Abstract

We investigated the high-sensitivity interferometric autocorrelation of ultrafast optical pulses utilizing two-photon absorption in sub-micrometer silicon p-i-n waveguides. The autocorrelation sensitivities were evaluated to be about 0.5 and 4.5 × 10−8 W2 for 1- and 0.5-mm devices, respectively. Such sensitivities are about 100 times higher than the traditional two-photon conductivity photodetectors in commercial autocorrelators; thus favor weak pulse characterization. We comprehensively studied the interferometric autocorrelation performances by the experiment and FDTD (finite-difference time-domain) simulation. The pulse energy dependences of measured autocorrelation photocurrents and pulse widths were well explained by the simulation with the free carrier absorption and free carrier plasma effect considered. The autocorrelation error tends to occur if the pulse energy is high enough to cause strong free carrier effects and the threshold pulse energy for error occurrence is increased for shorter devices, but accurate autocorrelation measurement was achieved for sub-Watts pulses at which the influences of free carrier effects on interferometric autocorrelation was negligible. The minimum applicable range of pulse widths was estimated from waveguide dispersion analysis to be ~0.09 and 0.13 ps with a 10% target error for 0.5-mm and 1-mm devices, respectively. The interferometric autocorrelation in sub-micrometer silicon p-i-n waveguides is promising as a monolithic photonic device for on-chip monitor and diagnostics of weak ultrafast pulses.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Ultrafast optical pulses in pico- or femto-seconds usually need autocorrelators for time-domain characterization [1]. Such autocorrelators adopt second harmonic generation (SHG) nonlinear crystals equipped with photomultipliers or two-photon conductivity (TPC) type photodetectors for detecting autocorrelated signals [2–4]. The former is featured by highest sensitivity (~10−8 W2) but needs careful crystal angle alignment for phase matching and is difficult to be integrated. The latter is usually of low cost, but relatively low sensitivity of ~10−6 W2. The autocorrelation technology is catalyzed into two types, intensity autocorrelation and interferometric one [5]. Basically, the intensity one is particularly used to measure pulse duration; while the interferometric one can extract more information such as chirps besides pulse duration because it is electric field resolved [6–8]. Recently, autocorrelation realized by silicon photonic devices is emerging towards ultrafast optical pulse measurement in a chip scale [9–12]. As self-reference method, the autocorrelation is easy to be implemented compared to the XPM-based frequency resolved optical gating (FROG) method [13] because the pulses in XPM-FROG need to be split into two polarizations, one of which requires much higher power over the other. Due to this reason, the XPM-FROG is applicable to the thick rib waveguide with a large mode area supporting two polarizations [13]; but is not suitable for thin rib waveguides on standard 220-nm SOI which cannot efficiently support TM polarization. Among previous reports, the intensity autocorrelation was mainly focused on; whereas the interferometric autocorrelation is less studied yet. Achieving optical interferometric autocorrelation with integrated photonic devices will offer additional novel solutions to chirp-related pulse diagnostics [6], which may find applications in on-chip signal processing and communications [14]. Regarding this purpose, the key difficulty is to realize high-sensitivity autocorrelation photodetectors on photonic chips because on-chip pulse signals are usually of less than sub-Watts, much weaker than the free-space lasers in ultrafast optical systems. In [15], we had demonstrated an interferometric autocorrelation of ultrafast optical pulses in silicon wire p-i-n waveguides with a sensitivity as high as 10−8 W2. In this study, we present the comprehensive study on the various performances of this interferometric autocorrelation from both experiment and simulation. This work will give a full understanding on the interferometric autocorrelation using sub-micrometer silicon p-i-n waveguides as two-photon absorption (TPA) pulse detectors, which specifies the application conditions for this silicon photonic device be applied to characterize ultrafast optical pulses at the telecommunication wavelengths.

This paper was organized in the following way. In section 2, we first introduced the principle, device, and measurement in details and then the FDTD (finite-difference time-domain) simulation which was for the first time to be utilized to simulation interferometric autocorrelation as far as we know. In section 3, the accurate pulse width measurement was demonstrated using the interferometric autocorrelation waveforms. Subsequently, the performances including responsivity, accuracy, and sensitivity were analyzed with the assistance of FDTD simulation results. Finally, the free carrier effect and pulse width limitation were also discussed. In section 4 was this paper concluded.

2. Experiments and methods

2.1 Interferometric autocorrelation principle

The principle schematic of interferometric autocorrelation in silicon p-i-n waveguides is shown in Fig. 1(a). An optical pulse is split into two replica pulses and one of them experiences a time delay (Δt). Then two replicas are combined and input into the silicon p-i-n waveguide which is reversely biased. TPA-induced carriers form the photocurrent under a reverse bias, which can be sensed by external current meter. The autocorrelation of two replica pulses is achieved through this TPA process in the p-i-n junction and the temporal waveform of photocurrent in relation of Δt stands for the autocorrelation signal. Since the TPA is proportional to the 4th power of the electric field, the induced photocurrent is phase sensitive and interferometric fringes can be resolved in photocurrent waveform as shown in the inset of Fig. 1(a). Therefore, such an autocorrelation is usually called as phase-sensitive or interferometric autocorrelation. The photocurrent waveform of interferometric autocorrelation has an important feature that the ratio of the peak (Δt = 0) to the swing (Δt >>0) equals eight in an ideal case, which is four times that of the intensity autocorrelation and favors weak pulse measurement.

 figure: Fig. 1

Fig. 1 (a) Principle schematic of interferometric autocorrelation using the silicon p-i-n waveguide as a photocurrent detector. (b) Fabricated device and its cross-section scanning capacitance microscope indicating carrier distribution in the rib waveguide. (c) Measurement system of interferometric autocorrelation. FL: fiber mode-lock laser. TDL: tunable delay line. PM: power meter. SM: source meter. PC: computer.

