Two-window heterodyne methods to characterize light fields

In this dissertation, I develop a novel Two-Window heterodyne technique for measuring the time-resolved Wigner function of light fields, which allows their complete characterization. A Wigner function is a quasi-probability density that describes the transverse position and transverse momentum of a light field and is Fourier-transform related to its mutual coherence function. It obeys rigorous transport equations and therefore provides an ideal way to characterize a light field and its propagation through various media. I first present the experimental setup of our Two-Window technique, which is based on a heterodyne scheme involving two phase-coupled Local Oscillator beams we call the Dual-LO. The Dual-LO consists of a focused beam (‘SLO’) which sets the spatial resolution, and a collimated beam (‘BLO’) which sets the momental resolution. The resolution in transverse position and transverse momentum can be adjusted individually by the size of the SLO and BLO, which enables a measurement resolution surpassing the uncertainty principle associated with Fourier-transform pairs which limits the resolution when just a single LO is used. We first use our technique to determine the beam size, transverse coherence length and radius of curvature of a Gaussian-Schell beam, as well as its longitudinal characteristics, which are related to its optical spectrum. We then examine Enhanced Backscattering at various path-lengths in the turbid medium. For the first time ever, we demonstrate the phase-conjugating properties of a turbid medium by observing the change in sign of the radius of curvature for a non-collimated field incident on the medium. We also perform time-resolved measurements in the transmission regime. In tenuous media we observe two peaks in phase-space confined by a hyperbola which are due to low-order scattering. Their distance depends on the chosen path-delay. Some coherence and even spatial properties of the incident field are preserved in those peaks as measurements with our Two-Window technique show. Various other applications are presented in less detail, such as the Wigner function of the field inside a speckle produced by a piece of glass containing air bubbles.