Highly sensitive ultrafast pulse characterization using hydrogenated amorphous silicon waveguides Keith G. Petrillo,1,2 Ke-Yao Wang,1,2 Amy C. Foster,1 and Mark A. Foster1,* 1
Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA 2 These authors contributed equally to this work. * [email protected]
Abstract: We experimentally demonstrate frequency resolved optical gating (FROG) via four-wave mixing (FWM) in ultrahigh nonlinearity hydrogenated amorphous silicon waveguides. We demonstrate FROG characterization using a FWM architecture that mimics second harmonic generation (SHG) FROG for pulsewidths as low as 360 fs. Additionally, we demonstrate for the first time a FWM architecture analogous to third harmonic generation (THG) FROG and validate its ability to overcome the direction of time ambiguity of the SHG-like architecture. Both architectures allow for sensitivities suitable for future telecommunications signals. ©2013 Optical Society of America OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (190.4390) Nonlinear optics, integrated optics; (320.7100) Ultrafast measurements.
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#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31230
1. Introduction Future telecommunication architectures such as optical time division multiplexing (OTDM) [1–5], orthogonal OTDM [6], optical orthogonal frequency division multiplexing (optical OFDM) [7], and optical code division multiple access (OCDMA) [8] rely on ultrawidebandwidth ultrafast sources such as mode-locked lasers and comb generators [9]. The performance of these systems relies heavily on the properties of the ultrafast source, and as data rates are increased, physical distortions such as dispersion and nonlinearities are consequently magnified [1–8]. Pulse characterization techniques are crucial for performance monitoring [10]; however, the ultrahigh-bandwidths required for these systems are difficult to measure by traditional means such as electronic and optical sampling [10–13]. Therefore, ultrafast self-referencing pulse characterization techniques such as frequency resolved optical gating (FROG) [14, 15], modified interferometric field autocorrelation (MIFA) [16, 17] and spectral interferometry for direct electric-field reconstruction (SPIDER) [18] will be indispensable for laser characterization. Among existing approaches, frequency resolved optical gating (FROG) is a highly effective and robust self-referencing optical pulse characterization technique that fully characterizes an ultra-short optical pulse [14, 15, 19–29]. The most sensitive FROG geometry utilizes second-harmonic generation (SHG) between the pulse and its time-delayed replica. However, due to the limited interaction length of bulk nonlinear crystal, conventional freespace architectures struggle to measure the high repetition rate and, therefore low peak power pulses often found in high speed communications architectures [19–22]. For FROG to be suitable for high repetition rate communications sources, architectures incorporating guidedwave nonlinear devices are required [23–28]. While impressive sensitivities (2.7 × 10−6 mW2 using FROG [28], and 2.7 × 10−9 mW2 using MIFA [17]) have been demonstrated utilizing the χ(2) nonlinearity of aperiodically-poled lithium niobate waveguides, the platform uses highly specialized materials and thereby presents a challenge for efficient integration with telecommunications hardware. In comparison, the vast majority of guided wave devices do not exhibit a χ(2) nonlinearity. For this reason, a prominent guided-wave FROG architecture utilizes the χ(3) nonlinear process of four-wave mixing (FWM) as a replacement to the SHG material thereby facilitating the use of more abundant and manufacturable materials such as highly nonlinear fibers (HNLF) [23], semiconductor optical amplifiers (SOA) [26] or crystalline silicon (c-Si) waveguides [24]. Sensitivities ranging from 0.1 to 60 mW2 have been demonstrated in these platforms for picosecond pulses. Here we investigate two FROG architectures utilizing FWM in hydrogenated amorphous silicon (a-Si:H) waveguides. This recently developed integrated waveguiding material is amenable to back-end-of-the-line (BEOL) CMOS integration and exhibits ultrahigh effective nonlinearities of as high as 3000 W−1m−1 [30, 31]; a value five orders of magnitude larger than highly nonlinear optical fiber and an order of magnitude larger than crystalline silicon (c-Si) waveguides. Furthermore, the group-velocity dispersion (GVD) of these structures can be designed to achieve phase-matching over a wide bandwidth (> 55 THz) [32]. Due to the combination of these beneficial properties, here we demonstrate characterization of pulses as short as 360 fs (with 2.5-THz bandwidth) with improved sensitivity (6 mW2) using the SHGlike FWM architecture. With improved fiber-waveguide coupling, we expect the sensitivity to reach < 0.5 mW2. Secondly, we demonstrate a novel THG-like FROG architecture using two stages of FWM and demonstrate highly sensitive direction-of-time unambiguous FROG characterization of pulses as short as 1-ps with a sensitivity of 1 × 106 mW3. To the best of our knowledge, this THG-like FWM architecture is the first and most sensitive self-referenced guided-wave approach that overcomes the direction of time ambiguity of SHG FROG.
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31231
2. Hydrogenated amorphous silicon waveguide A-Si:H is a back-end of the line (BEOL) CMOS-compatible material and is available in current standard fabrication process lines. The material can be deposited using lowtemperature plasma-enhanced chemical vapor deposition (PECVD) (300°C) and therefore allows vertical stacking and three-dimensional integration of photonic circuits without affecting the base-layer electronic devices at the front end. A-Si:H waveguides have recently been demonstrated with ultrahigh nonlinearities [30, 33, 34] and the total FWM bandwidth of these devices can be extremely broad due to the relatively short interaction lengths (< 1 cm) and dispersion engineering possible with these structures. The a-Si:H waveguide employed here is fabricated using standard CMOS techniques as described in [31]. The waveguide is designed to have a cross-section of 215 nm × 500 nm and is 8-mm long. The group velocity dispersion (GVD) of the waveguide, which is controlled by the waveguide geometry, is anomalous and near zero, allowing for efficient FWM over a broad bandwidth (> 55 THz) [32]. The waveguide has a propagation loss of ~3.2 dB/cm in the quasi-TE-mode with a lensed fiber-to-chip input coupling loss of ~8.5 dB.
