Abstract

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 107W2, which is equal to or even better than that of commercial scanning autocorrelators and 107-fold better than that of conventional single-shot autocorrelators.

© 2017 Optical Society of America

1. INTRODUCTION

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 [1] and single-shot [210]. 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 [11]. A scanning autocorrelator has been demonstrated by integrating a Si photonic crystal waveguide (PCW)-based delay scanner and two-photon absorption (TPA) PD [12] onto a silicon-on-insulator (SOI) using a complementary metal oxide semiconductor (CMOS) process [13]. The PCW has been extensively studied because it exhibits large first-order dispersion, which generates slow light [11,14], enables tunable delay [15], and enhances TPA [14,16]. Regarding single-shot autocorrelators, a SrxBa1xNb2O6 crystal [17], CdS nanowire [18], and Si PCW [19] 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 [20]. 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 [21]. 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 z in the LSPCW and time t, we denote the intensities of Gaussian pulse envelopes launched from left and right as I1(z,t) and I2(z,t), respectively, neglecting the cross-sectional profile. Then, I2(z,t)=I1(Lz,t) for the total length of the LSPCW, L, and the electric field of the two pulses are given by

E1(z,t)=I1(z,t)exp[jωt(jk+α)z],E2(z,t)=I2(z,t)exp[jωt(jk+α)(Lz)],
where ω is the frequency, k is the propagation constant, and α is the propagation loss. The density of TPA-induced free carriers is given by
N(z)|E1(z,t)+E2(z,t)|4dt.

 figure: Fig. 1.

Fig. 1. Schematic of proposed autocorrelator and correlation waveforms obtained from integrated TPA-PD array.

Download Full Size | PPT Slide | PDF

Substituting Eq. (1) into Eq. (2), N(z) 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 N(z), 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 α=0 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.

 figure: Fig. 2.

Fig. 2. Theoretical correlation waveforms. (a) The waveform observable with sufficient resolution, and (b) with practical resolution of 5 μm. In (b), dashed line depicts the envelope component. The red and blue lines show the intensities individually induced by pulses incident from the left and right, respectively. FWHM of pulse and ng of LSPCW are set at 3 ps and 20, respectively.

Download Full Size | PPT Slide | PDF

While the correlation in a scanning autocorrelator is a function of the temporal offset Δt, in our device it is a function of the spatial offset Δz. These offsets are related via Δt=2Δzng/c (where c is the light velocity in a vacuum and ng is the group index). The full width at half-maximum (FWHM) of the input pulse is given as Δτ=2Δzng/c for a Gaussian pulse (Δτ=2Δzng/1.54c for a sech2 pulse). As expressed in these equations, a higher ng compresses the pulse in space and shortens the correlation waveform on the TPA-PD array.

3. EXPERIMENT

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 μ-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 [22], 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).

 figure: Fig. 3.

Fig. 3. Fabricated device and its optical and electrical characteristics. (a) Total and magnified images. For clarity, p- and n-doped regions are red- and blue-colored, respectively. (b) Transmission and ng spectra of LSPCW with wavelength resolutions of 0.1 and 0.6 nm, respectively. The transmission is normalized to that of Si wire of the same length. (c) Responsivity characteristics of center TPA-PD (circles) and linear and square fittings to PpkPav and Ppk (gray line), respectively, which were obtained for 4.5-ps Gaussian pulse at 40-MHz repetition.

Download Full Size | PPT Slide | PDF

The transmission and ng 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 λ=15291544nm with ng24 and the second-order dispersion β2=2 to 2ps2/mm. The propagation loss of the LSPCW with pn 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 λ=1541nm 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 3V (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 1.8×104). The photocurrent is proportional to both the square of the peak power, Ppk, and the product of the peak and average power, PpkPav (both the peak and average power were evaluated in the input fiber). The square responsivity evaluated for PpkPav is 6.9×104A/W2. The responsivity begins to saturate at Ppk3W, 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 pin photodiode (responsivity of 0.8A/W) and low-noise preamplifier, the detectable limit power for 10-Gbps telecom transmission is 0.011mW [23], which corresponds to 0.9 fC/bit. In our device, on the other hand, the photocurrent of 1 μA was obtained for Ppk=3W, 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 Ppk=1W, changing the FWHM Δτ 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 Δτ 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 Δτ=7.1ps the fabricated device produces a waveform with a slightly lowered intensity. We believe that this error is caused by a combination of variations in ng and the PDs’ responsivity and insufficient phase averaging. The time resolution for a Gaussian pulse, 2png/c, where p is the pitch of the PDs, was measured to be 570 fs in the fabricated device; this can be improved by using a smaller p and ng, although doing so would degrade the responsivity.

 figure: Fig. 4.

