  Implanting fully polarized low energy muons on the nanometer scale beneath
the surface of a superconductor in the Meissner state enabled us to probe the
evanescent magnetic field profile B(z)(0<z<=200nm measured from the surface).
All the investigated samples [Nb: kappa \simeq 0.7(2), Pb: kappa \simeq 0.6(1),
Ta: kappa \simeq 0.5(2)] show clear deviations from the simple exponential B(z)
expected in the London limit, thus revealing the non-local response of these
superconductors. From a quantitative analysis within the Pippard and BCS models
the London penetration depth lambda_L is extracted. In the case of Pb also the
clean limit coherence length xi0 is obtained. Furthermore we find that the
temperature dependence of the magnetic penetration depth follows closely the
two-fluid expectation 1/lambda^2 \propto 1-(T/T_c)^4. While B(z) for Nb and Pb
are rather well described within the Pippard and BCS models, for Ta this is
only true to a lesser degree. We attribute this discrepancy to the fact that
the superfluid density is decreased by approaching the surface on a length
scale xi0. This effect, which is not taken self-consistently into account in
the mentioned models, should be more pronounced in the lowest kappa regime
consistently with our findings.