Fig. 1. Schematic of experimental setup for SHG-like FWM-FROG measurement. Two different pulses under test are generated by a mode-locked fiber laser with or without the compression stage. Inset: optical spectrum at the output of the a-Si:H waveguide. (PUT: pulse under test. HNLF: highly nonlinear fiber. VOA: variable optical attenuator. WDM: wavelength division multiplexer. EDFA: erbium-doped fiber amplifier. OBPF: optical bandpass filter. PC: polarization controller. OSA: optical spectrum analyzer.) Inset: the dispersion curve of the aSi:H waveguide showing anomalous group-velocity dispersion at operation wavelength for broad bandwidth operation.
3. SHG-like FWM-FROG In the SHG-like FWM-FROG architecture the pulse to be characterized is split, delayed, and recombined along with a continuous-wave (CW) laser [23, 24, 26]. Analogous to a traditional bulk χ(2) crystal SHG FROG approach, Eq. (1), the FWM architecture creates the mixing of three signals to generate a new signal at the idler frequency that resembles the traditional SHG FROG signal with a background, Esig (t ,τ ) ∝ E (t ) E (t − τ ), (1) * 2 2 Eidler (t ,τ ) ∝ ECW [E pump (t ) + E pump (t − τ ) + 2 E pump (t ) E pump (t − τ )]
(2)
where E is the electric field to be characterized, Esig is the developed FROG electric field, Epump is the electric field to be characterized acting as a pump in the FWM stage, ECW is the electric field of the CW laser, and Eidler is the electric field generated from the FWM process. The first two terms in the brackets of Eq. (2) represent a constant background that is subtracted from the measurement. Since the CW laser ideally does not exhibit ultrafast
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31232
temporal characteristics, the cross term (last term in Eq. (2)) in the FWM-generated signal is identical to the SHG FROG of the pulse and the electric field of the pulse can be recovered using standard SHG FROG algorithms accounting for the offset center frequency. Utilizing this FWM technique, HNLF has yielded the best sensitivity of 0.1 mW2 but was limited in signal pulsewidth to 7 ps due to the large interaction length required (and therefore significantly reduced bandwidth) for such sensitivity [23]. To decrease the interaction length while maintaining similar sensitivities, semiconductor optical amplifiers and crystalline silicon (c-Si) waveguides have demonstrated a sensitivity of about 50 mW2 and 60 mW2, respectively, with pulsewidths around 3 ps [24, 26].
Fig. 2. Pulse characterization of PUT 1 (left column), and PUT 2 (right column). (a),(e) Optical spectrum at the output of the waveguide. (b),(f) Measured and retrieved FROG. (c),(g) FROG retrieved auto-correlation and spectrum in comparison to the independent measurements. (d),(h) Retrieved amplitude and phase in both time and frequency domain.
To test the sensitivity of the conventional SHG-like FWM-FROG in an a-Si:H waveguide, Fig. 1, a 10-GHz 1.8-ps pulse under test (PUT 1) is split and combined using a free space Michelson interferometer with a variable delay arm. The fixed arm is spatially dithered to avoid interference fringes from the background [23]. The pulse and the delayed replica are coupled into the waveguide along with a CW laser using a lensed fiber. Polarization controllers are used in each path to match the quasi-TE mode of the waveguide, and the pulses and CW probe undergo FWM as described in Eq. (2). We operate the system with CW power of 5 mW. Although increasing the CW power in this FWM FROG architecture can improve the measurement sensitivity, in our device we found that raising the CW power above ~5 mW yields a negligible improvement in sensitivity due to power dependent free-carrier induced losses. The FROG spectrogram is formed from the idler spectrum recorded using an optical #200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31233
spectrum analyzer (OSA) as the delay is varied. The background spectrum is measured by increasing the delay until there is no overlap between the original and delayed pulses and subsequently subtracted from the FROG spectrogram. A typical FWM spectrum is shown in Fig. 2(a). The measured and retrieved spectrograms of the 1.8-ps pulses after background subtraction are shown in Fig. 2(b). We obtain a retrieval error of < 0.01 for the 64 x 64 grid. We compare the retrieved autocorrelation and spectrum with independently measured traces using an autocorrelator and OSA and find excellent agreement as shown in Fig. 2(c). The retrieved intensity and phase in frequency and time domain are plotted in Fig. 2(d). For this measurement, the input power to the FROG system is 900 μW. The retrieval error can be maintained below 0.015 while reducing the input power down to 320 μW, which corresponds to a sensitivity of 6 mW2. Furthermore, given that coupling losses to silicon waveguides of less than 3 dB have been demonstrated experimentally, we estimate that a sensitivity of better than 0.5 mW2 is fundamentally achievable in this system. The a-Si:H waveguide is dispersion-engineered for broad-bandwidth FWM and therefore allows characterization of ultra-short pulses. To demonstrate the broad bandwidth capability of the waveguide, we characterize a 360-fs pulse with 20-nm (2.5-THz) bandwidth. A compression stage that consists of dispersion shifted fiber, highly nonlinear fiber, and standard single-mode fiber is used to spectrally broaden and temporally compress the pulses from the 10-GHz laser, Fig. 1 (PUT 2). Figure 2(e) shows the overall optical spectrum depicting the broad bandwidth of the pulses. In order to separate the broad bandwidth pulse and idler using our available bandpass filters, the CW laser is tuned to 1528 nm. The measured and the retrieved FROG trace of the 360-fs pulse are plotted in Fig. 2(f) with retrieval error of 0.028. Independently measured auto-correlation and spectrum match well with the retrieved ones, Fig. 2(g), and the intensity and phase of the retrieved pulse are plotted in Fig. 2(h). Notably, this demonstration represents the shortest optical pulses characterized to-date using the FWM-FROG architecture. These results show a combination