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The coupling coefficients of the cladding-mode resonances of a tilted fiber Bragg grating (TFBG) are linearly increasing or decreasing in different wavelength regions. Based on the Kramers-Kronig relations, when the coupling coefficients are linearly increasing, the phase shifts are linearly increasing correspondingly. This feature is employed, for the first time, for the implementation of a multi-tap continuously tunable microwave photonic filter with complex coefficients by using a TFBG. By locating the optical carriers of single-sideband-modulated signals at the cladding-mode resonances of the TFBG which has linearly increasing depths, linearly increasing phase shifts are introduced to the optical carriers. By beating the optical carriers with the single sidebands, the phase shifts are translated to the microwave signals, and thus complex coefficients with the required linearly increasing phase shifts are generated. The tunability of the complex coefficients is realized by optically pumping the TFBG which is written in an erbium/ytterbium (Er/Yb) co-doped fiber. A proof-of-concept experiment is performed; a three- and four-tap filter with a frequency tunable range of 150 and 120 MHz, respectively, are demonstrated.

A continuously tunable multi-tap complex-coefficient microwave photonic filter based on a tilted fiber Bragg grating