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2.2 Device and measurement

Figure 1(b) shows the device with a length (L) of 1 mm. The device of 0.5 mm was also measured for comparison in this paper. These devices were fabricated on a 220-nm SOI wafer with a 3-μm buried oxide at the AIST SCR 300-mm silicon photonic platform. The phase shifter adopts the shallow-etched rib waveguide with a width of 500 nm and a slab thickness of ~110 nm, as shown in the inset of Fig. 1(b) that shows the measured scanning capacitance microscopy. Carrier distribution can also be clearly seen. The horizontal p-i-n junction was embedded at the waveguide center with doping densities of ~1 × 1018 cm−3 in both p- and n-doped regions. We used >1-μm-thick AlCu alloy as the electrode metal and 430-nm-wide channel waveguides for connection to the rib waveguide via low loss conversion structures.

Figure 1(c) shows the fiber-based measurement system. The optical pulse sequence with a repetition rate of 20 MHz and a full width at half maximum (FWHM) of 1 picosecond (ps) was emitted from a fiber mode-lock laser with a central wavelength of 1.55 μm. Optical pulses passed through a fiber-based Mach-Zehnder interferometer (MZI) and in each arm of MZI, we used a tunable delay line to control the time delay of each replica pulse and aligned the light to TE polarization. After MZI, a 20-dB coupler was used for monitoring the pulse energy in the fiber before the light was coupled into the chip. The lensed fibers were used for light coupling. The coupling loss and the linear propagation loss from the fact to the input end of p-i-n phase shifter were estimated about 4.2 dB in total. In this paper, the pulse energy in experimental description denotes the energy in the fiber before coupling except for specifically noted cases. A fixed reverse bias of 10 V was applied to the device through a source meter which was controlled by computer to automatically record the photocurrent when scanning the time delay with a 5-femtosecond (fs) step. In this way, we obtained the interferometric autocorrelation waveforms.

2.3 FDTD simulation

To simulate the interferometric autocorrelation, we extend the pulse envelope propagation simulation in our previous paper [16] to the FDTD simulation in this paper. Since it is not electric field resolved, the former can only give the envelope waveform rather than the interferometric one. In addition, it cannot include the free-carrier plasma effect. Therefore, FDTD method is necessary to analyze interferometric autocorrelation performance of silicon p-i-n waveguides. Here are the details related to our FDTD simulation explained. Considering two facts that (1) there are no complex geometries along the p-i-n waveguide and (2) the optical mode field keeps stable along the straight waveguide, we adopt one-dimensional FDTD for simplicity. We included linear absorption, TPA, plasma effect, and free-carrier absorption (FCA) into our simulation, while neglected the Kerr effect and the group index dispersion (GVD) of the rib waveguide based on our current experimental conditions.

It is necessary to explain why the self-phase modulation (SPM) due to the Kerr nonlinearity and GVD can be neglected in our simulation. To evaluate the pulse width change due to the SPM induced by the Kerr effect and GVD versus the pulse power, we first calculated the spectral broadening using the method in [17] and then retrieved the pulse width broadening. Under our experimental conditions (1-ps-wide pulse, 1 mm device, effective waveguide area of 0.1 μm2) using the Kerr coefficient n2 = 5 × 10−18 m2/W [18] and the calculated GVD (shown in section 3.4), the pulse width changes is less than 10 fs within a 20 W peak power. Obviously, this is negligible compared to the pulse width broadening of the TPA induced free-carrier dispersion (FCD) effect in explaining our experimental results. FCD is more efficient in the trailing edge than the leading edge and thus more efficient to induce pulse width broadening than the Kerr effect. Such a description is also seen in [18] (Page 5, Paragraph 6). Therefore, the TPA-induced FCD is dominant in causing the measurement error of pulse width in our autocorrelation experiment. This can also be understood from the dispersion length. The dispersion parameter D was calculated to be −6.8 × 10−4 ps/nm⋅mm at 1.55 μm, from which we can obtain the GVD parameter β2 = −2/2πc = 0.87 ps2/m. Then the dispersion length Ld ( = T022) is 1.15 m for 1-ps-wide pulse, which is thousands time longer than our devices of 1 and 0.5 mm. Similar descriptions can be seen in [18] that GVD was of minor effect for spectral broadening and in [19] the dispersion is negligible for picosecond pulses as the dispersion length is 50 times longer than the wavelength length. With the pulses become shorter, the influence of GVD gradually appears which determines the minimum applicable pulse width and will be discussed in the last part.

The calculation procedure follows the well-established method as introduced in [20,21]. The basic procedure is iteratively solving the Maxwell equations Eqs. (1) and (2) and the equation of electric displacement field (D) [Eq. (3)] in time domain. μ0 is the magnetic permeability. We first update the magnetic field H from the electric field E and D from H. Then, E is calculated from D and the sum of all polarizations (P) being considered. Equations (4)-(7) list the expressions of P considered in this study. For PFCA and Pplasma, we need Eqs. (8) and (9) to calculate the carrier absorption cross sections for electrons and holes and the refractive index change due to free carrier plasma effect [22], respectively. In Eq. (8), we calculated the mobility μe,h using Eq. (1) in [23] which took the carrier density dependence into consideration. A rate equation [Eq. (10)] was used to update the carrier density and the electron and hole densities were assumed identically generated by TPA excitation (Ne = Nh) for simplicity. Under the large electrical field at the 10 V reverse bias, the carrier lifetime (τ) is determined by the drift time instead of the recombination time, which is about 25 ps as we explained in our previous paper [16]. For photocurrent calculation, we assumed that all generated carriers are collected to form current and then it can be calculated by integrating the right first term of Eq. (10) in time and space. Thus, this ideal assumption will give an approximate to the intrinsic upper limit of photocurrent level. Finally, the photocurrent was normalized to the average in one pulse repetition period.