of high sensitivity and broad bandwidth capability, which cannot be obtained simultaneously in any other FWM platform [23, 24, 26]. Furthermore, from the dispersion of the a-Si:H waveguide, we estimate that this device is capable of characterizing pulses with a center wavelength in the range between the two zero-GVD wavelengths (1400 nm and 1700 nm). Additionally, the dispersion limits the FWM bandwidth and we estimate that the present device allows for the characterization of pulse widths approaching 100 fs. However, with further dispersion optimization [35], similar waveguides can allow for the characterization of pulses narrower than 50 fs. 4. THG-like FWM-FROG SHG FROG lacks the ability to distinguish the direction of time. However, an alternative geometry based on third harmonic generation (THG) allows for a compromise between the high sensitivity of SHG FROG and the ability to determine the direction of time as is achieved in the other geometries. The free space versions of THG FROG are roughly identical to SHG FROG except that a χ(3) crystal is utilized [29]. This is a difficult scheme to replicate in integrated and fiber platforms [36], however, since phase-matching of the THG process is challenging in guided wave structures, and since guided wave devices do not allow for spatial separation of the nonlinearly-generated signals [14, 15, 29]. In communications settings, the direction of time of signal distortions is critical for performance monitoring. For example, the fundamental characterization of whether GVD distortions are normal or anomalous is not possible with a simple SHG FROG measurement due to the direction of time ambiguity. THG FROG is one such architecture that eliminates this ambiguity at the cost of sensitivity. THG FROG combines a signal with a delayed replica in a third-order crystal to produce the signal field, Esig (t ,τ ) ∝ E (t ) 2 E (t − τ ), (3)
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31234
at the third harmonic frequency. Since the third-order process is weaker than second-order processes, free space THG architectures are highly impractical for measuring telecommunications pulses. Here we demonstrate for the first time a FROG architecture using two stages of FWM to mimic a THG FROG measurement. A block diagram of the THG-like architecture is shown in Fig. 3.
Fig. 3. A block diagram of the cascaded FWM THG FROG. A nonlinear copy creation stage develop a replica of the pulse to be measured on a second wavelength. The two signals are isolated and delayed with respect to each other prior to mixing. The result from the mixing is read on a spectrum analyzer.
The pulse to be characterized is combined with a CW laser prior to the first FWM stage. This initial FWM stage generates the complex conjugate of the pulse at a shifted wavelength. The CW source and higher order FWM content are removed using spectral filters while the spectrally distinct conjugate pulse and original pulse are separated. One pulse is delayed relative to the other prior to recombining. The delayed pulse and conjugate mix in the second FWM stage to generate a signal at a new frequency that mimics a THG process, 2 (4) Eidler (t ,τ ) ∝ E pump (t ) Econj (t − τ ), where Econj is the replica of the signal to be characterized represented by Epump. Notably, in contrast to other guided wave FROG architectures (FWM and SHG), this idler spectrum is background-free simplifying the signal recovery process. Finally, a standard THG FROG algorithm is applied to reconstruct the amplitude and phase of the pulse.
Fig. 4. The experimental setup of cascaded FWM stages for THG FROG (PM: phase modulator. D-38 fiber: Corning Vascade S1000 fiber. MLFL: mode locked fiber laser). Insets (a), (b), and (c) show the spectrum of the experimental setup after the initial HNLF stage, before the waveguide, and after the waveguide respectively where BWres is the bandwidth resolution of the OSA.
The THG-like FWM FROG experimental system is shown in Fig. 4. A CW laser is randomly phase modulated to mitigate stimulated Brillouin scattering (SBS) in the first FWM
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31235
medium (HNLF), amplified to 2 W by an erbium doped fiber amplifier (EDFA) and filtered by a 100-GHz filter centered at 1547 nm to provide a pump source for the first FWM stage. One hundred meters of HNLF is used for this stage to allow maximum conversion efficiency with minimal coupling loss. Since the CW pump is slowly varying, the generated signal retains the complex conjugate of the phase information of the original signal [37, 38]. The typical spectrum developed from this process is shown in Fig. 4(a). A wavelength-division multiplexer (WDM) isolates the conjugate pulse from the remainder of the signals in the system (including the CW pump, the original signal, and cascaded FWM effects). An additional WDM filter is used to fully suppress the CW pump energy that propagates through the first WDM. The conjugate pulse passes through a polarization controller (PC) and 3-m of Corning Vascade S1000 fiber to compensate for second and third-order dispersion of the PC and WDM filters. Another WDM combines the replica with the signal that propagates through its own PC, 4.5-m of compensating Corning Vascade S1000 fiber, and a tunable delay. The total single mode fiber length in our setup is < 10 m. Therefore, the residual fourth-order dispersion limits the characterization of pulses < 50 fs without further dispersion compensation or algorithmic correction. The combined signal and replica, Fig. 4(b), are coupled into the 8-mm a-Si:H waveguide for the second FWM stage to yield the THG-like FROG idler spectrum, Fig. 4(c). As the signal is delayed relative to the conjugate pulse, the FWM idler spectrum is collected on an OSA to generate the FROG traces found in Fig. 5. We note that the slight change (red shoulder 25-dB below peak) in signal spectrum out of the waveguide is the result of a small amount of self-phase modulation (SPM) that accompanies the FWM process within the waveguide. However, this SPM is minimal and was found to negligibly impact the pulse characterization performance.
