A simple and general approach for designing practical all-optical (all-fiber) arbitrary-order time differentiators is introduced here for the first time. Specifically, we demonstrate that the N^th time derivative of an input optical waveform can be obtained by reflection of this waveform in a single uniform fiber Bragg grating (FBG) incorporating N π-phase shifts properly located along its grating profile. The general design procedure of an arbitrary-order optical time differentiator based on a multiple-phase-shifted FBG is described and numerically demonstrated for up to fourth-order time differentiation. Our simulations show that the proposed approach can provide optical operation bandwidths in the tens-of-GHz regime using readily feasible FBG structures.

© 2007 Optical Society of America

1. J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special issue on "Optical Signal Processing," in J. Lightwave Technol. 24, 2484-2767 (2006). [CrossRef]
2. N. Q. Ngo, S. F. Yu, S. C. Tjin, and C.H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004). [CrossRef]
3. M. Kulishov and J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005). [CrossRef] [PubMed]
4. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators," Opt. Express 14, 10699-10707 (2006). [CrossRef] [PubMed]
5. N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, "Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating," Opt. Express 15, 371-381 (2007). [CrossRef] [PubMed]
6. Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-712 (2007). [CrossRef] [PubMed]
7. H. J. A. Da Silva, and J. J. O’Reilly, "Optical pulse modeling with Hermite - Gaussian functions," Opt. Lett. 14, 526-528 (1989). [CrossRef] [PubMed]
8. C. Wu and M. G. Raymer, "Efficient picosecond pulse shaping by programmable Bragg gratings," IEEE J. Quantum Electron. 42, 871-882 (2006). [CrossRef]
9. A. Papoulis, Fourier Integral and its Applications, (McGraw-Hill, New York, 1987).
10. R. Kashyap, Fiber Bragg Gratings, (Academic Press, San Diego, 1999).
11. T. Erdogan, "Fiber Grating Spectra," J. Lightwave Technol. 15, 1277-1294 (1997). [CrossRef]
12. J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, "Damman fiber Bragg gratings and phase-only sampling for high-channel counts," IEEE Photon. Technol. Lett. 14, 1309 - 1311 (2002). [CrossRef]

IEEE J. Quantum Electron.

• C. Wu and M. G. Raymer, "Efficient picosecond pulse shaping by programmable Bragg gratings," IEEE J. Quantum Electron. 42, 871-882 (2006). [CrossRef]

IEEE Photon. Technol. Lett.

• J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, "Damman fiber Bragg gratings and phase-only sampling for high-channel counts," IEEE Photon. Technol. Lett. 14, 1309 - 1311 (2002). [CrossRef]

J. Lightwave Technol.

• T. Erdogan, "Fiber Grating Spectra," J. Lightwave Technol. 15, 1277-1294 (1997). [CrossRef]

Opt. Commun.

• N. Q. Ngo, S. F. Yu, S. C. Tjin, and C.H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004). [CrossRef]

Opt. Express

• R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators," Opt. Express 14, 10699-10707 (2006). [CrossRef] [PubMed]
• N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, "Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating," Opt. Express 15, 371-381 (2007). [CrossRef] [PubMed]

Opt. Lett.

• Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-712 (2007). [CrossRef] [PubMed]
• H. J. A. Da Silva, and J. J. O’Reilly, "Optical pulse modeling with Hermite - Gaussian functions," Opt. Lett. 14, 526-528 (1989). [CrossRef] [PubMed]
• M. Kulishov and J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005). [CrossRef] [PubMed]

Other

• A. Papoulis, Fourier Integral and its Applications, (McGraw-Hill, New York, 1987).
• R. Kashyap, Fiber Bragg Gratings, (Academic Press, San Diego, 1999).
• J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special issue on "Optical Signal Processing," in J. Lightwave Technol. 24, 2484-2767 (2006). [CrossRef]

Click here to see a list of articles that cite this paper

Related Journal Articles

• Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating (OE)
• Ultrafast all-optical Nth-order differentiator based on chirped fiber Bragg gratings (OE)
• Simultaneous ultrafast optical pulse train bursts generation and shaping based on Fourier series developments using superimposed fiber Bragg gratings (OE)
• Ultrafast all-optical Nth-order differentiator and simultaneous repetition-rate multiplier of periodic pulse train (OE)
• Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings (OE)

Related Conference Papers

• Fully functional optical add and drop multiplexer using twin-core fiber based mach-zehnder interferometer with photoimprinted fiber bragg gratings
• Numerical simulation of decoherence-control processes in Quantum Computers
• Numerical simulation of decoherence-control processes in Quantum Computers
• Single-Photon-Level Nonlinear Optics Through Quantum Interference
• Single-Photon-Level Nonlinear Optics Through Quantum Interference
• Semiconductor quantum computer design with 100 nm separation of nuclear-spin qubits
• Semiconductor quantum computer design with 100 nm separation of nuclear-spin qubits
• Double helix quantum computer
• Double helix quantum computer