Abstract

An all-optical temporal differentiator with a record operation bandwidth of ~25 THz (~200 nm, at least one order of magnitude larger than any previously reported temporal differentiation technology) is experimentally demonstrated based on a simple and compact all-fiber wavelength-selective directional coupler. The fabricated directional coupler can be used to process optical signals with time features as short as a few tens of femtosecond. A Gaussian-like optical pulse with a time-width of 250-fs is experimentally differentiated with a processing error of 2.1%. As an application example, a chirp-free flat-top pulse with a time-width of 540-fs is also successfully generated.

© 2012 OSA

1. Introduction

The implementation of all-optical circuits for computing, information processing, and networking could overcome the severe speed limitations currently imposed by electronic-based systems [111]. A promising approach toward the implementation of ultrafast all-optical circuits is to emulate the developments in the electronic domain, i.e., to follow similar component and design strategies, using photonic technologies [1013]. For this purpose, high-speed optical signal processors, such as optical differentiator [1417], integrator [6, 1820], Fourier transformer [4, 2123] and Hilbert transformer [2426], have recently attracted an increasing interest for optical communications, pulse shaping or sensing applications that use optical signals. An all-optical temporal differentiator is a fundamental function for ultrafast signal processing, which provides the derivative of the time-domain complex envelope of an arbitrary input optical signal. In general, an all-optical temporal differentiator can be realized using a linear optical device that has a spectral transfer function proportional to the term (ω-ω0)N, where N is the differentiation order, ω is the optical frequency variable and ω0 is the optical carrier frequency of the optical signal to be processed. This functionality can be implemented using a linear optical filter providing a linear amplitude (V-shaped) spectral response over its operation bandwidth with a complex zero at the carrier frequency of the signal under test. All-optical differentiators have been designed by use of an integrated-optic transversal filter approach [11], fiber gratings [1215], silicon ring resonator [16] and Mach-Zehnder interferometers [17]. A practically useful optical differentiation scheme needs to provide a set of performance specifications in terms of simplicity, stability, compactness, and large bandwidth. However, although the current available techniques can be used to implement all-optical temporal differentiation in a compact fashion, they can hardly offer processing bandwidths above a few THz [12].

Recently, we proposed and numerically investigated a novel ultra-broadband all-optical differentiator scheme [27] based on a simple and widely available technology, namely a wavelength-selective directional coupler made of non-identical waveguides in an integrated-waveguide or optical fiber structure [28]. The distinctive feature of the differentiator based on a directional coupler is that it can offer an extremely broad bandwidth, > 10-THz [27]. In this Letter, an optical temporal differentiator with a record operation bandwidth of ~25-THz is fabricated and experimentally demonstrated based on a compact all-fiber wavelength-selective directional coupler. The operation bandwidth provided by this device is at least one order of magnitude larger than that offered by any previously reported temporal differentiation technology.

2. Fabrication and characterization

Figure 1 shows the schematic diagram of the wavelength-selective directional coupler. Details on the design of the coupler for optical differentiation can be found in Ref [27]. The resonance wavelength (i.e., carrier wavelength of the optical signal to be differentiated) is determined by the propagation constant curve, where the propagation constants of the two waveguides are identical. A π phase shift exactly at the signal’s central frequency is achieved. Operation bandwidth of the temporal differentiator based on a wavelength-selective directional coupler is directly proportional to the coupling coefficient of the coupler. By controlling the coupling coefficient between the two waveguides in the coupler, the operation bandwidth of the temporal differentiator can be tuned in the fabrication.

 

Fig. 1 Schematic diagram of the wavelength-selective directional coupler.