Fig. 5. Experimental results: from left to right the columns show the experimental FROG spectrogram traces, the reconstructed traces, the temporal reconstruction (solid) and its phase (dashed) with the corresponding experimental (dashed) and recovered (solid) autocorrelation in the inset, and the spectral reconstruction (solid) with its phase (dashed) and the measured spectrum (dotted) for the transform-limited (top row), anomalously chirped (second row), normally chirped (third row), and self-phase modulation with compression cases (bottom row).
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31236
Figure 5 shows the FROG traces from four different test pulses: a 1.8-ps 10-GHz harmonically mode-locked fiber laser, Fig. 4 (PUT 1), a 1.8-ps pulse anomalously chirped to 10 ps in 350 meters of Corning single mode (SMF-28) fiber, Fig. 4 (PUT 2), a 1.8-ps pulse normally chirped to 8 ps in 86 meters of Corning Vascade S1000 fiber, Fig. 4 (PUT 3), and the mode-locked laser pulse spectrally broadened via a 250-mW EDFA in conjunction with 100 meters of HNLF, compressed in 5 meters of SMF-28 fiber. For the last case, Fig. 4 (PUT 4), 30 meters of HNLF is used for the nonlinear copy creation stage to allow additional FWM bandwidth for the copy creation of a larger bandwidth signal. In each case, there is good agreement with the independent autocorrelations shown in the inset of the temporal reconstruction plots, and with the the independently measured spectrum. The details for grid size, error, pulse width, and spectral FWHM can be found in the respective plots. The elimination of the direction of time ambiguity is clearly shown in the chirped cases. For the anomalous chirp, the temporal phase is concave up and the spectral phase is concave down. For the normal chirp, the phase distortions are reversed indicating that the pulse is chirped in the opposite direction. This is directly observable in the respective FROG traces as the asymmetric wing in the upper right of the anomalously chirped trace switches to the upper left in the normally chirped trace. In the SPM and compressed case, the temporal reconstruction has asymmetric ripples in the trailing wing of the pulse. Additionally, the Vshaped spectral phase includes a cubic response with the downturn in phase on the end of the spectrum. The combination of these two features indicates that the pulse is predominately afflicted by SPM and third-order dispersion [15], as expected from the HNLF followed by SMF-28 fiber stages. The transform-limited trace is developed from a 7-mW average power 10-GHz pulse train illustrating the sensitivity of the system while acquiring a reconstruction error of less than 0.01. This measured sensitivity is 1x106 mW3 which is defined as the peak power squared multiplied to the average power of the ultrafast laser input to this self-referenced system [39]. In the chirped cases, the average power is increased to 16 mW to acquire lower reconstruction errors. Further improvements to the sensitivity of this device may be acquired through mitigating splice losses and reducing coupling losses to the waveguide. In the present system, the FWM bandwidth of the HNLF limits the signal bandwidth and therefore the minimum pulsewidth. The measured FWM bandwidth of the 100-m HNLF at 1550 nm is 1.7 THz on each side of the pump. We estimate that the FWHM pulse bandwidth should be less than half this FWM bandwidth for proper characterization corresponding to a minimum pulsewidth of approximately 500 fs. Additionally, the FWM bandwidth decreases as the center wavelength of the signal is changed. For example, at 1560 nm the bandwidth is 1.2 THz corresponding to a minimum pulsewidth of approximately 750 fs. However, replacing the HNLF with an additional dispersion managed integrated waveguide as the first FWM stage should allow for significantly more tunability in the center wavelength, as well as shorter pulsewidths. 5. Conclusion Using highly nonlinear a-Si:H waveguides, we demonstrate two FWM-based FROG architectures that mimic SHG and THG FROG interactions. The large nonlinearity of the aSi:H waveguides allow large nonlinear phase shifts to occur in very short (< 1 cm) interaction lengths allowing for bandwidths of 2.5 THz and extremely short pulsewidths of 360 fs to be characterized with a sensitivity of 6 mW2 (< 0.5 mW2 can be achieved with improved coupling). This sensitivity is an improvement on other integrated FWM devices [23–27] while achieving operation on significantly broader pulse bandwidths. Additionally, we present a novel THG-like FWM FROG architecture that allows self-referenced unambiguous directionof-time ultrafast pulse characterization with sensitivities of 1 × 106 mW3 and pulse energies of 0.7 pJ for 10-GHz repetition rates. To the best of our knowledge, this architecture is the most sensitive self-referenced FROG technique that eliminates the direction-of-time ambiguity.
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31237
Both of the architectures exhibit sensitivities suitable for the high-repetition-rate and widebandwidth sources of future communications systems. Acknowledgments This work was supported by the DARPA Young Faculty Award program under award number N66001-11-1-4153 and award number N66001-12-1-4248. The devices were fabricated in part at the Center for Nanoscale Science and Technology’s NanoFab at the National Institute of Standards and Technology.
