Binding between optically co-trapped micro-particles occurs when the scattered optical fields are sufficient to compete with the trapping forces. Such optical binding is seen as being pertinent to large-scale micro-manipulation due to the significant forces present within an optical trapping system comprising multiple micro-particles. One aspect of optical binding involves an inter-particle force relationship that is strongly dependent on optical frequency. In our study we theoretically show that a broadened spectral content associated with frequency doubled broadband ultrashort pulses can result in spatial overlap of contained frequencies. The binding force oscillations are averaged out when sufficient spectral content is present within the pulse.