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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 16526–16538
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Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry

Mohammad H. Asghari, Yongwoo Park, and José Azaña  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 16526-16538 (2010)
http://dx.doi.org/10.1364/OE.18.016526


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Abstract

Several methods are now available for single-shot measurement of the complex field (amplitude and phase profiles) of optical waveforms with resolutions down to the sub-picosecond range. As a main critical limitation, all these techniques exhibit measurement update rates typically slower than a few Hz. It would be very challenging to directly upgrade the update rate of any of these available methods beyond a few kHz. By combining spectral interferometry with dispersion-induced real-time optical Fourier transformation, here we demonstrate single-shot complex-field measurements of optical waveforms with a resolution of ~400 fs over a record length as long as ~350 ps, corresponding to a large record-length-to-resolution ratio of ~900. This performance is achieved at a measurement update rate of ~17 MHz, i.e. at least one thousand times faster than with any previous single-shot complex-field THz-bandwidth optical signal characterization method.

© 2010 OSA

1. Introduction

Future progress in a wide range of fields [1

1. C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Quantum Electron. 12(4), 843–858 (2006). [CrossRef]

-8

8. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009). [CrossRef] [PubMed]

] essentially depend on the development of improved temporal waveform measurement methods, capable of providing the stringent performance that is required to capture ultrafast phenomena, i.e. with resolutions down to the sub-picosecond range, in an entirely dynamic fashion, i.e. as these phenomena evolve at ultrahigh speeds. The capability of performing such advanced measurements is important for applications in which random (non-repetitive), rapidly-changing ultrafast waveforms need to be fully characterized and evaluated. These include real-time monitoring in ultrahigh-bit-rate optical telecommunication, computing and information processing systems [1

1. C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Quantum Electron. 12(4), 843–858 (2006). [CrossRef]

,2

2. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

,10

10. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010). [CrossRef]

]; testing of electronic and photonic materials, devices and sub-systems [3

3. T. J. Ahn, Y. Park, and J. Azaña, “Fast and accurate group delay ripple measurement technique for ultralong chirped fiber Bragg gratings,” Opt. Lett. 32(18), 2674–2676 (2007). [CrossRef] [PubMed]

-6

6. H. Xia, C. Wang, S. Blais, and J. Yao, “Ultrafast and precise interrogation of fiber Bragg grating sensor based on wavelength-to-time mapping incorporating higher order dispersion,” J. Lightwave Technol. 28(3), 254–261 (2010). [CrossRef]

]; and observation and analysis of a large variety of ultrafast dynamic events in physics, biology, chemistry etc [7

7. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007). [CrossRef] [PubMed]

,8

8. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009). [CrossRef] [PubMed]

].

In the past decades, new and improved methods for measuring the complex-field temporal (or spectral) profile of ultrafast optical signals have been developed [1

1. C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Quantum Electron. 12(4), 843–858 (2006). [CrossRef]

-10

10. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010). [CrossRef]

]. For characterization of non-repetitive events, single-shot measurement techniques are necessary [2

2. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

,10

10. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010). [CrossRef]

-18

18. N. K. Fontaine, R. P. Scott, J. P. Heritage, and S. J. B. Yoo, “Near quantum-limited, single-shot coherent arbitrary optical waveform measurements,” Opt. Express 17(15), 12332–12344 (2009). [CrossRef] [PubMed]

]. A main figure-of-merit to evaluate the performance of single-shot optical signal characterization techniques is the time-bandwidth product, calculated as the ratio between the maximum duration of the waveform that can be measured (record length) and the temporal resolution (inversely proportional to the spectral bandwidth) offered by the measurement setup. Well-established non-linear optical techniques exist for ultrafast signal measurement with few-femtosecond accuracy [12

12. D. J. Kane and R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18(10), 823–825 (1993). [CrossRef] [PubMed]

,13

13. M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, “SPIDER: A decade of measuring ultrashort pulses,” Laser Phys. Lett. 5(4), 259–266 (2008). [CrossRef]

]; linear counterparts of these techniques have been also developed with the aim of increasing the measurement sensitivity [14

14. C. Dorrer and I. Kang, “Highly sensitive direct characterization of femtosecond pulses by electro-optic spectral shearing interferometry,” Opt. Lett. 28(6), 477–479 (2003). [CrossRef] [PubMed]

