Critical Attributes of Narrow Band Interference Filters
The concept of a narrow band pass filter is simple. These are devices that let a specific range of wavelengths pass, while rejecting others. This article will present the salient aspects of a typical narrow band filter.
Characteristics of NBP Filters
The Peak Transmission is the highest level obtained in the pass band; Ripple is the variation in transmission in the pass band. The shape of the filter can be specified in many ways, the simplest is to specify the full width at one half of the peak transmission (Full Width at Half Maximum, FWHM). Other widths, such as the 90% and 10%, serve to further constrain the performance. The rejection band is the region in which most of the incident light is not transmitted. It can either be reflected or absorbed, and for filters that have wide rejection bands, both.
Figure 1: Simple narrow band filter in near IR. (right)
In this article, the filter is a 3 cavity Fabry-Perot filter. A Fabry-Perot filter consists of a dielectric reflecting stack, a spacer layer and a second matched reflector. If these structures are combined in series, they produce spectral characteristics with steeper slopes and greater rejection while maintaining the FWHM.
Filters like the one illustrated by Figure 1, use multiple layers of materials with differing refractive index. The change in speed of the light in the different materials results in light being split into reflected and transmitted portions. These portions then traverse different paths and recombine coherently with each other. If this interference is in-phase, the light becomes more intense. If out-of-phase, the waves combine destructively and the light becomes less intense. Obviously, the path length depends on the direction of propagation and hence the angle of incidence. The art and science of thin film design is in constructing layers that give the desired performance for the specified illumination conditions.
Choosing Materials for Interference Filters
In selecting materials for interference filters, the decision tree begins with choosing materials that are suitable for the region of interest. There are some cases in which metals (whose performance is dominated by the imaginary portion of their complex refractive index) are important, but for the most part filters are made of materials with very low absorption in the band of interest.
In most regions of the electromagnetic spectrum, there are several materials that can be selected that have the required low absorption. These materials are then down-selected by other criteria such as index contrast, stress levels and personal experience with their performance in the deposition systems available. In most deposition systems, two materials are used. These are arranged as an alternating series in what is referred to a discrete stack. It is also possible to produce filters using blends of materials to produce gradients in the optical properties, often referred to as Rugates, but this will not be addressed here.
The materials selected have a strong influence on the filter performance. The measure of the velocity of light in a material is called the refractive index, N=c/v. Where c is the speed of light in vacuum and v is the velocity in the material. In real materials, N is a complex quantity where the real part is responsible for the properties of propagation and the imaginary part is related to the loss of energy. At an interface between two materials, the amount of energy reflected is proportional to the difference in index of refraction, or as follows in the simplest case, the amplitude reflection coefficient can be written as:
The greater the index contrast, the more light is reflected at each interface.
There are numerous design techniques that can be applied to obtain the desired spectral characteristics, but the general rule is that the higher the index contrast (reflection coefficient) the fewer layers needed to obtain the desired level of performance. In general, fewer layers translate directly to lower cost.
Figure 2 shows the change in the observed spectral performance for several filters with identical structures, incorporating different materials for the high index layers. The width and depth of the rejection zone, as well as the ripple, are directly proportional to the index contrast. The FWHM is inversely proportional to the index contrast.
Figure 2: Change in spectral performance of the filter from figure 1 with index contrast.
All optical filters are used in some sort of system. As such, they are never used with plane waves at normal incidence. Filters are used in cones and at angles. The effect of illuminating a filter at an angle introduces a shift in the performance to shorter wavelengths and introduces a split in the characteristic between the two orthogonal planes of polarization. As the angles increase, these effects become more pronounced.
The effect of the angle-of-incidence is shown for two filters of identical design but differing high index material as in the previous example. Both of these designs use SiO2 for the low index material. In this figure, we see that the materials with the higher index of refraction, the Si shifts in wavelength only about half as much (13 nm) as does the filter with lower refractive index, Ta2O5 (24 nm).
Filters can be readily designed to work at any angle-of-incidence, but at angles beyond about 20° in air, polarization effects become important. These will not be addressed here.
Figure 3 and Figure 3A: Angle shift for angles up to 20° in air for a Silicon and a Tantalum Pentoxide bandpass filter.
The large discrepancy in the bandwidths somewhat obscures the angle shift. Of concern for optical systems as a result of this angle shift is the change of the shape of filters.
In Figure 4, the designs have been altered so that the FWHM of each filter is approximately the same, as seen by the 0° curves. In order to achieve similar FWHM, the Tantala filter has much more material. Both filters use high index spacers to produce the low angle shift. As the yellow and aqua curves show, the performance of these filters in an F/1.5 cone is noticeably different.
Figure 4: F/1.5 (about 20°) cone on two filters with similar bandwidths.
In most applications of narrow band filters, the ideal response is that of a shape similar to a door frame with steep cut-on and cut-off sides and a flat top. The effect of utilizing filters in a cone causes them to diverge from this ideal with a subsequent deterioration in signal-to-noise ratio and other figures of merit.
In this article, we have reviewed some of the behavior of simple bandpass filters. It is important to note that the materials selected to fabricate the filters have a strong impact on the performance of these devices. In particular, we have observed how the spectral properties of filters depend on the angle-of-illumination and how this angle shift results in the degradation of the filters performance when illuminated with a range of angles.
Materion Narrow Band Filters
As one of the world’s largest producers of optical filters, we have the expertise to offer a full range of customized interference filters for an array of applications. For more information, contact Bob Sprague, Director of Technology, Robert.Sprague@Materion.com