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The asymmetric fiber coupler was fabricated with flame brushing technique [29] in which the butane (C3H8) and oxygen (O2) flame torch are used as heat source. During the coupler fabrication, the output power from the two fiber coupler arms was monitored in real time. The coupling ratio and excess loss were determined as a function of the coupler elongation. In addition, the spectral response of the coupler output was observed during the fabrication process, looking for a close matching with the target transfer function of the optical differentiators. We made the coupler with two different commercially available optical fibers, i.e. SMF-28 (Corning Inc.), with a core radius of 4.1 μm and an index difference of 0.47%, and CL980-20(OFS Inc.), with a core radius of 1.8 μm and an index difference of 0.96%, since their propagation constants are matched only at ~1550 nm. The elongation length was about 10 mm.

Figure 2 shows the spectral magnitude and phase responses of the designed wavelength-selective directional coupler, where the parameters of the optical fibers and structure applied in the simulation match those used in the fabrication. In Fig. 2(a), it can be seen that the desired V-shaped spectral amplitude response is achieved over an operation bandwidth of ~25-THz, centered at 1,550nm. In addition, as shown in Fig. 2(b), the spectral phase response exhibits a linear variation over the entire resonance bandwidth, besides the needed π phase shift at the central notch wavelength. Hence, the complex (amplitude and phase) spectral transfer function of the simulated directional coupler corresponds to that of an optical temporal first-order differentiator with a processing bandwidth of ~25 THz.

 

Fig. 2 Simulated spectral magnitude (a) and phase (b) responses of a fiber-optics directional coupler based on the practical parameters used in the fabrication.

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Figure 3 shows the magnitude and phase spectral responses of a fabricated optical differentiator, measured using an optical vector analyzer (OVA). Since the measurement bandwidth of the OVA is limited to about 10 THz (i.e., ~80 nm), only a fraction of the entire resonance bandwidth is covered. Figure 4(a) shows the measured magnitude spectral response of the directional coupler by using a superluminescent light emitting diodes (SLED) and an optical spectrum analyzer (OSA). It can be seen that the measured transmission spectrum agrees very well with the numerically simulated spectrum, in particular, within the operation bandwidth. The small deviation between the simulated and fabricated spectra is caused by the nonlinearity of the propagation-constant curves (dispersion curves) of the two waveguides in the directional coupler. In addition, based on the simulated results in Fig. 2(b), the spectral phase response can be reconstructed along the uncovered operation bandwidth, assuming a linear phase variation, as shown in Fig. 4(b).

 

Fig. 3 Magnitude (a) and phase (b) spectral responses of the fabricated directional coupler measured by use of an OVA; the inset shows a zoom-in view of the π phase shift at the central notch wavelength.

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Fig. 4 Magnitude spectral response (a) of the fabricated directional coupler by using a SLED and an OSA (simulated magnitude response is also included for comparison), and the numerically reconstructed spectral phase response using the measured phase response shown in Fig. 3(b), both extending over the entire operation bandwidth

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The processing error as a function of the input pulse bandwidth is then investigated based on the measured transfer function of the directional coupler shown in Fig. 2. Figure 5(a) shows the simulated results of an input Gaussian pulse with a pulse time-width (FWHM) of 35.2-fs (i.e., full-width bandwidth is 25-THz) and the output pulse from the directional coupler. Here, the pulse time-width is defined as 3-dB time-width, whereas the full-width bandwidth is defined as twice the full width at half maximum (FWHM) bandwidth. The simulated output pulse agrees well with an ideally differentiated optical pulse. To further evaluate the processing errors, the spectral response of the fabricated differentiator in Fig. 4 is employed to estimate the processing error vs. the input pulse full-width bandwidth/time-width, results shown in Fig. 5(b). There exists an optimal operation bandwidth (17-THz) where the root mean square error (RMSE) is minimized to ~0.24%. The processing error is largely increased when the input pulse bandwidth approaches the tens-of-GHz regime. This is mainly attributed to the insufficient measured depth at the central resonance notch due to the limited measurement resolution and sensitivity of the OSA.