μ0Ht=×E
Dt=×H
D=εrE+Pi
Pα=c0ε0n0αiωE
PFCA,e,h=c0ε0n0σe,hNe,hiωE
Pplasma=2ε0n0Δn(Ne,Nh)E
PTPA=c02ε02n02βTPA2iω|E|2
σe,h=e3λ24π2c03ε0n01m*e,h2μe,h
Δn=e2λ28π2c02ε0n0ΔNe,hm*e,h
dNe,hdt=c02ε02n02βTPA8ω|E|4Ne,hτ

Next, we introduce the parameters and conditions in our simulation. The pulse source was sech2-shaped with a 1-ps FWHM and the effective area of the waveguide was 0.1 μm2 which was used to calculate the electrical field. The refractive index n0 and propagation loss were 3.4 and 1 dB/cm, respectively. The TPA coefficient βTPA will be discussed in section 3.2. All other symbols in above equations have their usual meanings and values which can also be referred to in [20,21]. Perfect matching conditions were used at simulation boundary. Note that the pulse energy in simulation means the input one before separating into two autocorrelated pulses and all calculations were done at λ = 1.55 μm.

3. Results

3.1 Interferometric autocorrelation waveform

Figure 2(a) and 2(b) show the measured interferometric autocorrelation waveforms for the device lengths of L = 1 mm at 1.22 pJ and L = 0.5 mm at 0.93 pJ, respectively. As mentioned above, different from the intensity autocorrelation, these waveforms are fringe resolved. The zero delay time was aligned to the peak. For pulse width characterization, we can infer the original pulse widths from the autocorrelated envelopes of the autocorrelation waveforms. The envelopes shown in Figs. 2(a) and 2(b) have the widths of ~1.62 and ~1.46 ps, from which the original pulse widths can be measured to be ~1.05 and ~0.95 ps using the deconvolution factor ( = 1.54) of sech2-pulses [5]. For comparison, a commercial autocorrelator was also used to measure the pulse width which was about 1.03 ~1.05 ps. Therefore, the interferometric autocorrelation using silicon p-i-n waveguides as TPA photodetectors can offer correct pulse width characterization for ultrafast optical pulses. For FDTD simulation, we need consider the loss from the fiber to the input end of p-i-n waveguide to determine the simulated pulse energy. As mentioned in section 2.2, we estimated it about 4.2 dB and then for the energies in fiber of approximately 1.22 and 1.00 pJ, we did the simulation at 0.50 and 0.38 pJ, respectively, for 1 mm and 0.5 mm devices. Figures 2(c) and 2(d) show the simulated interferometric autocorrelation waveforms for L = 1 mm and L = 0.5 mm, respectively. The pulse widths of the envelopes are 1.53 and 1.52 ps, which correspond to the inferred widths of about 0.99 ps, reasonably matching the experimental values.

 figure: Fig. 2

Fig. 2 Experimental interferometric autocorrelation waveforms of the device lengths (a) L = 1 mm and (b) L = 0.5 mm. FDTD simulated autocorrelation waveforms without phase noise for (c) L = 1 mm and (d) L = 0.5 mm, and with phase noise (e) L = 1 mm and (f) L = 0.5 mm.

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In addition, the fringes in the simulated waveforms are uniform; whereas they are likely random in the experimental ones. We believe that this noise nature comes from the mechanical optical delay lines in which the random phase fluctuations happen in the delay lines within the mechanical moving time. A promising solution to eliminate this noise nature is to adopt the integrated delay lines that allow faster and more stable delay tuning and then the chirp could be extracted using the method in [6]. To reproduce the noise effect on the waveform, we introduced the Gaussian random phase noises to one of the pulse replicas in the simulation under the condition that the total phase noise accumulated along the device was between −π and π. Figures 2(e) and 2(f) show the waveforms with phase noises, simulated at the same conditions as Figs. 2(c) and 2(d). As seen, these waveforms give very similar fringe features to the experimental ones. Meanwhile, the autocorrelated pulse widths of 1.53 ps in Fig. 2(e) and 1.52 ps in Fig. 2(f) both indicate ~0.99 ps inferred widths. Therefore, to reproduce the experimental fringe feature, phase noise should be considered in FDTD simulation; whereas for pulse width and photocurrent analysis, FDTD simulation without considering phase noise also gives reasonable results. In the following sections, the phase noise was not included in simulation for responsivity and accuracy analysis.

3.2 Responsivity, accuracy, and sensitivity

We performed similar autocorrelation measurements and simulation as we did in section 3.1 for other pulse energies in order to obtain the pulse energy dependence of photocurrent and pulse widths. From the autocorrelation waveform of each pulse energy, we can extract the peak photocurrent that is the maximum around zero time delay (Δt = 0) and the swing current that can be the average between −4 and −5 ps or between 4 and 5 ps. These photocurrents from both measurement and simulation are given in Fig. 3(a) in a relation of the pulse energy. In the low energy region, the ratio of the peak to swing almost equals eight for both experiment and simulation as indicated by the green arrow. This suggests that the interferometric autocorrelation is close to the ideal case for weak pulses. Both the experimental peak and swing photocurrents follow the relation of IR⋅P2 at the low energy side, where the coefficient R and P is the responsivity and power. As shown in Fig. 3(a), this square power dependence is well explained by our FDTD simulation. The experimental R is estimated to be about 1.5 μA/W2 which is much higher than that of thick rib waveguides in [10].

 figure: Fig. 3

Fig. 3 Pulse energy dependences of (a) peak and swing photocurrents of L = 1 mm and (b) pulse widths measured from autocorrelation waveforms as explained in section 3.1. The unit of βTPA is cm/GW. To be noted that the pulse energy in this figure is the calibrated one using the 4.2-dB loss.

