A widely-tunable single-mode 1.3 mu m vertical-cavity surface-emitting laser structure incorporating a microelectromechanical system-tunable high-index-contrast subwavelength grating (HCG) mirror is suggested and numerically investigated. A linear tuning range of 100 nm and a wavelength tuning efficiency of 0.203 are predicted. The large tuning range and efficiency are attributed to the incorporation of the tuning air gap as part of the optical cavity and to the use of a short cavity structure. The short cavity length can be achieved by employing a HCG design of which the reflection mechanism does not rely on resonant coupling. The absence of resonance coupling leads to a 0.59 lambda-thick penetration depth of the HCG and enables to use a 0.25 lambda-thick tuning air gap underneath the HCG. This considerably reduces the effective cavity length, leading to larger tuning range and efficiency. The basic properties of this new structure are analyzed, and shown to be explained by analytical expressions that are derived in the paper. In this context, the penetration depth of the HCG is introduced and shown to be an important characteristic length scale. Throughout the tuning wavelength range, strong single mode operation was maintained and uniform output power is expected.