 

Fig. 5 (a) Simulated input pulse with a full-width bandwidth of 25-THz, simulated output pulse from the directional coupler with the magnitude and phase spectral responses shown in Fig. 4, and output pulse from an ideal first-order differentiator. (b) Device processing error as a function of the input pulse bandwidth/time-FWHM

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3. Experimental demonstration

The experiment setup for time-domain characterization of the fabricated optical temporal differentiator is shown in Fig. 6 . The characterization principle is based on self-referenced Fourier-transform spectral interferometry (FTSI), which can be used to retrieve the complex temporal waveform of the pulse at the differentiator output [3032]. A nearly transform-limited Gaussian-like optical pulse from an optical parametric oscillator (OPO) laser is launched into the fabricated wavelength-selective directional coupler. To minimize the dispersion effect on pulse propagation through optical fibers, the fiber pigtails before and after the directional coupler are entirely removed and the optical pulse is directly launched into the directional coupler through a minimized fiber length (~30 cm). In the reference arm, a tunable delay line is used to tune the time spacing between the signals in the two arms (input/reference and output pulses). A short dispersion shifted fiber (DSF) is employed to direct the result of linear interference between the input (reference) pulse and the output waveform to be measured into an OSA, which is used to measured the resulting spectral interferogram. In addition, the intensity profile of the input (reference) optical pulse is measured using an autocorrelator at the output of the DSF. These data are employed for numerical reconstruction of the waveform at the coupler output.

 

Fig. 6 Experimental setup for the characterization of the fabricated 25-THz bandwidth all-optical temporal differentiator. OPO: optical parametric oscillator; OSA: optical spectrum analyzer; DSF: dispersion shifted fiber.

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In the first experiment, a nearly transform-limited Gaussian-like optical pulse with a FWHM of ~250-fs is launched into the directional coupler. The carrier wavelength of the optical pulse is tuned to match the central notch wavelength of the directional coupler, thus operating as a first-order differentiator. The measured spectra of the optical pulses before and after the directional coupler are shown in Fig. 7(a) . The temporal waveforms before and after the directional coupler are measured using the described FTSI setup, with the results shown in Fig. 7(b). The measured time-domain output pulse agrees well (RMSE is 2.1%) with the simulated ideal one (numerical derivative of the input Gaussian pulse), including the anticipated discrete π phase shift between the two consecutive Gaussian-like lobes.

 

Fig. 7 (a) Spectra of a femtosecond optical pulse before and after propagation through the fabricated directional coupler, when the pulse carrier wavelength matches the central resonance wavelength; (b) Time-domain intensity profiles of the input pulse, the measured output pulse and the numerical ideal output. The time-domain phase profile of the measured output pulse is also shown in (b).

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As an application example, a flat-top pulse generation experiment is implemented by re-shaping an input Gaussian-like optical pulse with a slightly wavelength-detuned optical differentiator [33], which in our implementation is realized using the directional coupler. Similar to the LPG-based technique reported in Ref [33], when the wavelength shift between the pulse carrier wavelength and the directional coupler's central notch wavelength is tuned to ~8 nm, as shown in Fig. 8(a) , a nearly chirp-free flat-top pulse with a FWHM of 540-fs is generated at the directional coupler's output, as shown in Fig. 8(b). It is worth noting that a key feature of this optical pulse re-shaping technique (wavelength-shifted differentiator) is that flat-top waveforms with various durations can be synthesized by use of input pulses with different time widths [33]. Using the newly reported fiber device, the duration of the generated flat-top waveform can be changed from a few picoseconds to tens of femtoseconds by simply tuning the time-width of the input pulse and correspondingly shifting the pulse carrier wavelength with respect to the directional coupler's notch.

 

Fig. 8 (a) Spectra of a femtosecond pulse before and after propagation through the fabricated directional coupler when the pulse carrier wavelength is shifted from the central resonance wavelength by ~8 nm; (b) Time-domain intensity profiles of the input pulse, the measured output pulse and the numerical ideal output. The time-domain phase profile of the measured output pulse is also shown in (b).

