OWLS is a method for detecting interfacial adsorption based on the guided light modes excited in a planar, dielectric waveguide sandwiched between media of lower refractive index (Ramsden 1993; Voros et al. 2002). The OWLS detection mechanism may be understood through a four-layer model, consisting of a glass support (S), a waveguiding film (F), a second film (F'), and a cover solution (C)(Brusatori and Van Tassel 2003; Tiefenthaler and Lukosz 1989). In what follows, the F' layer may represent an adsorbed layer or a second layer to a two-layer waveguiding film. A polarized laser beam of wavelength A is directed through the glass support toward an optical grating at the FF'C interface at an angle a. The corresponding effective refractive index (N) is:
where nF is the film's refractive index, 0F is the propagation angle within the film, nair is the refractive index of air, £ is the diffraction order of the grating, and A is the grating period. The condition under which coherent propagation occurs in the direction parallel to the film is:
where kz,F is the component of the wave vector normal to the waveguiding film, dF is the thickness of the waveguiding film, ^F,S and F, C are the phase shifts associated with the reflections at the F,S and the F,F',C interfaces, respectively, and the integer m is the mode number.
The phase shift at a given interface is related to its reflection coefficient via r = \r\elf. For a simple interface between films a and ft, kz,a kzft na nft raft = T-^ (14)
where a, ft = F, F', or C, na is the refractive index of film a, and kza is the component of the wave vector normal to the film a:
where is the propagation angle in the a film (by Snell's law, cos = [1 -N2/Re(na)2]1/2 is the real part of na. In Eq. 14, p = 0 or 1 for electric field vectors oriented normal (transverse electric, or TE) or parallel (transverse magnetic, or TM) to the plane of incidence, respectively. The reflection coefficient across the F,F',C interface is:
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