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31238
Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA 2 These authors contributed equally to this work. * [email protected]
Abstract: We experimentally demonstrate frequency resolved optical gating (FROG) via four-wave mixing (FWM) in ultrahigh nonlinearity hydrogenated amorphous silicon waveguides. We demonstrate FROG characterization using a FWM architecture that mimics second harmonic generation (SHG) FROG for pulsewidths as low as 360 fs. Additionally, we demonstrate for the first time a FWM architecture analogous to third harmonic generation (THG) FROG and validate its ability to overcome the direction of time ambiguity of the SHG-like architecture. Both architectures allow for sensitivities suitable for future telecommunications signals. ©2013 Optical Society of America OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (190.4390) Nonlinear optics, integrated optics; (320.7100) Ultrafast measurements.
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#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31230
1. Introduction Future telecommunication architectures such as optical time division multiplexing (OTDM) [1–5], orthogonal OTDM [6], optical orthogonal frequency division multiplexing (optical OFDM) [7], and optical code division multiple access (OCDMA) [8] rely on ultrawidebandwidth ultrafast sources such as mode-locked lasers and comb generators [9]. The performance of these systems relies heavily on the properties of the ultrafast source, and as data rates are increased, physical distortions such as dispersion and nonlinearities are consequently magnified [1–8]. Pulse characterization techniques are crucial for performance monitoring [10]; however, the ultrahigh-bandwidths required for these systems are difficult to measure by traditional means such as electronic and optical sampling [10–13]. Therefore, ultrafast self-referencing pulse characterization techniques such as frequency resolved optical gating (FROG) [14, 15], modified interferometric field autocorrelation (MIFA) [16, 17] and spectral interferometry for direct electric-field reconstruction (SPIDER) [18] will be indispensable for laser characterization. Among existing approaches, frequency resolved optical gating (FROG) is a highly effective and robust self-referencing optical pulse characterization technique that fully characterizes an ultra-short optical pulse [14, 15, 19–29]. The most sensitive FROG geometry utilizes second-harmonic generation (SHG) between the pulse and its time-delayed replica. However, due to the limited interaction length of bulk nonlinear crystal, conventional freespace architectures struggle to measure the high repetition rate and, therefore low peak power pulses often found in high speed communications architectures [19–22]. For FROG to be suitable for high repetition rate communications sources, architectures incorporating guidedwave nonlinear devices are required [23–28]. While impressive sensitivities (2.7 × 10−6 mW2 using FROG [28], and 2.7 × 10−9 mW2 using MIFA [17]) have been demonstrated utilizing the χ(2) nonlinearity of aperiodically-poled lithium niobate waveguides, the platform uses highly specialized materials and thereby presents a challenge for efficient integration with telecommunications hardware. In comparison, the vast majority of guided wave devices do not exhibit a χ(2) nonlinearity. For this reason, a prominent guided-wave FROG architecture utilizes the χ(3) nonlinear process of four-wave mixing (FWM) as a replacement to the SHG material thereby facilitating the use of more abundant and manufacturable materials such as highly nonlinear fibers (HNLF) [23], semiconductor optical amplifiers (SOA) [26] or crystalline silicon (c-Si) waveguides [24]. Sensitivities ranging from 0.1 to 60 mW2 have been demonstrated in these platforms for picosecond pulses. Here we investigate two FROG architectures utilizing FWM in hydrogenated amorphous silicon (a-Si:H) waveguides. This recently developed integrated waveguiding material is amenable to back-end-of-the-line (BEOL) CMOS integration and exhibits ultrahigh effective nonlinearities of as high as 3000 W−1m−1 [30, 31]; a value five orders of magnitude larger than highly nonlinear optical fiber and an order of magnitude larger than crystalline silicon (c-Si) waveguides. Furthermore, the group-velocity dispersion (GVD) of these structures can be designed to achieve phase-matching over a wide bandwidth (> 55 THz) [32]. Due to the combination of these beneficial properties, here we demonstrate characterization of pulses as short as 360 fs (with 2.5-THz bandwidth) with improved sensitivity (6 mW2) using the SHGlike FWM architecture. With improved fiber-waveguide coupling, we expect the sensitivity to reach < 0.5 mW2. Secondly, we demonstrate a novel THG-like FROG architecture using two stages of FWM and demonstrate highly sensitive direction-of-time unambiguous FROG characterization of pulses as short as 1-ps with a sensitivity of 1 × 106 mW3. To the best of our knowledge, this THG-like FWM architecture is the first and most sensitive self-referenced guided-wave approach that overcomes the direction of time ambiguity of SHG FROG.
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31231
2. Hydrogenated amorphous silicon waveguide A-Si:H is a back-end of the line (BEOL) CMOS-compatible material and is available in current standard fabrication process lines. The material can be deposited using lowtemperature plasma-enhanced chemical vapor deposition (PECVD) (300°C) and therefore allows vertical stacking and three-dimensional integration of photonic circuits without affecting the base-layer electronic devices at the front end. A-Si:H waveguides have recently been demonstrated with ultrahigh nonlinearities [30, 33, 34] and the total FWM bandwidth of these devices can be extremely broad due to the relatively short interaction lengths (< 1 cm) and dispersion engineering possible with these structures. The a-Si:H waveguide employed here is fabricated using standard CMOS techniques as described in [31]. The waveguide is designed to have a cross-section of 215 nm × 500 nm and is 8-mm long. The group velocity dispersion (GVD) of the waveguide, which is controlled by the waveguide geometry, is anomalous and near zero, allowing for efficient FWM over a broad bandwidth (> 55 THz) [32]. The waveguide has a propagation loss of ~3.2 dB/cm in the quasi-TE-mode with a lensed fiber-to-chip input coupling loss of ~8.5 dB.
