On-Chip Tunable Second-Order Differential-Equation Solver Based on a Silicon Photonic Mode-Split Microresonator

We propose and experimentally demonstrate an on-chip all-optical differential-equation solver capable of solving second-order ordinary differential equations (ODEs) characterizing continuous-time linear time-invariant systems. The photonic device is implemented by a self-coupled microresonator on a silicon-on-insulator platform with mutual coupling between the cavity modes. Owing to the mutual mode coupling within the same resonant cavity, the resonance wavelengths induced by different cavity modes are self-aligned, thus avoiding precise wavelength alignment and unequal thermal wavelength drifts as in the case of cascaded resonators. By changing the mutual mode coupling strength, the proposed device can be used to solve second-order ODEs with tunable coefficients. System demonstration using the fabricated device is carried out for 10-Gb/s optical Gaussian and super-Gaussian input pulses. The experimental results are in good agreement with theoretical predictions of the solutions, which verify the feasibility of the fabricated device as a tunable second-order photonic ODE solver.

[1]  Tao Wang,et al.  Pulse Delay and Advancement in SOI Microring Resonators With Mutual Mode Coupling , 2009, Journal of Lightwave Technology.

[2]  Linjie Zhou,et al.  All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator , 2014, Scientific Reports.

[3]  Peter A. Beerel,et al.  The design and verification of a high-performance low-control-overhead asynchronous differential equation solver , 1998, IEEE Trans. Very Large Scale Integr. Syst..

[4]  R. Magnusson,et al.  Concept of multiorder multimode resonant optical filters , 2002, IEEE Photonics Technology Letters.

[5]  Lech Wosinski,et al.  Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling. , 2008, Optics express.

[6]  G. R. Carmichael,et al.  The evaluation of numerical techniques for solution of stiff ordinary differential equations arising from chemical kinetic problems , 1988 .

[7]  Linjie Zhou,et al.  Coherent interference induced transparency in self-coupled optical waveguide-based resonators. , 2011, Optics letters.

[8]  Pan Cao,et al.  Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems. , 2014, Optics express.

[9]  K. Qu,et al.  Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems , 2013, 1301.3070.

[10]  Sisi Tan,et al.  All-optical computation system for solving differential equations based on optical intensity differentiator. , 2013, Optics express.

[11]  F. Courvoisier,et al.  Multimode resonances in square-shaped optical microcavities. , 2001, Optics letters.

[12]  Xinwan Li,et al.  Tunable silicon Fabry-Perot comb filters formed by Sagnac loop mirrors. , 2013, Optics letters.

[13]  Jie Hou,et al.  All-optical 1st- and 2nd-order differential equation solvers with large tuning ranges using Fabry-Pérot semiconductor optical amplifiers. , 2015, Optics express.

[14]  Po Dong,et al.  High-speed low-voltage single-drive push-pull silicon Mach-Zehnder modulators. , 2012, Optics express.

[15]  P. Lions,et al.  Ordinary differential equations, transport theory and Sobolev spaces , 1989 .

[16]  Tao Wang,et al.  Compact all-optical differential-equation solver based on silicon microring resonator , 2012 .

[17]  Yikai Su,et al.  Coupled mode theory analysis of mode-splitting in coupled cavity system. , 2010, Optics express.

[18]  Claes Johnson,et al.  Introduction to Adaptive Methods for Differential Equations , 1995, Acta Numerica.

[19]  J. Azaña,et al.  Photonic temporal integrator for all-optical computing. , 2008, Optics express.

[20]  Jose Azaa,et al.  Ultrafast Analog All-Optical Signal Processors Based on Fiber-Grating Devices , 2010, IEEE Photonics Journal.

[21]  Yi Xuan,et al.  An All-Silicon Passive Optical Diode , 2012, Science.

[22]  D. J. Moss,et al.  On-chip CMOS-compatible all-optical integrator , 2010, Nature communications.

[23]  Guangyuan Li,et al.  Multiple magnetic mode-based Fano resonance in split-ring resonator/disk nanocavities. , 2013, ACS nano.

[24]  G. F. Simmons.  Differential Equations With Applications and Historical Notes , 1972 .

[25]  Shanhui Fan,et al.  Coupling of modes analysis of resonant channel add-drop filters , 1999 .

[26]  Kouki Totsuka,et al.  Slow light in coupled-resonator-induced transparency. , 2007, Physical review letters.

[27]  V. Fock.  Proper time in classical and quantum mechanics , 1937 .

[28]  Xinliang Zhang,et al.  High-order all-optical differential equation solver based on microring resonators. , 2013, Optics letters.

[29]  Peter J. Winzer,et al.  Advanced Optical Modulation Formats , 2006, Proceedings of the IEEE.

[30]  Xiaofeng Hu,et al.  Push–Pull Optical Nonreciprocal Transmission in Cascaded Silicon Microring Resonators , 2013, IEEE Photonics Journal.

[31]  Pan Cao,et al.  Nested Configuration of Silicon Microring Resonator With Multiple Coupling Regimes , 2013, IEEE Photonics Technology Letters.

[32]  T. ElAli,et al.  An Analog Computer to Solve any First Order Differential Equation , 2007 .