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An optical true time delay line (OTTDL) is an essential component in optical signal processing. A Bragg grating structure is usually employed in OTTDL design, which makes it possible to achieve a slow-light effect. Here, we present the design and experimental demonstration of a cladding modulated waveguide Bragg grating (CMWBG) that supports transverse magnetic polarization for OTTDL application. In contrast to traditional waveguide Bragg gratings that support transverse electric polarization, the proposed structure has low propagation loss and high fabrication tolerance characteristics. The slow-light effect of the CMWBG was experimentally demonstrated with a high group index value. An averaged maximum group delay value of up to 84.4 ps was achieved at a length of 1 mm CMWBG, and a tuning range of about 81.4 ps was obtained.