Fig. 1. Schematic of experimental setup for SHG-like FWM-FROG measurement. Two different pulses under test are generated by a mode-locked fiber laser with or without the compression stage. Inset: optical spectrum at the output of the a-Si:H waveguide. (PUT: pulse under test. HNLF: highly nonlinear fiber. VOA: variable optical attenuator. WDM: wavelength division multiplexer. EDFA: erbium-doped fiber amplifier. OBPF: optical bandpass filter. PC: polarization controller. OSA: optical spectrum analyzer.) Inset: the dispersion curve of the aSi:H waveguide showing anomalous group-velocity dispersion at operation wavelength for broad bandwidth operation.
3. SHG-like FWM-FROG In the SHG-like FWM-FROG architecture the pulse to be characterized is split, delayed, and recombined along with a continuous-wave (CW) laser [23, 24, 26]. Analogous to a traditional bulk χ(2) crystal SHG FROG approach, Eq. (1), the FWM architecture creates the mixing of three signals to generate a new signal at the idler frequency that resembles the traditional SHG FROG signal with a background, Esig (t ,τ ) ∝ E (t ) E (t − τ ), (1) * 2 2 Eidler (t ,τ ) ∝ ECW [E pump (t ) + E pump (t − τ ) + 2 E pump (t ) E pump (t − τ )]
(2)
where E is the electric field to be characterized, Esig is the developed FROG electric field, Epump is the electric field to be characterized acting as a pump in the FWM stage, ECW is the electric field of the CW laser, and Eidler is the electric field generated from the FWM process. The first two terms in the brackets of Eq. (2) represent a constant background that is subtracted from the measurement. Since the CW laser ideally does not exhibit ultrafast
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31232
temporal characteristics, the cross term (last term in Eq. (2)) in the FWM-generated signal is identical to the SHG FROG of the pulse and the electric field of the pulse can be recovered using standard SHG FROG algorithms accounting for the offset center frequency. Utilizing this FWM technique, HNLF has yielded the best sensitivity of 0.1 mW2 but was limited in signal pulsewidth to 7 ps due to the large interaction length required (and therefore significantly reduced bandwidth) for such sensitivity [23]. To decrease the interaction length while maintaining similar sensitivities, semiconductor optical amplifiers and crystalline silicon (c-Si) waveguides have demonstrated a sensitivity of about 50 mW2 and 60 mW2, respectively, with pulsewidths around 3 ps [24, 26].
Fig. 2. Pulse characterization of PUT 1 (left column), and PUT 2 (right column). (a),(e) Optical spectrum at the output of the waveguide. (b),(f) Measured and retrieved FROG. (c),(g) FROG retrieved auto-correlation and spectrum in comparison to the independent measurements. (d),(h) Retrieved amplitude and phase in both time and frequency domain.
To test the sensitivity of the conventional SHG-like FWM-FROG in an a-Si:H waveguide, Fig. 1, a 10-GHz 1.8-ps pulse under test (PUT 1) is split and combined using a free space Michelson interferometer with a variable delay arm. The fixed arm is spatially dithered to avoid interference fringes from the background [23]. The pulse and the delayed replica are coupled into the waveguide along with a CW laser using a lensed fiber. Polarization controllers are used in each path to match the quasi-TE mode of the waveguide, and the pulses and CW probe undergo FWM as described in Eq. (2). We operate the system with CW power of 5 mW. Although increasing the CW power in this FWM FROG architecture can improve the measurement sensitivity, in our device we found that raising the CW power above ~5 mW yields a negligible improvement in sensitivity due to power dependent free-carrier induced losses. The FROG spectrogram is formed from the idler spectrum recorded using an optical #200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31233
spectrum analyzer (OSA) as the delay is varied. The background spectrum is measured by increasing the delay until there is no overlap between the original and delayed pulses and subsequently subtracted from the FROG spectrogram. A typical FWM spectrum is shown in Fig. 2(a). The measured and retrieved spectrograms of the 1.8-ps pulses after background subtraction are shown in Fig. 2(b). We obtain a retrieval error of < 0.01 for the 64 x 64 grid. We compare the retrieved autocorrelation and spectrum with independently measured traces using an autocorrelator and OSA and find excellent agreement as shown in Fig. 2(c). The retrieved intensity and phase in frequency and time domain are plotted in Fig. 2(d). For this measurement, the input power to the FROG system is 900 μW. The retrieval error can be maintained below 0.015 while reducing the input power down to 320 μW, which corresponds to a sensitivity of 6 mW2. Furthermore, given that coupling losses to silicon waveguides of less than 3 dB have been demonstrated experimentally, we estimate that a sensitivity of better than 0.5 mW2 is fundamentally achievable in this system. The a-Si:H waveguide is dispersion-engineered for broad-bandwidth FWM and therefore allows characterization of ultra-short pulses. To demonstrate the broad bandwidth capability of the waveguide, we characterize a 360-fs pulse with 20-nm (2.5-THz) bandwidth. A compression stage that consists of dispersion shifted fiber, highly nonlinear fiber, and standard single-mode fiber is used to spectrally broaden and temporally compress the pulses from the 10-GHz laser, Fig. 1 (PUT 2). Figure 2(e) shows the overall optical spectrum depicting the broad bandwidth of the pulses. In order to separate the broad bandwidth pulse and idler using our available bandpass filters, the CW laser is tuned to 1528 nm. The measured and the retrieved FROG trace of the 360-fs pulse are plotted in Fig. 2(f) with retrieval error of 0.028. Independently measured auto-correlation and spectrum match well with the retrieved ones, Fig. 2(g), and the intensity and phase of the retrieved pulse are plotted in Fig. 2(h). Notably, this demonstration represents the shortest optical pulses characterized to-date using the FWM-FROG architecture. These results show a combination