## New design for photonic temporal integration with combined high processing speed and long operation time window |

Optics Express, Vol. 19, Issue 2, pp. 425-435 (2011)

http://dx.doi.org/10.1364/OE.19.000425

Acrobat PDF (1146 KB)

### Abstract

We propose and experimentally prove a novel design for implementing photonic temporal integrators simultaneously offering a high processing bandwidth and a long operation time window, namely a large time-bandwidth product. The proposed scheme is based on concatenating in series a time-limited ultrafast photonic temporal integrator, e.g. implemented using a fiber Bragg grating (FBG), with a discrete-time (bandwidth limited) optical integrator, e.g. implemented using an optical resonant cavity. This design combines the advantages of these two previously demonstrated photonic integrator solutions, providing a processing speed as high as that of the time-limited ultrafast integrator and an operation time window fixed by the discrete-time integrator. Proof-of-concept experiments are reported using a uniform fiber Bragg grating (as the original time-limited integrator) connected in series with a bulk-optics coherent interferometers’ system (as a passive 4-points discrete-time photonic temporal integrator). Using this setup, we demonstrate accurate temporal integration of complex-field optical signals with time-features as fast as ~6 ps, only limited by the processing bandwidth of the FBG integrator, over time durations as long as ~200 ps, which represents a 4-fold improvement over the operation time window (~50 ps) of the original FBG integrator.

© 2011 OSA

## 1. Introduction

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

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

11. M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. **35**(8), 1191–1193 (2010). [CrossRef] [PubMed]

*complex-field envelope*of arbitrary optical signals with bandwidths easily above a few hundreds of GHz, well beyond the reach of any analog or digital electronic solution. Photonic temporal integrators have already been proposed for various interesting applications, including ultra-short pulse shaping [2

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

4. N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. **24**(1), 563–572 (2006). [CrossRef]

**2**(3), 359–386 (2010). [CrossRef]

5. 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]

6. Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express **17**(15), 12835–12848 (2009). [CrossRef] [PubMed]

**2**(3), 359–386 (2010). [CrossRef]

11. M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. **35**(8), 1191–1193 (2010). [CrossRef] [PubMed]

3. N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. **45**(26), 6785–6791 (2006). [CrossRef] [PubMed]

6. Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express **17**(15), 12835–12848 (2009). [CrossRef] [PubMed]

7. N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. **32**(20), 3020–3022 (2007). [CrossRef] [PubMed]

3. N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. **45**(26), 6785–6791 (2006). [CrossRef] [PubMed]

6. Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express **17**(15), 12835–12848 (2009). [CrossRef] [PubMed]

**2**(3), 359–386 (2010). [CrossRef]

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

11. M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. **35**(8), 1191–1193 (2010). [CrossRef] [PubMed]

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

9. Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express **16**(22), 17817–17825 (2008). [CrossRef] [PubMed]

9. Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express **16**(22), 17817–17825 (2008). [CrossRef] [PubMed]

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

9. Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express **16**(22), 17817–17825 (2008). [CrossRef] [PubMed]

**2**(3), 359–386 (2010). [CrossRef]

**33**(1), 4–6 (2008). [CrossRef]

**35**(8), 1191–1193 (2010). [CrossRef] [PubMed]

3. N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. **45**(26), 6785–6791 (2006). [CrossRef] [PubMed]

7. N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. **32**(20), 3020–3022 (2007). [CrossRef] [PubMed]

*N*amplitude and phase equalized time impulses in response to an input temporal impulse (

*N*= 2, 3, 4 …). We demonstrate that if the time period of the resonant cavity is properly fixed, then this simple scheme enables increasing the operation time window of the original time-limited ultrafast optical integrator by

*N*times without affecting the processing bandwidth of the original time-limited integrator (i.e. simultaneously offering the ultra-high processing bandwidth of the time-limited integrator). If an active optical resonant cavity, with

*N*→ ∞, were used, then an unlimited integration time window could be achieved. For proof-of-concept demonstrations, here we have experimentally extended the operation time window of a 5 mm FBG integrator, capable of accurate integration of optical signals with time features as fast as ~6 ps, by four times, from ~50 ps (original value) to ~200 ps, using a cascaded coherent two-arm interferometer operating as a 4-point discrete-time optical integrator.

