Large tunable fractional delay of slow light pulse and its application to fast optical correlator

The slow light device based on photonic crystal coupled waveguide was fabricated, and a tunable delay of 72 ps was obtained for 2ps-wide slow light pulses by local heating, which corresponds to a tunable fractional delay of 36. This value was further enhanced to 110 by compressing the output pulses through self-phase modulation and dispersion compensation in external fibers. We applied this device to optical correlator as a delay scanner, where the fractional delay determines the resolution of the delay scanning. Using this correlator, we successfully observed sub-picosecond pulses at a scan frequency up to 2 kHz, which is 100 times faster than that of mechanical scanners in conventional correlators. ©2011 Optical Society of America OCIS codes: (130.5296) Photonic crystal waveguides; (230.3120) Integrated optics devices; (070.4550) Correlators. References and links 1. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: capabilities and fundamental limitations,” J. Lightwave Technol. 23(12), 4046–4066 (2005). 2. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). 3. T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2(8), 448–450 (2008). 4. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). 5. F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65– 71 (2007). 6. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008). 7. A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable Delay Lines in Silicon Photonics: Coupled Resonators and Photonic Crystals, a Comparison,” IEEE Photonics J. 2(2), 181–194 (2010). 8. J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express 18(25), 26525–26534 (2010). 9. 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). 10. D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13(23), 9398–9408 (2005). 11. T. Kawasaki, D. Mori, and T. Baba, “Experimental observation of slow light in photonic crystal coupled waveguides,” Opt. Express 15(16), 10274–10281 (2007). 12. T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16(12), 9245–9253 (2008). 13. J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide Range Tuning of Slow Light Pulse in SOI Photonic Crystal Coupled Waveguide via Folded Chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). 14. G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, “High-speed phaseand group-delay scanning with a gratingbased phase control delay line,” Opt. Lett. 22(23), 1811–1813 (1997). 15. E. Margallo-Balbás, M. Geljon, G. Pandraud, and P. J. French, “Miniature 10 kHz thermo-optic delay line in silicon,” Opt. Lett. 35(23), 4027–4029 (2010). #154729 $15.00 USD Received 16 Sep 2011; revised 26 Oct 2011; accepted 28 Oct 2011; published 10 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24102


Introduction
Slow light with a group velocity much lower than that in vacuum yields a long delay in a compact device [1][2][3][4][5][6][7][8][9].The performance of slow light is often evaluated by the delaybandwidth product (DBP) and fractional delay.The former is an essential figure-of-merit (FOM) of the device because its bandwidth determines the shortest transmittable optical pulse, and hence the DBP constrains the largest buffering capacity.The latter is a more practical FOM giving the net buffering capacity of pulses broadened by higher order dispersion.If targeting advanced time-domain optical signal processing such as optical buffering, the tunable fractional delay is more crucial.The photonic-crystal coupled waveguide (PCCW) is a promising device because it generates wideband and dispersion-free slow light pulse on a chip at room temperature [10,11] and its delay can be tuned by sloping the equivalent modal index along the waveguide (chirped structure) [12].So far, we have obtained fixed and tunable fractional delays of 80 and 22, respectively, in a 280-μm-long PCCW by using local heating [13].This tunable value is larger than those of any other onchip slow-light devices (< 10).In a longer PCCW, however, the dispersion became noticeable due to small disordering in the fabricated device, so the values were rather degraded.
In this study, we fabricated the device using e-beam lithography with a higher extraction voltage than in our previous studies.Consequently, the dispersion was reduced and larger fixed and tunable fractional delays were obtained.In addition, we enhanced the fractional delays drastically by compressing output pulses through the self-phase modulation and dispersion compensation in external fibers.Since the pulse spectrum is changed in this case, we cannot count these values as buffering capacities.However, we can consider the tunable value as the resolution of the delay scanning.Therefore, we applied the device to optical correlator as a delay scanner.Optical correlators are widely used to observe fs-to ps-wide optical pulses.They usually use a mechanical delay scanner with a typical scan frequency f of no higher than 10 Hz.A faster scanner is required for high-volume multi-dimensional data acquisition in optical coherent tomography, terahertz time-domain spectroscopy, and so on.A grating-based delay line [14] and thermo-optic effect in Si waveguides [15] have been studied for this purpose.However, the former needs a large and complex optical system, while the latter only achieves a narrow scan range of around 1 ps.In this study, we used the PCCW and successfully observed sub-ps pulses at f < 2 kHz.