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4. Conclusions

In conclusion, we have reported the experimental realization of an optical temporal differentiator with a record operation bandwidth of 25 THz using an extremely simple and compact all-fiber wavelength-selective directional coupler. The reported optical temporal differentiator can be used to generate and process optical signal with temporal features down to a few tens of femtoseconds. A Gaussian-like optical pulse with a time-width of ~250-fs was accurately differentiated using this device. As an application example, a chirp-free flat-top pulse with a time-width of ~540-fs was also successfully generated.

Acknowledgments

This work was financially supported by Chosun University (2011-2012) and by the Natural Sciences and Engineering Research Council of Canada (NSERC).

References and links

1. L. Venema, “Photonics technologies,” Nat. Insight 424(6950), 809 (2003). [CrossRef]  

2. H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010). [CrossRef]  

3. R. S. Tucker, “The role of optics in computing,” Nat. Photonics 4(7), 405 (2010). [CrossRef]  

4. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011). [CrossRef]  

5. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010). [CrossRef]  

6. M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef]   [PubMed]  

7. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009). [CrossRef]  

8. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]  

9. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef]   [PubMed]  

10. J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, “Special issue on “Optical signal processing,” J. Lightwave Technol. 24(7), 2484–2486 (2006). [CrossRef]  

11. 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(1-3), 115–129 (2004). [CrossRef]  

12. J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2(3), 359–386 (2010). [CrossRef]  

13. M. Li, D. Janner, J. P. Yao, and V. Pruneri, “Arbitrary-order all-fiber temporal differentiator based on a fiber Bragg grating: design and experimental demonstration,” Opt. Express 17(22), 19798–19807 (2009). [CrossRef]   [PubMed]  

14. 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. 23(4), 251–253 (2011). [CrossRef]  

15. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006). [CrossRef]   [PubMed]  

16. F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y. Su, “Compact optical temporal differentiator based on silicon microring resonator,” Opt. Express 16(20), 15880–15886 (2008). [CrossRef]   [PubMed]  

17. Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett. 32(6), 710–712 (2007). [CrossRef]   [PubMed]  

18. M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29–33 (2010). [CrossRef]   [PubMed]  

19. J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008). [CrossRef]   [PubMed]  

20. R. Slavík, Y. Park, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008). [CrossRef]   [PubMed]  

21. T. Hirooka and M. Nakazawa, “Optical adaptive equalization of high-speed signals using time-domain optical Fourier transformation,” J. Lightwave Technol. 24(7), 2530–2540 (2006). [CrossRef]  

22. K. Dolgaleva, A. Malacarne, P. Tannouri, L. A. Fernandes, J. R. Grenier, J. S. Aitchison, J. Azaña, R. Morandotti, P. R. Herman, and P. V. S. Marques, “Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide,” Opt. Lett. 36(22), 4416–4418 (2011). [CrossRef]   [PubMed]  

23. M. A. Muriel, J. Azaña, and A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. 24(1), 1–3 (1999). [CrossRef]   [PubMed]  

24. M. H. Asghari and J. Azaña, “All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis,” Opt. Lett. 34(3), 334–336 (2009). [CrossRef]   [PubMed]  

25. M. Li and J. Yao, “All-fiber temporal photonic fractional Hilbert transformer based on a directly designed fiber Bragg grating,” Opt. Lett. 35(2), 223–225 (2010). [CrossRef]   [PubMed]  

26. M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber Bragg grating,” IEEE Photon. Technol. Lett. 22(21), 1559–1561 (2010). [CrossRef]  

27. T.-J. Ahn and J. Azaña, “Wavelength-selective directional couplers as ultrafast optical differentiators,” Opt. Express 19(8), 7625–7632 (2011). [CrossRef]   [PubMed]  

28. R. Zengerle and O. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol. 4(7), 823–827 (1986). [CrossRef]  

29. F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused coupler: Fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6(10), 1476–1482 (1988). [CrossRef]  

