

Figure 1: Two distinct filter spectra emerge for s– and ppolarized light as AOI increases.  


Figure 2: MaxLine filter spectral response to AOI shift


Figure 3: U and Sgrade StopLine filter spectra


Figure 4: Egrade StopLine filter spectra 
While most applications call for optical filters to be used at normal incidence, it is important to understand how the spectral properties of different types of filters change when using these filters a nonnormal angles of incidence (AOI). There are two main effects exhibited by all filter spectrum as the angle is increased from normal:
1. The features of the spectrum shift to shorter wavelengths.
2. Two distinct spectra emerge – one for spolarized light and one for ppolarized light.
RazorEdge^{®} Edge Filters
The graph on the right (Figure 1) shows a series of spectra derived from a typical RazorEdge longwavepass (LWP) filter design, and can be applied to any of the RazorEdge edge filters. Here, the resulting wavelength λ is compared to the wavelength λ_{0} of the edge location at normal incidence. As the angle increases from normal incidence, the filter edge shifts toward shorter wavelengths and the edges associated with s and ppolarized light shift by different amounts. For LWP filters, the response of ppolarized light shifts more than spolarized light. The opposite is true for SWP filters. This polarization splitting causes the unpolarized spectrum to show a “shelf” near the 50% transmission point, but note that the edge steepness remains intact, even for polarized light.
The shift of almost any spectral feature can be approximated by a simple model of the wavelength of the feature vs. angle of incidence , given by the equation:
where neff is the effective index of refraction, which varies with AOI and polarization, and λ0 is the wavelength of the spectral feature of interest at normal incidence. For the RazorEdge family of edge filters, the shift of the 90% transmission point on the edge is described by this equation with neff = 2.08 and 1.62 for s and ppolarized light, respectively. To learn more about determining the spectral change of RazorEdge filters, click here.
MaxLine^{®} Laserline Filters
Varying filter designs will respond to changes in AOI in different ways, but still show marked differences between s and ppolarized light. The spectra of a MaxLine laserline filter (Figure 2) shows that as the angle increases from normal incidence, the center wavelength shifts toward shorter wavelengths and the bandwidth broadens slightly for ppolarized light while narrowing for spolarized light. The most striking feature is the decrease in transmission for spolarized light, while the ppolarized light maintains high transmission. The center wavelength shifts are described by the above equation with neff = 2.19 and 2.13 for s and ppolarized light, respectively, for many of the MaxLine filters. To learn more about how the spectral features of the MaxLine filters will change with AOI, please contact our Applications Engineers.
StopLine^{®} Notch Filters
The StopLine series of filters has a different response to AOI depending on the grade of filter used. For the standard U and Sgrade filters (Figure 3), as the angle is increased from normal incidence, the notch center wavelength shifts to shorter wavelengths, the notch depth decreases, and the notch bandwidth decreases (with a greater decrease for ppolarized light than for spolarized light). The shift of the notch center wavelength is described by the above equation with neff = 1.76 for both s and ppolarized light.
Egrade filter (Figure 4), which is based on a different type of filter design, shows a large increase in OD for spolarized light as the AOI increases. As the angle is increased from normal incidence, the notch center wavelength shifts to shorter wavelengths; however, the shift is greater for ppolarized light than it is for spolarized light. The shift is described by the above equation with neff = 1.71 for ppolarized light and neff = 1.86 for spolarized light. To learn more about the spectral shifts of notch filters due to AOI, click here.
Modeling Data for nonnormal angles of incidence
Try angle tuning on selected filters, by using MyLight™. Select your filter and click on the blue “MyLight” button at the top right of the filter spectra to model the theory data at whatever angle you desire.