RESUMEN
We present an on-chip filter with a broad tailorable working wavelength and a single-mode operation. This is realized through the application of topological photonic crystal nanobeam filters employing synthesis parameter dimensions. By introducing the translation of air holes as a new synthetic parameter dimension, we obtained nanobeams with tunable Zak phases. Leveraging the bulk-edge correspondence, we identify the existence of topological cavity modes and establish a correlation between the cavity's interface morphology and working wavelength. Through experiments, we demonstrate filters with adjustable filtering wavelengths ranging from 1301 to 1570 nm. Our work illustrates the use of the synthetic translation dimension in the design of on-chip filters, and it holds potential for applications in other devices such as microcavities.