A multiple narrow bandpass filter with both high factor and complete transmission using quasi-periodic Thue–Morse dielectric multilayers is proposed. The factor of the system increases exponentially with the generation order. Even though the factor of resonances increases as the generation order of the multilayers increases, these resonances are still complete resonances. The number of resonance peaks for the bandpass filter of the system also increases as the generation order increases. These resonance peaks have a multifractal distribution throughout the frequency range, which is different from that in traditional periodical multilayers.
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