  Filters are key devices in optical systems and are usually applied to signal
suppression or selection based on their amplitude frequency responses.
Different from amplitude filtering, an all-pass filter (APF) is a unique type
of filter that exhibits a uniform amplitude and variable phase in the frequency
response. Traditionally, an APF is designed to be ideal and lossless, which is
impossible in practice. Here we demonstrate a method of realizing an APF even
when transmission loss exists, and a possible structure for realizing the lossy
APF is proposed. The method indicates that a lossy APF can be realized by
introducing self-compensation of loss to the structure of an ideal single-stage
APF, and an APF based on silicon-on-insulator (SOI) foundry is fabricated and
demonstrated. The method of self-compensation of loss can also be used to
realize APFs in the electrical domain. We anticipate that our work will inspire
realizations of more APF-related devices that once seemed impossible in
practice.