,15

15. J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, “Highly sensitive, single-shot characterization for pulse widths from 0.4 to 85 ps using electro-optic shearing interferometry,” Opt. Lett. 31(23), 3523–3525 (2006). [CrossRef] [PubMed]

]. However, these widely used methods typically suffer from relatively short single-shot record lengths of a few tens of picoseconds. Ultrafast optical signal measurement techniques based on the time-lens concept have been explored to overcome this limitation [2

2. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

,11

11. R. Salem, M. A. Foster, A. C. Turner-Foster, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “High-speed optical sampling using a silicon-chip temporal magnifier,” Opt. Express 17(6), 4324–4329 (2009). [CrossRef] [PubMed]

]. In a recent state-of-the-art demonstration, single-shot optical waveform measurements were carried out with sub-picosecond resolutions over total durations up to the sub-nanosecond range, corresponding to an estimated time-bandwidth product of ~450, using a non-linear silicon chip-based time-lens [2

2. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

]. However, time-lens based methods are typically restricted to measuring the temporal amplitude profile of the optical signal under test and they do not provide any information on the signal’s phase profile. This information is essential to achieve a full (complex-field) signal characterization. Fontaine et al. [10

10. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010). [CrossRef]

] recently demonstrated an interferometric method that performs parallel coherent detection on spectral slices of arbitrary optical waveforms for real-time, complex-field optical waveform measurements. While it would be challenging to extend the capabilities of this method to measure optical signals with bandwidths in the THz range using present technology, this technique has enabled the measurement of waveforms with very large time-bandwidth products (320,000).

In this manuscript, we propose and develop a simple and practical (fiber-optics) method for complex-field ultrafast optical signal characterization using a balanced Fourier-transform spectral interferometry (FTSI) scheme [15

15. J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, “Highly sensitive, single-shot characterization for pulse widths from 0.4 to 85 ps using electro-optic shearing interferometry,” Opt. Lett. 31(23), 3523–3525 (2006). [CrossRef] [PubMed]

-19

19. L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]

] combined with RT-OFT. Using this new linear approach, we demonstrate single-shot characterization of complex optical events (including accurate measurement of continuous and discrete-time phase variations), with a large time-bandwidth products (up to ~900) and average powers as low as ~26 nW, at update rate of ~17 MHz, i.e. at least thousand times faster than with spectrometer-based solutions. In a remarkable application example, we fully characterize the dynamic ultrashort pulse response of an intensity electro-optic modulator (EOM) as its bias condition is rapidly swept at a measurement update rate of ~17 MHz.

2. Operation principle

FTSI is a simple and very sensitive linear technique for complex-field characterization of ultrafast optical signals [19

19. L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]

]. This technique is based on measuring the spectral energy density of the interference pattern between the optical SUT and a well-characterized reference signal (ultrashort optical pulse with a spectral content extending over that of the SUT). Let us assume an optical signal defined as (analytic representation) E(t) ej2πf0t, where E(t) is the signal’s complex envelope (t is the time variable), and f0 is the optical carrier frequency. The FTSI method is based on measuring an interference spectral pattern (also called spectral interferogram), SI(ω), that is generated by combining a reference pulse (R(t) ej2πf0t) and the SUT (E(t) ej2πf0t), relatively delayed by τ, e.g. using an optical coupler,
SI(ω)=|R(ω)+E(ω)×ejωτ|2                           =|R(ω)|2+|E(ω)|2background signals+2   Re{R*(ω)×E(ω)×ejωτ}interference part                           =                     SIB(ω)                         +                                           SII(ω)(1)
where Re{} means the real part, j=√-1, ω=2πf and f is the base-band frequency variable. Since the information on the complex-field of SUT, E(ω), is embedded in the interference part of SI(ω) (i.e. SII(ω) in Eq. (1)), this part should be isolated from the background signal, SIB(ω), in the spectral interferogram. For this purpose, the reference signal is suitably delayed with respect to the SUT using an optical delay line (τ) in such a way that the interference part can be isolated from the background signal in the time domain, i.e. after taking the inverse Fourier transform of the spectral interferogram in Eq. (1). Moreover, a time delay between the reference pulse and SUT is always needed to ensure there is no phase ambiguity in reconstruction of the SUT. In particular, the interference spectral pattern is recorded using a conventional optical spectrum analyzer (OSA). The amplitude and phase profiles of the SUT in the frequency domain can be accurately recovered from the measured spectral interferogram using the following Fourier-based procedure:
E(ω)=[Θ(tτ)×1[SI(ω)]]ejωτR*(ω)
(2)
where is the Fourier transform and Θ(t-τ) represents the Heaviside function that is used to single out the term centered at τ in the temporal function 1[SI(ω)] (i.e. term corresponding to the interference signal). The time-domain complex-field profile of the SUT can be then numerically calculated by taking an inverse Fourier transform of E(ω). Full knowledge of the reference pulse amplitude and phase profiles is assumed. Despite all its well-proved advantages, the measurement update rate offered by this technique is severely limited by the update rate of current spectrometers. In addition, the measurable time duration of the SUT (record length) is also limited by the frequency resolution of the spectral interference measurement [16

