OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 23153–23161
« Show journal navigation

All-optical 1st and 2nd order integration on a chip

Marcello Ferrera, Yongwoo Park, Luca Razzari, Brent E. Little, Sai T. Chu, Roberto Morandotti, David J. Moss, and José Azaña  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 23153-23161 (2011)
http://dx.doi.org/10.1364/OE.19.023153


View Full Text Article

Acrobat PDF (1912 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate all-optical temporal integration of arbitrary optical waveforms with temporal features as short as ~1.9ps. By using a four-port micro-ring resonator based on CMOS compatible doped glass technology we perform the 1st- and 2nd-order cumulative time integral of optical signals over a bandwidth that exceeds 400GHz. This device has applications for a wide range of ultra-fast data processing and pulse shaping functions as well as in the field of optical computing for the real-time analysis of differential equations.

© 2011 OSA

1. Introduction

All-optical integrated circuits bring the promise of overcoming the limitations of electronic circuits in terms of processing speed, power consumption, and isolation from possible sources of data corruption [1

1. G. P. Agrawal, “Fiber-optic Communication Systems,” in Microwave and Optical Engineering, 3rd ed. (John Wiley & Sons, Inc. New York, 2002).

]. One of the key factors that have made electronics a dominant technology for the past 60 years is the ability to perform quite a broad range of fundamental operations using only a small number of basic building blocks [2

2. P. Kinget and M. Steyaert, “Analog VLSI Integration of Massive Parallel Processing Systems,” in The Springer International Series in Engineering and Computer Science, ed. (Kluwer Academic Publishers, Boston, Dordrecht, London, 2010).

,3

3. M. Tooley, “Electronic Circuits - Fundamentals & Applications,” in Advanced Technological and Higher National Certificates Kingston University, ed. (Elsevier Ltd., Oxford UK, 2006).

]. These include temporal differentiators and integrators, which have played a major role in the development of the first electronic ALUs (Arithmetic Logic Units). Because of its superior signal to noise ratio, the integrator is often preferred to the differentiator [4

4. A. Mehrotra and A. L. Sangiovanni-Vincentelli, Noise Analysis of Radio Frequency Circuits, ed. (Kluwer Academic Publishers, Massachusetts, 2010).

,5

5. C. W. Hsue, L. C. Tsai, and K.-L. Chen, “Implementation of First-Order and Second-Order Microwave Differentiator,” IEEE Trans. Microw. Theory Tech. 52(5), 1443–1448 (2004). [CrossRef]

] for high frequency applications.

A temporal integrator is a device that is capable of performing the time integral of an arbitrary input waveform [6

6. 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]

], and is characterized by its ability to store energy in one form or another (e.g. optical, electrical). In electronics, a simple parallel plate capacitor can achieve this, due to its inherent capability to store electrical charge, whereas to accomplish the same task in the optical domain, photons need to be stored and localized in the same fashion as a capacitor accumulates electrical charge – a well-known and difficult challenge for photonics.

The realization of an optical integrator in an integrated and monolithic form would represent a fundamental step for many ultra-fast data processing applications, including photonic bit counting [7

7. 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]

], pulse waveform shaping [1

1. G. P. Agrawal, “Fiber-optic Communication Systems,” in Microwave and Optical Engineering, 3rd ed. (John Wiley & Sons, Inc. New York, 2002).

,7

7. 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

8. 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]

], data storage [9

9. M. H. Asghari and J. Azaña, “Photonic Integrator-Based Optical Memory Unit,” IEEE Photon. Technol. Lett. 23(4), 209–211 (2011). [CrossRef]

,10

10. 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]

], analog-to-digital conversion [11

11. Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

], and real time computation of linear differential equations [12

12. 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]

]. For many of these applications, and particularly for the last-mentioned, the ability to perform optical integration even just up to the second order would be extremely useful. Indeed, a very broad family of phenomena in applied physics, engineering, and biology can be modeled by second order differential equations [13

13. G. F. Simmons, Differential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, New York, 1991).

]. In addition, the intrinsic sensitivity of optical integrators to the phase of the signal is in stark contrast to their electronic counterparts that operate on real valued temporal signals. This phase sensitivity can in principle allow for the realization of a new class of functions such as complex optical pulse shaping methods and optical memories [7

7. 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

9. M. H. Asghari and J. Azaña, “Photonic Integrator-Based Optical Memory Unit,” IEEE Photon. Technol. Lett. 23(4), 209–211 (2011). [CrossRef]

].

