Abstract
We propose and numerically demonstrate an ultrafast real-time ordinary differential equation (ODE) computing unit in optical field based on a silicon microring resonator, operating in the critical coupling region as an optical temporal differentiator. As basic building blocks of a signal processing system, a subtractor and a splitter are included in the proposed structure. This scheme is featured with high speed, compact size and integration on a silicon-on-insulator (SOI) wafer. The size of this computing unit is only 35 μm × 45 μm. In this paper, the performance of the proposed structure is theoretically studied and analyzed by numerical simulations.
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Liu F F, Wang T, Qiang L, Ye T, Zhang Z, Qiu M, Su Y. Compact optical temporal differentiator based on silicon microring resonator. Optics Express, 2008, 16(20): 15880–15886
Slavík R, Park Y, Kulishov M, Morandotti R, Azaña J. Ultrafast alloptical differentiators. Optics Express, 2006, 14(22): 10699–10707
Azaña J, Slavik R, Park Y, Kulishoy M. Ultrafast all-optical differentiators based on fiber gratings. In: Proceedings of International Conference on Transparent Optical Networks, 2007, 101–104
Ferrera M, Park Y, Razzari L, Little B E, Chu S T, Morandotti R, Moss D J, Azaña J. On-chip CMOS-compatible all-optical integrator. Nature Communications, 2010, 1(29): 29
Ngo N Q, Yu S F, Tjin S C, Kam C H. A new theoretical basis of higher-derivative optical differentiators. Optics Communications, 2004, 230(1–3): 115–129
Lenz G, Eggleton B J, Madsen C K, Slusher R E. Optical delay lines based on optical filters. IEEE Journal of Quantum Electronics, 2001, 37(4): 525–532
Berger N K, Levit B, Fischer B, Kulishov M, Plant D V, Azaña J. Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating. Optics Express, 2007, 15(2): 371–381
Xu K, Niu J, Dai Y T, Sun X, Dai J, Wu J, Lin J. All-optical analogto-digital conversion scheme based on Sagnac loop and balanced receivers. Applied Optics, 2011, 50(14): 1995–2000
Tang X G, Liao J K, Lu R G, Li H P, Zhang X X, Zhang L, Liu Y Z. Optical coding scheme for all-optical analog-to-digital conversion using asymmetrical Y-branch waveguide. Optics Communications, 2011, 284(9): 2298–2302
Oppenheim A V, Willsky A S, Hamid S. Signals and Systems. 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1996
Simmons G F. Differential Equations with Applications and Historical Notes. 2nd ed. New York: McGraw-Hill, 1991
Xu J, Zhang X L, Dong J J, Liu D M, Huang D X. All-optical differentiator based on cross-gain modulation in semiconductor optical amplifier. Optics Letters, 2007, 32(20): 3029–3031
Sakai A, Fukazawa T, Baba T. Low loss ultra-small branches in a silicon photonic wire waveguide. IEICE Transactions on Electronics. E (Norwalk, Conn.), 2002, 85-C(4): 1033–1038
Zhang Z Y, Dainese M, Wosinski L, Qiu M. Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling. Optics Express, 2008, 16(7): 4621–4630
Liu F F, Li Q, Zhang Z Y, Qiu M, Su Y K. Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect. IEEE Journal on Selected Topics in Quantum Electronics, 2008, 14(3): 706–712
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Lu, L., Wu, J., Wang, T. et al. Compact all-optical differential-equation solver based on silicon microring resonator. Front. Optoelectron. 5, 99–106 (2012). https://doi.org/10.1007/s12200-012-0186-9
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DOI: https://doi.org/10.1007/s12200-012-0186-9