of high sensitivity and broad bandwidth capability, which cannot be obtained simultaneously in any other FWM platform [23, 24, 26]. Furthermore, from the dispersion of the a-Si:H waveguide, we estimate that this device is capable of characterizing pulses with a center wavelength in the range between the two zero-GVD wavelengths (1400 nm and 1700 nm). Additionally, the dispersion limits the FWM bandwidth and we estimate that the present device allows for the characterization of pulse widths approaching 100 fs. However, with further dispersion optimization [35], similar waveguides can allow for the characterization of pulses narrower than 50 fs. 4. THG-like FWM-FROG SHG FROG lacks the ability to distinguish the direction of time. However, an alternative geometry based on third harmonic generation (THG) allows for a compromise between the high sensitivity of SHG FROG and the ability to determine the direction of time as is achieved in the other geometries. The free space versions of THG FROG are roughly identical to SHG FROG except that a χ(3) crystal is utilized [29]. This is a difficult scheme to replicate in integrated and fiber platforms [36], however, since phase-matching of the THG process is challenging in guided wave structures, and since guided wave devices do not allow for spatial separation of the nonlinearly-generated signals [14, 15, 29]. In communications settings, the direction of time of signal distortions is critical for performance monitoring. For example, the fundamental characterization of whether GVD distortions are normal or anomalous is not possible with a simple SHG FROG measurement due to the direction of time ambiguity. THG FROG is one such architecture that eliminates this ambiguity at the cost of sensitivity. THG FROG combines a signal with a delayed replica in a third-order crystal to produce the signal field, Esig (t ,τ ) ∝ E (t ) 2 E (t − τ ), (3)
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31234
at the third harmonic frequency. Since the third-order process is weaker than second-order processes, free space THG architectures are highly impractical for measuring telecommunications pulses. Here we demonstrate for the first time a FROG architecture using two stages of FWM to mimic a THG FROG measurement. A block diagram of the THG-like architecture is shown in Fig. 3.
Fig. 3. A block diagram of the cascaded FWM THG FROG. A nonlinear copy creation stage develop a replica of the pulse to be measured on a second wavelength. The two signals are isolated and delayed with respect to each other prior to mixing. The result from the mixing is read on a spectrum analyzer.
The pulse to be characterized is combined with a CW laser prior to the first FWM stage. This initial FWM stage generates the complex conjugate of the pulse at a shifted wavelength. The CW source and higher order FWM content are removed using spectral filters while the spectrally distinct conjugate pulse and original pulse are separated. One pulse is delayed relative to the other prior to recombining. The delayed pulse and conjugate mix in the second FWM stage to generate a signal at a new frequency that mimics a THG process, 2 (4) Eidler (t ,τ ) ∝ E pump (t ) Econj (t − τ ), where Econj is the replica of the signal to be characterized represented by Epump. Notably, in contrast to other guided wave FROG architectures (FWM and SHG), this idler spectrum is background-free simplifying the signal recovery process. Finally, a standard THG FROG algorithm is applied to reconstruct the amplitude and phase of the pulse.
Fig. 4. The experimental setup of cascaded FWM stages for THG FROG (PM: phase modulator. D-38 fiber: Corning Vascade S1000 fiber. MLFL: mode locked fiber laser). Insets (a), (b), and (c) show the spectrum of the experimental setup after the initial HNLF stage, before the waveguide, and after the waveguide respectively where BWres is the bandwidth resolution of the OSA.
The THG-like FWM FROG experimental system is shown in Fig. 4. A CW laser is randomly phase modulated to mitigate stimulated Brillouin scattering (SBS) in the first FWM
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31235
medium (HNLF), amplified to 2 W by an erbium doped fiber amplifier (EDFA) and filtered by a 100-GHz filter centered at 1547 nm to provide a pump source for the first FWM stage. One hundred meters of HNLF is used for this stage to allow maximum conversion efficiency with minimal coupling loss. Since the CW pump is slowly varying, the generated signal retains the complex conjugate of the phase information of the original signal [37, 38]. The typical spectrum developed from this process is shown in Fig. 4(a). A wavelength-division multiplexer (WDM) isolates the conjugate pulse from the remainder of the signals in the system (including the CW pump, the original signal, and cascaded FWM effects). An additional WDM filter is used to fully suppress the CW pump energy that propagates through the first WDM. The conjugate pulse passes through a polarization controller (PC) and 3-m of Corning Vascade S1000 fiber to compensate for second and third-order dispersion of the PC and WDM filters. Another WDM combines the replica with the signal that propagates through its own PC, 4.5-m of compensating Corning Vascade S1000 fiber, and a tunable delay. The total single mode fiber length in our setup is < 10 m. Therefore, the residual fourth-order dispersion limits the characterization of pulses < 50 fs without further dispersion compensation or algorithmic correction. The combined signal and replica, Fig. 4(b), are coupled into the 8-mm a-Si:H waveguide for the second FWM stage to yield the THG-like FROG idler spectrum, Fig. 4(c). As the signal is delayed relative to the conjugate pulse, the FWM idler spectrum is collected on an OSA to generate the FROG traces found in Fig. 5. We note that the slight change (red shoulder 25-dB below peak) in signal spectrum out of the waveguide is the result of a small amount of self-phase modulation (SPM) that accompanies the FWM process within the waveguide. However, this SPM is minimal and was found to negligibly impact the pulse characterization performance.
