A semiconductor laser under external optical injection exhibits a wide range of nonlinear dynamics [1] and it is known that injection into multimode lasers leads to complex dynamics between the modes [2]. Here we report on orthogonal optical injection into a 1550 nm vertical-cavity surface-emitting laser (VCSEL) that exhibits two modes corresponding to the orthogonal polarisations of the fundamental transverse mode of the device. We show, for the first time to our knowledge, an analysis of the time series of simultaneously-measured orthogonal polarisations of the fundamental mode.