One-chip integration of optical correlator based on slow-light devices

We propose and demonstrate an on-chip optical correlator, in which two types of photonic crystal slow-light waveguides are integrated and operated as an optical delay scanner and a two-photon-absorption photodetector. The footprint of the device, which was fabricated using a CMOS-compatible process, was 1.0 × 0.3 mm, which is substantially smaller than that of conventional optical correlators with free-space optics. We observed optical pulses using this device and confirmed the correspondence of pulse waveforms with those observed using a commercial correlator when the pulse width was 5−7 ps. This device will achieve one-chipping of an optical correlator and related measurement instruments. ©2015 Optical Society of America OCIS codes: (130.5296) Photonic crystal waveguides; (230.3120) Integrated optics devices. References and links 1. J. An, K. Pyun, O. Kwon, and D. E. Kim, “An autocorrelator based on a Fabry-Perot interferometer,” Opt. Express 21(1), 70–78 (2013). 2. C. Monat, C. Grillet, M. Collins, A. Clark, J. Schroeder, C. Xiong, J. Li, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Integrated optical auto-correlator based on third-harmonic generation in a silicon photonic crystal waveguide,” Nat. Commun. 5(2), 3246 (2014). 3. H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, “Single nanowire optical correlator,” Nano Lett. 14(6), 3487–3490 (2014). 4. F. R. Laughton, J. H. Marsh, D. A. Barrow, and E. L. Portnoi, “The Two-Photon-Absorption Semiconductor Waveguide Autocorrelator,” IEEE J. Quantum Electron. 30(3), 838–845 (1994). 5. T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for autocorrelation measurements,” Appl. Phys. Lett. 81(7), 1323 (2002). 6. Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multipleand single-shot autocorrelator based on twophoton conductivity in semiconductors,” Opt. Lett. 17(9), 658–660 (1992). 7. J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22(17), 1344– 1346 (1997). 8. D. J. Kane and R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18(10), 823–825 (1993). 9. A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Subpicosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photonics 5(10), 618–623 (2011). 10. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26(12), 932–934 (2001). 11. P. Gabolde and R. Trebino, “Single-frame measurement of the complete spatiotemporal intensity and phase of ultrashort laser pulses using wavelength-multiplexed digital holography,” J. Opt. Soc. Am. B 25(6), A25–A33 (2008). 12. P. Bowlan, U. Fuchs, R. Trebino, and U. D. Zeitner, “Measuring the spatiotemporal electric field of tightly focused ultrashort pulses with sub-micron spatial resolution,” Opt. Express 16(18), 13663–13675 (2008). 13. N. Ishikura, R. Hosoi, R. Hayakawa, T. Tamanuki, M. Shinkawa, and T. Baba, “Photonic crystal tunable slow light device integrated with multi-heaters,” Appl. Phys. Lett. 100(22), 221110 (2012). 14. R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “High-speed delay tuning of slow light in pin-diodeincorporated photonic crystal waveguide,” Opt. Lett. 38(15), 2680–2682 (2013). 15. R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “Two-photon absorption photodiodes in Si photoniccrystal slow-light waveguides,” Appl. Phys. Lett. 102(3), 031114 (2013). #242716 Received 11 Jun 2015; revised 26 Jul 2015; accepted 28 Jul 2015; published 30 Jul 2015 (C) 2015 OSA 10 Aug 2015 | Vol. 23, No. 16 | DOI:10.1364/OE.23.020767 | OPTICS EXPRESS 20767 16. M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011). 17. T. Tamura, K. Kondo, Y. Terada, Y. Hinakura, N. Ishikura, and T. Baba, “Silica-Clad Silicon Photonic Crystal Waveguides for Wideband Dispersion-Free Slow Light,” J. Light. Technol. (2015, presently available on line). 18. F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011).


Introduction
An optical correlator is widely used to observe short optical pulses with a time duration of less than 10 ps, which is difficult for optoelectronic devices.It fundamentally comprises an optical delay scanner and a nonlinear photodetector.Because a movable mirror is usually used as the delay scanner, commercial optical correlators are box-sized devices.Thus far, downsizing of optical correlators has been studied using a Fabry-Perot resonator as a delay scanner, a photonic crystal waveguide (PCW) or wire waveguide as a second harmonic generator (SHG) in front of the photodetector [1][2][3], and two-photon-absorption photodetector (TPA-PD) instead of SHG [4][5][6][7].Furthermore, some methods other than optical correlators exist for measuring short optical pulses, which include frequency-resolved optical gating (FROG) [8,9], simplified FROG [10], digital holography [11], and near-field scanning microscopy [12], among others.However, all these methods involve large systems with free-space optics.Thus far, no precedents exist for demonstrating on-chip optical correlators and short pulse measurement instruments.
Si photonics is a fascinating platform that enables not only large-scale photonic integration on a silicon-on-insulator (SOI) wafer with high uniformity and reproducibility but also low-cost mass production via a CMOS-compatible process.We have studied an Si PCW fabricated by such a process and its slow-light generation, demonstrating tunable delays [13,14] and a TPA-PD [15] at telecom wavelengths.In this study, we propose and demonstrate an on-chip optical correlator in which the two basic components are integrated monolithically.