## 2. Time-limited passive photonic temporal integrators

*h(t),*i.e. response to the temporal impulse

*δ*(

*t*) (Dirac-delta), is proportional to the unit step function

*u*(

*t*) [1]where

*t*is the time variable. A time-limited version of this ideal impulse response can be realized using a single weak-coupling uniform FBG operating in reflection [8

**33**(1), 4–6 (2008). [CrossRef]

*T*,

*h*,where

_{T}(t)*T*is the round-trip propagation time through the total FBG length, and

*∏*((

*t−T/2*)

*/T*) is the square function of duration

*T*, centered at

*T*/2, i.e. this is a constant in the interval

*0≤t≤T*. The corresponding reflection field spectrum is given by

*H*where

_{T}(f)∝ sinc(fT)exp(-jπfT)*sinc(f)*=

*sin(πf)/(πf)*and

*f*is the base-band frequency variable (around the Bragg frequency of the FBG, which should be made to coincide with the input signal optical carrier frequency) [10

10. M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. **27**(17), 3888–3895 (2009). [CrossRef]

*H*) and the corresponding temporal impulse response are plotted in Fig. 1(a) and (b) with red-solid lines, respectively. The artifacts (overshoots) in the temporal impulse response plotted in Fig. 1(b), generally known as Gibbs phenomenon, are due to the limited sweeping frequency range in the numerical simulation. It should be noted that the output signal from the integrator device is not necessarily zero outside the integration time window (0≤

_{T}(f)*t*≤

*T*). The additional feature in the output signal outside the operation time window of the FBG integrator (unwanted signal) is associated with the tail of the convolution between the input signal and the time-limited impulse response of the FBG integrator. If necessary, an additional temporal modulation mechanism may be used to extract the valid integrated waveform from the full temporal pattern of the output signal. One potential solution for this purpose can be the use of intensity electro-optic modulation (EOM) of the output optical signal from the FBG integrator with a square-like electronic temporal window. As a main critical limitation, the weak-coupling FBG filter performs accurate temporal integration only over a limited time window, i.e. the time duration of the grating impulse response,

*T*, which in turns is fixed by the round-trip propagation time through the entire FBG length.

**16**(22), 17817–17825 (2008). [CrossRef] [PubMed]

13. R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. **18**(1), 90–101 (2000). [CrossRef]

*sinc*function only over a limited bandwidth around the grating resonance (Bragg) frequency. Thus, the processing bandwidth of the FBG integrator is ultimately determined by the frequency bandwidth over which the grating reflection spectrum approaches the ideal sinc function (notice that this bandwidth is typically larger than the frequency extend of the main lobe in the FBG reflectivity).

## 3. Operation principle of the proposed solution for extending the operation time-window of the time-limited integrators

*T*), see Fig. 2 . Mathematically, in the temporal domain, the impulse response of the proposed configuration,

*h(t)*, can be derived as the convolution of the temporal impulse response of the discrete-time optical integrator,

*N*= 2, 3, 4 …), with that of the original time-limited integrator, as defined by Eq. (2):where ⊗ represents convolution. Equation (3) implies that the temporal impulse response of the proposed configuration emulates the impulse response of an ideal integrator (unit-step function) over an increased temporal duration, i.e.

*N*×

*T*. The idea is illustrated graphically in Figure 2: Multiple (

*N*) copies of the input impulse are first generated with a repetition period of

*T*which is the temporal impulse response of the employed discrete-time optical integrator.

*T*) for each impulse in the generated train, is a squared temporal function extending over the FBG operation time window,

*T*(the FBG impulse response is plotted with a dashed red line). In this way, a squared temporal impulse response with a duration

*N*times longer than that of the original FBG integrator is obtained at the device’s output. In the case of using an active optical resonant cavity as the discrete-time optical integrator, in which

*N*→

*∞*, an unlimited operation time window could be achieved using this configuration. Considering the case of using a passive discrete-time optical integrator, the operation time window of the proposed device is still limited (

*N*×

*T*), thus an additional time-modulation mechanism may be used to eliminate the unwanted signals outside the extended operation time window (

*N*×

*T*), e.g. using EOM, as described above.

*H(f)*, the reflection field spectrum of the time-limited FBG integrator,

*H*[10

_{T}(f) ∝ sinc(fT)exp(-jπfT)10. M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. **27**(17), 3888–3895 (2009). [CrossRef]

*N*-point discrete-time optical integrator with a free-spectral-range equal to the inverse of the operation time window of the time-limited integrator,

*N*= 4) integrators, with the definitions given above, are plotted in Fig. 3(a) with red-dotted and blue-dashed lines, respectively. The spectral response of a system which cascades these two integrators in series, obtained by numerical multiplication of the two individual spectral responses, is plotted in Fig. 3(a) with a green-solid line. In general, the combined spectral response can be analytically derived as follows

*N*-fold increased operation time window, i.e. with an operation time window of

*N*×

*T*.

