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A novel planar waveguide Time Domain Optical Fourier Transformer (TD-OFT), which is composed of waveguide lenses and blazed phase gratings, is proposed. A detailed mathematical derivation based on scalar diffraction optics is presented. In order to verify the theoretical analysis, the reciprocity in TD-OFT is also studied. Three different pulse examples, including the Gaussian pulse, square pulse and square pulse train, are implemented by analytical formulations. To evaluate the device performance, the similarity coefficient is defined. The results show that the similarity increases as the device aperture increases. However, there is trade-off between the similarity and the spectra resolution. For the input pulse, under the circumstance of same similarity, the shorter temporal pulse duration (larger bandwidth) needs smaller aperture size. Improved waveguide lens is particularly designed and then the whole device is simulated by Extension of BPM (EX-BPM) with two specific pulses, Gaussian and raised cosine pulse. The simulation results are also verified by reciprocity theorem using the numerical method. The designed TD-OFT occupies a size about 600μm (in width)×5mm (in length) for an ultrafast pulse around 10fs. It is possible to make the device size even smaller either by reducing the focal length of the collimating lens or enlarging the bandwidth of input pulse. Compared with currently proposed TD-OFT made by discrete photonic and optoelectronic components, this design can be integrated with a more compact size and seems more appealing on the simulated performance and fabrication cost. As a result, the planar waveguide TD-OFT has great potential in the next ultrafast optical network.

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