Spatial correlation properties and the spectral intensity distributions of focused Gaussian Schell-model array beams

The spatial correlation properties and the spectral intensity distributions of focused Gaussian Schell-model (GSM) array beams are studied in detail. The closed-form expressions for the spectral degree of coherence and the spectral intensity of focused GSM array beams are derived. It is shown that the spectral degree of coherence of focused GSM array beams is the same as that of focused GSM beams in the focal plane. On the other hand, it is found that, in the focal plane the spectral intensity distribution of focused GSM array beams is the fringe pattern when the value of the coherence length is small. However, it becomes one peak located at the center as the value of the coherence length is large enough. In the focal plane, the spectral intensity maximum increases and the width of the normalized spectral intensity distribution decreases as the beam number increases. In general, for GSM array beams, the width of the modulus of the spectral degree of coherence in the focal plane always exceeds that of the normalized spectral intensity distribution, which is different from the behavior of focused GSM beams. In addition, the power in the bucket (PIB) and the beam propagation factor (M2 factor) are also discussed. The main results are explained physically.