Design
Figure 1 shows a schematic of the device structure.Si-wire waveguides terminated by spotsize converters at end facets of the chip were used for optical wiring.To avoid nonlinear induced absorption and pulse distortion in the wire waveguides, straight sections of the optical wiring was widened through a taper so that the optical intensity was suppressed.The input optical pulse was divided into a reference branch and a delay scanner branch through a multi-mode interferometer (MMI) 1 × 2 branch.A heater was integrated into the reference branch for phase tuning, where the change of the delay by the heating was negligible.In a delay scanner based on a lattice-shifted photonic crystal waveguide (LSPCW) [13][14][15][16], the delay is scanned by integrated heaters integrated beside the LSPCW.This delay scanner is followed by a LSPCW dispersion controller operated by other heaters.The operation of the delay scanner and dispersion controller can be observed by tapping off the light via an MMI 10% tap placed adjacent to the LSPCW and extracting it through monitor port #1 for observation using an external cross-correlator.Eventually, pulses in the two branches are joined through a 2 × 1 MMI combiner, where the in-phase condition between the two branches is maintained by the heater of the reference branch; the pulses are subsequently launched into the LSPCW with a pn junction, which functions as a TPA-PD.The TPA efficiency is enhanced by low-dispersion slow light.A heater was also placed on the LSPCW to adjust the slow-light band.We obtained an auto-correlation waveform by measuring the photocurrent from the TPA-PD as a function of the delay.Now, we obtain the expression for the photocurrent.The temporal electric field of the pulse in each branch is represented as where ω and φ i are the center frequency and phase, respectively, and i = 1 and 2 correspond to reference and delay scanner branch, respectively.I i (t) is the envelope intensity of the pulse, which is given by the intensity of the incident pulse, I 0 (t), and attenuation in each branch, L i , as Here, 1/2 shows the first division of the pulse.The photocurrent as a function of the delay τ is where and 1 2 in Eq. ( 3) shows the field fraction at the combiner.As described later, we fixed the delay τ in each measurement and adjusted the Δφ with the phase tuner in the reference branch so that cos(ωτ + Δφ) and cos2(ωτ + Δφ) became unity and i(τ) took the maximum value.The first and second terms in the integral of C 0 (τ) denote the background components which are independent of τ.Other terms depend on τ and form a pulse peak.Therefore, the peak to background ratio at τ = 0 is In the lossless case, i.e., L 1 = L 2 = 1, this ratio becomes 8: 1.If τ is scanned so fast that the detector cannot respond, the terms of the cosine functions in Eq. ( 3) vanish and the ratio becomes 3: 1.With a loss, this ratio changes, as shown later.

