page_title: Metal-mesh optical filter
section_title: Theory
hierarchical_section_title: Metal-mesh optical filter / Theory
caption_attribution_description: English: Diagram of capacitive and inductive grids used in metal mesh optical filters.
context_page_description: Metal-mesh optical filters are optical filters made from stacks of metal meshes and dielectric. They are used as part of an optical path to filter the incoming light to allow frequencies of interest to pass while reflecting other frequencies of light.
  Metal-mesh filters have many applications for use in the far infrared and submillimeter regions of the electromagnetic spectrum. These filters have been used in FIR and submillimeter astronomical instruments for over 4 decades, in which they serve two main purposes: bandpass 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, and bandpass 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.
  Transmission line theory can be applied to metallic meshes to understand how they work and the overall light transmission properties of groups of metallic meshes grouped together.
context_section_description: In 1967 Ulrich showed that the optical transmission properties of a metallic mesh can be modeled by considering the mesh to be a simple circuit element on a free space transmission line. To develop the theory of metallic meshes, he focused on the properties of two types of mesh structure: a metallic grid with square openings; and a grid of metallic squares supported on a thin dielectric substrate. Using the transmission line method, he then modeled the behavior of each of these meshes as either lumped inductance (square openings) or a lumped capacitance (free-standing squares). These two types of meshes are commonly referred to as inductive or capacitive meshes.
  The theory developed by Ulrich to explain light transmission by metallic meshes makes a few assumptions and idealizations, which will be used here as well in explaining the theory. This theory is valid for thin meshes, i.e. , but the following equations assume that the grid is infinitely thin, the metallic parts are perfectly conducting, and the supporting dielectric film in the capacitive grids has no effect. 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 ().
caption: Capacitive and inductive grids used in metal-mesh filters. g is the cell size, t is the thickness, 2a is the spacing between elements in capacitive grids and the width of the elements in inductive grids.
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