In this paper, new expressions for spot size, radius of curvature, and Rayleigh length of a linearly and negatively chirped Gaussian beam are presented in paraxial approximation self-consistently. It is shown that there is a slight modification in those relations in comparison to that of used in literatures. These modifications change the tailored parameters in some laser beam interactions such as laser electron vacuum acceleration. At propagation distances much grater than the Rayleigh length, the modifications indicate that the temporal shape of the chirped laser beam will be changed. This effect indicates an asymmetric pulse with a slowly increasing front part and a suddenly dropping tail. For propagation distances less than the Rayleigh length, the change in laser pulse shape is not considerable. Finally, the modifications are employed in modeling of a single electron acceleration by the chirped Gaussian laser pulse.

In this paper, we propose and apply two novel schemes of multi-band carrierless amplitude and phase (m-CAP) modulation for spatial modulation (SM) based visible light communications (VLC) systems. In SM, both spatial and signal constellation are utilised to improve the performance of the m-CAP system. Here, we have adopted the non-DC m-CAP which is a power efficient technique with no DC-bias. The bit error rate (BER) performance and the spectral efficiency of the proposed systems are compared with single-input single-output (SISO) and multiplexing multiple-input multiple-output (MIMO) m-CAP systems. Results demonstrate that non-DC m-CAP, with the same spectral efficiency as that of SISO m-CAP, outperforms other schemes in terms of BER due to its power efficiency, however a higher spectral efficiency can be achieved by the SM-MIMO m-CAP scheme.

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