Topological operations around exceptional points1-8-time-varying system configurations associated with non-Hermitian singularities-have been proposed as a robust approach to achieving far-reaching open-system dynamics, as demonstrated in highly dissipative microwave transmission3 and cryogenic optomechanical oscillator4 experiments. In stark contrast to conventional systems based on closed-system Hermitian dynamics, environmental interferences at exceptional points are dynamically engaged with their internal coupling properties to create rotational stimuli in fictitious-parameter domains, resulting in chiral systems that exhibit various anomalous physical phenomena9-16. To achieve new wave properties and concomitant device architectures to control them, realizations of such systems in application-abundant technological areas, including communications and signal processing systems, are the next step. However, it is currently unclear whether non-Hermitian interaction schemes can be configured in robust technological platforms for further device engineering. Here we experimentally demonstrate a robust silicon photonic structure with photonic modes that transmit through time-asymmetric loops around an exceptional point in the optical domain. The proposed structure consists of two coupled silicon-channel waveguides and a slab-waveguide leakage-radiation sink that precisely control the required non-Hermitian Hamiltonian experienced by the photonic modes. The fabricated devices generate time-asymmetric light transmission over an extremely broad spectral band covering the entire optical telecommunications window (wavelengths between 1.26 and 1.675 micrometres). Thus, we take a step towards broadband on-chip optical devices based on non-Hermitian topological dynamics by using a semiconductor platform with controllable optoelectronic properties, and towards several potential practical applications, such as on-chip optical isolators and non-reciprocal mode converters. Our results further suggest the technological relevance of non-Hermitian wave dynamics in various other branches of physics, such as acoustics, condensed-matter physics and quantum mechanics.