Fig. 4. Autocorrelation waveforms produced by fabricated device (orange circle and fitting curve) and commercial scanning autocorrelator (gray line). In each curve, the peak value is 1.0 and other values are estimated by counting the number of divisions in the vertical axis. Inset shows the relation of pulse FWHM measured by the device to that by a commercial one.

Download Full Size | PPT Slide | PDF

4. PRECISION

To show the potential of the fabricated device for practical use, we evaluated the precision of the correlation at various values of Δτ, center wavelength λ, pulse power Ppk, 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 σ in the correlation, measured by each TPA-PD that was normalized by a value on the Gaussian fitting curve. Figure 5 summarizes the measured σ values for the four parameters, where the respective default values/settings were Δτ=3.04.5ps, λ=1,541nm, Ppk=0.71.5W, and TE polarization. From Figs. 4 and 5(a), it is seen that σ remains small for Δτ=17ps. By elongating the LSPCW or reducing p and ng, 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.

 figure: Fig. 5.

Fig. 5. Precision (standard deviation σ from Gaussian fitting) of observed correlation waveforms evaluated for (a) pulse FWHM Δτ, (b) center wavelength λ, (c) input pulse power Ppk, (and PpkPav), and (d) polarization angle. σ>0.2 is not acceptable even for rough observation of the correlation.

Download Full Size | PPT Slide | PDF

In Fig. 5(b), σ is small at the shorter wavelengths but increases toward the photonic band edge on the long wavelength side because the fluctuation in the loss, ng, and the phase are enhanced by the band edge slow light. This confirms an effective Δλ 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 ng to 10.

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 PpkPav in the proposed device was estimated to be on the order of 107W2, which is equivalent or even better than that in a commercial scanning autocorrelator, and better by a factor of 107 than that of a conventional single-shot correlator [5]. 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, σ increases as the angle approaches 90°. However, as σ 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.

5. SUMMARY

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.

Funding

New Energy and Industrial Technology Development Organization (NEDO).

Acknowledgment

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.

REFERENCES

1. A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, Semicond. Sci. Technol. 26, 083001 (2011). [CrossRef]  

2. J. Janszky and G. Corradi, Opt. Commun. 23, 293 (1977). [CrossRef]  

3. R. N. Gyuzalian, S. B. Sogomonian, and Z. G. Horvath, Opt. Commun. 29, 239 (1979). [CrossRef]  

4. F. Salin, P. Georges, G. Roger, and A. Brun, Appl. Opt. 26, 4528 (1987). [CrossRef]  

5. D. T. Reid, W. Sibbett, J. M. Dudley, L. P. Barry, B. Thomsen, and J. D. Harvey, Appl. Opt. 37, 8142 (1998). [CrossRef]  

6. Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, Opt. Lett. 17, 658 (1992). [CrossRef]  

7. K. Oba, P. C. Sun, T. T. Mazurenko, and Y. Fainman, Appl. Opt. 38, 3810 (1999). [CrossRef]  

8. D. J. Kane and R. Trebino, Opt. Lett 18, 823 (1993). [CrossRef]  

9. G. Figueira, L. Cardoso, N. Lopes, and J. Wemans, J. Opt. Soc. Am. B 22, 2709 (2005). [CrossRef]  

10. D. Javorkova and V. Bagnoud, Opt. Express 15, 5439 (2007). [CrossRef]  

11. J. Li, T. P. White, L. O’Faolain, A. G. Iglesias, and T. F. Krauss, Opt. Express 16, 6227 (2008). [CrossRef]  

12. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005). [CrossRef]  