16. P. Bowlan, P. Gabolde, A. Shreenath, K. McGresham, R. Trebino, and S. Akturk, “Crossed-beam spectral interferometry: a simple, high-spectral-resolution method for completely characterizing complex ultrashort pulses in real time,” Opt. Express 14(24), 11892–11900 (2006). [CrossRef] [PubMed]

-19

19. L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]

]. The record length could be increased by improving the resolution of the spectrometer, but this in turn would negatively affect the measurement update rate. We overcome these fundamental limitations using RT-OFT of each interference waveform induced by a simple linear propagation through a highly-dispersive fiber-optics element [20

20. Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997). [CrossRef]

,21

21. J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000). [CrossRef]

].

3. Experiments and discussions

A detailed diagram of the used setup for the experimental demonstration of the proposed real-time complex-field ultrafast optical signal measurement is shown in Fig. 2.

A balanced spectral-interferometry scheme combined with RT-OFT was employed. The mode-locked fiber laser (MLFL) source (Pritel Inc.) generated nearly transform-limited Gaussian-like optical pulses at a repetition rate of 5 MHz (or 17 MHz, depending on the experiment), with a full-width (defined at 1% of the energy density peak) spectral bandwidth of ~ 16 nm (FWHM of ~2.9 nm), centered at a wavelength of ~1550 nm. We confirmed that the ultrashort pulses generated from the MLFL were nearly transform-limited through autocorrelation and spectral measurements. In particular, the measured autocorrelation of the laser pulses was nearly identical to that calculated from the measured laser spectrum assuming a uniform (flat) spectral phase profile.

The laser pulses were split using a 90:10 fiber-optic coupler; one of the resulting pulse trains was used as the optical reference source whereas the other pulse train was properly re-shaped, using a combination of dispersive optical fibers, intensity EOM and/or bulk-optics Michelson interferometers, to obtain the optical SUT (E(t)) with prescribed amplitude and phase profiles (depending on the specific measurement experiment). The shaped SUT and the optical reference were combined using a 2x2 single-mode fiber-optic 50:50 coupler (centered at 1,550 nm with 3-dB power coupling ratio). The time delay between the signal and the reference was adjusted using an optical delay line (SMF-28). Two different spectral interference patterns were generated at the two outputs of the 2x2 fiber coupler, SI+(ω) and SI-(ω). In particular, as expected for such a coupler, the phase of these two spectral interferograms were shifted by π, namely:

SI(ω)+=0.5|R(ω)+E(ω)×ejωτ|2                                 =0.5|R(ω)|2+0.5|E(ω)|2+   Re{R*(ω)×E(ω)×ejωτ},(3a)
SI(ω)=0.5|R(ω)E(ω)×ejωτ|2                                 =0.5|R(ω)|2+0.5|E(ω)|2   Re{R*(ω)×E(ω)×ejωτ} (3b)

Hence, after subtraction, the background-free spectral interferogram is numerically recovered by use of the frequency-to-time mapping law defined by the group-delay characteristic of the LCFG. In practice, this is first measured by using a transform-limited optical pulse (e.g. same pulse as the reference) as the SUT in our experimental setup [3

3. T. J. Ahn, Y. Park, and J. Azaña, “Fast and accurate group delay ripple measurement technique for ultralong chirped fiber Bragg gratings,” Opt. Lett. 32(18), 2674–2676 (2007). [CrossRef] [PubMed]

]. The reconstructed spectral phase profile of the signal at the LCFG output provides precise information on the group-delay response of the dispersive fiber grating [3

3. T. J. Ahn, Y. Park, and J. Azaña, “Fast and accurate group delay ripple measurement technique for ultralong chirped fiber Bragg gratings,” Opt. Lett. 32(18), 2674–2676 (2007). [CrossRef] [PubMed]

]. Finally, the amplitude and phase profiles of the optical SUT can be recovered from the spectral interferogram by means of the well-known FTSI algorithm based on the use of discrete Fourier transforms, as described in Section 2 above (see Eq. (2)). The reference spectrum is grabbed using the same configuration, i.e. using an LCFG followed by the photo-detector and the real-time oscilloscope. Signals that are further from the reference cause higher frequency modulation in the resulting interferogram. A higher frequency modulation translates into a decreased amplitude in the captured interference signal due to the expected frequency-dependant roll-off of the photo-detector. This artificial decay in the captured interferograms for signals delayed further from the reference could be calibrated in the numerical signal recovery stage using the information first obtained from multiple measurements with a single pulse that is subsequently delayed with a constant time delay step for each measurement. A similar procedure, including a demonstration example, is described in greater detail in [22

22. Y. Park, T. J. Ahn, J. C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15(8), 4597–4616 (2007). [CrossRef] [PubMed]

]. Since this calibration was not considered necessary to demonstrate the main goal of our paper, we have manually increased the power of the input individual pulses as they were located further from the reference in order to display a normalized individual peak power for the pulses with different delays from the reference without the need to do any further numerical calibration.

The reference signal in our first set of experiments, which was directly generated from a wavelength-tunable passively MLFL, was a periodic train of transform-limited Gaussian-like pulses, each with a full-width spectral bandwidth of ~2 THz (~16 nm) centered at a wavelength of ~1550 nm, with a repetition rate of ~5 MHz. We first experimentally evaluated the resolution/record-length specifications of our optical oscilloscope through characterization of individual ultrashort pulses, each identical to those of the reference signal, delayed from the corresponding reference by different times. Since the time resolution of the used real-time digitizer was ~20 ps, we estimated that our configuration provided an equivalent spectral resolution of ~20 ps×(2 ns/nm)-1 ~10 pm, corresponding to an approximate record length of ~350 ps. The inset of Fig. 3
Fig. 3 Result of a real-time and single-shot measurement of an optical waveform (SUT) composed by two sub-picosecond (FWHM time-width ~600-fs) Gaussian-like pulses delayed from each other by ~336-ps. The plot in the inset shows the result of real-time and single-shot measurements of various individual sub-picosecond Gaussian-like pulses with different delays, ranging from 4ps to 350ps, with respect to the corresponding reference pulse. The presented plots show the recovered time intensity profiles (in normalized unit (n.u.)) of the SUTs (the recovered phase profile for each pulse was nearly linear and is not shown here).
shows the results (recovered time intensity profiles) from real-time and single-shot measurements of randomly selected individual pulses with delays ranging from 4 ps to 350 ps from the reference. Considering that the measured rising time (10% to 90% of the amplitude peak) of each of these pulses is ~400 fs, ultimately limited by the input optical source bandwidth, a remarkable time-bandwidth product of ~900 was experimentally estimated for our measurement setup. The minimum average optical power of the optical SUT that was required for accurate characterization varied from ~26 nW, for the pulse delayed by ~4 ps, to ~1 μW, for the pulse delayed by ~350 ps. In a complementary experiment, we characterized the time intensity profile of an optical signal composed by two replicas of the ultrashort laser pulse, relatively delayed by ~336 ps. Characterization of such a signal is particularly challenging because the fringes in the spectral interference pattern change very rapidly due to environmental fluctuations, making necessary the use of a single-shot and real-time measurement technique. The obtained results are shown in Fig. 3.

We evaluated the anticipated capabilities of our setup by measuring the amplitude and phase temporal profiles of an optical signal with sub-picosecond time features and a total duration in the sub-nanosecond range, i.e. with an ultra-large time-bandwidth product approaching ~900. This complex SUT was prepared using a similar strategy to that followed in [2

2. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

], i.e. by first interfering two replicas of the ultrashort laser pulse, relatively delayed by ~145.4 ps, which were subsequently linearly dispersed through a ~1,220 m long section of standard single-mode fiber, SMF-28e (Corning inc.). The optical signal average power was ~500 nW. The measured spectral amplitude of the SUT is shown in the inset of Fig. 4
Fig. 4 Real-time and single-shot complex-field characterization of an interference optical signal (SUT) having a time-bandwidth product of ~900: Recovered amplitude (a) and phase (b) time-domain profiles of the experimentally measured SUT (blue, solid) compared to the theoretically simulated phase profile (red, dashed). Insets are zoomed plots over the time interval between 210 ps to 220 ps. The measured spectral amplitude of the optical SUT is plotted in the inset of (a).
. An example of real-time, single-shot amplitude and phase characterization of this target signal is plotted in Fig. 4 (solid curves) compared to the theoretically simulated phase temporal profile of the SUT (dashed curve). Figure 4 shows that the recovered temporal phase profile for each dispersed pulse matches very accurately that expected from numerical simulations, according to the nominal group delay characteristics of the used dispersive fiber section. As shown in the plotted zooms (insets of Fig. 4), the predicted discrete phase shifts between the interference-induced sub-picosecond time lobes were also recovered with a fairly high precision. In the experiments carried out here, a long section of optical fiber (~1,220 m) was used for inducing a partial temporal interference between the two time-delayed pulses. Since the optical path length of the fiber section was disturbed by environmental perturbations such as temperature variations and/or vibrations, the interference amplitude envelope changed very rapidly in time, thus necessarily requiring the use of a single-shot acquisition technique. Only the period of the interference fringes and phase profile of the resulting interference waveform could be precisely predicted through numerical simulations, both being in excellent agreement with the experimentally recovered profiles (comparison between period of interference fringes and numerical calculations are not shown in the paper). It is worth noting that the amplitude roll-off due to the frequency response characteristics of the photodiode and amplifier may affect the measured waveform amplitude profile, i.e. the experimentally recovered amplitude envelope profile of the interference signal might be attenuated with respect to time, as compared with the actual signal’s envelope. As mentioned above, this could be precisely estimated and calibrated through a pre-acquisition of the roll-off amplitudes (an example of this procedure and acquisition is discussed in [22

22. Y. Park, T. J. Ahn, J. C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15(8), 4597–4616 (2007). [CrossRef] [PubMed]

]). It is worth noting that according to the MLFL repetition rate of ~5 MHz, a sequence of interference SUTs was generated with a corresponding period of ~200 ns. Our technique allowed us to capture and characterize each of these SUTs separately, which clearly proves the capability of our method to provide the anticipated fast update rates.

In another set of experiments, we demonstrated the unique capability of our optical oscilloscope to characterize rapidly-changing, non-periodic THz-bandwidth optical waveforms at very fast (17-MHz) update rates. The complex waveforms to be tested were generated using the setup shown in Fig. 5(a)
Fig. 5 (a) Experimental setup for generating rapidly-changing ultrafast optical signals by intensity modulation of dispersed broadband pulses using an EOM driven by a synchronized train of electronic pulses in which the DC bias level is rapidly swept (the bias is driven by a 1.6-MHz electrical sinusoids). Amplitude (b) and phase (c) time profiles of 30 rapidly-changing ultrafast waveforms as measured at the EOM output with an update rate of ~17 MHz, expanding over a total duration of ~1.773μs. Results corresponding to the individual characterization of 3 of these ultrafast waveforms at the measurement times of 236.4 ns, 354.6 ns and 827.4 ns are plotted in (d).
. The references were nearly transform-limited Gaussian-like optical pulses, each with a full-width bandwidth of ~2 THz, directly generated from our MLFL at an increased repetition rate of ~17 MHz. The sequence of varying optical waveforms to be characterized was generated by linearly dispersing the ultrashort laser pulses through a ~500-m long SMF section followed by intensity electro-optic modulation (EOM) (EOspace Inc., 40 Gb/s modulator) with Vπ≈6.5 V in which the bias level was rapidly swept. In particular, the EOM’s driving signal was a 17-MHz train of electronic pulses, each with a time-width of ~50 ps and a peak voltage of ~1 V, which was prepared by photo-detecting the reference pulses with a 40-GHz photo-detector (New focus Inc.) followed by electronic amplification with a 20-GHz RF-amplifier (New focus Inc.). The EOM’s DC bias was controlled by an RF signal generator producing a sinusoid waveform at a frequency of ~1.6 MHz, with an average voltage of ~0.3 V and a peak-to-peak voltage of ~1.3 V.

The fast sine variation of the EOM’s DC bias combined with the EOM’s driver voltages caused temporal modulation of the dispersed Gaussian-like optical signal, resulting in fast (MHz rate) variations of the amplitude and phase profiles of the optical waveform obtained at the modulator output (SUT). Notice that each of these ultra-broadband waveforms (full-width spectral bandwidth ~ 2 THz) extended over a full-width temporal duration of ~110 ps, and the temporal separation between any two consecutive SUTs was ~59.1 ns, as determined by the laser pulse repetition rate. In each experiment, we grabbed 8,300 spectral interference profiles, corresponding to 8,300 consecutive single-shot optical waveforms, captured over a total time window of ~490.53 μs with our real-time oscilloscope. In this way, we successfully tracked the changes in the amplitude and phase profiles of the modulated ultrafast optical waveforms at every time period of ~59.1-ns. The recovered amplitude and phase temporal profiles of 30 consecutive modulated waveforms are plotted in Figs. 5(b) and 5(c), respectively. A 3D representation is used to better illustrate the measured rapid changes in the recovered profiles. Fig. 5(d) also shows the individual characterization of some of these complex optical waveforms at the measurement times of 236.4 ns, 354.6 ns and 827.4 ns, respectively. For comparison, the numerically predicted quadratic phase curve corresponding to propagation through a 500-m SMF section is also represented in the same plot, showing an excellent agreement with the experimentally recovered quadratic phase variations. Moreover, a discrete phase-jump on each quadratic phase profile was accurately observed at the zero-crossing point of the corresponding amplitude profile as this point was swept in time along the modulated signal duration.

In our experimental setup, the power of the input waveform to be characterized should be kept low enough to avoid non-linearities in the fiber devices, including fiber interleaver (with a DSF spool), LCFG and fiber spools; considering that the signal will propagate through a total equivalent length of conventional single-mode fiber of approximately 50 m, we estimate that the maximum allowed input average power to operate in the linear regime is about 67 μW, assuming an input pulse temporal duration of ~1 ps with a repetition rate of 5 MHz. Considering that the minimum measurable input average power for the same input pulse was ~26 nW (see above experimental results), a dynamic range of ~34 dB is estimated for our specific experimental measurement system.

4. Conclusions

We have proposed and experimentally demonstrated a simple and practical (fiber-optics) method for complex-field ultrafast optical signal characterization using a balanced FTSI scheme combined with dispersion-induced real-time optical Fourier transformation. Using this new linear approach, we demonstrated single-shot characterization of complex-field optical events (including accurate measurement of continuous and discrete-time phase variations), with a resolution of ~400 fs over a record length as long as ~350 ps and average powers as low as ~26 nW, at update rates in the MHz range, i.e. at least thousand times faster than with spectrometer-based solutions. In a remarkable application example, we fully characterized the dynamic ultrashort pulse response of an intensity EOM as its bias condition was rapidly swept at a measurement update rate of ~17 MHz.

Our experimental demonstrations clearly prove the outstanding performance provided by the developed real-time THz-bandwidth optical signal measurement method, including its capability for accurate characterization of the amplitude and phase profiles of sub-microwatt ultrafast waveforms over sub-nanosecond record lengths in a single shot and at update rates well in the MHz range. The latter is the most distinctive feature of the demonstrated concept. Using LCFGs with higher GVD factors and/or faster detection stages, the measurement record length could be readily extended to the nanosecond range without essentially affecting the rest of the system specifications. The simple strategy demonstrated here, namely incorporating dispersion-induced RT-OFT in a spectrometer-based measurement system, could be potentially used in many other well-established ultrafast signal characterization schemes to achieve a significant improvement in the system performance, particularly in terms of measurement update rates, as required for full and accurate characterization of rapidly-changing ultrafast waveforms in a variety of engineering and scientific fields.

Acknowledgements

This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by le Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT).

References and links

1.

C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Quantum Electron. 12(4), 843–858 (2006). [CrossRef]

2.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

3.

T. J. Ahn, Y. Park, and J. Azaña, “Fast and accurate group delay ripple measurement technique for ultralong chirped fiber Bragg gratings,” Opt. Lett. 32(18), 2674–2676 (2007). [CrossRef] [PubMed]

4.

Y. Park, T. J. Ahn, and J. Azaña, “Real-time complex temporal response measurements of ultrahigh-speed optical modulators,” Opt. Express 17(3), 1734–1745 (2009). [CrossRef] [PubMed]

5.

R. T. Schermer, F. Bucholtz, C. A. Villarruel, J. Gil Gil, T. D. Andreadis, and K. J. Williams, “Investigation of electrooptic modulator disruption by microwave-induced transients,” Opt. Express 17(25), 22586–22602 (2009). [CrossRef]

6.

H. Xia, C. Wang, S. Blais, and J. Yao, “Ultrafast and precise interrogation of fiber Bragg grating sensor based on wavelength-to-time mapping incorporating higher order dispersion,” J. Lightwave Technol. 28(3), 254–261 (2010). [CrossRef]

7.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007). [CrossRef] [PubMed]

8.

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009). [CrossRef] [PubMed]

9.

I. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1(2), 308–437 (2009). [CrossRef]

10.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010). [CrossRef]

11.

R. Salem, M. A. Foster, A. C. Turner-Foster, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “High-speed optical sampling using a silicon-chip temporal magnifier,” Opt. Express 17(6), 4324–4329 (2009). [CrossRef] [PubMed]

12.

D. J. Kane and R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18(10), 823–825 (1993). [CrossRef] [PubMed]

13.

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, “SPIDER: A decade of measuring ultrashort pulses,” Laser Phys. Lett. 5(4), 259–266 (2008). [CrossRef]

14.

C. Dorrer and I. Kang, “Highly sensitive direct characterization of femtosecond pulses by electro-optic spectral shearing interferometry,” Opt. Lett. 28(6), 477–479 (2003). [CrossRef] [PubMed]

15.

J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, “Highly sensitive, single-shot characterization for pulse widths from 0.4 to 85 ps using electro-optic shearing interferometry,” Opt. Lett. 31(23), 3523–3525 (2006). [CrossRef] [PubMed]

16.

P. Bowlan, P. Gabolde, A. Shreenath, K. McGresham, R. Trebino, and S. Akturk, “Crossed-beam spectral interferometry: a simple, high-spectral-resolution method for completely characterizing complex ultrashort pulses in real time,” Opt. Express 14(24), 11892–11900 (2006). [CrossRef] [PubMed]

17.

V. R. Supradeepa, D. E. Leaird, and A. M. Weiner, “Single shot amplitude and phase characterization of optical arbitrary waveforms,” Opt. Express 17(16), 14434–14443 (2009). [CrossRef] [PubMed]

18.

N. K. Fontaine, R. P. Scott, J. P. Heritage, and S. J. B. Yoo, “Near quantum-limited, single-shot coherent arbitrary optical waveform measurements,” Opt. Express 17(15), 12332–12344 (2009). [CrossRef] [PubMed]

19.

L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]

20.

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997). [CrossRef]

21.

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000). [CrossRef]

22.

Y. Park, T. J. Ahn, J. C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15(8), 4597–4616 (2007). [CrossRef] [PubMed]

23.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008). [CrossRef]

24.

R. M. Fortenberry, W. V. Sorin, H. Lin, and S. A. Newton, “Low-power ultrashort optical pulse characterization using linear dispersion,” in Conference on Optical Fiber Communication, 290-291 (1997).

25.

C. Dorrer, “Chromatic dispersion characterization by direct instantaneous frequency measurement,” Opt. Lett. 29(2), 204–206 (2004). [CrossRef] [PubMed]

26.

T. J. Ahn, Y. Park, and J. Azaña, “Improved optical pulse characterization based on feedback-controlled Hilbert transformation temporal interferometry,” IEEE Photon. Technol. Lett. 20(7), 475–477 (2008). [CrossRef]

27.

C. Dorrer, “Single-shot measurement of the electric field of optical waveforms by use of time magnification and heterodyning,” Opt. Lett. 31(4), 540–542 (2006). [CrossRef] [PubMed]

28.

http://www.thorlabs.com/NewGroupPage9_PF.cfm?Guide=10&Category_ID=219&ObjectGroup_ID=2005

29.

S. Moon and D. Y. Kim, “Normalization detection scheme for high-speed optical frequency-domain imaging and reflectometry,” Opt. Express 15(23), 15129–15146 (2007). [CrossRef] [PubMed]

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(200.4740) Optics in computing : Optical processing
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Ultrafast Optics

History
Original Manuscript: May 21, 2010
Revised Manuscript: June 23, 2010
Manuscript Accepted: June 24, 2010
Published: July 22, 2010

Citation
Mohammad H. Asghari, Yongwoo Park, and José Azaña, "Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry," Opt. Express 18, 16526-16538 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16526


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References

  1. C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Quantum Electron. 12(4), 843–858 (2006). [CrossRef]
  2. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]
  3. T. J. Ahn, Y. Park, and J. Azaña, “Fast and accurate group delay ripple measurement technique for ultralong chirped fiber Bragg gratings,” Opt. Lett. 32(18), 2674–2676 (2007). [CrossRef] [PubMed]
  4. Y. Park, T. J. Ahn, and J. Azaña, “Real-time complex temporal response measurements of ultrahigh-speed optical modulators,” Opt. Express 17(3), 1734–1745 (2009). [CrossRef] [PubMed]
  5. R. T. Schermer, F. Bucholtz, C. A. Villarruel, J. Gil Gil, T. D. Andreadis, and K. J. Williams, “Investigation of electrooptic modulator disruption by microwave-induced transients,” Opt. Express 17(25), 22586–22602 (2009). [CrossRef]
  6. H. Xia, C. Wang, S. Blais, and J. Yao, “Ultrafast and precise interrogation of fiber Bragg grating sensor based on wavelength-to-time mapping incorporating higher order dispersion,” J. Lightwave Technol. 28(3), 254–261 (2010). [CrossRef]
  7. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007). [CrossRef] [PubMed]
  8. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009). [CrossRef] [PubMed]
  9. I. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1(2), 308–437 (2009). [CrossRef]
  10. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010). [CrossRef]
  11. R. Salem, M. A. Foster, A. C. Turner-Foster, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “High-speed optical sampling using a silicon-chip temporal magnifier,” Opt. Express 17(6), 4324–4329 (2009). [CrossRef] [PubMed]
  12. D. J. Kane and R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18(10), 823–825 (1993). [CrossRef] [PubMed]
  13. M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, “SPIDER: A decade of measuring ultrashort pulses,” Laser Phys. Lett. 5(4), 259–266 (2008). [CrossRef]
  14. C. Dorrer and I. Kang, “Highly sensitive direct characterization of femtosecond pulses by electro-optic spectral shearing interferometry,” Opt. Lett. 28(6), 477–479 (2003). [CrossRef] [PubMed]
  15. J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, “Highly sensitive, single-shot characterization for pulse widths from 0.4 to 85 ps using electro-optic shearing interferometry,” Opt. Lett. 31(23), 3523–3525 (2006). [CrossRef] [PubMed]
  16. P. Bowlan, P. Gabolde, A. Shreenath, K. McGresham, R. Trebino, and S. Akturk, “Crossed-beam spectral interferometry: a simple, high-spectral-resolution method for completely characterizing complex ultrashort pulses in real time,” Opt. Express 14(24), 11892–11900 (2006). [CrossRef] [PubMed]
  17. V. R. Supradeepa, D. E. Leaird, and A. M. Weiner, “Single shot amplitude and phase characterization of optical arbitrary waveforms,” Opt. Express 17(16), 14434–14443 (2009). [CrossRef] [PubMed]
  18. N. K. Fontaine, R. P. Scott, J. P. Heritage, and S. J. B. Yoo, “Near quantum-limited, single-shot coherent arbitrary optical waveform measurements,” Opt. Express 17(15), 12332–12344 (2009). [CrossRef] [PubMed]
  19. L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]
  20. Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997). [CrossRef]
  21. J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000). [CrossRef]
  22. Y. Park, T. J. Ahn, J. C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15(8), 4597–4616 (2007). [CrossRef] [PubMed]
  23. D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008). [CrossRef]
  24. R. M. Fortenberry, W. V. Sorin, H. Lin, and S. A. Newton, “Low-power ultrashort optical pulse characterization using linear dispersion,” in Conference on Optical Fiber Communication, 290-291 (1997).
  25. C. Dorrer, “Chromatic dispersion characterization by direct instantaneous frequency measurement,” Opt. Lett. 29(2), 204–206 (2004). [CrossRef] [PubMed]
  26. T. J. Ahn, Y. Park, and J. Azaña, “Improved optical pulse characterization based on feedback-controlled Hilbert transformation temporal interferometry,” IEEE Photon. Technol. Lett. 20(7), 475–477 (2008). [CrossRef]
  27. C. Dorrer, “Single-shot measurement of the electric field of optical waveforms by use of time magnification and heterodyning,” Opt. Lett. 31(4), 540–542 (2006). [CrossRef] [PubMed]
  28. http://www.thorlabs.com/NewGroupPage9_PF.cfm?Guide=10&Category_ID=219&ObjectGroup_ID=2005
  29. S. Moon and D. Y. Kim, “Normalization detection scheme for high-speed optical frequency-domain imaging and reflectometry,” Opt. Express 15(23), 15129–15146 (2007). [CrossRef] [PubMed]

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