*N*→ ∞, as the discrete optical integrator, the spectral field response of the discrete-time integrator can be expressed as

*H*[7

_{C}(f) = 1/(1-e^{-j2πfT})7. N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. **32**(20), 3020–3022 (2007). [CrossRef] [PubMed]

## 4. Experimental demonstrations and discussions

*Δλ*≈8 nm around the FBG central wavelength of

*λ*≈1550.5 nm. The coherence time of this FBG integrator is

_{0}*τ*≈

_{c}*λ*

_{0}^{2}/

*cΔλ*= 1 ps where

*c*is the speed of light in the vacuum. The grating physical length fixed a maximum integration time window of

*T*~50 ps. This same grating was previously demonstrated for temporal integration of ultrafast optical signals with time features as fast as ~6 ps, corresponding to a processing bandwidth of a few hundreds of GHz [9

**16**(22), 17817–17825 (2008). [CrossRef] [PubMed]

_{1}and I

_{2}in the figure) with relative delays Δτ

_{1}~Δτ

_{2}/2 ~

*T*~50 ps. The relative time delays of the two stage interferometric setup were adjusted accurately using high-resolution actuators (with 30 nanometer spatial resolution) (Newport Inc.) to generate four in-phase replicas of the input ultra-short impulse with a repetition period equal to

*T*. The time period of the input optical carrier at a wavelength of ~1550.5 nm is ~5.2 fs. Since this period is much shorter than the coherence time of the FBG integrator (~1 ps), the copies of the output signal are coherently superimposed. This shows that the proposed integrator is working as a coherent integrator.

**16**(22), 17817–17825 (2008). [CrossRef] [PubMed]

15. 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]

_{1}) and an integrator with four times the original operation time window (using the 4-point discrete-time integrator based on two concatenated interferometers, I

_{1}and I

_{2}) are plotted with solid-curves in Figs. 5(a) to (c) , respectively. For comparison, the numerically calculated integral of the input temporal impulse waveform is also plotted in each figure with a dashed-curve (shifted from origin for better comparison). As expected, the operation time window of the original FBG integrator was increased up to four times using a passive 4-point discrete-time optical integrator (two cascaded interferometers). Using our experimental setup, we have demonstrated accurate temporal integration of complex-field optical signals with time-features as fast as ~6 ps, over time durations as long as ~200 ps. This translates into a time-bandwidth product (TBP) of ~33.33 which is ~4 times higher than that of the original time-limited integrator.

*coherent*optical temporal integration process. As a result, the four replicas of the input signal generated in the cascaded interferometers must be all in phase while also having the exact relative delay fixed by the operation time window of the original integrator. High-resolution actuators in our bulk-optics interferometric setup were necessary to achieve these stringent specifications. We believe that the proposed concept would greatly benefit from implementation in a robust and stable integrated-waveguide format.

**16**(22), 17817–17825 (2008). [CrossRef] [PubMed]

10. M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. **27**(17), 3888–3895 (2009). [CrossRef]

*N*-point discrete-time optical integrator), the temporal impulse response of the new integrator is

*N*times longer than that of the original FBG integrator and as a result, the corresponding spectral response exhibits a pass-band frequency width that is

*N*times narrower than that of the original FBG integrator. Thus, the EE of an integrator composed by a time-limited integrator concatenated with an

*N*-point discrete-time optical integrator is

*N*times lower than that of the time-limited integrator. In other words, in this new scheme, the longer operation time window for the integrator is achieved at the expense of a reduced power efficiency of the device. This trade-off could be overcome by use of an active resonant cavity for implementing the discrete-time optical integrator.

## 5. Conclusions

## Acknowledgements

## References and links

1. | A. V. Oppenheim, A. S. Willsky, and S. Hamid, Signals and Systems, 2nd ed. Upper Saddle River, (NJ: Prentice Hall, 1996). |

2. | J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. |

3. | N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. |

4. | N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. |

5. | 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 |

6. | Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express |

7. | N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. |

8. | J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. |

9. | Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express |

10. | M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. |

11. | M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. |

12. | Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE |

13. | R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. |

14. | T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. |

15. | 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 |

**OCIS Codes**

(050.2770) Diffraction and gratings : Gratings

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

(120.2440) Instrumentation, measurement, and metrology : Filters

(320.5540) Ultrafast optics : Pulse shaping

(070.7145) Fourier optics and signal processing : Ultrafast processing

**ToC Category:**

Optics in Computing

**History**

Original Manuscript: November 8, 2010

Revised Manuscript: December 15, 2010

Manuscript Accepted: December 16, 2010

Published: January 3, 2011

**Citation**

Mohammad H. Asghari, Yongwoo Park, and José Azaña, "New design for photonic temporal integration with combined high processing speed and long operation time window," Opt. Express **19**, 425-435 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-425

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### References

- A. V. Oppenheim, A. S. Willsky, and S. Hamid, Signals and Systems, 2nd ed. Upper Saddle River, (NJ: Prentice Hall, 1996).
- J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2(3), 359–386 (2010). [CrossRef]
- N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006). [CrossRef] [PubMed]
- N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. 24(1), 563–572 (2006). [CrossRef]
- 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]
- Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009). [CrossRef] [PubMed]
- N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007). [CrossRef] [PubMed]
- J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008). [CrossRef]
- Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008). [CrossRef] [PubMed]
- M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. 27(17), 3888–3895 (2009). [CrossRef]
- M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010). [CrossRef] [PubMed]
- Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).
- R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. 18(1), 90–101 (2000). [CrossRef]
- T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]
- 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]

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