13. S. Kinugasa, N. Ishikura, H. Ito, N. Yazawa, and T. Baba, Opt. Express 23, 20767 (2015). [CrossRef]  

14. M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, Opt. Express 19, 22208 (2011). [CrossRef]  

15. C. Monat, B. Corcoran, M. E. Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Opt. Express 17, 2944 (2009). [CrossRef]  

16. N. Ishikura, T. Baba, E. Kuramochi, and M. Notomi, Opt. Express 19, 24102 (2011). [CrossRef]  

17. R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007). [CrossRef]  

18. H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014). [CrossRef]  

19. 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, Nat. Commun. 5, 3246 (2014). [CrossRef]  

20. E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007). [CrossRef]  

21. Y. Hamachi, S. Kubo, and T. Baba, Opt. Lett. 34, 1072 (2009). [CrossRef]  

22. L. H. Frandsen, A. V. Lavrinenko, J. F. Pedersen, and P. I. Borel, Opt. Express 14, 9444 (2006). [CrossRef]  

23. “G12072-54: InGaAs PIN photodiode with preamp,” Spec Sheet (Hamamatsu Photonics, 2011).

References

  • View by:
  • |
  • |
  • |

  1. A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, Semicond. Sci. Technol. 26, 083001 (2011).
    [Crossref]
  2. J. Janszky and G. Corradi, Opt. Commun. 23, 293 (1977).
    [Crossref]
  3. R. N. Gyuzalian, S. B. Sogomonian, and Z. G. Horvath, Opt. Commun. 29, 239 (1979).
    [Crossref]
  4. F. Salin, P. Georges, G. Roger, and A. Brun, Appl. Opt. 26, 4528 (1987).
    [Crossref]
  5. D. T. Reid, W. Sibbett, J. M. Dudley, L. P. Barry, B. Thomsen, and J. D. Harvey, Appl. Opt. 37, 8142 (1998).
    [Crossref]
  6. Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, Opt. Lett. 17, 658 (1992).
    [Crossref]
  7. K. Oba, P. C. Sun, T. T. Mazurenko, and Y. Fainman, Appl. Opt. 38, 3810 (1999).
    [Crossref]
  8. D. J. Kane and R. Trebino, Opt. Lett 18, 823 (1993).
    [Crossref]
  9. G. Figueira, L. Cardoso, N. Lopes, and J. Wemans, J. Opt. Soc. Am. B 22, 2709 (2005).
    [Crossref]
  10. D. Javorkova and V. Bagnoud, Opt. Express 15, 5439 (2007).
    [Crossref]
  11. J. Li, T. P. White, L. O’Faolain, A. G. Iglesias, and T. F. Krauss, Opt. Express 16, 6227 (2008).
    [Crossref]
  12. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005).
    [Crossref]
  13. S. Kinugasa, N. Ishikura, H. Ito, N. Yazawa, and T. Baba, Opt. Express 23, 20767 (2015).
    [Crossref]
  14. M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, Opt. Express 19, 22208 (2011).
    [Crossref]
  15. C. Monat, B. Corcoran, M. E. Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Opt. Express 17, 2944 (2009).
    [Crossref]
  16. N. Ishikura, T. Baba, E. Kuramochi, and M. Notomi, Opt. Express 19, 24102 (2011).
    [Crossref]
  17. R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
    [Crossref]
  18. H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
    [Crossref]
  19. 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, Nat. Commun. 5, 3246 (2014).
    [Crossref]
  20. E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
    [Crossref]
  21. Y. Hamachi, S. Kubo, and T. Baba, Opt. Lett. 34, 1072 (2009).
    [Crossref]
  22. L. H. Frandsen, A. V. Lavrinenko, J. F. Pedersen, and P. I. Borel, Opt. Express 14, 9444 (2006).
    [Crossref]
  23. “G12072-54: InGaAs PIN photodiode with preamp,” Spec Sheet (Hamamatsu Photonics, 2011).

2015 (1)

2014 (2)

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (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, Nat. Commun. 5, 3246 (2014).
[Crossref]

2011 (3)

2009 (2)

2008 (1)

2007 (3)

D. Javorkova and V. Bagnoud, Opt. Express 15, 5439 (2007).
[Crossref]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

2006 (1)

2005 (2)

G. Figueira, L. Cardoso, N. Lopes, and J. Wemans, J. Opt. Soc. Am. B 22, 2709 (2005).
[Crossref]

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005).
[Crossref]

1999 (1)

1998 (1)

1993 (1)

D. J. Kane and R. Trebino, Opt. Lett 18, 823 (1993).
[Crossref]

1992 (1)

1987 (1)

1979 (1)

R. N. Gyuzalian, S. B. Sogomonian, and Z. G. Horvath, Opt. Commun. 29, 239 (1979).
[Crossref]

1977 (1)

J. Janszky and G. Corradi, Opt. Commun. 23, 293 (1977).
[Crossref]

Baba, T.

Bagnoud, V.

Barry, L. P.

Benech, P.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Blaize, S.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Borel, P. I.

Brun, A.

Cardoso, L.

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, Nat. Commun. 5, 3246 (2014).
[Crossref]

Coarer, E. L.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

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, Nat. Commun. 5, 3246 (2014).
[Crossref]

Corcoran, B.

Corradi, G.

J. Janszky and G. Corradi, Opt. Commun. 23, 293 (1977).
[Crossref]

Dudley, J. M.

Eggleton, B. 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, Nat. Commun. 5, 3246 (2014).
[Crossref]

C. Monat, B. Corcoran, M. E. Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Opt. Express 17, 2944 (2009).
[Crossref]

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005).
[Crossref]

Fainman, Y.

Fang, W.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Fedeli, J. M.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Figueira, G.

Fischer, R.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

Frandsen, L. H.

Fu, L.

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005).
[Crossref]

Georges, P.

Ginzburg, P.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, Semicond. Sci. Technol. 26, 083001 (2011).
[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, Nat. Commun. 5, 3246 (2014).
[Crossref]

C. Monat, B. Corcoran, M. E. Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Opt. Express 17, 2944 (2009).
[Crossref]

Gyuzalian, R. N.

R. N. Gyuzalian, S. B. Sogomonian, and Z. G. Horvath, Opt. Commun. 29, 239 (1979).
[Crossref]

Hama, Y.

Hamachi, Y.

Harvey, J. D.

Hayat, A.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

Heidari, M. E.

Horvath, Z. G.

R. N. Gyuzalian, S. B. Sogomonian, and Z. G. Horvath, Opt. Commun. 29, 239 (1979).
[Crossref]

Iglesias, A. G.

Imamura, S.

Ishikura, N.

Ito, H.

Janszky, J.

J. Janszky and G. Corradi, Opt. Commun. 23, 293 (1977).
[Crossref]

Javorkova, D.

Kane, D. J.

D. J. Kane and R. Trebino, Opt. Lett 18, 823 (1993).
[Crossref]

Kern, P.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Kinugasa, S.

Kivshar, Y. S.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

Kobayashi, T.

Krauss, T. F.

Krolikowski, W.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

Kubo, S.

Kuramochi, E.

Lavrinenko, A. V.

Leblond, G.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Lérondel, G.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

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, Nat. Commun. 5, 3246 (2014).
[Crossref]

J. Li, T. P. White, L. O’Faolain, A. G. Iglesias, and T. F. Krauss, Opt. Express 16, 6227 (2008).
[Crossref]

Lin, X.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Littler, I.

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005).
[Crossref]

Liu, W.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Lopes, N.

Mazurenko, T. T.

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, Nat. Commun. 5, 3246 (2014).
[Crossref]

C. Monat, B. Corcoran, M. E. Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Opt. Express 17, 2944 (2009).
[Crossref]

Morand, A.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

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, Nat. Commun. 5, 3246 (2014).
[Crossref]

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005).
[Crossref]

Neshev, D. N.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

Nevet, A.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

Notomi, M.

O’Faolain, L.

Oba, K.

Orenstein, M.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

Pedersen, J. F.

Reid, D. T.

Roger, G.

Royer, P.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Salin, F.

Saltiel, S. M.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

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, Nat. Commun. 5, 3246 (2014).
[Crossref]

Shen, Y. R.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Shinkawa, M.

Sibbett, W.

Sogomonian, S. B.

R. N. Gyuzalian, S. B. Sogomonian, and Z. G. Horvath, Opt. Commun. 29, 239 (1979).
[Crossref]

Stefanon, I.

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Sukhorukov, A. A.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

Sun, P. C.

Suzuki, K.

Takagi, Y.

Thomsen, B.

Tong, L.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Trebino, R.

D. J. Kane and R. Trebino, Opt. Lett 18, 823 (1993).
[Crossref]

Wang, A.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Wemans, J.

White, T. P.

Wu, X.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Xiong, 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, Nat. Commun. 5, 3246 (2014).
[Crossref]

Yazawa, N.

Yoshihara, K.

Yu, H.

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 91, 031104 (2007).
[Crossref]

Electron. Lett. (1)

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, Electron. Lett. 41, 320 (2005).
[Crossref]

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

H. Yu, W. Fang, X. Wu, X. Lin, L. Tong, W. Liu, A. Wang, and Y. R. Shen, Nano Lett. 14, 3487 (2014).
[Crossref]

Nat. Commun. (1)

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, Nat. Commun. 5, 3246 (2014).
[Crossref]

Nat. Photonics (1)

E. L. Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photonics 1, 473 (2007).
[Crossref]

Opt. Commun. (2)

J. Janszky and G. Corradi, Opt. Commun. 23, 293 (1977).
[Crossref]

R. N. Gyuzalian, S. B. Sogomonian, and Z. G. Horvath, Opt. Commun. 29, 239 (1979).
[Crossref]

Opt. Express (7)

Opt. Lett (1)

D. J. Kane and R. Trebino, Opt. Lett 18, 823 (1993).
[Crossref]

Opt. Lett. (2)

Semicond. Sci. Technol. (1)

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

Other (1)

“G12072-54: InGaAs PIN photodiode with preamp,” Spec Sheet (Hamamatsu Photonics, 2011).

Supplementary Material (1)

NameDescription
» Supplement 1       Supplement 1

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. Schematic of proposed autocorrelator and correlation waveforms obtained from integrated TPA-PD array.
Fig. 2.
Fig. 2. Theoretical correlation waveforms. (a) The waveform observable with sufficient resolution, and (b) with practical resolution of 5 μm. In (b), dashed line depicts the envelope component. The red and blue lines show the intensities individually induced by pulses incident from the left and right, respectively. FWHM of pulse and ng of LSPCW are set at 3 ps and 20, respectively.
Fig. 3.
Fig. 3. Fabricated device and its optical and electrical characteristics. (a) Total and magnified images. For clarity, p- and n-doped regions are red- and blue-colored, respectively. (b) Transmission and ng spectra of LSPCW with wavelength resolutions of 0.1 and 0.6 nm, respectively. The transmission is normalized to that of Si wire of the same length. (c) Responsivity characteristics of center TPA-PD (circles) and linear and square fittings to PpkPav and Ppk (gray line), respectively, which were obtained for 4.5-ps Gaussian pulse at 40-MHz repetition.
Fig. 4.
Fig. 4. Autocorrelation waveforms produced by fabricated device (orange circle and fitting curve) and commercial scanning autocorrelator (gray line). In each curve, the peak value is 1.0 and other values are estimated by counting the number of divisions in the vertical axis. Inset shows the relation of pulse FWHM measured by the device to that by a commercial one.
Fig. 5.
Fig. 5. Precision (standard deviation σ from Gaussian fitting) of observed correlation waveforms evaluated for (a) pulse FWHM Δτ, (b) center wavelength λ, (c) input pulse power Ppk, (and PpkPav), and (d) polarization angle. σ>0.2 is not acceptable even for rough observation of the correlation.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

E1(z,t)=I1(z,t)exp[jωt(jk+α)z],E2(z,t)=I2(z,t)exp[jωt(jk+α)(Lz)],
N(z)|E1(z,t)+E2(z,t)|4dt.

Metrics