Tunable delay
Structural details of the PCCW have been reported in Refs [11][12][13].It is fabricated on SOI substrate with a Si layer of 210 nm thickness.The photonic crystal slab consists of a triangular lattice of air-holes, with a pitch of 460 nm and diameter of mostly 270 nm.However, some airholes are position-shifted and/or down/up-sized in the range of 120  380 nm, particularly around the junctions with input and output (I/O) photonic crystal waveguides (PCWs).In previous studies, the device was fabricated by using 50 kV e-beam lithography.In this study, we employed 100 kV and expected the disordering to be reduced.
Figure 1(a) and (b) show the fabricated device.The magnified view of the photonic crystal suggests the high uniformity of airholes.The PCCW is 400 μm long, and is connected to I/O PCWs of 2700 μm total length.Around the PCCW, air-slots are aligned to enhance the thermal isolation and heating efficiency.Figure 1(c) shows the delay spectrum measured by using the modulation phase shift method at 300 MHz.Raw data of the spectrum exhibit some oscillations, but it is much smaller than previously.In previous studies, we usually used 10 GHz modulation in dispersion analyzer Alnair CDA 2100 although the measurable delay range was limited.If 300 MHz was used, higher coherence severely increased the phase noise caused by the internal reflection and localization of slow light due to the disordering.In this study, on the other hand, we could observe a reasonable spectrum with acceptable noise at 300 MHz.This is evidence that the disordering was reduced by the improved process.The spectrum exhibits a delay peak corresponding to the flat photonic band of the PCCW [11].Neglecting the delay in the I/O PCWs, the peak group index evaluated after taking the moving  The transmission and delay characteristics of short optical pulses were measured using setups in Refs [12,13].that include mode-locked fiber laser, erbium-doped fiber amplifier (EDFA), band-pass filter (BPF), and a commercial cross-correlator.In this observation, we again confirmed the small disordering of the device from the lower dispersion in the pulse transmission measurement.In previous studies, the low dispersion transmission of 3-ps-wide pulses was observed reasonably for devices shorter than 300 μm.In this study, on the other hand, low dispersion was obtained for < 2-ps-wide pulses even in the 400 μm device.For the tunable delay, the device was locally heated by irradiating the device top with 442 nm laser light.The laser spot was adjusted to an elliptical shape parallel to the PCCW, with major and minor axes of 510 μm and 230 μm respectively by using cylindrical lens.The power P and central position x of the laser spot were optimized so that the delay tuning range was maximized while maintaining the low dispersion condition.
Figure 2(a) demonstrates the delay tuning of the slow light pulse.Here, 1.3-ps-wide pulses with center wavelength λ ~1.54 μm and bandwidth (FWHM) Δλ = 4.5 nm were incident on the device.The relatively large total delay includes the fixed delay in the long I/O PCWs.The maximum delay in the device was 169 ps, the continuous tuning range was 72 ps, and the average output pulse width (FWHM) Δτ 0 was 2.0 ps.Thus the fixed and tunable fractional delays are 85 and 36, respectively.In previous studies, the maximum value of the fixed delay was obtained for a narrow pulse width of 0.9 ps.The transmission of such narrow pulse was not observed in this experiment, which may be due to the dispersion in the long I/O PCWs.Nevertheless the long delay and the reasonably narrow pulse slightly improved the fixed fractional delay.On the other hand, the tunable value was enhanced by 1.6-fold than previously by the narrowed average pulse width.Of course, this pulse width is still limited by the bandwidth and the remnant dispersion.As a simple method that breaks this limit, we compressed the output pulse.In this experiment, we amplified the peak power of output pulse from 6 to 37 dBm by an EDFA and expanded its spectrum through the self-phase modulation in highly nonlinear fiber (HNLF).We used a 22 m HNLF with a dispersion of 1.4 ps/nm/km (0.030 ps/nm).Then we successively connected 10 m long single-mode fiber (SMF) with a dispersion of 16 ps/nm/km (0.17 ps/nm) to compensate for the total dispersion including the device, other fibers and optics.Consequently, the pulse width was reduced to an average of 0.52 ps.This changes the delay tuning, as shown in Fig. 2(b) and (c).Fixed and tunable fractional delays increased to 290 and 110, respectively.As mentioned above, this tunable value can be regarded as the resolution of the delay scanning in the optical correlator.The correlation is obtained from the convolution integral of two pulses.In this study, we used the cross-correlation method where one pulse goes through the device under test (DUT) and the other is the reference (REF).Therefore, if the REF is narrower, we can measure narrower DUT pulses.

