  We have analyzed spectra of localized microwave transmitted through quasi-1D
random samples to obtain the central frequency, linewidth and field speckle
pattern of the modes for an ensemble of samples at three lengths. We find
strong correlation between modal field speckle patterns. This leads to
destructive interference between modes which explain strong suppression of
steady state transmission and of pulsed transmission at early times. We have
also studied the statistics of mode spacings and widths in localized samples.
The distribution of mode spacings between adjacent modes is close to the Wigner
surmise predicted for diffusive waves, which exhibit strong level repulsion.
However, a deviation from Wigner distribution can be seen in the distribution
of spacings beyond the nearest ones. A weakening in the rigidity of the modal
spectrum is also observed as the sample length increases because of reduced
level repulsion for more strongly localized waves. In contrast to residual
diffusive behavior for level spacing statistics, the distribution of level
widths are log-normal as predicted for localized waves. We also measured the
steady state and dynamic fluctuations and correlation of localized wave
transmitted through random waveguides. We find the degree of intensity
correlation first increases, and then decays with time delay, before increasing
dramatically. The variation in the spatial correlation of intensity with time
delay is due to the changing effective number of modes that contribute to
transmission. A minimum in correlation is reached when the number of modes
contributing appreciably to transmission peaks. At long times, the degree of
intensity correlation and the variance of total transmission increase
dramatically. This reflects the reduced role of short-lived states and the
growing weight of long-lived modes.
