A solid etalon filter, or a solid spacer filter, is a high-order single-cavity (Fabry–Perot) filter where the cavity consists of an optically worked plate or a cleaved crystal. Thin-film reflectors are deposited on either side of the cavity or spacer, which also acts as the substrate.
Unlike all-thin-film narrowband filters, solid etalon filters avoid uniformity issues, and their thick cavities do not suffer from the scattering losses common to higher-order thin-film cavities. These filters are more robust and stable than conventional air-spaced Fabry–Perot etalons, while their manufacturing challenges are comparable.
Features and Early Development
The high order of these filters implies a small interval between orders, requiring a conventional thin-film narrowband filter in series to eliminate unwanted orders. Dobrowolski described the use of mica for constructing such filters, achieving half-widths as narrow as 0.3 nm. Despite complications due to mica’s natural birefringence, splitting of the pass band can be avoided by designing the mica thickness as a half-wave plate (or multiple half-waves) at the desired wavelength.
For such cavities:
\[
2\pi \frac{(n_o – n_e)d}{\lambda} = p
\]
where \( n_o \) and \( n_e \) are refractive indices, \( d \) is thickness, and \( p \) is an integer. Filters with mica layers around 60 μm thick have achieved half-widths of 0.1 nm, with peak transmittance ranging up to 50% for narrower filters and 80% for broader filters with 0.3 nm half-width.
Optically Worked Cavities
Recent advances use optically worked materials like fused silica for cavities. Austin reported production of fused silica discs as thin as 50 μm, enabling half-widths as narrow as 0.1 nm in the visible spectrum. Thicker discs yield bandwidths as low as 0.005 nm. However, optical working introduces errors in parallelism, denoted by \( \Delta d \), which affect peak wavelength and resolving power.
The resolving power is:
\[
\text{Resolving Power} = \frac{\lambda_0}{\Delta \lambda_h} = mF
\]
where \( m \) is the order number, \( F \) is the finesse, and \( \Delta \lambda_h \) is the half-width. The attainable \( \Delta D \) in the visible region is around \( \lambda / 100 \), limiting finesse to approximately 25. For example, a resolving power of 50,000 (half-width 0.01 nm at 500 nm) requires a finesse of 25 and order number \( m = 2000 \), corresponding to a cavity optical thickness of 500 μm.
Infrared Applications
Solid etalon filters are also employed in the infrared spectrum. Smith and Pidgeon used polished germanium slabs, achieving a reflectance of 62% with half-widths of 0.1 cm\(^{-1}\). Roche and Title extended the use of solid etalon filters for infrared wavelengths, utilizing Yttralox for longer wavelengths and achieving resolving powers of \( 3 \times 10^4 \).
Advances in Telecommunications
Floriot et al. adapted solid etalon filters for telecommunication, combining multiple cavities coherently to enhance edge steepness and achieve a rectangular response. The coupling between cavities is achieved using air layers, adjustable via piezoelectric translators. A typical design involves over 100 discrete layers, refined for optimal performance.
An example design with four cavities is as follows:
\[
1.09H(LH)^2 246C (HL)^2 1.05H 20.66A 1.13H(LH)^2 500C (HL)^2 1.09H 24.79A 1.06H(LH)^2 412C (HL)^2 1.02H 31.11A 0.73H(LH)^2 298C (HL)^2 1.27H
\]
Where:
– \( H \): High-index quarter-wave (\( n = 2.09 \), Ta\(_2\)O\(_5\)),
– \( L \): Low-index quarter-wave (\( n = 1.46 \), SiO\(_2\)),
– \( C \): Silica cavity (\( n = 1.44 \)),
– \( A \): Air quarter-wave.
Performance
The calculated performance of such filters, shown in Figure 8.11, demonstrates exceptional ripple control. The solid etalon filter’s response remains robust even at oblique incidence, with minimal distortion.
