Semrock's steep RazorEdge® Raman filters have been optimized for use with light at or near normal incidence. However, for many applications it is desirable to understand how the spectral properties change for larger angles of incidence.

There are two main effects exhibited by the spectrum as the angle is increased from normal: (1) the filter edge shifts toward shorter wavelengths; and (2), there is a splitting that occurs between the edges associated with s-polarized light and p-polarized light. Because
of the latter effect, the spectrum for unpolarized light demonstrates a "shelf" near 50% transmission when the splitting significantly exceeds the edge steepness. These effects are demonstrated in the graph below, which shows spectra derived from a typical design
curve for Semrock's Long-Wave-Pass (LWP) Raman edge filters. Because the designs are so similar for all of the RazorEdge filters
in the series, the set of curves in the graph can be applied approximately to any of the filters. Therefore, the spectra are plotted as a function of "normalized wavelength" / , where is the wavelength of light associated with a particular feature on the spectral curve and is the wavelength of that feature when light is normally incident on the filter.

For LWP filters, the edge associated with p-polarized light shifts more than the edge associated with s-polarized light. For Short-Wave-Pass (SWP) filters, both edges shift toward shorter wavelengths, but the s-polarized edge shifts more than the p-polarized edge. It is important to note that whereas the polarization splitting causes an apparently drastic reduction in the edge steepness for unpolarized light, the edge steepness for polarized light changes very little.

The edge shift and polarization splitting effects can be quantified by a simple model of the wavelength vs. angle of incidence . The following expression accurately describes this dependence:

where n_eff is called the "effective index of refraction," and is the wavelength of the spectral feature of interest at normal incidence. Curve fits of this equation to data taken from the spectra above are shown in the graph below. Edge positions at both 90% and 50% transmission are plotted for both s- and p-polarized light.

Again, because the designs for all RazorEdge filters in the series are similar, the above applies approximately to any of the filters.
The parameters used for the curve fits in this graph are listed in the table below.

Edge		neff
s polarization; T = 90%	1.0000	2.0815
s polarization; T = 50%	0.9995	2.0860
p polarization; T = 90%	1.0000	1.6191
p polarization; T = 50%	1.9995	1.6199