Metal-mesh optical filter
Metal-mesh filters have many applications for use in the far infrared (FIR)[1] and submillimeter regions of the electromagnetic spectrum.
These filters have been used in FIR and submillimeter astronomical instruments for over 4 decades,[2] in which they serve two main purposes: band-pass or low-pass filters are cooled and used to lower the noise equivalent power of cryogenic bolometers (detectors) by blocking excess thermal radiation outside of the frequency band of observation,[3] and band-pass filters can be used to define the observation band of the detectors.
Metal-mesh filters can also be designed for use at 45° to split an incoming optical signal into several observation paths, or for use as a polarizing half-wave plate.
The electromagnetic theory can then be applied to develop a model of an oscillating circuit on a transmission line model that explains the transmission properties of these meshes quite well as long as the wavelength of light is larger than the size of the metallic element (
Since we are neglecting losses, the amplitude squared of the reflected and transmitted waves must equal unity:
in the complex plane is a unit half circle centered on the point
are independent of polarization, we can apply Babinet's principle to the capacitive and inductive grids.
Babinet's principle states that if we swap the metallic parts of a grid for the gaps, (i.e., make a complementary mesh), then the sum of the transmitted wave from the original structure and the structure's complement must equal the original incident wave.
However, in an inductive grid the metal is continuous, and hence DC currents can exist.
, the inductive grid must reflect the entire incident wave[5] because of the boundary conditions for the electric field at the surface of a conductor.
[7] The relations derived above therefore show that a capacitive mesh will transmit the entire incident wave in this case.
[5] Up until now, the theory has only been considering the ideal case where the grids are infinitely thin and perfectly conducting.
[5] For microwave and infrared radiation incident on copper, this unitless absorptivity comes out to be
, which means that the initial assumption that absorption could be ignored in this ideal model was a good one.
[5] For single layer metallic grids, the simple theory Ulrich laid out works quite well.
Measurements of very thin nearly ideal grids show the expected behavior and have very low absorptive loss.
[5] In order to build filters out of metallic meshes with the desired properties, it is necessary to stack many metallic meshes together, and while the simple electromagnetic theory laid out above works well for one grid, it becomes more complicated when more than one element is introduced.
If, for example, three identical grids were stacked, then there would be three admittance shunts in parallel across the transmission line.
At low frequencies, a reasonable model is to replace the shunt in the transmission line with a capacitor of value
However, at high frequencies this model fails to reflect the behavior of real metallic meshes correctly.
included in the 2-element equivalent circuit is consistent with the earlier calculation of absorptivity, which gives
[5] The real power in this model is it allows prediction of the transmission properties of many metallic grids stacked together with spacers to form interference filters.
Stacks of capacitive grids make a low-pass filter with a sharp frequency cutoff above which transmission is almost zero.
Likewise, stacks of inductive grids make a high-pass filter with a sharp frequency cutoff below which transmission is almost zero.
Stacked inductive and capacitive meshes can be used to make band-pass filters.
[2] The manufacture of metal-mesh filters starts with photolithography of copper on a substrate, which allows fine control over the parameters
The metallic grids are made of thin copper film on top of a dielectric substrate such as mylar or polypropylene.
Hot pressed filters are mechanically robust and when impedance matched to vacuum show a pass-band fringe due to Fabry-Perot interference in the underlying dielectric material.
[2] These filters have been used in FIR and submillimeter astronomical instruments for over 4 decades,[2] in which they serve two main purposes: band-pass or low-pass filters are cooled and used to lower the noise equivalent power of cryogenic bolometers by blocking excess thermal radiation outside of the frequency band of observation,[3] and band-pass filters can be used to define the observation band of the detectors.
Metal-mesh filters can also be designed for use at 45° to split an incoming optical signal into several observation paths, or for use as a polarizing half-wave plate.