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For simulation, we have to discuss the TPA coefficient βTPA because it has been seen obvious dependence on the carrier density from the past papers [24–27]. It is usually believed within 0.5 ~0.9 cm/GW for intrinsic silicon [24,25]. While βTPA around 2 cm/GW was also reported for silicon under an excitation carrier density of 6 × 1016 cm−3 [26]. βTPA was also estimated to be ~6.8 cm/GW for an excitation carrier density of 5.5 × 1018 cm−3 [27]. Considering this uncertainty and our doping density (~1 × 1018 cm−3), we determined to compare two cases of βTPA = 0.9 and 4.5 cm/GW in this section. The following three phenomena were observed in our experiment. (1) In Fig. 3(a), it is suggested that the simulation using these two βTPA well covers the measured photocurrents considering the assumption in section 2.3 that all carriers generated by TPA are collected and the actual collection efficiency be 100% in circuits. (2) The saturation feature of peak current in higher pulse energy regions (>1 pJ) due to FCA appears earlier in experiment than in simulation using βTPA = 0.9 cm/GW with increase in the pulse energy, but matches well with the simulation using βTPA = 4.5 cm/GW. (3) The pulse energy dependence of measured pulse width can also be well explained by the simulation using βTPA = 4.5 cm/GW, as shown in Fig. 3(b). While, the simulation using βTPA = 0.9 cm/GW tends to underestimate the pulse width. Considering the uncertainty of parameter, we believe that our FDTD simulation of interferometric autocorrelation gives reasonable explanations to the experimental results.

Besides responsivity, accuracy and sensitivity are another two important performances for pulse characterization using interferometric autocorrelation. As shown in Fig. 3(b), the measured pulse width starts to deviate from the original width around 1 pJ (the peak power = 1W for 1 ps pulse) due to the free carrier effect for the 1-mm device. The free carrier effect is obvious only provided that high free carrier densities are caused at high pulse energies. Its influence on the interferometric autocorrelation measurement is negligible for sub-Watts pulses and becomes weak when the device length is shortened, which is illustrated by both the measured and simulated data in Fig. 3(b). Shorter devices have higher threshold pulse energy for error occurrence. Therefore, the sub-Watts pulses can be correctly characterized by the interferometric autocorrelation in silicon p-i-n waveguides. For on-chip characterization, the pulse is usually in a region of sub-Watts or less [9] and if necessary we can also utilize integrated splitters or attenuators for pulses of high powers. How the free carrier effect induces the measurement error will be explained in the next section. For sensitivity of the interferometric autocorrelation, we try to measure waveforms with a minimum target peak current around 400 pA since it is detectable by most of digital current meters. As seen in Fig. 3(b), the detectable power being input into the waveguide is up to ~0.016 pJ (~0.042 pJ in fiber) and ~0.048 pJ (~0.127 pJ in fiber) for 1-and 0.5-mm-long devices, respectively. Thus, the sensitivity, described by the product of the peak power and average power at the minimum detectable power level, is of ~0.5 × 10−8 and 4.6 × 10−8 W2 for the 1- and 0.5-mm devices, respectively. This sensitivity in a level of 10−8 W2 is almost 100 times higher than that of traditional TPA-type photodetectors used in commercial autocorrelators and comparable or even better than that of SHG nonlinear crystals equipped with photomultipliers. Therefore, such a high sensitivity makes the silicon p-i-n waveguides much suitable for weak pulse characterization.

3.3 Free carrier effect

In this section, we explain how the free carrier effect induces the pulse width errors at high pulse energies in interferometric autocorrelation as we observed in section 3.2. It has two paths to influence the autocorrelation accuracy, FCA and free carrier induced index change Δn. To clarify the free carrier effect, we first observe the electric field (Ex) of pulses at the input and output of the waveguide under different pulse energies in FDTD simulation. Figure 4(a) shows these Ex of two correlated pulse replicas with a time delay of 1 ps of 1 and 10 pJ input energies. Comparing these two energies, we can notice that (1) the relative pulse attenuation at 10 pJ is stronger than that at 1 pJ, which indicates a stronger FCA at 10 pJ. (2) the shape of the output Ex becomes obviously asymmetric at 10 pJ, which means that the latter pulse experiences more attenuation from the FCA that is caused by the former pulse.

 figure: Fig. 4

Fig. 4 (a) Electric field (Ex) of two autocorrelated pulses with a time delay Δt = 1 ps before and after propagation along the 1 mm p-i-n waveguide for the pulse energies of 1 and 10 pJ. x denotes the TE polarization. (b) Corresponding temporal response of the index change Δn due to the TPA-induced free carrier effect monitored at z = 0.5 mm, the center of waveguide. z denotes the optical propagation direction along waveguide.

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We next show the free-carrier induced Δn in Fig. 4(b) that was monitored at the waveguide center z = 0.5 mm. Ten times higher pulse energy also induces almost ten times larger Δn. Δn also exhibits a temporal asymmetry with a characteristic time determined by the carrier lifetime as discussed in section 2.3. Thus, the latter pulse of two correlated pulse replicas experiences different index change which is automatically included in FDTD equations. It is these two asymmetries in time domain that causes the autocorrelation errors in pulse width measurement at higher pulse energies. In sub-Watt (1 pJ of 1 ps) peak power region, the free carrier induced errors are negligible and accurate measurement is guaranteed. Therefore, the interferometric autocorrelation using silicon p-i-n waveguide is suitable for weak pulses less than sub-Watts, which is true for the application of on-chip ultrafast pulse characterization.

