  We theoretically study the low energy electromagnetic response of BCS type
superconductors focusing on propagating collective modes that are observable
with THz near field optics. The interesting frequency and momentum range is
$\omega < 2\Delta$ and $q < 1/\xi$ where $\Delta$ is the gap and $\xi$ is the
coherence length. We show that it is possible to observe the superfluid
plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes and
Carlson-Goldman modes using THz near field technique, although none of these
modes couple linearly to far field radiation. Coupling of THz near field
radiation to the amplitude mode requires particle-hole symmetry breaking while
coupling to the Bardasis-Schrieffer mode does not and is typically stronger.
For parameters appropriate to layered superconductors of current interest, the
Carlson-Goldman mode appears in the near field reflection coefficient as a weak
feature in the sub-THz frequency range. In a system of two superconducting
layers with nanometer scale separation, an acoustic phase mode appears as the
antisymmetric density fluctuation mode of the system. This mode produces well
defined resonance peaks in the near-field THz response and has strong
anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their
response. In a slab consisting of many layers of quasi-two dimensional
superconductors, realized for example in samples of high T$_c$ cuprate
compounds, many branches of propagating Josephson plasmon modes are found to
couple to the THz near field radiation.