Recently, we demonstrated ultra-fast all optical integration in a monolithic passive device, based on a high-quality factor (Q>106) micro-ring resonator [14

14. 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 (2010) [CrossRef]

] in a CMOS compatible platform. We achieved 1st-order temporal integration of complex field optical waveforms, with a time resolution of ~8ps over an integration window exceeding 800ps, for an overall time-bandwidth product (TBP>100) well beyond the reach of electronics. However, a limitation of that device was its reduced throughput (0.015%) imposed by its very narrow resonance linewidth.

In this work, we explore the trade-off between integration bandwidth and overall energy efficiency by performing all-optical integration in a micro ring resonator with a reduced Q factor (~65.000). By lowering the Q factor, we gain multiple benefits such as increasing the time resolution as well as the efficiency of the device, together with reducing its physical dimensions. Of course, this comes at the expense of a shorter integration time window since a smaller Q results in faster energy dissipation for each round-trip. In addition, we investigate the possibility of implementing 2nd-order integration using the same device by directing the output to the secondary input of our four-port device. By doing so, we achieve 1st- and 2nd-order temporal integration of arbitrary input waveforms with time features down to ~1.9ps, with an input to output power efficiency of 1.5%, an integration bandwidth exceeding 400GHz, and an integration time window of ~12.5ps. This device offers significant promise for integrated ultrafast optical information processing, measurement and computing systems.

2. Theory

The approach to realizing an optical integrator relies on emulating the spectral transfer function of an ideal 1st-order integrator (linear optical filter), that is proportional to the following expression:
H(ω)=1j(ωω0)
(1)
where ω0 is the central frequency of the signal to be processed and ω is the optical carrier frequency. This characteristic stems from the fact that in the time domain, the temporal impulse response of the ideal 1st-order integrator hint(t) must be proportional to the unit step function u(t), which is defined by:

u(t)={0 for t<0;1 for t0;
(2)

It is immediately clear that in order to have such a response, an optical device has to be capable of storing energy (photons). We now compare H(ω) to the spectral transfer function of an optical resonant cavity, such as a Fabry-Perot resonator, in which ω0 is one of its resonant frequencies. From Fig. 1
Fig. 1 Integrator transfer function, showing a comparison between the spectral transfer function of an ideal integrator (black curve) with that of a Fabry-Perot cavity (red curve) in which one resonance matches the integrator operative frequency ω0. The figure shows the main discrepancies between these two curves around the operative frequency and at the lobes of the characteristic resonance. It also shows (blue arrows) how largely the operation (processing) bandwidth of the resonator can exceed its linewidth when it is used as integrator.
, we note that these two curves have a very similar behavior for a frequency range (defined as “integration bandwidth” in Fig. 1) that significantly exceeds the cavity linewidth (the full width at half maximum (FWHM) of the resonance). Thus, in photonics, the behavior of a 1st-order optical integrator can be emulated by means of an optical resonant cavity.

However, this technique has some limitations. From Fig. 1 we see that the two transfer functions differ from each other (i) at the lobes of the Lorentzian function that approximates the resonance spectral shape (over the cavity free spectral range) and (ii) around ω0 where the ideal integrator diverges to infinity. To understand this we consider the temporal impulse response of a resonant cavity (e.g. Fabry-Perot) for an input pulse centered at ω0 and with a time duration longer than the cavity round-trip propagation time:
hcavity(t)=exp(Kt)u(t)
(3)
where K = -(1/T)ln(r2γ), r is the field reflectivity (e.g. in the Fabry-Perot mirrors), T the round-trip propagation time in the cavity, and γ the gain in the cavity medium (γ>1 in active media and <1 in lossy materials), respectively. Notice that the field reflectivity in a Fabry-Perot cavity is equivalent to the cross-coupling field coefficient in a ring resonator. Equation (3) implies that in a resonator, for each round-trip, part of the propagating light is coupled out, causing an exponential decay of the stored light over time. To ensure that a cavity behaves as a temporal integrator, the condition r2γ = 1 (i.e. K = 0) must be met, which can be achieved in two ways: i) compensating both propagation and coupling losses by using an active device with gain (γ>1; r<1; r2γ≈1) or ii) using an ultra low-loss material platform (γ≈1) which is also mature enough to allow for a very high mirror reflectivity (r≈1). However, the first strategy implies the use of gain in the cavity and this introduces other drawbacks such as limited processing speed <20GHz as well as increased signal to noise ratio, in addition to adding fabrication steps that may not be CMOS compatible [12