30. A. Trisorio, S. Grabielle, M. Divall, N. Forget, and C. P. Hauri, “Self-referenced spectral interferometry for ultrashort infrared pulse characterization,” Opt. Lett. 37(14), 2892–2894 (2012). [CrossRef]   [PubMed]  

31. L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]  

32. C. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17(10), 1795–1802 (2000). [CrossRef]  

33. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express 14(26), 12670–12678 (2006). [CrossRef]   [PubMed]  

References

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  1. L. Venema, “Photonics technologies,” Nat. Insight424(6950), 809 (2003).
    [CrossRef]
  2. H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics4(5), 261–263 (2010).
    [CrossRef]
  3. R. S. Tucker, “The role of optics in computing,” Nat. Photonics4(7), 405 (2010).
    [CrossRef]
  4. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
    [CrossRef]
  5. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics4(3), 182–187 (2010).
    [CrossRef]
  6. M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
    [CrossRef] [PubMed]
  7. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
    [CrossRef]
  8. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
    [CrossRef]
  9. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature456(7218), 81–84 (2008).
    [CrossRef] [PubMed]
  10. J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, “Special issue on “Optical signal processing,” J. Lightwave Technol.24(7), 2484–2486 (2006).
    [CrossRef]
  11. 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(1-3), 115–129 (2004).
    [CrossRef]
  12. J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J.2(3), 359–386 (2010).
    [CrossRef]
  13. M. Li, D. Janner, J. P. Yao, and V. Pruneri, “Arbitrary-order all-fiber temporal differentiator based on a fiber Bragg grating: design and experimental demonstration,” Opt. Express17(22), 19798–19807 (2009).
    [CrossRef] [PubMed]
  14. 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.23(4), 251–253 (2011).
    [CrossRef]
  15. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express14(22), 10699–10707 (2006).
    [CrossRef] [PubMed]
  16. F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y. Su, “Compact optical temporal differentiator based on silicon microring resonator,” Opt. Express16(20), 15880–15886 (2008).
    [CrossRef] [PubMed]
  17. Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett.32(6), 710–712 (2007).
    [CrossRef] [PubMed]
  18. M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun1(3), 29–33 (2010).
    [CrossRef] [PubMed]
  19. J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett.33(1), 4–6 (2008).
    [CrossRef] [PubMed]
  20. R. Slavík, Y. Park, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express16(22), 18202–18214 (2008).
    [CrossRef] [PubMed]
  21. T. Hirooka and M. Nakazawa, “Optical adaptive equalization of high-speed signals using time-domain optical Fourier transformation,” J. Lightwave Technol.24(7), 2530–2540 (2006).
    [CrossRef]
  22. K. Dolgaleva, A. Malacarne, P. Tannouri, L. A. Fernandes, J. R. Grenier, J. S. Aitchison, J. Azaña, R. Morandotti, P. R. Herman, and P. V. S. Marques, “Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide,” Opt. Lett.36(22), 4416–4418 (2011).
    [CrossRef] [PubMed]
  23. M. A. Muriel, J. Azaña, and A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett.24(1), 1–3 (1999).
    [CrossRef] [PubMed]
  24. M. H. Asghari and J. Azaña, “All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis,” Opt. Lett.34(3), 334–336 (2009).
    [CrossRef] [PubMed]
  25. M. Li and J. Yao, “All-fiber temporal photonic fractional Hilbert transformer based on a directly designed fiber Bragg grating,” Opt. Lett.35(2), 223–225 (2010).
    [CrossRef] [PubMed]
  26. M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber Bragg grating,” IEEE Photon. Technol. Lett.22(21), 1559–1561 (2010).
    [CrossRef]
  27. T.-J. Ahn and J. Azaña, “Wavelength-selective directional couplers as ultrafast optical differentiators,” Opt. Express19(8), 7625–7632 (2011).
    [CrossRef] [PubMed]
  28. R. Zengerle and O. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol.4(7), 823–827 (1986).
    [CrossRef]
  29. F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused coupler: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6(10), 1476–1482 (1988).
    [CrossRef]
  30. A. Trisorio, S. Grabielle, M. Divall, N. Forget, and C. P. Hauri, “Self-referenced spectral interferometry for ultrashort infrared pulse characterization,” Opt. Lett.37(14), 2892–2894 (2012).
    [CrossRef] [PubMed]
  31. L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B12(12), 2467–2474 (1995).
    [CrossRef]
  32. C. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B17(10), 1795–1802 (2000).
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M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber Bragg grating,” IEEE Photon. Technol. Lett.22(21), 1559–1561 (2010).
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Ayotte, N.

