maximum (FWHM) of far field pattern (FFP) of the 5\(\uplambda\)- and 10-\(\uplambda\) cavity VCSELs with 5.5-\(\upmu\)m aperture as a function of light output power. The insets show the FFP images at around 1 mW and 5 mW.  
cavity mirror reflectivity, resulted in the highest slope efficiency value so far recorded of 0.87 W/A and the highest \(\eta_{d}\)\({}^{total}\) of 32% under pulsed operation, in addition to a maximum output power of 6 mW under CW operation. It is evident that controlling the cavity mirror and lowering the internal loss are both important with regard to increasing external differential quantum efficiency, slope efficiency and output power. On this basis, the present study obtained output power values of 15.7 and 2.7 mW at 20 and 110 \({}^{\circ}\)C, respectively. These represent the highest power values reported to date for a blue VCSEL based on GaN, and were achieved by reducing the reflectivity of the front cavity mirror to 99.1% while incorporating a long (10\(\lambda\)) structure. The thermal resistance of the device relative to that of a 5\(\lambda\) analogue was lowered from 1100 to 710 K/W, and these VCSELs were found to exhibit an elevated internal temperature of 434 K at their rollover point. Tuning the front mirror reflectivity in conjunction with these other modifications improved the device performance, giving an 8.9% wall-plug efficiency, 31% differential efficiency and an output power of 15.7 mW at 20 \({}^{\circ}\)C. In transverse mode control, the 10\(\lambda\)-cavity VCSEL with a 5.5-\(\mu\)m aperture exhibited a very narrow divergence beam of around 5\({}^{\circ}\) even at around 5 mW output power. These technologies and their superior performances may open the door to the practical use of VCSEL eyewear display. In a future study, we will investigate a W-class high-power VCSEL array in the blue wavelength range, with potential use in highly functional automotive headlamps.  
Conceptualization and device design, M.K.; epitaxial growth, T.A. and K.T. ([PERSON]); fabrication process, S.K. and K.T. ([PERSON]); measurement and evaluation, M.K. and K.T. ([PERSON]); project administration, T.S.; supervision, T.T.; writing and original draft preparation, M.K.; writing, review and editing, T.T. and M.K.  
This research received no external funding.  
The authors thank [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] for their support during fabrication of the device and for helpful discussions. We also thank [PERSON] and [PERSON] for their encouragement during this work.  
The authors declare no conflict of interest.