  The extraordinary concept of weak value amplification and a number of other
seemingly counter-intuitive wave phenomena are manifestations of fine
interference effects. Taking example of one such intriguing wave interference
phenomenon, namely, optical Fano resonance, we show that weak value
amplification naturally arises in such scenario due to near destructive
spectral interference between a continuum mode and a narrow resonance mode
which mimics the corresponding near destructive interference between the
eigenstates of the measuring observable as a consequence of nearly mutually
orthogonal pre and post selections of the system states. In order to elucidate
this, we first experimentally demonstrate a weak measurement concept that uses
near destructive interference of two paths of an interferometer having slightly
rotated linear polarization states of light. By generating nearly destructive
interference between the two paths with small amplitude and phase offsets of
the waves, we observe both real and imaginary (respectively) weak value
amplification of the small polarization rotation leading to large rotation of
the polarization vector orientation and dramatic changes in the circular
polarization descriptor 4th Stokes vector element of light, respectively. We go
on to demonstrate that the giant enhancement of small Faraday rotation in the
vicinity of the Fano spectral dip in waveguided magneto-plasmonic crystal is a
manifestation of such natural interferometric weak value amplification.