Optical correlator
Now we propose an optical correlator using the PCCW and pulse compressor as a delay scanner of the REF pulse, as shown in Fig. 3. Here, P is modulated by a pulsed current from the signal generator (SG) to the laser so that the delay is scanned like a saw-tooth wave.The (C) 2011 OSA interval between currents is set to be sufficiently longer than the thermal relaxation time in the PCCW.The heating position x and the amplification in the EDFA cannot be changed dynamically with P. With such limited control parameters, the delay changed nonlinearly and the intensity and dispersion fluctuated nonuniformly.To avoid these problems, we limited the scan range to 22 ps, transformed the pulsed current appropriately, and the cross-correlation trace was calibrated by post-processing of the signal.This scan range is still sufficient for measuring ps to sub-ps pulses.After passing the PCCW, the REF pulse was compressed as mentioned above.Meanwhile, the branched pulse passed through the DUT.Here, fibers with bandwidth-and wavelength-tunable band-pass filter (BPF) were considered as DUT.The correlation waveform was observed through second-harmonic generation (SHG) using photomultiplier (PMT) connected with oscilloscope (OSC).Here, the DUT pulse width Δτ DUT and REF pulse width Δτ REF were fixed at 0.2 and 0.5 ps, respectively.Assuming these pulses to be Gaussian, the width of the correlation waveform, Δτ cor , is given by the relation Δτ cor 2 = Δτ DUT 2 + Δτ REF 2 .Therefore, Δτ REF is dominant in this observation.For a scan range of 22 ps, the waveform was maintained at f < 1 kHz, while it trailed at higher f due to the slow thermal response.When the scan range was limited to 5 ps, the tail was not so evident up to f = 2 kHz. Figure 4(b) shows the normalized Δτ cor for different f and scan ranges.The waveform broadened at higher frequencies, but the broadening was suppressed by narrowing the scan range.If 10% broadening in Δτ cor is acceptable, the highest f reaches 2 and ~3 kHz with scan ranges of 5 and 3 ps, respectively.
To estimate the thermal response time of the delay scan, we modulated P with a step-like current and switched the delay between the REF (0.5 ps) and DUT (0.2 ps) pulses, from completely separated to just overlapped.In this case, the cross-correlation waveform is given by the convolution integral of the ideal waveform and thermal response.The thermal response is derived by deconvoluting the ideal waveform for two Gaussian pulses of 0.2 and 0.5 ps widths from the correlation waveform.Figure 5 shows the normalized separation between two pulses, which corresponds to the delay scan of the REF pulse.The obtained response curve fits well to the exponential function with a 1/e time constant of 19 μs.Taking the Fourier transform of this exponential function, 50 and 90% frequency bandwidths are derived to be 8.3 and 2.8 kHz, respectively.The 90% bandwidth is in good agreement with the result of Fig. 4(b) with the shortest scan range.Within this bandwidth, the error in the delay scan for Fig. 4(a) can be smaller than 10%.The response time is determined by the thermal equilibrium between the PCCW area and outer area.As aforementioned, the heating laser spot was elliptical with a 230 μm width across the PCW.Therefore, the outer area having a larger thermal capacity was heated simultaneously, and this might delay the equilibrium.If the laser spot is narrowed so that only the PCCW area is irradiated, the response time will be shortened and the frequency bandwidth will be enhanced.Figure 6 shows the waveforms for different Δτ DUT , which were controlled by changing the bandwidth of the BPF.Here, the small nonlinearity of Δt and intensity fluctuation in the PCCW were calibrated by the waveform at Δτ DUT = 6.0 ps, which was measured separately using a commercial auto-correlator.As Δτ DUT decreased from 6.0 ps, the waveform narrowed and converged at Δτ DUT < Δτ REF = 0.5 ps.It shows that the proposed system functions as a correlator.