12. 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]

,15

15. 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]

]. On the other hand, typical passive photonic integrators such as those based on fiber Bragg gratings (FBG), either suffer from a very limited integration time window [16

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

,17

17. M. A. Preciado and M. A. Muriel, “Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design,” Opt. Lett. 33(12), 1348–1350 (2008). [CrossRef] [PubMed]

] or require a reflectivity approaching 100% [18

18. 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]

], which is quite a stringent requirement. In this work we show that, despite some of the limitations inherent in using a resonant optical cavity to approximate an ideal optical integrator (e.g. its limited integration time window), we can achieve a level of performance that in many respects (e.g. integration speed, I/O power efficiency, etc.) succeeds much better than other approaches proposed to date (FBGs, etc.).

3. Experiment

The device is a doped silica glass high index-contrast micro ring resonator with a Q~65.000 and a FSR~575GHz. The waveguide cross section is 1.5x1.45µm2 while the ring radius is 47.5µm. The ring geometry, together with its operating principle as well as a SEM image of the device cross section, are shown in Fig. 2
Fig. 2 Schematic of the all-optical integrator. The image on the left shows a SEM image of the micro-ring resonator cross section (taken prior to the deposition of the SiO2 cladding). The figure on the right depicts the ring resonator device and illustrates the overall I/O scheme of the cavity when it operates as an integrator.
.

The glass films were deposited by plasma enhanced chemical vapor deposition (PECVD) while the waveguide pattern was implemented using photolithography and reactive ion etching. The fabrication process is CMOS compatible with no need for post annealing at high temperature to reduce losses. The most important characteristic of this device that enabled us to exploit our cavities as all-optical integrators is their extremely low propagation loss, at less than 0.06dB/cm [19

19. M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. T. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008). [CrossRef]

,20

20. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. T. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4(1), 41–45 (2010). [CrossRef]

].

As we can see from Fig. 3, in the case of single integration (block-a), the device simply consisted of the micro ring resonator plus an input polarization controller used to set the polarization state to TM. For the double integration scheme (block-b), the 1st order integration signal coming out from the drop port was re-directed to the through port to be integrated for a second time. In this configuration, a second polarization controller was placed right before the through port to reset the polarization to TM since the propagation inside the ring slightly changed the signal polarization state. For the 2nd-order integration scheme (Fig. 3-block-b) an optical isolator was necessary in order to block any residual signal that was not completely coupled into the ring from the input port, since the bandwidth of the input waveforms exceeded the resonator linewidth.

The optical power spectra of both the input and output of the device are shown in Fig. 4a
Fig. 4 (a) Optical spectra of the laser pulses (input of the integrator, dashed line) and output of the resonator (solid line) recorded at the drop port. (b) The experimentally measured temporal profile of the output of the device (black solid curve), representing the 1st-order integral of the laser pulses, as well as the theoretically calculated integral (blue dashed curve), and the theoretical response of an equivalent cavity (magenta solid curve) with the same photon-life time of our resonator (~12.5ps). The inset in (b) is the input laser pulse temporal profile (red curve). All experimental measurements were obtained using the FTSI based approach mentioned in the text.
, while the corresponding temporal measurements (normalized field amplitude Vs time in ps) are shown in Fig. 4b.

Figure 4b reports both the experimental (black solid curve - retrieved by FTSI) and the theoretical (blue dashed line) 1st order integral of the input signal as generated by the laser. The red curve in the inset represents the temporal profile of the optical pulses generated by the laser.

The theoretical integral is evaluated considering an ideal integrator, thus an infinite photon life-time inside the cavity. This plot estimates how well our ring emulates a perfect integrator. However, another important comparison can be made by reporting the theoretical response of an equivalent cavity with the same photon-life time of our resonator (~12.5ps). This is described by the magenta solid line in Fig. 4b, and it allows us to judge how far our ring is from an ideal equivalent cavity affected by the same losses. This plot was evaluated by performing the convolution between Eq. (3) (in which K was estimated respect to a photon life-time of 12.5ps) and the ideal pulse train as emitted by the laser (Fig. 4b inset).

