  We construct the three dimensional mirror theory of SO(2k) and SO(2k+1) gauge
groups by using O3-planes. An essential ingredient in constructing the mirror
is the splitting of a physical brane (NS-brane or D5-brane) on O3-planes. In
particular, matching the dimensions of moduli spaces of mirror pair (for
example, the SO(2k+1) and its mirror) there is a D3-brane creation or
annihilation accompanying the splitting. This novel dynamical process gives a
nontrivial prediction for strongly coupled field theories, which will be very
interesting to check by Seiberg-Witten curves. Furthermore, applying the same
idea, we revisit the mirror theory of Sp(k) gauge group and find new mirrors
which differ from previously known results. Our new result for Sp(k) gives
another example to a previously observed fact, which shows that different
theories can be mirror to the same theory. We also discussed the phenomena such
as "hidden FI-parameters" when the number of flavors and the rank of the gauge
group satisfy certain relations, ``incomplete Higgsing'' for the mirror of
SO(2k+1) and the ``hidden global symmetry''. After discussing the mirror for a
single Sp or SO gauge group, we extend the study to a product of two gauge
groups in two different models, namely the elliptic and the non-elliptic
models.
