Irradiance variance for convergent Gaussian beams using nondimensional beam parameters

摘要

The longitudinal and radial irradiance variance for a convergent Gaussian beam is examined in terms of two pairs of nondimensional beam parameters, the first pair approximately ega $EQ $lambda@L/$pi@W$-o$/$+2$/ and approximately ega$-o$/ $EQ 1 $MIN L/R$-o$/ associated with the beam when transmitted, and the second pair given by $Lambda $EQ $lambda@L/$pi@W$+2$/ and $Theta $EQ 1 $PLU L/R associated with the received beam. Here, $lambda is wavelength, L is path length, R$-o$/ and R are radii of curvature of the phase front at the transmitter and receiver, respectively, and W$-o$/ and W are the beam radii at the transmitter and receiver. With the addition of $lambda and L, either of these beam parameter pairs completely characterizes the diffractive propagation environment for a lowest-order paraxial Gaussian beam, and is fundamental in the analytic expression of the irradiance variance. Special attention is paid to differences between the perfectly focused beam and the nearly focused beam. We also show that every beam has a convergent counterpart with identical diffractive irradiance behavior at the receiver, but decreased irradiance variance.