Controllable Emergence of Multiple Topological Anderson Insulator Phases in Photonic Su-Schrieffer-Heeger Lattices

We investigate the emergence and control of multiple topological Anderson insulator (TAI) phases in a one-dimensional Su-Schrieffer-Heeger (SSH) waveguide lattice with generalized Bernoulli-type disorder introduced in the intradimer couplings. By systematically varying the disorder configuration - including the values and probabilities of the multivariate distribution - we demonstrate that both the number and width of TAI phases can be precisely engineered. Analytical determination of topological phase boundaries via the inverse localization length shows excellent agreement with numerical simulations. Our results reveal a rich landscape of disorder-induced topological phase transitions, including multiple reentrant TAI phases that arise as the disorder amplitude increases. Furthermore, we show that the mean chiral displacement serves as a sensitive probe for detecting these topological transitions, providing a practical route for experimental realization in photonic waveguide lattices. This work establishes a versatile framework for designing quantum and photonic materials with customizable topological properties driven by tailored disorder.