## 3 High-Power and Narrow Divergent Beam Performance Using a Long Cavity Structure
A maximum output power of 8.2 mW at 20 \({}^{\circ}\)C and a 20 mA operating current are seen in Figure 6a, and these results are attributed to the differential quantum efficiency (\(\eta_{d}\)) of 25.4% and the significant slope efficiency (\(\eta_{s}\)) of 0.71 W/A. Thermal rollover limited the maximum output power obtainable from the VCSEL, while the maximum output power and rollover operating current were both decreased as the heat sink temperature was increased. Therefore, it was anticipated that reducing the thermal resistance would result in a relatively high rollover current and thus provide an enhanced output power over a significant range of temperatures. The I-L/I-V data acquired from the 10-\(\lambda\) cavity VCSEL from 20 to 110 \({}^{\circ}\)C are summarized in Figure 6b. These data demonstrate that the rollover operating current and maximum output power were both greatly increased as a result of this structure. An \(\eta_{s}\) value of 0.87 W/A together with an increased \(\eta_{d}\) of 31% and an elevated output power of 15.7 mW were observed at 20 \({}^{\circ}\)C. The threshold voltage, threshold current density and threshold current at 20 \({}^{\circ}\)C were 5.1 V, 9.0 kA/cm\({}^{2}\) and 4.5 mA, respectively. Relative to the 5\(\lambda\)-cavity analogue, a much higher rollover operating current was obtained (20 vs. 29 mA at 20 \({}^{\circ}\)C). This result can likely be ascribed to a lowering of the thermal resistance, together with a higher slope efficiency stemming from the reduced front mirror reflectivity [20]. Figure 6: (a) I-L/I-V characteristics of the VCSEL having a 5-\(\lambda\) cavity structure over a temperature range from 20 to 100 \({}^{\circ}\)C. (b) I-L/I-V characteristics of the VCSEL having a 10-\(\lambda\) cavity structure over the temperature range from 20 to 110 \({}^{\circ}\)C.  
Consequently, the light output power was close to double the original value at 20 \({}^{\circ}\)C. The 10-\(\lambda\) cavity device showed a maximum wall-plug efficiency of 8.9% at 20 \({}^{\circ}\)C together with an elevated lasing temperature of 110 \({}^{\circ}\)C at an output power of 2.7 mW (see Figure 6b). This operating temperature together with a differential quantum efficiency of 31% and output power of 15.7 mW are, to our knowledge, the best results yet obtained from a GaN-based VCSEL in the CW mode. The emission spectra acquired at current injection levels of \(0.9l_{th}\), \(0.95l_{th}\), \(l_{th}\) and \(1.05l_{th}\) from the VCSELs with both cavity structures are presented in Figure 7a,b. A significant increase in the peak intensities once a threshold value is exceeded is apparent in both figures. During CW operation at 20 \({}^{\circ}\)C, the 5-\(\lambda\) and 10-\(\lambda\) cavity structures generated narrow 0.08 nm lasing linewidths at 443.5 and 440.1 nm, respectively. Incorporating a long cavity structure lowered the thermal resistance, and this effect was assessed by monitoring the thermal resistance (\(R_{th}\)) values. These values were obtained from experimental data via the equation:  
\[R_{th}=\frac{\Delta T}{\Delta P_{diss}}=\frac{\frac{\Delta\lambda}{\Delta T_{ diss}}}{\frac{\Delta\lambda}{\Delta T_{hs}}}, \tag{4}\]  
where \(\Delta\lambda/\Delta P_{diss}\) is the wavelength shift over the power dissipation value and \(\Delta\lambda/\Delta T_{hs}\) is the wavelength shift over the variation in the heat sink temperature [34; 35; 36; 37]. \(\Delta\lambda/\Delta T_{hs}\) values from 0.012 to 0.0185 nm/K have been previously reported for these types of devices [34; 35; 37; 38]. Herein, thermal effects were negated by obtaining the \(\Delta\lambda/\Delta T_{hs}\) data in conjunction with pulsed operation, and the 5\(\lambda\)- and 10\(\lambda\)-cavity devices were determined to have values of 0.0142 and 0.0146 nm/K, respectively, which are in agreement with previously reported data. These same two VCSELs were found to have \(\Delta\lambda/\Delta P_{diss}\) values of 0.015 and 0.0103 nm/mW, respectively, and \(R_{th}\) values of 1100 and 710 K/W were calculated based on Equation (4).