In this paper, we propose three plasmon-induced transparency(PIT) hybrid models based on the coupling of black phosphorus (BP) nanorods. By using the bright-bright mode coupling between BP nanorods with different lengths, and according to the weak hybrid effect after the detuning of each bright mode unit, we can trigger the single-band, dual-band and triple-band PIT effects.

Secondly, by changing the relaxation rate of BP, the resonant frequency can be adjusted in each PIT model. When the relaxation rate of BP changes from small to large, the resonance frequencies of the transparent windows in those three PIT models all increase and the blue shifts occur. In a single-band PIT model, when the relaxation rate of BP changes from 0.8 \times 10^ - 14 to 1.4 \times 10^ - 14\;\rmcm^ - 2, the resonant frequency of transparent window increases 7.5628 THz. In a dual-band PIT model, under the same change of relaxation rate, the resonant frequencies of the two transparent windows increase 6.8593 and 9.1457 THz, at the same time, and the resonant frequencies of the three transparent windows in triple-band PIT model increase 6.8593, 8.7939 and 11.2563 THz respectively. In addition to the resonant frequency, the transmittance at the dip frequency in each model gradually decreases, and the depth of depression gradually increases.

Finally, the sensing characteristics of the single-band PIT model are further studied. When the refractive index of the background changes from small to large, the dip frequency and the resonant frequency of the transparent window will be significantly red-shifted. The change of frequency is approximately linear with refractive index. The model has a sensitivity of 6110.6 (nm/RIU) and a figure of merit of 7.39 (1/RIU) which is better than the same type of sensor. This model provides a theoretical reference for designing the multiband filtering and ultrasensitive sensors.