We show that by breaking the symmetry of a beam subjected to tight focusing, namely by obscuring half of it or, equivalently, shifting the beam away from the lens axis, it is possible to obtain novel light properties in the focal spot which, to the best of our knowledge, have not been observed before. For example, a linearly polarized beam half-obstructed or shifted from the axis generates longitudinal and transverse electrical field components, both of which peak on-axis. The ratio of the intensities of these two components can be tuned by changing the shift distance, the size, and the azimuthal location of the displaced incoming beam. Moreover, such symmetry breaking of a linearly polarized beam acts as a catalyst for producing distributions of circular polarization/longitudinal spin angular momentum, as well as orbital angular momentum, in the focal plane. The simple method for generating co-incident longitudinal and transverse components with a controllable ratio may find applications in laser machining, particle manipulation, etc.