Fig. 5. Experimental results: from left to right the columns show the experimental FROG spectrogram traces, the reconstructed traces, the temporal reconstruction (solid) and its phase (dashed) with the corresponding experimental (dashed) and recovered (solid) autocorrelation in the inset, and the spectral reconstruction (solid) with its phase (dashed) and the measured spectrum (dotted) for the transform-limited (top row), anomalously chirped (second row), normally chirped (third row), and self-phase modulation with compression cases (bottom row).
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31236
Figure 5 shows the FROG traces from four different test pulses: a 1.8-ps 10-GHz harmonically mode-locked fiber laser, Fig. 4 (PUT 1), a 1.8-ps pulse anomalously chirped to 10 ps in 350 meters of Corning single mode (SMF-28) fiber, Fig. 4 (PUT 2), a 1.8-ps pulse normally chirped to 8 ps in 86 meters of Corning Vascade S1000 fiber, Fig. 4 (PUT 3), and the mode-locked laser pulse spectrally broadened via a 250-mW EDFA in conjunction with 100 meters of HNLF, compressed in 5 meters of SMF-28 fiber. For the last case, Fig. 4 (PUT 4), 30 meters of HNLF is used for the nonlinear copy creation stage to allow additional FWM bandwidth for the copy creation of a larger bandwidth signal. In each case, there is good agreement with the independent autocorrelations shown in the inset of the temporal reconstruction plots, and with the the independently measured spectrum. The details for grid size, error, pulse width, and spectral FWHM can be found in the respective plots. The elimination of the direction of time ambiguity is clearly shown in the chirped cases. For the anomalous chirp, the temporal phase is concave up and the spectral phase is concave down. For the normal chirp, the phase distortions are reversed indicating that the pulse is chirped in the opposite direction. This is directly observable in the respective FROG traces as the asymmetric wing in the upper right of the anomalously chirped trace switches to the upper left in the normally chirped trace. In the SPM and compressed case, the temporal reconstruction has asymmetric ripples in the trailing wing of the pulse. Additionally, the Vshaped spectral phase includes a cubic response with the downturn in phase on the end of the spectrum. The combination of these two features indicates that the pulse is predominately afflicted by SPM and third-order dispersion [15], as expected from the HNLF followed by SMF-28 fiber stages. The transform-limited trace is developed from a 7-mW average power 10-GHz pulse train illustrating the sensitivity of the system while acquiring a reconstruction error of less than 0.01. This measured sensitivity is 1x106 mW3 which is defined as the peak power squared multiplied to the average power of the ultrafast laser input to this self-referenced system [39]. In the chirped cases, the average power is increased to 16 mW to acquire lower reconstruction errors. Further improvements to the sensitivity of this device may be acquired through mitigating splice losses and reducing coupling losses to the waveguide. In the present system, the FWM bandwidth of the HNLF limits the signal bandwidth and therefore the minimum pulsewidth. The measured FWM bandwidth of the 100-m HNLF at 1550 nm is 1.7 THz on each side of the pump. We estimate that the FWHM pulse bandwidth should be less than half this FWM bandwidth for proper characterization corresponding to a minimum pulsewidth of approximately 500 fs. Additionally, the FWM bandwidth decreases as the center wavelength of the signal is changed. For example, at 1560 nm the bandwidth is 1.2 THz corresponding to a minimum pulsewidth of approximately 750 fs. However, replacing the HNLF with an additional dispersion managed integrated waveguide as the first FWM stage should allow for significantly more tunability in the center wavelength, as well as shorter pulsewidths. 5. Conclusion Using highly nonlinear a-Si:H waveguides, we demonstrate two FWM-based FROG architectures that mimic SHG and THG FROG interactions. The large nonlinearity of the aSi:H waveguides allow large nonlinear phase shifts to occur in very short (< 1 cm) interaction lengths allowing for bandwidths of 2.5 THz and extremely short pulsewidths of 360 fs to be characterized with a sensitivity of 6 mW2 (< 0.5 mW2 can be achieved with improved coupling). This sensitivity is an improvement on other integrated FWM devices [23–27] while achieving operation on significantly broader pulse bandwidths. Additionally, we present a novel THG-like FWM FROG architecture that allows self-referenced unambiguous directionof-time ultrafast pulse characterization with sensitivities of 1 × 106 mW3 and pulse energies of 0.7 pJ for 10-GHz repetition rates. To the best of our knowledge, this architecture is the most sensitive self-referenced FROG technique that eliminates the direction-of-time ambiguity.
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31237
Both of the architectures exhibit sensitivities suitable for the high-repetition-rate and widebandwidth sources of future communications systems. Acknowledgments This work was supported by the DARPA Young Faculty Award program under award number N66001-11-1-4153 and award number N66001-12-1-4248. The devices were fabricated in part at the Center for Nanoscale Science and Technology’s NanoFab at the National Institute of Standards and Technology.
#200210 - $15.00 USD Received 28 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 11 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031229 | OPTICS EXPRESS 31238
