Ultrafast All-Optical Temporal Differentiator in Integrated
Silicon-on-Insulator Phase-shifted Bragg Gratings
Weifeng Zhang
wzhan088@uottawa.ca
Abstract
Nowadays, optical signal processing has become an integral part of modern computing, networking and
communication technologies. The implementation of all-optical systems is promising for overcoming the
speed limitations of conventional electronic systems. Transition to new alternatives involves the
development of photonic equivalents of fundamental devices, which are used in electronic circuits as
basic building blocks, e.g., for mathematical and logical operations. One of these fundamental signalprocessing devices is a temporal differentiator. In our plan, we will combine the advantages of an
integrated-optical platform with the filtering and pulse shaping functionalities of phase-shifted Bragg
gratings. For this purpose we take advantage of phase-shifted Bragg gratings fabricated in Silicon-onInsulator (SOI) waveguides. The proposed devices offer several distinctive features when compared to
their fiber counterparts, including being less sensitive to environmental conditions, having a negligible
dispersion and allowing for a full compatibility with all-optical integrated circuits, and thus offering the
possibility of performing full signal processing and computing tasks on a single chip.
Design
The spectral features required for the efficient realization of the first-order temporal derivative of the
complex time envelope of optical signals can be provided by an uniform π-phase-shifted Bragg grating
operating in reflection in Fig.1in [1]. In such a case, the necessary linear optical filtering is obtained in the
vicinity of the Bragg wavelength (i.e. within the reflection notch) with the operation bandwidth depending
on the grating properties (e.g., increasing with κ).
Figure.1 The ideal frequency response of a ultrafast photonic temporal differentiator
An ideal reflection response of the proposed device is obtained by assuming that the two parts of a πphase shifted Bragg grating are exactly the same and by setting the grating parameters in such a way that
2κL=π. Fig.2 in [2] shows the schematic diagram of a phase shifted Bragg grating. In the figure W and
∆W represents the width and etch depth of the grating, respectively. Λ is the grating period and Λp is the
half- wave phase shift length. The grating period lengths l g and lw are related by Bragg condition as
lg n1  lw n2 
mB
2
where n1 and n2 are the effective indices of the grating region and waveguide region, respectively, m is
the order of the grating and B is the Bragg wavelength.
Figure.2 Schematic diagram (top side view) of phase shifted Bragg grating
Simulation
I plan to firstly, using MODE solution to get the effective index of the grating and then use Propagator to
2D simulation. At last, I will use FDTD to get 3D simulation.
Reference
[1] M. Li, L. Shao, J. Albert, and J. P. Yao, "Continuously tunable photonic fractional temporal differentiator based
on a tilted fiber Bragg grating," IEEE Photon. Technol. Lett., vol. 23, no. 4, pp. 251-253, Feb. 2011
[2] Prabhathan, P., Murukeshan, V., Jing, Z., and Ramana, P., “Compact SOI nanowire refractive index sensor using
phase shifted bragg grating,” Optics Express 17(17), 15330–15341 (2009).