We propose an ultra-compact solid-state autocorrelator fabricated using Si photonics technology that obtains correlation by detecting the overlap of two slow light pulses counter-propagating in a photonic crystal waveguide integrated with a two-photon absorption photodiode array. As the device does not require a mechanical delay scanner, it can be integrated onto a chip and operated without alignment. Using the correlator, we successfully acquired the autocorrelation of picosecond pulses. The nonlinear enhancement of slow light improves sensitivity, resulting in an evaluated detection limit in terms of the product of the peak and average power on the order of , which is equal to or even better than that of commercial scanning autocorrelators and -fold better than that of conventional single-shot autocorrelators.
© 2017 Optical Society of America
Autocorrelators are used to measure the length of pico- and femtosecond pulses, which are not directly observable using a simple photodiode (PD). These tools are commonly used in lab experiments involving such short pulses and in the development of related applications such as optical coherence tomography, optical frequency combs, chirped-pulse amplification, and supercontinuum generation, and have therefore been the subject of continuous study. There are two types of autocorrelators: delay-scanning  and single-shot [2–10]. The former is in widespread use but is bulky and requires complicated and fragile free-space optics with a mechanical delay scanner. The latter can take a correlation from a single pulse, but requires large optics, precise beam tilting, and much more intense pulses.
In recent years, a variety of optical devices have been substantially miniaturized through the application of Si photonics and photonic crystal technology . A scanning autocorrelator has been demonstrated by integrating a Si photonic crystal waveguide (PCW)-based delay scanner and two-photon absorption (TPA) PD  onto a silicon-on-insulator (SOI) using a complementary metal oxide semiconductor (CMOS) process . The PCW has been extensively studied because it exhibits large first-order dispersion, which generates slow light [11,14], enables tunable delay , and enhances TPA [14,16]. Regarding single-shot autocorrelators, a crystal , CdS nanowire , and Si PCW  were used to generate second and third harmonics as a probe that reflects the correlation between pairs of pulses in the waveguides. Direct detection of the stationary wave using a near-field nanoprobe has also been reported . However, full integration has not yet been reported in single-shot autocorrelators, as an external charge-coupled device (CCD) camera would be needed to observe the harmonics.
In this Letter, we demonstrate a single-shot autocorrelator that is fully integrated via a CMOS process. In the device, a linear array of TPA-PDs is integrated onto a Si PCW to enable the acquisition of correlations between pulse pairs that are split from an incident pulse and counter-propagate in the Si PCW through the TPA photocurrent. Owing to its ultra-compact size, ease of fabrication, and nonmechanical robust operation without alignment, this autocorrelator is advantageous for the measurement of short pulses and its applications. Furthermore, its strong confinement and nonlinear enhancement of slow light improves the sensitivity of the TPA-PDs, which overcomes the very low sensitivity of conventional single-shot autocorrelators. In this Letter, we describe the principle of the proposed autocorrelator in greater detail and discuss its theoretical correlation waveform. We then discuss experimental results in terms of detecting picosecond pulses and evaluate its practical performance.
2. PRINCIPLE AND THEORY
A schematic of the device is shown in Fig. 1. It comprises a spot-size converter (SSC), Si wire waveguides, 50:50 splitter, and a TPA-PD linear array embedded onto the PCW. The dispersion of the PCW is tailored via photonic lattice shifts along the waveguide (which we call lattice-shifted PCW, or LSPCW) so that picosecond pulses do not suffer from dispersion . After an optical pulse coupled to the SSC is split in two, the split pulses impact the LSPCW from opposite ends and induce free carriers through the TPA during the propagation, which are observed as the photocurrent. When the counter-propagating pulses overlap, the photocurrent increases, producing autocorrelation, described as follows. For position in the LSPCW and time , we denote the intensities of Gaussian pulse envelopes launched from left and right as and , respectively, neglecting the cross-sectional profile. Then, for the total length of the LSPCW, , and the electric field of the two pulses are given by
Substituting Eq. (1) into Eq. (2), becomes the sum of an envelope component and oscillating components arising from the carrier wave terms (see Supplement 1). Figure 2 shows some examples of calculations of normalized , which corresponds to the correlation. As shown later, the pitch of the TPA-PDs was experimentally set at 5 μm. Under this condition, the fast oscillation in Fig. 2(a) cannot be resolved but is averaged; thus, only the envelope component remains, as plotted in Fig. 2(b). It exhibits an autocorrelation waveform of the input pulse with a background of 0.333 in normalized intensity, which is produced by the individual TPA of each pulse. The orange and purple plots represent the case for and 220 dB/cm (experimental value), respectively. The difference is small because the carrier densities gradually decay from each input end due to the loss, as depicted by the red and blue lines, but they are moderately canceled by each other.