It is worth mentioning that the 1st-order integral reported in Fig. 4b is approximately equal to the temporal impulse response of the integrator, since the spectral content of the pulse very nearly matches the processing bandwidth of the device. This information was preliminary obtained by comparing the (experimentally measured) operative resonance with the power spectrum of an ideal integrator, and then roughly estimating the frequency range within which these two curves almost overlap. The resulting integration bandwidth was estimated to be >400GHz, a value which is comparable to the FSR of the device (~575GHz) but much wider than the resonator linewidth (~3GHz).

The input pulse shown in the inset of Fig. 4b was measured by using the set-up in Fig. 3 from which we removed the integrator block and shielded one arm of the interferometer. The pulse temporal profile was obtained by fitting the FTSI-obtained waveform with a Gaussian profile whose full width at half maximum resulted in a pulse-width of ~1.9ps (see inset Fig. 4b). From Fig. 4b, we were also able to measure the device integration time window to be as long as ~12.5ps, defined as the decay time of the integrator impulse response, required to reach 90% of the maximum field amplitude.

Figure 5
Fig. 5 Experimental results. (a) the 1st- and (b) 2nd-order integrals of the in-phase signal; (c) the 1st- and (d) the 2nd-order integrals for the π-shifted pulses. For all these plots, the solid black curves represent the experimentally measured temporal profiles obtained using the FTSI based method described in the text. The dashed blue lines correspond to the theoretical cumulative time integrals. Finally, the solid green lines are temporal convolution products. For the case of the 1st order integral, the convolution was performed between the corresponding ideal input and the impulse response of Fig. 4b. For the 2nd order integral, the convolution is performed between the FTSI-recovered signal of the 1st integral and the same impulse response. All the input waveforms represented by the red curves of the insets in Fig. 4b and Fig. 5a,c are ideal Gaussian approximations of the experimentally measured input signals, and they were used to evaluate the correspondent theoretical cumulative time integral.
shows the results of the second set of experiments, where the Michelson interferometer was used to generate two additional input signals, represented by the red curves in the insets of Fig. 5a,c. These two input waveforms consisted of in-phase (Inset Fig. 5a) and π-phase-shifted (Inset Fig. 5c) pulse couplets, respectively. By coarsely varying the optical path difference of the interferometer, the temporal distance between these pulses was set to ~30ps for both the in-phase and π-phase-shifted pulses. The phase shift between pulses was precisely fine-tuned using a piezo-controller mounted on one of the two mirrors of the pulse shaper. The magnitude of the phase shift was monitored by measuring the optical spectral interference between the two pulses (for example, a π (zero)-phase shift between the two delayed pulses translates into a zero (peak) in the spectral interference pattern at the pulses’ central frequency).

The main plots in Fig. 5 represent: (a) the 1st- and (b) 2nd-order integrals of the in-phase pulses, while (c) the 1st- and (d) the 2nd-order integrals of the π-shifted pulse train. For all plots, the solid black curves are the experimentally measured temporal profiles, as directly recovered from the experimental spectra. The dashed blue lines correspond to the theoretical cumulative time integrals of the corresponding ideal input waveforms. Finally, the solid green lines are temporal convolution products.

For the case of the 1st order integral, the convolution was performed between the corresponding ideal input and the impulse response of Fig. 4b. For the 2nd -order integral, the convolution is performed between the FTSI-recovered signal of the 1st -order and the same impulse response. The convolution plots, besides being a further demonstration of the robustness of our system, also prove our original assumption that the 1st-order integral (black solid curve) reported in Fig. 4b can be considered the impulse response of our system. In fact, only under this condition we can have good agreement between the convolution plots and the experimentally calculated integrals. All the input waveforms represented by the red curves of the insets in Fig. 4b and Fig. 5a,c are ideal Gaussian approximations of the experimentally measured input signals, and they were used to evaluate the correspondent theoretical cumulative time integral.