Fabrication
Figure 2 shows the device fabricated on an 8-inch SOI wafer with a 210-nm-thick Si layer and a 2-µm-thick silica BOX layer using a CMOS-compatible process whose minimum feature size is 180 nm.The spot size converter has a 200-µm-long Si-wire inverse taper with a 180-nm-tip width, which is cladded by a silica waveguide of 4 × 4 µm 2 cross-section [16].
The insertion loss between the spotsize converter and lensed fiber with a spot diameter of 3 µm was approximately 2 dB.The Si-wire waveguides for the optical wiring were 400 nm wide.They were partially widened to 4 µm via a 50-µm-long taper in the long straight section to avoid the nonlinear effects, as previously discussed.Even in the widened waveguide, the excitation of unnecessary higher-order modes was negligible.The reference branch comprised four wire waveguides (total length of 99.6 µm and calculated group index n g = 4.15), six tapers (300 µm, average n g = 3.93), and three widened waveguides (2224 µm, n g = 3.71).The total group delay was expected to be 34 ps.The resistance of a TiN heater placed on the longest widened waveguide was 2.5 kΩ .The measured excess loss of the 1 × 2 branch described in Fig. 2 was 0.23 dB.The measured tap ratio and excess loss of the tap also described in Fig. 2 were 10% and 1.7 dB, respectively, at λ = 1550 nm.They were sufficient for measuring waveforms using the external correlator.We used the third-row-shifted LSPCW to generate low-dispersion slow light.The 250µm-long air-bridge LSPCW with a lattice constant a = 450 nm, hole diameter 2r = 255 nm, and lattice shift s = 90 nm was used as the delay scanner and dispersion controller.A bow-tie heater of 230-Ω resistance was employed in the delay scanner, aiming to form a temperature slope and index chirp.Here three types of slow-light bands were produced in the LSPCW, as shown in Fig. 3: (1) a highly dispersive band on the short-wavelength side; (2) a slow-light band in which tunable delay and dispersion compensation are available via the index chirp; and (3) a low-dispersion slow-light band on the long-wavelength side.We first planned to tune the delay using band (2).In this study, however, the desirable tunable slow light was not obtained because of some damages in the air-bridge LSPCW, which might be caused by the chemical eching prosess of the BOX layer beneath the Si layer.Therefore, we set the center wavelength of the input pulse at band (1).Here the delay τ was tuned from 3 ps to 21 ps simply by the spectral shift due to the heating (red and orange lines in Fig. 3).The loss caused by the delay, which was evaluated through the tap, was as high as 3.0-7.4dB (3.0 dB for τ < 11 ps and 0.44τ − 1.8 dB for τ > 11 ps, 3.5 dB at the center) due to the damage.The dispersion slope of band (1) was measured to be 1.7−7.5 ps/nm.When the full-width at halfmaximum (FWHM) of the pulse duration is 5 ps, the corresponding spectral FWHM in wavelength becomes 1.3 nm, which suggests that the pulse could be broadened to >10 ps.Actually it was compensated in the dispersion controller.Because heaters in the dispersion controller were not operated in this study, the wavelengths of the bands were shorter than those in the delay scanner under heating.This means that the band (1) in the delay scanner overlaps with band (2) in the dispersion controller and the dispersion is compensated.The group delay of the dispersion controller was approximately 8 ps, and that at wire waveguides, including the widened ones, was 14 ps, resulting in a total delay of 25−43 ps in this branch.This delay is comparable to that in the reference branch.The 300-µm-long silica-cladded LSPCW with a = 400 nm, 2r = 220 nm, and s = 130 nm were used as the TPA-PD.Here we used band (3) so that the TPA efficiency was enhanced with the pulse shape sustained.The resistance of the heater above this LSPCW is 420 Ω.The footprint including all these components falls inside 1.0 × 0.3 mm 2 .