While the correlation in a scanning autocorrelator is a function of the temporal offset , in our device it is a function of the spatial offset . These offsets are related via (where is the light velocity in a vacuum and is the group index). The full width at half-maximum (FWHM) of the input pulse is given as for a Gaussian pulse ( for a pulse). As expressed in these equations, a higher compresses the pulse in space and shortens the correlation waveform on the TPA-PD array.
Figure 3(a) shows the device fabricated on a SOI chip. The orange lines indicate the optical paths, which comprise Si wires. Beyond the splitter, one path has a TiN -heater for tuning the inter-path phase relation. The phase relation influences only the fast oscillating components, which are averaged if there are no local phase fluctuations in the LSPCW. However, the fabricated LSPCW has some fluctuations, which make the averaging imperfect. Furthermore, because slow light propagates in the LSPCW as a Bloch wave, and its mode profile is defined by the lattice position , the instantaneous mode overlap efficiency between the counter-propagating pulses strongly depends on the phase relation. Therefore, the initial phase relation and local phase fluctuations can deform the correlation waveform. Hence, a sinusoidal voltage is applied to the heaters to average them. The pulses are launched from both ends of the LSPCW with the same timing. Along the LSPCW, 17 TPA-PDs were formed at a 5-μm pitch by boron- and phosphorus-ion implantation; of these, only 15 are used, with the outer two remaining redundant. As the number of PDs is limited only by the number of electrical probes used in the measurement, their number can be increased as desired if they are directly connected to an electronic circuit. The length of each PD is 3 μm and, to achieve electrical separation, the inter-PD spacing in the undoped region is 2 μm (see Supplement 1 for more details).
The transmission and spectra of the LSPCW (different device but fabricated simultaneously using the same design) were measured by coupling transverse-electric (TE) polarized continuous wave laser light into the SSC using lensed fibers [Fig. 3(b)]. The guided mode appears with low-dispersion characteristics at with and the second-order dispersion to . The propagation loss of the LSPCW with doping is dominated by the free carrier absorption and is 220 dB/cm. In evaluating the TPA-PDs, TE-polarized Gaussian pulses of a desired FWHM centered at were produced using a mode-locked fiber laser with a repetition of 40 MHz, an erbium-doped fiber amplifier, and a band-pass filter coupled to the device (see Supplement 1 for more details). The photocurrent was detected independently via Al electrodes and probes, revealing a measured dark current in the PDs of less than 2 pA under a reverse bias of (this value was used throughout this study). Figure 3(c) shows the responsivity characteristics of the center PD, at which the correlation peak was obtained. The length of the Gaussian pulse was set at 4.5 ps (the duty ratio was ). The photocurrent is proportional to both the square of the peak power, , and the product of the peak and average power, (both the peak and average power were evaluated in the input fiber). The square responsivity evaluated for is . The responsivity begins to saturate at , as the overly strong TPA and free carrier absorption at this point begin to distort the correlation waveforms.
Meanwhile, we know that when using a standard photodiode (responsivity of ) and low-noise preamplifier, the detectable limit power for 10-Gbps telecom transmission is , which corresponds to 0.9 fC/bit. In our device, on the other hand, the photocurrent of 1 μA was obtained for , which corresponds to an output electric charge of 25 fC for a single pulse, considering the repetition of 40 MHz. Since the signal-to-noise ratio is maintained for arbitrary charge extraction speed under the restriction of thermal noise, the large output charge in our device means that single-shot observation of picossecond pulses will be possible if we prepare a comparably low-noise preamplifier.
