Apodization of Silicon Integrated Bragg Gratings Through Periodic Phase Modulation

The sinusoidal phase modulation apodization technique, owing to its high precision and resolution and very low phase noise, shows great promise for spectral tailoring of silicon integrated Bragg grating (IBG) devices for optical telecommunications and signal processing. Here, we extend this promising sinusoidal phase modulation technique by showing that phase modulation apodization of a silicon IBG can actually be accomplished based on any periodic function. This paper also shows a dependence of the apodization characteristic, physical grating structure, and actual apodized grating performance on the periodic function used. Then, we propose a general implementation process of the periodic phase modulation apodization to achieve a desired response on a silicon IBG, and study the limiting factors of the apodization performance, design tradeoffs and optimization, and grating robustness against fabrication constraints for different periodic phase functions, using a computational lithography model together with a structure-aware grating emulator. Finally, the extended periodic phase modulation apodization technique is validated by demonstrating a series of differently designed phase-modulated silicon IBGs, including Gaussian-apodized gratings, single- and multi-channel flat-top filters, and flat-top dispersion-compensating filters, using different periodic phase functions. The work offers an additional degree of freedom for the design and optimization of phase-modulated gratings, and has significant implications for practical implementation of the phase modulation apodization for spectral engineering of silicon Bragg grating devices.