Journal of Physical Chemistry A, Vol.103, No.49, 10619-10629, 1999
Femtosecond heterodyne-detected four-wave-mixing studies of deterministic protein motions. II. Theory and experimental technique of diffractive optics-based spectroscopy
Analytic relations are developed to describe the coupling between experimentally observed optically heterodyne-detected (OHD) transient grating (TG) signals and the underlying molecular dynamics of heme proteins. The heterodyne detection was implemented using a diffractive optical element to generate the phase-matched beam pattern along with a reference beam for OHD. The phase stability between the reference and signal fields using this approach is shown to be excellent over several hours of signal collection. Under small signal conditions this leads to an enhancement in signal-to-noise of several orders of magnitude. The grating excitation provides an inherent acoustic reference that can be used to determine the absolute signal phase. This enables separation of the real and imaginary components to the nonlinear susceptibility as well as determination of both the absorption anisotropy and its real counterpart, the phase anisotropy. The relationship between the phase anisotropy and the observed OHD TG signals is expressed in terms of the complex molecular polarizability specific to heme proteins but can be readily extended to all other systems. Access to the material anisotropy provides a direct probe of mode selective coupling in proteins, i.e., the nonuniform displacements determined by the underlying asymmetric protein structure.