3.4 Pulse width limitation

It is necessary to examine the applicable range of pulse width for ultrafast pulse characterization using silicon p-i-n waveguides as autocorrelation detector because of existence of GVD. In other words, the pulse width limitation is determined by the GVD of the rib waveguide. Even though the free carrier effect discussed in section 3.3 also induces temporal pulse asymmetry due to absorption and dispersion and thus causes measurement errors, it is not an intrinsic restriction because it only occurs at high pulse powers and can be solved by adopting an external or integrated attenuator to decrease the input pulse power to a reasonable region for correct measurement. It is the GVD that limits the pulse width. Obviously, the pulse width has no upper limits since this dispersion is negligible for much wider pulses; whereas there is a lower limit of pulse width because the narrow pulse experiences pulse broadening due to the GVD.

The limitation can be known from the pulse broadening which can be calculated from the wavelength dependent group index (ng). Figure 5(a) show the calculated ng for the rib waveguide described in section 2.2 using the mode solver [28]. The corresponding dispersion parameter D was calculated using D = 1/c⋅dng/dλ, as shown in Fig. 5(b). Based on this wavelength dependent D, we can calculate the pulse broadening which is shown in Fig. 5(c) as the output-vs-input relation of pulse widths. In this figure, a conventional SHG nonlinear crystal, LiIO3, was also calculated for comparison, which is often used in autocorrelators due to wide phase-matching bandwidth. Usually, it requires 1 mm thickness in conventional SHG-based autocorrelators to achieve necessary sensitivity. The parameters (ng and D) of LiIO3 were cited from [29]. For p-i-n waveguides, three lengths (0.1, 0.5, and 1 mm) were calculated. As seen in Fig. 5(c), the influence of GVD is negligible for the pulse width larger than 0.2 ps; thus, for 1-ps-width, even though we did not include the GVD in our FDTD simulation as mentioned in section 2.3, the reasonableness is reserved. With the shrinking of the pulse, the pulse broadening becomes obvious. The 0.1-mm p-i-n waveguide shows almost same pulse broadening as the nonlinear LiIO3 crystal; however, the 0.5 and 1 mm p-i-n waveguides have larger broadening for the input pulse width < 0.2 ps. To quantify the minimum applicable limitation of pulse widths, we need determine how much the broadening is acceptable. For this purpose, we define the broadening error ratio 10 × log(Δw/w0) in the unit of decibel (dB), where w0 and Δw are the input pulse width and pulse broadening, respectively. The calculated error ratios are shown in Fig. 5(d). If considering the −10 dB as the target maximum error, the pulse limitations are 36.9, 41.1, 91.8, and 129.8 fs for LiIO3, 0.1-, 0.5-, and 1.0-mm p-i-n waveguides, respectively. Therefore, <10% error is guaranteed for >0.13 ps pulses in the autocorrelation measurement using p-i-n waveguides less than 1 mm. In fact, for actual applications, we can determine the waveguide length after comprehensively considering the range of pulse widths to be measured, error tolerance, and required sensitivity. It is worth commenting that to further decrease the error for pulses <100 fs, it requires at least >25 nm flat dispersion profile that could be achieved by exploring dispersion engineering for the rib waveguide on the 220-nm SOI.

 figure: Fig. 5

Fig. 5 Wavelength dependences of (a) group index and (b) dispersion parameter D. (c) Pulse broadening due to GVD. (c) Error ratio in a relation to the input pulse width. Error ratio is defined as 10 × log(Δw/w0) where w0 and Δw are the input pulse width and pulse broadening, respectively.

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Above discussion on the pulse width limitation focuses on the central wavelength of 1.55 μm and actually, to examine the applicable bandwidth, the pulse broadening was also calculated versus the wavelength and pulse width (not shown). Since it can be seen from [24,26] that the bandwidth of TPA coefficient covers 1.5 − 1.6 μm, the bandwidth is mainly dominated by GVD. For the 10% error and 1 mm device, the pulse width is ~176 fs at 1.6 μm. With the decrease in the wavelength, the error decreases due to the decrease in GVD as shown in Fig. 5(b). More wide the pulse width, more large the bandwidth is. Therefore, at least 100 nm bandwidth from 1.5 to 1.6 μm is guaranteed for >176 fs pulses, covering the whole C and L bands.

4. Summary

The interferometric autocorrelation in silicon p-i-n waveguides was demonstrated to measure ultrafast optical pulses and comprehensively studied by the experiment and FDTD simulation with the FCA and free carrier plasma effect considered. The pulse energy dependences of measured photocurrents and pulse widths were well explained by the simulation. The autocorrelation sensitivities were evaluated to be about 0.5 and 4.5 × 10−8 W2 for 1- and 0.5-mm devices, respectively. Such high sensitivities favor weak pulse characterization. At high pulse energies, the autocorrelation error happened due to strong free carrier effects; but accurate autocorrelation was achieved for sub-Watts pulses where the influences of free carrier effects on interferometric autocorrelation was negligible. The waveguide dispersion determines the minimum applicable range of pulse widths, which was around 0.09 and 0.13 ps with 10% error for 0.5-mm and 1-mm devices, respectively. The interferometric autocorrelation in sub-micrometer silicon p-i-n waveguides is promising for on-chip monitor and diagnostics of weak ultrafast pulses.

Funding

Japan Society for the Promotion of Science (JSPS) (KAKENHI 16K18097).

