Heterodyne and homodyne detection in fluctuating smectic membranes by photon correlation spectroscopy at X-ray and visible wavelengths

We discuss heterodyne and homodyne detection in photon correlation spectroscopy (PCS) performed at X-ray and visible wavelengths. Fluctuating smectic membranes in a reflection geometry have been used as model systems. At X-ray wavelength (XPCS), under specular conditions a strong elastic signal is present that acts as a time-independent internal reference source. This leads to a transition from heterodyne detection at the specular ridge to homodyne detection off-specular giving rise to a difference in relaxation time of a factor 2. In addition by comparing similar propagating modes at the specular ridge (XPCS) and at off-specular positions (PCS with visible light), cos-like and cos2-like oscillations have been observed as expected for heterodyne and homodyne mixing, respectively.