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We present the design and fabrication of an optically pumped vertical-external-cavity surface-emitting lasers with double-well resonant periodic gain structure. Each double-well consists of two 4-nm-thick InGaAs strained quantum wells. The double-well provides optimum overlap between the quantum wells and the antinodes of the standing wave of laser signal at high-power and high-temperature operation. The structure is more tolerant to variation of the growth, processing, and operating temperature for maintaining high modal gain. For a 230-μm diameter pump spot, over 4-W continuous-wave output with a slope efficiency of 39% is demonstrated at 30°C without thermal rollover.