Slepian developed the prolate spheroidal wavefunction (PSW) spatial-mode basis, which forms the normal modes of the Fresnel-propagation kernel of a free-space optical communications channel bookended by hard-circular apertures. The zero-th-order PSW mode exhibits the highest power-transfer eigenvalue, thereby maximizing transmissivity for single-spatial-mode communications [ Bell Syst. Tech. J. 43 , 3009 ( 1964 ) BSTJAN 0005-8580 10.1002/j.1538-7305.1964.tb01037.x , J. Opt. Soc. Am. 55 , 1110 ( 1965 ) 10.1364/JOSA.55.001110 ]. We show that the transmissivity performance of this fundamental PSW mode can be obtained by an aperture-truncated Gaussian beam of an optimized beam waist, despite the two mode shapes deviating from one another in the near-field regime.
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