Spectral and nonlinear optical properties of the new tricarbocyanine dyes, derivatives of the benzo[cd]indole, which absorb efficiently in the region 1.05–1.08 µm, have been investigated. Based on these compounds, the liquid (ethanol solutions) and polymer (in a form of triplexes, where dye-doped polyurethane films are placed between two optical glass substrates) passive Q-switches for the neodymium lasers have been developed. The modulation depth of 100% at the generation of the ultrashort pulse (USP) trains has been obtained. The high-stable regime of passive mode-locking has been realized; it is characterized with the 100% probability appearance of a single pulse in an axial period with average durability 25–30 ps and energy 1–2 mJ, depending on the dye structure. Advantages of the new Q-switches over the corresponding analogues, based on organic dyes, nanotubes, graphene, inorganic semiconductors and mirrors (SESAM), LiF:F2ˉ and Cr4+:YAG, have been demonstrated.