A Bessel function‐based design method of a periodic multireflection optical filter

• Published in: Electronics & communications in Japan. Part 2, Electronics Vol. 81; no. 10; pp. 19 - 29
• Main Authors: Takata, Haruhisa, Yamada, Minoru, Yamane, Yasuhiro, Ahmed, Moustafa
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01.10.1998
• Subjects: Bessel function; dielectric multilayered film; Fourier transform; optical filter; waveguide
• ISSN: 8756-663X; 1520-6432
• DOI: 10.1002/(SICI)1520-6432(199810)81:10<19::AID-ECJB3>3.0.CO;2-R

A method of design of optical filters with periodic reflectivity peaks on the wave number axis is proposed for a dielectric multilayered film type and a waveguide type. There is approximately a Fourier transform relationship between the refractive index profile and the reflectivity of the filter. This relationship resembles the one between the time domain waveform of a signal and its frequency response in communication. By using this resemblance, the refractive index profile is described as an FM modulation function so that the filter characteristics based on the Bessel function can be realized. Since the magnitudes of the reflectivity peaks are not identical if a monotonic FM modulation function is used, higher‐order terms are introduced into the phase term of the function for correction. Also, the (effective) index of refraction used for transformation of the variation of the refractive index profile to a rectangular waveform is only binary valued. From the results of the analysis, a filter design method is proposed. In both the multilayer type and the waveguide type, the results are very close to the desired filter characteristics. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(10): 19–29, 1998