A vertical cavity surface emitting laser (VCSEL) in which a higher order lasing mode produces a Gaussian-like single mode far field beam intensity pattern. Such a VCSEL includes a protective surface deposition on a VCSEL structure, and phase filter elements on the surface deposition. The surface deposition and the phase filter elements implement an optical phase filter that induces optical path difference such that a single mode far field beam intensity pattern results when the VCSEL operates in a higher order lasing mode. The VCSEL can include structures that enhance a selected higher-order operating mode and/or that suppress unwanted operating modes.