Overlapping orders

If we have a two-level sample we expect to see a series of resonances separated by half the inverse of the repetition rate of the laser as the carrier frequency is scanned. If a second transition is within the bandwidth of the laser then this too will give rise to a series of resonances. The resulting spectrum is rather like that obtained from a Fabry-Perot interferometer with overlapping orders. However, in the mode-locked case the modes are precisely equally spaced in frequency. 

Because of small imperfections and the finite size of the circular aperture the practically achievable resolution is frequently reduced. Because of its high resolution the Fabry-Perot interferometer has been much used for measuring hyperfine structure and isotope shifts. The spectral line of interest is then first selected by a monochromator or an interference filter. First, a free spectral range of sufficient width to accomodate all the spectral components of the line is chosen to allow the correct order of components to be determined. Then the plates are moved fiurther apart, resulting in an increased resolution but also the mclusion of overlapping orders. 

The grating instrument is not without its problems. Until recently, gratings were very expensive and very scarce. With new replica techniques, this problem has been considerably reduced. Another problem is overlapping orders i.e., at the exit slit would be found X cm" along with 2x, 3a , 4x, ... cm To cancel out the unwanted wavelengths, some form of order sorting must be employed. Two methods are commonly used. 

Another, less costly, unique alternative is the introduction of an angular overlap order parameter. Before we define it, let us first discuss the characteristic features of free-energy landscape parametrized by angular degrees of freedom. 

Such a variant is the angular overlap order parameter [46,47,189,195,196]. It is based on the idea of defining a simple and computationally low-cost measure for the similarity of two conformations, where the differences of the angular degrees of freedom are calculated. We define the overlap parameter as follows ... 

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