Abstract: For the first time we show that optical diffraction is a wavelet transform with the electromagnetic wavelets, which are reduced to Hyugens' wavelets by a temporal. Fourier analysis in the case of monochromatic field. We define the non-diffracting electromagnetic wavelet by integrating a subset of the electromagnetic wavelets. A non-diffracting field can be constructed by a linear combination of the non- diffracting electromagnetic wavelets, which are the one-side windowed Fourier transform of the Bessel beams with a temporal frequency window and are spatially localized in the lateral direction, translated in the propagation direction and scaled in the time and the temporal frequency.!3
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