Because of the intrinsic similarities in terms of general concept and experimental set-up, it might be worth recalling the work of A. P. Heberle and associates in which the formation and the recombination of excitons is controlled by using phase-locked femtosecond pulses [24

24. A. P. Heberle, J. J. Baumberg, and K. Köhler, “Ultrafast coherent control and destruction of excitons in quantum wells,” Phys. Rev. Lett. 75(13), 2598–2601 (1995). [CrossRef] [PubMed]

]. By looking at this experiment one can think to use the quantum well in which the excitons formation takes place as a sort of loadable capacity in the same manner we used our ring resonator. However, while our integrator storage capability is mostly limited by technological issues (e.g. by reducing losses in principle we can indefinitely extend the integration window), the possibility of employing Heberle's quantum well in a capacitor fashion is forbidden by fundamental physical phenomena such as the limited excitons phase coherence time.

Going back to our optical integrator, our results clearly show that this device effectively acts as a complex-field cumulative temporal integrator with an operational bandwidth that exceeds 400GHz. The signal profiles were chosen to demonstrate the ability to perform important functions such as ultra-fast optical counting (in-phase pulses) and memories (π-shifted pulses) [7

7. 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

9. M. H. Asghari and J. Azaña, “Photonic Integrator-Based Optical Memory Unit,” IEEE Photon. Technol. Lett. 23(4), 209–211 (2011). [CrossRef]

]. The 2nd order integrals also fit quite well to both the theoretical cumulative integral and the convolution signal, thus proving the robustness of this device. One of the most efficient ways to perform higher order optical integration makes use of FBG-based components [6

6. 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]

]. Our approach avoids the need to concatenate identical fundamental (1st-order integration) devices to achieve higher order integration, while drastically reduces the technological requirements that would otherwise be needed with FBG based approaches. Our results demonstrate that the micro-ring cavity solution to attain higher order integration, is an effective scheme to maximize scalability while at the same time minimizing the complexity of the device.

While the relatively limited integration window of our low-Q resonators may still preclude their use for some applications such as optical memories [9

9. M. H. Asghari and J. Azaña, “Photonic Integrator-Based Optical Memory Unit,” IEEE Photon. Technol. Lett. 23(4), 209–211 (2011). [CrossRef]

] at least in the present passive configuration, their integration bandwidth compares very favorably with state-of-the-art electronic systems. When combined with their simple design and well accepted fabrication processes, this demonstrates their potential as fundamental components for future ultra-fast optical processing circuits.

4. Conclusions

We report a 1st- and 2nd-order on-chip ultra-fast all-optical integrator, achieving a processing speed greater than 400GHz (corresponding to a time resolution of ~1.9ps). By adopting comparatively low-Q cavities (Q~65.000) we improve the device throughput as well as the processing speed, thus demonstrating that higher order integration can be obtained with almost no increase in the overall device complexity. This work represents an important step towards the realization of efficient optical signal-processing circuits capable of overcoming the limitations in bandwidth and power consumption imposed by electronics.

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) contract no. PDF-387780-2010 and the Australian Research Council (ARC) Discovery Projects and Centres of Excellence programs.

References and links

1.

G. P. Agrawal, “Fiber-optic Communication Systems,” in Microwave and Optical Engineering, 3rd ed. (John Wiley & Sons, Inc. New York, 2002).

2.

P. Kinget and M. Steyaert, “Analog VLSI Integration of Massive Parallel Processing Systems,” in The Springer International Series in Engineering and Computer Science, ed. (Kluwer Academic Publishers, Boston, Dordrecht, London, 2010).

3.

M. Tooley, “Electronic Circuits - Fundamentals & Applications,” in Advanced Technological and Higher National Certificates Kingston University, ed. (Elsevier Ltd., Oxford UK, 2006).

4.

A. Mehrotra and A. L. Sangiovanni-Vincentelli, Noise Analysis of Radio Frequency Circuits, ed. (Kluwer Academic Publishers, Massachusetts, 2010).

5.

C. W. Hsue, L. C. Tsai, and K.-L. Chen, “Implementation of First-Order and Second-Order Microwave Differentiator,” IEEE Trans. Microw. Theory Tech. 52(5), 1443–1448 (2004). [CrossRef]

6.

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]

7.

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.

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]

9.

