Difference between revisions of "Reflectivity oscillations below critical angle"
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| − | In [[reflectivity]] experiments, when the angle of incidence is below the [[critical angle]], the beam experiences [[total external reflection]]. | + | In [[reflectivity]] experiments, when the angle of incidence is below the [[critical angle]], the beam experiences [[total external reflection]]. Thus, the reflectivity goes to 100% (<math>\scriptstyle R =1 </math>) for any <math>\scriptstyle \theta \lt \theta_c</math>, or for <math>\scriptstyle q \lt q_c</math>. |
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| + | However, one sometimes sees oscillations of the reflectivity even below this angle (especially in [[x-ray]] reflectivity, though it is also possible in neutron reflectivity). These oscillations can be thought of as [[waveguide]] modes appearing while the reflectivity angle is in between the critical angle of the substrate, and the critical angle of the film. Notably, these variations are only visible (in reflectivity) due to the non-zero absorption of the film. However, even a very small absorption can be measured, because the waveguide modes inherently travel through the film many times. | ||
[[Image:Reflectivity example-real density.png|thumb|center|400px|Reflectivity calculation in a film with purely-real density (no absorption).]] | [[Image:Reflectivity example-real density.png|thumb|center|400px|Reflectivity calculation in a film with purely-real density (no absorption).]] | ||
[[Image:Reflectivity example-complex density.png|thumb|center|400px|Reflectivity calculation in a film with a complex density (finite value of the imaginary part of the complex potential; corresponds to film absorption).]] | [[Image:Reflectivity example-complex density.png|thumb|center|400px|Reflectivity calculation in a film with a complex density (finite value of the imaginary part of the complex potential; corresponds to film absorption).]] | ||
Revision as of 14:56, 15 October 2014
In reflectivity experiments, when the angle of incidence is below the critical angle, the beam experiences total external reflection. Thus, the reflectivity goes to 100% () for any Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle \theta \lt \theta_c} , or for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle q \lt q_c} .
However, one sometimes sees oscillations of the reflectivity even below this angle (especially in x-ray reflectivity, though it is also possible in neutron reflectivity). These oscillations can be thought of as waveguide modes appearing while the reflectivity angle is in between the critical angle of the substrate, and the critical angle of the film. Notably, these variations are only visible (in reflectivity) due to the non-zero absorption of the film. However, even a very small absorption can be measured, because the waveguide modes inherently travel through the film many times.