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12. K. Kondo and T. Baba, “On-chip autocorrelator using counter-propagating slow light in a photonic crystal with two-photon absorption photodiodes,” Optica 4(9), 1109–1112 (2017). [CrossRef]  

13. E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009). [CrossRef]  

14. M. Dinu, D. C. Kilper, and H. R. Stuart, “Optical performance monitoring using data stream intensity autocorrelation,” J. Lightwave Technol. 24(3), 1194–1202 (2006). [CrossRef]  

15. G. W. Cong, Y. Maegami, M. Ohno, M. Okano, and K. Yamada, “High-sensitivity Autocorrelation Measurement of Ultrafast Optical Pulses Using Silicon Wire P-I-N Waveguides,” in Proceedings of 43rd European Conference on Optical Communication (ECOC, 2017), paper P1.SC2.21. [CrossRef]  

16. G. Cong, M. Ohno, Y. Maegami, M. Okano, and K. Yamada, “Optical autocorrelation performance of silicon wire p-i-n waveguides utilizing the enhanced two-photon absorption,” Opt. Express 24(26), 29452–29458 (2016). [CrossRef]   [PubMed]  

17. S. C. Pinault and M. J. Potasek, “Frequency broadening by self-phase modulation in optical fibers,” J. Opt. Soc. Am. B 2(8), 1318–1319 (1985). [CrossRef]  

18. E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef]   [PubMed]  

19. Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Cross-phase modulation-induced spectral broadening in silicon waveguides,” Opt. Express 24(1), 443–451 (2016). [CrossRef]   [PubMed]  

20. N. Suzuki, “FDTD Analysis of Two-Photon Absorption and Free-Carrier Absorption in Si High-Index-Contrast Waveguides,” J. Lightwave Technol. 25(9), 2495–2501 (2007). [CrossRef]  

21. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

22. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]  

23. D. M. Caughey and R. E. Thomas, “Carrier Mobilities in Silicon Empirically Related to Doping and Field,” in Proceedings of the IEEE (1967), pp. 2192–2193. [CrossRef]  

24. Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007). [CrossRef]  

25. A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004). [CrossRef]   [PubMed]  

26. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007). [CrossRef]  

27. A. J. Sabbah and D. M. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B 66(16), 165217 (2002). [CrossRef]  

28. Lumerical Solutions, Inc., https://www.lumerical.com/tcadproducts/mode/.

29. M. M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14(4), 1693–1706 (1976). [CrossRef]  

References

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  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).
    [Crossref] [PubMed]
  2. R. Niigaki, Y. Kida, and T. Imasaka, “Mode-locked laser with a repetition rate of 17.6 THz,” Appl. Opt. 56(27), 7636–7641 (2017).
    [Crossref] [PubMed]
  3. E. Z. Chong, T. F. Watson, and F. Festy, “Autocorrelation measurement of femtosecond laser pulses based on two-photon absorption in GaP photodiode,” Appl. Phys. Lett. 105(6), 062111 (2014).
    [Crossref]
  4. T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
    [Crossref]
  5. Autocorrelators, https://www.rp-photonics.com/autocorrelators.html
  6. T. Hirayama and M. Sheik-Bahae, “Real-time chirp diagnostic for ultrashort laser pulses,” Opt. Lett. 27(10), 860–862 (2002).
    [Crossref] [PubMed]
  7. D. A. Bender, M. P. Hasselbeck, and M. Sheik-Bahae, “Sensitive ultrashort pulse chirp measurement,” Opt. Lett. 31(1), 122–124 (2006).
    [Crossref] [PubMed]
  8. M. M. Karkhanehchi, C. J. Hamilton, and J. H. Marsh, “Autocorrelation Measurements of Modelocked Nd:YLF Laser Pulses Using Two-Photon Absorption Waveguide Autocorrelator,” IEEE. Photonics Tech. Lett. 9(5), 645–647 (1997).
    [Crossref]
  9. 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(1), 3246 (2014).
    [Crossref] [PubMed]
  10. 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), 1323–1325 (2002).
    [Crossref]
  11. R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “Two-photon-absorption photodiodes in Si photonic-crystal slow-light waveguides,” Appl. Phys. Lett. 102(3), 031114 (2013).
    [Crossref]
  12. K. Kondo and T. Baba, “On-chip autocorrelator using counter-propagating slow light in a photonic crystal with two-photon absorption photodiodes,” Optica 4(9), 1109–1112 (2017).
    [Crossref]
  13. E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
    [Crossref]
  14. M. Dinu, D. C. Kilper, and H. R. Stuart, “Optical performance monitoring using data stream intensity autocorrelation,” J. Lightwave Technol. 24(3), 1194–1202 (2006).
    [Crossref]
  15. G. W. Cong, Y. Maegami, M. Ohno, M. Okano, and K. Yamada, “High-sensitivity Autocorrelation Measurement of Ultrafast Optical Pulses Using Silicon Wire P-I-N Waveguides,” in Proceedings of 43rd European Conference on Optical Communication (ECOC, 2017), paper P1.SC2.21.
    [Crossref]
  16. G. Cong, M. Ohno, Y. Maegami, M. Okano, and K. Yamada, “Optical autocorrelation performance of silicon wire p-i-n waveguides utilizing the enhanced two-photon absorption,” Opt. Express 24(26), 29452–29458 (2016).
    [Crossref] [PubMed]
  17. S. C. Pinault and M. J. Potasek, “Frequency broadening by self-phase modulation in optical fibers,” J. Opt. Soc. Am. B 2(8), 1318–1319 (1985).
    [Crossref]
  18. E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006).
    [Crossref] [PubMed]
  19. Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Cross-phase modulation-induced spectral broadening in silicon waveguides,” Opt. Express 24(1), 443–451 (2016).
    [Crossref] [PubMed]
  20. N. Suzuki, “FDTD Analysis of Two-Photon Absorption and Free-Carrier Absorption in Si High-Index-Contrast Waveguides,” J. Lightwave Technol. 25(9), 2495–2501 (2007).
    [Crossref]
  21. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).
  22. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
    [Crossref]
  23. D. M. Caughey and R. E. Thomas, “Carrier Mobilities in Silicon Empirically Related to Doping and Field,” in Proceedings of the IEEE (1967), pp. 2192–2193.
    [Crossref]
  24. Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
    [Crossref]
  25. A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004).
    [Crossref] [PubMed]
  26. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
    [Crossref]
  27. A. J. Sabbah and D. M. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B 66(16), 165217 (2002).
    [Crossref]
  28. Lumerical Solutions, Inc., https://www.lumerical.com/tcadproducts/mode/ .
  29. M. M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14(4), 1693–1706 (1976).
    [Crossref]

