We report the design, fabrication and characterization of oxide-confined large-area rectangular-shaped VCSELs that emit a single higher-order transverse mode. The mode selection mechanism is based on an inverted surface relief. In this method, extra losses are induced by a quarter-wavelength-thick antiphase layer, into which a multi-spot pattern is etched in a single step. The main parameters that control the selected mode, such as the threshold gain and the three-dimensional confinement factor, are calculated as a function of the active aperture dimensions for various structures, patterns, and aspect ratios, aiming to achieve single-higher-order transverse mode emission. Based on the design rules, 850 nm wavelength top-emitting GaAs/AlGaAs VCSELs have been fabricated and characterized. Devices with an aperture area of about 6 x 68 mu m(2) show high output powers of 12 mW in the (8, 1) order mode and differential resistances of only 18 ohms. In addition, the asymmetric transverse cavity can be used to achieve oscillation on a single polarization. Optical manipulation of micro-particles is a promising biophotonic application area for the investigated VCSELs. In an optical tweezers setup, a multi-spot VCSEL is positioned under an angle of about 25 degrees with respect to the fluidic flow direction. Lateral all-optical deflection of flowing 10 mu m diameter polystyrene particles is achieved, which is of particular interest for non-mechanical sorting in a microfluidic chip. With the multi-spot VCSEL, the distance between the intensity spots is 9 mu m, which cannot be easily achieved with conventional linear VCSEL arrays. Trapping and stacking of polystyrene microspheres are also shown.