In the observation of correlation waveforms, we coupled the TE-polarized pulses with , changing the FWHM in the range 1.0–7.1 ps. Figure 4 shows those observed using this device and a commercial scanning autocorrelator. The inset shows a comparison of the pulse width as measured by the fabricated device and the commercial autocorrelator. Although the waveforms are in close agreement in the range 1.0–4.5 ps, at the fabricated device produces a waveform with a slightly lowered intensity. We believe that this error is caused by a combination of variations in and the PDs’ responsivity and insufficient phase averaging. The time resolution for a Gaussian pulse, , where is the pitch of the PDs, was measured to be 570 fs in the fabricated device; this can be improved by using a smaller and , although doing so would degrade the responsivity.
To show the potential of the fabricated device for practical use, we evaluated the precision of the correlation at various values of , center wavelength , pulse power , and polarization, with the premise that once high precision could be confirmed, sufficient accuracy could be obtained by calibration. For each factor, precision was evaluated using the standard deviation in the correlation, measured by each TPA-PD that was normalized by a value on the Gaussian fitting curve. Figure 5 summarizes the measured values for the four parameters, where the respective default values/settings were , , , and TE polarization. From Figs. 4 and 5(a), it is seen that σ remains small for . By elongating the LSPCW or reducing and , in addition to calibrations, pulses above and below this width range are also acceptable. Increasing the number of TPA-PDs is also effective, and more than one hundred PDs can be made available by using appropriate electronic circuits.
In Fig. 5(b), is small at the shorter wavelengths but increases toward the photonic band edge on the long wavelength side because the fluctuation in the loss, , and the phase are enhanced by the band edge slow light. This confirms an effective of 10–15 nm in the proposed device. It could be extended up to 35 nm so that it fully covers the C-band (1530–1565 nm) by optimizing the LSPCW and accepting the reduced sensitivity arising from the corresponding slight decrease of to .
Because power was measured in the input fiber, the results shown in Fig. 5(c) reflect all loss components. Too low or too high power levels result in degradation in precision from noise or nonlinear saturation, respectively. The minimum detectable square power in the proposed device was estimated to be on the order of , which is equivalent or even better than that in a commercial scanning autocorrelator, and better by a factor of than that of a conventional single-shot correlator . This detection limit is compatible with single-shot operation at a reasonably low power if the photocurrent is effectively amplified, as mentioned in the previous section. At high power, the optical Kerr effect and overly enhanced TPA and so-induced carrier plasma dispersion degrade performance; however, power levels of up to 10 W are acceptable, and this figure can be exceeded through simple attenuation of the incident power.
Figure 5(d) reflects changing the polarization angle from 0 (TE) to 90° (transverse-magnetic: TM) by rotating the input fiber. As the LSPCW allows only a TE-like mode to propagate as slow light and enhance the TPA, increases as the angle approaches 90°. However, as is sufficiently low in the range 0–60°, the device does not require significant polarization adjustment at sufficiently high power levels. Inserting a flexible fiber connector into the input fiber to enable polarization adjustment will allow for easy optimization.
We demonstrated an ultra-compact on-chip autocorrelator comprising a TPA-PD-loaded photonic crystal slow light waveguide and several Si photonics components. Owing to its structural simplicity and absence of delay-scanning components, the device can be easily fabricated through a CMOS process. Practical high sensitivity and operational ease are achieved through this structural simplification and the dramatic miniaturization of the pulse measurement tools, making the proposed autocorrelator adaptable for pulse length monitoring tasks in instruments such as mode-locked pulse lasers, filters, amplifiers, and optical pulse synthesizers. The autocorrelator also has the potential to achieve real single-shot operation by optimizing the TPA-PD to further improve its sensitivity and preparing appropriate low-noise amplifiers.
New Energy and Industrial Technology Development Organization (NEDO).
This study was supported by New Energy and Industrial Technology Development Organization (NEDO) and Japan Science and Technology Agency ACCEL Project.
See Supplement 1 for supporting content.
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