M. H. Asghari and J. Azaña, “Photonic Integrator-Based Optical Memory Unit,” IEEE Photon. Technol. Lett. 23(4), 209–211 (2011). [CrossRef]

10.

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]

11.

Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

12.

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]

13.

G. F. Simmons, Differential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, New York, 1991).

14.

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 (2010) [CrossRef]

15.

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]

16.

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

17.

M. A. Preciado and M. A. Muriel, “Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design,” Opt. Lett. 33(12), 1348–1350 (2008). [CrossRef] [PubMed]

18.

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]

19.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. T. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008). [CrossRef]

20.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. T. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4(1), 41–45 (2010). [CrossRef]

21.

Y. Park, F. Li, and J. Azaña, “Characterization and optimization of optical pulse differentiation using spectral interferometry,” IEEE Photon. Technol. Lett. 18(17), 1798–1800 (2006). [CrossRef]

22.

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]

23.

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]

24.

A. P. Heberle, J. J. Baumberg, and K. Köhler, “Ultrafast coherent control and destruction of excitons in quantum wells,” Phys. Rev. Lett. 75(13), 2598–2601 (1995). [CrossRef] [PubMed]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(070.7145) Fourier optics and signal processing : Ultrafast processing

ToC Category:
Integrated Optics

History
Original Manuscript: September 14, 2011
Revised Manuscript: October 18, 2011
Manuscript Accepted: October 18, 2011
Published: October 31, 2011

Citation
Marcello Ferrera, Yongwoo Park, Luca Razzari, Brent E. Little, Sai T. Chu, Roberto Morandotti, David J. Moss, and José Azaña, "All-optical 1st and 2nd order integration on a chip," Opt. Express 19, 23153-23161 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23153


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. P. Agrawal, “Fiber-optic Communication Systems,” in Microwave and Optical Engineering, 3rd ed. (John Wiley & Sons, Inc. New York, 2002).
  2. P. Kinget and M. Steyaert, “Analog VLSI Integration of Massive Parallel Processing Systems,” in The Springer International Series in Engineering and Computer Science, ed. (Kluwer Academic Publishers, Boston, Dordrecht, London, 2010).
  3. M. Tooley, “Electronic Circuits - Fundamentals & Applications,” in Advanced Technological and Higher National Certificates Kingston University, ed. (Elsevier Ltd., Oxford UK, 2006).
  4. A. Mehrotra and A. L. Sangiovanni-Vincentelli, Noise Analysis of Radio Frequency Circuits, ed. (Kluwer Academic Publishers, Massachusetts, 2010).
  5. C. W. Hsue, L. C. Tsai, and K.-L. Chen, “Implementation of First-Order and Second-Order Microwave Differentiator,” IEEE Trans. Microw. Theory Tech.52(5), 1443–1448 (2004). [CrossRef]
  6. 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]
  7. Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express16(22), 17817–17825 (2008). [CrossRef] [PubMed]
  8. 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]
  9. M. H. Asghari and J. Azaña, “Photonic Integrator-Based Optical Memory Unit,” IEEE Photon. Technol. Lett.23(4), 209–211 (2011). [CrossRef]
  10. 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. Express17(15), 12835–12848 (2009). [CrossRef] [PubMed]
  11. Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE7797, 1–8 (2010).
  12. 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]
  13. G. F. Simmons, Differential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, New York, 1991).
  14. 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 (2010) [CrossRef]
  15. 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]
  16. J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett.33(1), 4–6 (2008). [CrossRef] [PubMed]
  17. M. A. Preciado and M. A. Muriel, “Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design,” Opt. Lett.33(12), 1348–1350 (2008). [CrossRef] [PubMed]
  18. 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]
  19. M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. T. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics2(12), 737–740 (2008). [CrossRef]
  20. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. T. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010). [CrossRef]
  21. Y. Park, F. Li, and J. Azaña, “Characterization and optimization of optical pulse differentiation using spectral interferometry,” IEEE Photon. Technol. Lett.18(17), 1798–1800 (2006). [CrossRef]
  22. 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]
  23. 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). [CrossRef]
  24. A. P. Heberle, J. J. Baumberg, and K. Köhler, “Ultrafast coherent control and destruction of excitons in quantum wells,” Phys. Rev. Lett.75(13), 2598–2601 (1995). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited