Measurement of the Depression of the Velocity of Focused Beams of Light with a Gouy-Phase Interferometer

An apparatus is demonstrated that was constructed to show the depression in group velocity $v_g $ of a focused Gaussian (HeNe laser) beam, and arguments presented for the effects of this demonstration on the theoretical basis of Special Relativity. An exploration is conducted of Einstein's theoretical underpinnings for Special Relativity, that light pulses travel at a fixed group velocity $v_g =c$. This is accompanied by theoretical proof that $v_g $ for a focused Gaussian beam is depressed upon focusing, if the beam has a frequency-independent radius, related to the Gouy phase shift. An account of the operation of the apparatus is presented, and data from the operations related, verifying the change in $v_g $. This contradiction of Einstein's assumption, without effect on the experimental validity of Special Relativity, is reconciled by referring to Poincar\'{e}'s derivation of Special Relativity's equations, which assumes simply that Maxwell's equations retain their form across inertial reference frames.