Tutorial #30
Filmetrics

Spectral Reflectance Basics

Single interface reflection occurs whenever light crosses the interface between different materials.

The fraction of light that is reflected by an interface is determined by the discontinuity in n and k. For light reflected off of a material in air as shown by

To see how spectral reflectance can be used to measure optical constants, consider the simple case of light reflected by a single nonabsorbing material (k=0).

Clearly, n of the material can be determined from a measurement of R. In real materials, n varies with wavelength (that is to say, real materials exhibit dispersion), but since the reflectance is known at many wavelengths, n at each of these wavelengths is also known, as shown here.

Multiple Interfaces

Consider now a thin film on top of another material. In this case both the top and bottom of the film reflect light. The total amount of reflected light is the sum of these two individual reflections. Because of the wavelike nature of light, the reflections from the two interfaces may add together either constructively (intensities add) or destructively (intensities subtract), depending upon their phase relationship.

Their phase relationship is determined by the difference in optical path lengths of the two reflections, which in turn is determined by thickness of the film, its optical constants, and the wavelength of the light. Reflections are in-phase and therefore add constructively when the light path is equal to one integral multiple of the wavelength of light. For light perpendicularly incident on a transparent film, this occurs when where d is the thickness of the film and i is an integer (the factor of two is due to the fact that the light passes through the film twice.) Conversely, reflections are out of phase and add destructively when the light path is one half of a wavelength different from the in-phase condition, or when

The qualitative aspects of these reflections may be combined into a single equation:

From this, we can see that the reflectance of a thin film will vary periodically with 1/wavelength, which is illustrated below. Also, thicker films will exhibit a greater number of oscillations over a given wavelength range, while thinner films will exhibit fewer oscillations, and oftentimes only part of an oscillation, over the same range.

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