How do I design a frequency-selective waveguide window for a high power application?

Designing a frequency-selective waveguide window for a high-power application creates a dielectric barrier in the waveguide that passes the desired frequency band while blocking or reflecting other frequencies, and simultaneously seals the waveguide for pressurization or vacuum isolation. The frequency-selective window combines two functions: a hermetic seal (the dielectric disc or plate seals the waveguide to maintain gas pressure (for preventing arcing in high-power waveguides) or vacuum (for connecting to a vacuum system in a particle accelerator or plasma source)), and frequency selectivity (the window's dielectric properties and thickness create a resonant structure that provides low insertion loss at the desired frequency and higher loss or reflection at other frequencies). The design: the simplest window is a half-wave thick dielectric disc (thickness = n × lambda_d/2, where lambda_d = lambda_0/sqrt(epsilon_r); at n = 1: the disc is electrically transparent at the design frequency because the reflections from the two surfaces cancel). For wider bandwidth: multi-layer windows (alternating layers of different dielectrics) create a bandpass filter response. Window materials for high-power applications: alumina (Al2O3, epsilon_r = 9.8, tan_delta = 0.0001, high thermal conductivity: approximately 25 W/m-K, excellent for high-power CW applications), beryllium oxide (BeO, epsilon_r = 6.8, tan_delta = 0.0001, highest thermal conductivity: approximately 250 W/m-K, best for extreme power handling but: toxic dust requires careful handling), and CVD diamond (epsilon_r = 5.7, tan_delta < 0.00005, thermal conductivity: approximately 2000 W/m-K, the ultimate window material for the highest power levels but: very expensive, $5,000-50,000 per window).