Auto-correlation waveform
In the measurement of the correlation waveform, the temporal FWHM of the incident pulse was 3−10 ps, the corresponding spectral FWHM was 2.2−0.66 nm, respectively, the center wavelength was 1548.7 nm, and the repetition frequency was 40 MHz.The upper panel of Fig. 4(a) shows the delay of the 5-ps pulse and change of the cross-correlation waveform for heater power P H applied to the delay scanner; this pulse and waveform were observed through monitor port #1.The tuning range was 18 ps (τ = 3-21 ps), and the relative delay to the reference branch became zero at P H = 230 mW.Thus, this tuning range was suitable for observing the 5-ps pulse.The lower panel of Fig. 4(a) shows the change of the temporal FWHM.The dispersion appeared at low heating powers, but it finally converged to approximately 5 ps because of the dispersion compensation, as previously mentioned.The FWHM slightly smaller than the incident one might be due to the slight pre-chirping in the incident pulse; we observed that the spectral broadening caused by some nonlinear effects in the LSPCW was negligible.
Figure 4(b) shows the responsivity characteristics of the TPA-PD measured by inserting the pulse through monitor port #2 directly from outside and applying a −3 V bias.Here the pulse peak power P is derived from the time-averaged power P av with considering the duty ratio of the pulse.The photocurrent at P < 2 W is approximated as indicating that the current is generated by TPA.The saturation of the photocurrent at P > 3 W might be caused by the TPA in the optical wiring before the TPA-PD [15].The dark current of the TPA-PD was measured to be approximately 40 pA when noise was suppressed by averaging sufficiently.However, in the absence of averaging, the noise level was increased to 30 nA; thus, the lowest detectable power P ≈0.09 W (P av ≈17 μW).Now let us estimate the power range at the input port, which is detectable by the TPA-PD.The loss in the reference branch was estimated to be ∼0.5 dB (L 1 ∼0.89).On the other hand, the loss in the delay scanner branch was 0.44τ + 1 = 6.3 dB (L 2 = 0.23) at the center delay including 0.1 dB loss in the wire waveguide, ∼1 dB total loss at two junctions between the LSPCW delay scanner/ dispersion compensator and wire waveguides and 1.7 dB loss at the MMI tap.Therefore, the total loss summing the 2 dB coupling loss at the SSC, ∼3 dB total loss between the MMI branch and combiner on the in-phase condition, and ∼0.5 dB loss at the junction between the LSPCW TPA-PD and wire waveguide was ∼5.5 dB.Considering this value, the detectable range is P = 0.3-7 W. The lowest value will be lowered by increasing the responsivity of the TPA-PD with a higher group index in addition to the noise reduction by averaging.The highest value will be enhanced by further suppressing the nonlinear effects in the delay scanner.Finally, we operated the entire device to measure the correlation waveform of the pulse of 3, 5, 7 and 10 ps in FWHM (blue open and closed circles in Fig. 5).The incident peak power was set at 3.8, 2.3, 1.6, and 1.7 W, respectively.For comparison, we also calculated the waveform (blue line) using Eqs.( 3) and ( 4).Here, we assumed the above L 1 and L 2 and set the cosine functions in Eq. ( 3) to be unity because we manually measured each plot one-byone, adjusting the delay, phase, and optical alignment misaligned by the strong heating.Then the peak to background ratio calculated from Eq. ( 5) becomes 4.9: 1.For the 5-and 7-ps pulses, the measured waveforms were in good agreement with the calculated ones.For the 3ps pulse, the plots on the right side at lower heating powers did not agree with the calculated waveform.This discrepancy might stem from the imperfect dispersion compensation for a wider pulse spectrum.It is understood from the temporal FWHM of the pulse tapped from the delay scanner (red dotted line).The dispersion was particularly increased on the right side.For the 10-ps pulse, the entire waveform could not be acquired because of the limited delay scanning range.Moreover, the measured correlation intensity was unstable due to relatively low power levels at the tail of the waveform.If we scanned the delay synchronously with the phase using a saw-tooth drive signal and measured the waveform repeatedly on an oscilloscope, a more stable waveform would be observed after averaging.However, because the heating power for the delay scanning was as large as hundreds of milliwatts, the detected signal at the TPA-PD contained substantial noise when the heating power was scanned continuously and the photocurrent was particularly weak.This noise is caused by the poor heating efficiency to the air-bridge LSPCW.As a solution, a silica-cladded LSPCW designed for tunable delay [17] and a micro-ring-based tunable delay line [18], in which heaters are placed above them, will be effective.

Conclusion
In conclusion, we fabricated an on-chip optical correlator incorporating two photonic crystal slow-light waveguides and demonstrated its operation.The footprint of this device was only 1.0 × 0.3 mm 2 , which is substantially smaller than that of conventional correlators with freespace optics.It enables the measurement of optical pulses shorter than 10 ps; it was limited to 5-7 ps in this study but will be extended to 1-10 ps in future studies by reducing the dispersion and using wider tunable delay.The detectable incident peak power ranged from 0.3-7 W but it will also be extended particularly in the lower power level by reducing the noise in the TPA-PD.A working spectrum of up to 10 nm can be achieved by thermally tuning each component.This device will also enable one-chipping of more advanced optical measurement instruments.

Fig. 2 .
Fig. 2. Fabricated device and details of the MMI branch, 10% tap, and LSPCW.Figures in the branch and 10% tap are in units of microns.The doped region in the right-upper picture of TPA-PD is colored schematically.

Fig. 3 .
Fig. 3. Group delay spectrum showing three different bands (1)−(3).Black line shows no heating condition, while red and orange show heating conditions with heating powers of 293 and 835 mW, respectively.

Fig. 4 .
Fig. 4. Operation of two LSPCW components.(a) Delay tuning characteristics.The inset of the upper panel shows the cross-correlation waveform of the output pulse measured off-chip, where the FWHM of the reference pulse was 1.0 ps.(b) Responsivity characteristics of the TPA-PD.

Fig. 5 .
Fig. 5. Auto-correlation waveforms (blue) measured using the developed on-chip optical correlator (circles) and a simulated one (solid lines).Temporal FWHMs of incident pulse was 3, 5, 7 and 10 ps from upper to lower pannels.Open and closed circles depict those obtained in two different measurement trials.Red dotted lines show the temporal FWHM of the pulse tapped from the delay scanner and measured externally for each incident pulse width.