Topological insulators are unique physical structures that exhibit insulating properties in their interior while being conductive on their surface. Here, we present an observation of distinct first-order and second-order topological insulators in photonic martini lattices fabricated by femtosecond laser writing technology. By using direct femtosecond laser writing techniques, we experimentally construct two types of photonic nontrivial martini lattices with tailored boundary conditions (i.e., the martini-up lattice and the martini-down lattice), enabling direct experimental observation of topological edge states and corner states with distinct phase structures. Remarkably, these lattices support different second-order topological phases, each giving rise to distinct classes of topological corner states under varying phase transition conditions. Furthermore, we uncover striking differences in their edge state behavior: while the martini-down lattice sustains only in-phase topological edge states, the martini-up lattice hosts both in-phase and out-of-phase configurations. This work not only introduces a novel framework for exploring higher-order topology, but also provides the possibility for innovative approaches to light manipulation and the development of advanced photonic devices.

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• Topological effects in photonic systems
• Waveguide arrays