## 3 High-Power and Narrow Divergent Beam Performance Using a Long Cavity Structure  
The data in Figure 4(a) demonstrate that thermal rollover limited the maximum output power, meaning that it is vital to lower the thermal resistance (\(R_{th}\)) to increase output power. Figure 4(b) shows the structure having a 10.5-pair SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) DBR, 4.5\(\lambda\) cavity and 42-pair AlInN/GaN DBR, which was found to generate the highest output power. Because the DBR materials in this device, such as AlInN, have comparatively low thermal conductivities [29; 30], while GaN (the primary cavity material) possesses significant thermal conductivity [31; 32], \(R_{th}\) is expected to be reduced as a result of implementing a long-cavity structure [33; 34; 35]. A previous theoretical study by [PERSON] et al. [35] assessed the effect of cavity length on \(R_{th}\) in the case of a VCSEL based on GaN and having an AlInN/GaN DBR. This prior work employed a cylindrical model and estimated that a longer cavity would result in a 43% decrease in \(R_{th}\). Similarly, the present section demonstrates that incorporating a long cavity (of 10\(\lambda\)) results in the fabrication of a blue VCSEL based on GaN that exhibits a greater output power of 15.7 mW. A 5\(\lambda\)-cavity VCSEL was also fabricated so as to compare the I-L data from the two different devices at various thermal resistance values and temperatures. The far field pattern (FFP) narrow divergent angle was also assessed to evaluate the effect of adding the long cavity. The 5\(\lambda\)- and 10\(\lambda\)-cavity devices comprised a 10.5-pair SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) DBR, 5\(\lambda\) or 10\(\lambda\) cavity and 42 or 41-pair AlInN/GaN DBR. As discussed in Section 2, the AlInN/GaN DBR mirror reflectivity in the 10\(\lambda\)-cavity VCSEL was lowered to offset any reduction in the slope efficiency stemming from the  
Figure 5: I-L/I-V characteristics (**a**) and emission spectrum (**b**) of the fabricated GaN-based VCSELs with 42 (solid line), 44 (dashed line), and 46 (dotted line) AlInN/GaN DBR pairs during CW operation at room temperature. long cavity configuration. It should also be noted that, between the DBRs, the epitaxial structure was essentially identical to that shown in Figure 2b, and that the thicknesses of the n-GaN layers in the 5\(\lambda\)- and 10\(\lambda\)-cavity VCSELs were 660 and 1570 nm, respectively. A 20 nm thick SiO\({}_{2}\)-buried structure was also incorporated into each device as a means of lowering the internal loss (see Figure 4). As described above (in Equation (2)), the AlInN/GaN DBR reflectivity values were calculated as the ratio of the front slope efficiency to the rear slope efficiency. The 41-pair and 42-pair AlInN/GaN DBRs were found to have reflectivities of 99.1% and 99.3%, respectively. Prior to testing, each 8 \(\upmu\)m aperture VCSEL was bonded to a heat sink made of Cu with its p-side facing downwards (equivalent to flip-chip bonding) and tests were performed in conjunction with CW conditions. The I-L/I-V data obtained from a 5\(\lambda\)-cavity VCSEL between heat-sink temperatures of 20 and 100 \({}^{\circ}\)C are presented in Figure 6a. The VCSEL showed high temperature lasing to a temperature of 100 \({}^{\circ}\)C, in conjunction with a threshold voltage, threshold current density and threshold current (\(I_{th}\)) at 20 \({}^{\circ}\)C of 5.1 V, 8.4 kA/cm\({}^{2}\) and 4.2 mA, respectively. This \(I_{th}\) is somewhat greater than the value in Figure 5a as a result of the increased front mirror loss that, in turn, stemmed from the decreased front mirror reflectivity. A combination of high efficiency and enhanced output power was obtained by lowering the front mirror reflectivity, although it should be noted that this raised the threshold current.