2017 (2)

2016 (2)

2014 (2)

E. Z. Chong, T. F. Watson, and F. Festy, “Autocorrelation measurement of femtosecond laser pulses based on two-photon absorption in GaP photodiode,” Appl. Phys. Lett. 105(6), 062111 (2014).
[Crossref]

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(1), 3246 (2014).
[Crossref] [PubMed]

2013 (2)

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).
[Crossref] [PubMed]

R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “Two-photon-absorption photodiodes in Si photonic-crystal slow-light waveguides,” Appl. Phys. Lett. 102(3), 031114 (2013).
[Crossref]

2009 (1)

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

2007 (3)

N. Suzuki, “FDTD Analysis of Two-Photon Absorption and Free-Carrier Absorption in Si High-Index-Contrast Waveguides,” J. Lightwave Technol. 25(9), 2495–2501 (2007).
[Crossref]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

2006 (3)

2004 (2)

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004).
[Crossref] [PubMed]

2002 (3)

A. J. Sabbah and D. M. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B 66(16), 165217 (2002).
[Crossref]

T. Hirayama and M. Sheik-Bahae, “Real-time chirp diagnostic for ultrashort laser pulses,” Opt. Lett. 27(10), 860–862 (2002).
[Crossref] [PubMed]

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), 1323–1325 (2002).
[Crossref]

1997 (1)

M. M. Karkhanehchi, C. J. Hamilton, and J. H. Marsh, “Autocorrelation Measurements of Modelocked Nd:YLF Laser Pulses Using Two-Photon Absorption Waveguide Autocorrelator,” IEEE. Photonics Tech. Lett. 9(5), 645–647 (1997).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

1985 (1)

1976 (1)

M. M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14(4), 1693–1706 (1976).
[Crossref]

Agrawal, G. P.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

An, J.

Asghari, M.

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), 1323–1325 (2002).
[Crossref]

Baba, T.

K. Kondo and T. Baba, “On-chip autocorrelator using counter-propagating slow light in a photonic crystal with two-photon absorption photodiodes,” Optica 4(9), 1109–1112 (2017).
[Crossref]

R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “Two-photon-absorption photodiodes in Si photonic-crystal slow-light waveguides,” Appl. Phys. Lett. 102(3), 031114 (2013).
[Crossref]

Barry, L. P.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Bender, D. A.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Boyd, R. W.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

Boyraz, O.

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

Bradley, A. L.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Byer, R. L.

M. M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14(4), 1693–1706 (1976).
[Crossref]

Caughey, D. M.

D. M. Caughey and R. E. Thomas, “Carrier Mobilities in Silicon Empirically Related to Doping and Field,” in Proceedings of the IEEE (1967), pp. 2192–2193.
[Crossref]

Chen, X.

Chong, E. Z.

E. Z. Chong, T. F. Watson, and F. Festy, “Autocorrelation measurement of femtosecond laser pulses based on two-photon absorption in GaP photodiode,” Appl. Phys. Lett. 105(6), 062111 (2014).
[Crossref]

Choy, M. M.

M. M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14(4), 1693–1706 (1976).
[Crossref]

Clark, A.

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(1), 3246 (2014).
[Crossref] [PubMed]

Cohen, O.

Collins, M.

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(1), 3246 (2014).
[Crossref] [PubMed]

Cong, G.

Day, I. E.

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), 1323–1325 (2002).
[Crossref]

Dinu, M.

Donegan, J. F.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Drake, J.

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), 1323–1325 (2002).
[Crossref]

Dulkeith, E.

Eggleton, B. J.

Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Cross-phase modulation-induced spectral broadening in silicon waveguides,” Opt. Express 24(1), 443–451 (2016).
[Crossref] [PubMed]

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(1), 3246 (2014).
[Crossref] [PubMed]

Fauchet, P. M.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

Festy, F.

E. Z. Chong, T. F. Watson, and F. Festy, “Autocorrelation measurement of femtosecond laser pulses based on two-photon absorption in GaP photodiode,” Appl. Phys. Lett. 105(6), 062111 (2014).
[Crossref]

Folliot, H.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Grillet, C.

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(1), 3246 (2014).
[Crossref] [PubMed]

Hak, D.

Hamilton, C. J.

M. M. Karkhanehchi, C. J. Hamilton, and J. H. Marsh, “Autocorrelation Measurements of Modelocked Nd:YLF Laser Pulses Using Two-Photon Absorption Waveguide Autocorrelator,” IEEE. Photonics Tech. Lett. 9(5), 645–647 (1997).
[Crossref]

Hasselbeck, M. P.

Hayakawa, R.

R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “Two-photon-absorption photodiodes in Si photonic-crystal slow-light waveguides,” Appl. Phys. Lett. 102(3), 031114 (2013).
[Crossref]

Hill, G.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Hirayama, T.

Husko, C.

Imasaka, T.

Ishikura, N.

R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “Two-photon-absorption photodiodes in Si photonic-crystal slow-light waveguides,” Appl. Phys. Lett. 102(3), 031114 (2013).
[Crossref]

Karkhanehchi, M. M.

M. M. Karkhanehchi, C. J. Hamilton, and J. H. Marsh, “Autocorrelation Measurements of Modelocked Nd:YLF Laser Pulses Using Two-Photon Absorption Waveguide Autocorrelator,” IEEE. Photonics Tech. Lett. 9(5), 645–647 (1997).
[Crossref]

Kida, Y.

Kilper, D. C.

Kim, D. E.

Knights, A. P.