Conclusion
We improved the tunable slow light characteristics obtained by locally heating the photonic crystal coupled waveguide.A tunable fractional delay of 36 was obtained for picosecond pulses, which is the highest record for on-chip slow light.By compressing output pulses externally, this value was further enhanced to 110.We considered this as tunable resolution and applied to the delay scanning in the optical correlator.We successfully observed the subpicosecond pulse with a scan frequency up to 2 kHz, which is at least 100 times faster than mechanical scanners in conventional correlators.It is limited by the thermal response time of 19 μs, and will be improved by limiting the heating area.In this study, we employed the external laser heating, but it can be replaced by integrated heaters.In addition to the delay, heaters can be incorporated to tune the target wavelength in the range of several 10 nm.Such a compact and flexible tunable delay will allow one-chip correlation systems.

#
154729 -$15.00USD Received 16 Sep 2011; revised 26 Oct 2011; accepted 28 Oct 2011; published 10 Nov 2011 (C) 2011 OSA average is 95.The peak delay is 198 ps and the bandwidth (full-width at half maximum: FWHM in the PCCW) is 4.4 nm, which give the DBP of 110.

Fig. 1 .
Fig. 1.Fabricated PCCW and group delay spectrum.(a) Optical micrograph of the entire device.(b) Scanning electron micrograph of PCCW connected to PCW.(c) Delay in the entire device (left axis) and group index only in the PCCW (right axis).Gray and black lines show raw data and moving average around ± 0.3 nm, respectively.

Fig. 2 .
Fig. 2. Cross-correlation waveforms showing the delay tuning of slow light pulse in PCCW by local heating.(a) Result for optimized power P and central position x of the laser heating.(b) Result with pulse compressor in Fig. 3. (c) (Media 1) Animation of measured time shift of waveform in (b) with detailed condition of P and x.

Figure 4 (
Figure 4(a) shows correlation waveforms for different scan frequencies f and scan ranges.Here, the DUT pulse width Δτ DUT and REF pulse width Δτ REF were fixed at 0.2 and 0.5 ps, respectively.Assuming these pulses to be Gaussian, the width of the correlation waveform, Δτ cor , is given by the relation Δτ cor 2 = Δτ DUT 2 + Δτ REF2 .Therefore, Δτ REF is dominant in this observation.For a scan range of 22 ps, the waveform was maintained at f < 1 kHz, while it trailed at higher f due to the slow thermal response.When the scan range was limited to 5 ps, the tail was not so evident up to f = 2 kHz.Figure4(b) shows the normalized Δτ cor for different f and scan ranges.The waveform broadened at higher frequencies, but the broadening was suppressed by narrowing the scan range.If 10% broadening in Δτ cor is acceptable, the highest f reaches 2 and ~3 kHz with scan ranges of 5 and 3 ps, respectively.To estimate the thermal response time of the delay scan, we modulated P with a step-like current and switched the delay between the REF (0.5 ps) and DUT (0.2 ps) pulses, from completely separated to just overlapped.In this case, the cross-correlation waveform is given by the convolution integral of the ideal waveform and thermal response.The thermal response is derived by deconvoluting the ideal waveform for two Gaussian pulses of 0.2 and 0.5 ps widths from the correlation waveform.Figure5shows the normalized separation between two pulses, which corresponds to the delay scan of the REF pulse.The obtained response curve fits well to the exponential function with a 1/e time constant of 19 μs.Taking the Fourier transform of this exponential function, 50 and 90% frequency bandwidths are derived to be 8.3 and 2.8 kHz, respectively.The 90% bandwidth is in good agreement with the result of Fig.4(b) with the shortest scan range.Within this bandwidth, the error in the delay scan for Fig.4(a) can be smaller than 10%.The response time is determined by the thermal equilibrium between the PCCW area and outer area.As aforementioned, the heating laser spot was elliptical with a 230 μm width across the PCW.Therefore, the outer area having a larger thermal capacity was heated simultaneously, and this might delay the equilibrium.If the laser spot is narrowed so that only the PCCW area is irradiated, the response time will be shortened and the frequency bandwidth will be enhanced.

Fig. 4 .
Fig. 4. Cross-correlation waveforms and their width Δτobs for different f.(a) Waveforms with scan range of 22 ps (red) and 5 ps (purple).(b) Δτobs measured for different scan ranges.Values are normalized by that at f = 100 Hz.

Fig. 6 .
Fig.6.Cross-correlation waveforms at f = 1 kHz for different widths of DUT pulse measured by using the proposed correlator.