Angle of Incidence and Polarization

Most interference coatings are designed to filter collimated light (i.e. parallel rays of light) at a normal angle of incidence (i.e. where the coated surface is perpendicular to the light path). However, interference coatings have certain unique properties that can be used effectively at off-normal angles of incidence. Dichroic beamsplitters and tunable bandpass filters are two common products which take advantage of these properties.

The primary effect of an increase in the incident angle on an interference coating is a shift in spectral performance toward shorter wavelengths. In other words, the principal wavelength of all types of interference filters decreases as the angle of incidence increases. For example, the 665LP longpass filter (50% T at 665nm) in Figure 1 becomes a 605LP filter at a 45° angle of incidence.

To a near approximation, the relationship between this shift and angle of incidence is described as:

Where: = angle of incidence
= principal wavelength at angle of incidence

= principal wavelength at 0º angle of incidence

N = effective refractive index of the coating

The effective refractive index of a coating is determined by the coating materials used and the sequence of thin-film layers in the coating, both of which can be influenced in the design process. For filters with common coating materials such as zinc sulfide and cryolite, effective refractive index values are typically 1.45 or 2.0, depending upon which material is used for the spacer layer. This relationship is plotted in Figure 1. The actual shifts will vary slightly from calculations based solely on the above equation.

Figure 1: Decrease in CWL as a function of angle of incidence for two bandpass filters with the same coating materials (zinc sulfide and cryolite) but different effective refractive indices (N). N = 2.0 for the filter with a zinc sulfide spacer. N = 1.45 for the filter with a cryolite spacer

A secondary effect of angle of incidence is polarization. At angles greater than 0°, the component of lightwaves vibrating parallel to the plane of incidence and reflection (P-plane) will be filtered differently than the component vibrating perpendicular to the plane of incidence (S-plane). The plane of incidence is geometrically defined by a line along the direction of lightwave propagation and an intersecting line perpendicular to the coating surface. Polarization effects increase as the angle of incidence increases. Figures 2 & 3 illustrate the effects of polarization on a longpass and a bandpass filter. Coating designs can minimize polarization effects when necessary.

Figure 2: Angle of Incidence Polarization Effects—Longpass Filter
Longpass filter has cut-on at normal incidence of 665nm and at 45¼ incidence of 605nm. Graph illustrates the separation of the P- and S-planes of polarization at 45¼ angle of incidence.

Figure 3: Angle of Incidence Polarization Effects—Bandpass Filters
A bandpass filter at normal incidence with a CWL at 590nm and a FWHM of 40nm. At 45° angle of
incidence, in random polarization, the CWL is 547nm and the FWHM is 42nm. At 45° angle of incidence, there is a separation of the P- and S-planes of polarization.

Angle of Incidence and Decalage in HLG

This is one of the real secrets of HLG flying. A stubborn glider that does not launch well can often be transformed into a fine performer by changing the angle of incidence of the stab or the wing.

The photo (left) is DOGEAR, a 6 inch span hand launched glider that I designed and built. It did not launch well until I replaced the stab and now it's great. Its first ever timed flight was 38 seconds. Why and how?

Angle of Incidence is the angle between the wing's surface and the fuselage axis. (Usually for polyhedral wing models, you can place a ruler flat with the underside of the wing near the root chord to get an idea of the incidence).

Decalage, geometrically and simply speaking, is the angle between the wing's surface and the stab's surface. If you were to use a ruler under the wing and another ruler under the stab as described above, then it is the angle between the rulers. See the diagram here.

0-0 (said "zero-zero") is when the two surfaces (or rulers in the example above) are parallel.

Some HLG modellers swear that 0-0 is the best setting. On the other hand, many others (including me) say that a HLG should have a small decalage. When I say small, I mean small.

For example, if the stab has zero angle of incidence, then the wing should have just a few degrees positive, e.g. the LE of the wing is 1-2 mm higher than the TE. What I can say is that the vast majority of HLG pilots say that "large" decalage is bad.

Now, bear in mind that it is not easy to measure AOI accurately even with rulers and "large" is really a referring to a small measurement.