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), 1323–1325 (2002).
[Crossref]

Kondo, K.

Krauss, T. F.

Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Cross-phase modulation-induced spectral broadening in silicon waveguides,” Opt. Express 24(1), 443–451 (2016).
[Crossref] [PubMed]

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(1), 3246 (2014).
[Crossref] [PubMed]

Krug, T.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Kwon, O.

Lefrancois, S.

Li, J.

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(1), 3246 (2014).
[Crossref] [PubMed]

Liang, T. K.

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), 1323–1325 (2002).
[Crossref]

Lin, Q.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

Liu, A.

Lynch, M.

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

Maegami, Y.

Marsh, J. H.

M. M. Karkhanehchi, C. J. Hamilton, and J. H. Marsh, “Autocorrelation Measurements of Modelocked Nd:YLF Laser Pulses Using Two-Photon Absorption Waveguide Autocorrelator,” IEEE. Photonics Tech. Lett. 9(5), 645–647 (1997).
[Crossref]

Monat, C.

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(1), 3246 (2014).
[Crossref] [PubMed]

Moss, D. J.

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(1), 3246 (2014).
[Crossref] [PubMed]

Nguyen, H. C.

R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “Two-photon-absorption photodiodes in Si photonic-crystal slow-light waveguides,” Appl. Phys. Lett. 102(3), 031114 (2013).
[Crossref]

Niigaki, R.

O’Faolain, L.

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(1), 3246 (2014).
[Crossref] [PubMed]

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Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

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[Crossref]

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[Crossref]

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T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
[Crossref]

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[Crossref]

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A. J. Sabbah and D. M. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B 66(16), 165217 (2002).
[Crossref]

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E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

Schröder, J.

Schroeder, J.

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(1), 3246 (2014).
[Crossref] [PubMed]

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Song, Q.

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
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E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
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A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
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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(1), 3246 (2014).
[Crossref] [PubMed]

Yamada, K.

Zhang, J.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
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Appl. Opt. (1)

Appl. Phys. Lett. (6)

E. Z. Chong, T. F. Watson, and F. Festy, “Autocorrelation measurement of femtosecond laser pulses based on two-photon absorption in GaP photodiode,” Appl. Phys. Lett. 105(6), 062111 (2014).
[Crossref]

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), 1323–1325 (2002).
[Crossref]

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[Crossref]

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

IEEE J. Quantum Electron. (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

IEEE Photonics Technol. Lett. (1)

T. Krug, M. Lynch, A. L. Bradley, J. F. Donegan, L. P. Barry, H. Folliot, J. S. Roberts, and G. Hill, “High-Sensitivity Two-Photon Absorption Microcavity Autocorrelator,” IEEE Photonics Technol. Lett. 16(6), 1543–1545 (2004).
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M. M. Karkhanehchi, C. J. Hamilton, and J. H. Marsh, “Autocorrelation Measurements of Modelocked Nd:YLF Laser Pulses Using Two-Photon Absorption Waveguide Autocorrelator,” IEEE. Photonics Tech. Lett. 9(5), 645–647 (1997).
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[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

Optica (1)

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[Crossref]

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Autocorrelators, https://www.rp-photonics.com/autocorrelators.html

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Figures (5)

Fig. 1
Fig. 1 (a) Principle schematic of interferometric autocorrelation using the silicon p-i-n waveguide as a photocurrent detector. (b) Fabricated device and its cross-section scanning capacitance microscope indicating carrier distribution in the rib waveguide. (c) Measurement system of interferometric autocorrelation. FL: fiber mode-lock laser. TDL: tunable delay line. PM: power meter. SM: source meter. PC: computer.
Fig. 2
Fig. 2 Experimental interferometric autocorrelation waveforms of the device lengths (a) L = 1 mm and (b) L = 0.5 mm. FDTD simulated autocorrelation waveforms without phase noise for (c) L = 1 mm and (d) L = 0.5 mm, and with phase noise (e) L = 1 mm and (f) L = 0.5 mm.
Fig. 3
Fig. 3 Pulse energy dependences of (a) peak and swing photocurrents of L = 1 mm and (b) pulse widths measured from autocorrelation waveforms as explained in section 3.1. The unit of βTPA is cm/GW. To be noted that the pulse energy in this figure is the calibrated one using the 4.2-dB loss.
Fig. 4
Fig. 4 (a) Electric field (Ex) of two autocorrelated pulses with a time delay Δt = 1 ps before and after propagation along the 1 mm p-i-n waveguide for the pulse energies of 1 and 10 pJ. x denotes the TE polarization. (b) Corresponding temporal response of the index change Δn due to the TPA-induced free carrier effect monitored at z = 0.5 mm, the center of waveguide. z denotes the optical propagation direction along waveguide.
Fig. 5
Fig. 5 Wavelength dependences of (a) group index and (b) dispersion parameter D. (c) Pulse broadening due to GVD. (c) Error ratio in a relation to the input pulse width. Error ratio is defined as 10 × log(Δw/w0) where w0 and Δw are the input pulse width and pulse broadening, respectively.

Equations (10)

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μ 0 H t =×E
D t =×H
D= ε r E+ P i
P α = c 0 ε 0 n 0 α iω E
P FCA,e,h = c 0 ε 0 n 0 σ e,h N e,h iω E
P plasma =2 ε 0 n 0 Δn( N e , N h )E
P TPA = c 0 2 ε 0 2 n 0 2 β TPA 2iω | E | 2
σ e,h = e 3 λ 2 4 π 2 c 0 3 ε 0 n 0 1 m * e,h 2 μ e,h
Δn= e 2 λ 2 8 π 2 c 0 2 ε 0 n 0 Δ N e,h m * e,h
d N e,h dt = c 0 2 ε 0 2 n 0 2 β TPA 8ω | E | 4 N e,h τ

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