We show that nonlinear dynamics in diode lasers with optical injection leads to frequency tunable microwave sidebands which are suitable for atomic physics experiments. We demonstrate the applicability of the sidebands in an experiment where rubidium atoms are magneto-optically trapped with both the trap and the re-pump optical frequencies derived from one optically injected laser. We find linewidth narrowing in the optical spectrum of the injected laser at both the injection frequency and the sideband frequency. With strong optical injection which leads to frequency locking we find a complete linewidth transfer from the master to the slave. Further applications are discussed.High power and narrowband emission are typical prerequisites of continuous wave lasers. Applications in atomic physics such as laser cooling and trapping [1] often require two or more lasers with these qualities. Laser cooling of carefully selected molecules [2] is possible, but several lasers are necessary to close the transitions for efficient cooling. A cost-effective way to produce high power narrowband light is to injection lock a diode slave laser with high power but often poor spectral properties to a narrow linewidth master laser [3]. This technique utilises one of the many nonlinear dynamical states of a diode laser with external optical injection [4]. Recently, another dynamical state in the slave laser, the period one (P1) oscillation limit cycle of undamped relaxation oscillations, has received increasing attention [5][6][7]. Remarkably, the frequency of the P1 oscillation can far exceed the modulation bandwidth of free running diode lasers. As a consequence, optical injection can be used to produce fast modulations in the microwave range of the spectrum even at frequencies not typically covered by standard external modulators.In this letter we report on the general applicability of P1 oscillation dynamics to experiments in atomic physics. We show that by carefully controlling the injection we can produce tunable sidebands. We demonstrate the sideband stability by creating a magneto-optical trap (MOT) with light solely from the optically injected slave laser. We show that the frequencies needed for a MOT can be produced both with weak injection which does not lead to frequency locking of the slave and strong injection with frequency locking on the master laser frequency. We measure the optical spectrum of the slave laser with a heterodyne technique and find that the spectral features at both the injection frequency and at the sidebands frequency are narrower than the free running slave laser. In the frequency locked case we find a complete linewidth transfer from master to slave. The sidebands in the optically injected slave laser can extend to several tens of GHz [5]. We discuss applications of the sideband technique beyond laser cooling of alkalis.In an edge emitting diode laser typical values of the laser gain and cavity decay rates lead to relaxationoscillations in the population inversion and the intensity. The optical spec...