Azaña, J.

K. Dolgaleva, A. Malacarne, P. Tannouri, L. A. Fernandes, J. R. Grenier, J. S. Aitchison, J. Azaña, R. Morandotti, P. R. Herman, and P. V. S. Marques, “Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide,” Opt. Lett.36(22), 4416–4418 (2011).
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M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun1(3), 29–33 (2010).
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Cincontti, G.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, “Special issue on “Optical signal processing,” J. Lightwave Technol.24(7), 2484–2486 (2006).
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L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics4(3), 182–187 (2010).
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M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
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C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
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Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
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Doucet, S.

Dreschmann, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
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F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused coupler: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6(10), 1476–1482 (1988).
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Ferrera, M.

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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature456(7218), 81–84 (2008).
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Geluk, E.-J.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics4(3), 182–187 (2010).
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M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature456(7218), 81–84 (2008).
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Grenier, J. R.

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F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused coupler: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6(10), 1476–1482 (1988).
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M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
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Hillerkuss, D.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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Hoh, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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Huebner, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011).
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L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics4(3), 182–187 (2010).
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Janner, D.

Joffre, M.

Johnson, D. C.

F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused coupler: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6(10), 1476–1482 (1988).
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Opt. Commun. (1)

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the wavelength-selective directional coupler.

Fig. 2
Fig. 2

Simulated spectral magnitude (a) and phase (b) responses of a fiber-optics directional coupler based on the practical parameters used in the fabrication.

Fig. 3
Fig. 3

Magnitude (a) and phase (b) spectral responses of the fabricated directional coupler measured by use of an OVA; the inset shows a zoom-in view of the π phase shift at the central notch wavelength.

Fig. 4
Fig. 4

Magnitude spectral response (a) of the fabricated directional coupler by using a SLED and an OSA (simulated magnitude response is also included for comparison), and the numerically reconstructed spectral phase response using the measured phase response shown in Fig. 3(b), both extending over the entire operation bandwidth

Fig. 5
Fig. 5

(a) Simulated input pulse with a full-width bandwidth of 25-THz, simulated output pulse from the directional coupler with the magnitude and phase spectral responses shown in Fig. 4, and output pulse from an ideal first-order differentiator. (b) Device processing error as a function of the input pulse bandwidth/time-FWHM

Fig. 6
Fig. 6

Experimental setup for the characterization of the fabricated 25-THz bandwidth all-optical temporal differentiator. OPO: optical parametric oscillator; OSA: optical spectrum analyzer; DSF: dispersion shifted fiber.

Fig. 7
Fig. 7

(a) Spectra of a femtosecond optical pulse before and after propagation through the fabricated directional coupler, when the pulse carrier wavelength matches the central resonance wavelength; (b) Time-domain intensity profiles of the input pulse, the measured output pulse and the numerical ideal output. The time-domain phase profile of the measured output pulse is also shown in (b).

Fig. 8
Fig. 8

(a) Spectra of a femtosecond pulse before and after propagation through the fabricated directional coupler when the pulse carrier wavelength is shifted from the central resonance wavelength by ~8 nm; (b) Time-domain intensity profiles of the input pulse, the measured output pulse and the numerical ideal output. The time-domain phase profile of the measured output pulse is also shown in (b).

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