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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 21618–21627
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Coherent time-stretch transformation for real-time capture of wideband signals

Brandon W. Buckley, Asad M. Madni, and Bahram Jalali  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 21618-21627 (2013)
http://dx.doi.org/10.1364/OE.21.021618


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Abstract

Time stretch transformation of wideband waveforms boosts the performance of analog-to-digital converters and digital signal processors by slowing down analog electrical signals before digitization. The transform is based on dispersive Fourier transformation implemented in the optical domain. A coherent receiver would be ideal for capturing the time-stretched optical signal. Coherent receivers offer improved sensitivity, allow for digital cancellation of dispersion-induced impairments and optical nonlinearities, and enable decoding of phase-modulated optical data formats. Because time-stretch uses a chirped broadband (>1 THz) optical carrier, a new coherent detection technique is required. In this paper, we introduce and demonstrate coherent time stretch transformation; a technique that combines dispersive Fourier transform with optically broadband coherent detection.

© 2013 OSA

1. Introduction

Analog-to-Digital Converters (ADCs) [1

1. R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999). [CrossRef]

] map signals from the physical world to the discrete realm of computing, where they can be analyzed, manipulated, and shared. The speed and accuracy (number of bits) at which ADCs capture analog signals are their key performance metrics. For example, high-throughput biomedical imaging and screening systems, such as flow cytometers, rely on high-speed, high-resolution ADCs to gather and process data in real-time [2

2. A. Yen, Flow Cytometry: Advanced Research and Clinical Applications (CRC Press, Inc., 1989), Vol. 1.

, 3

3. J. M. d. Silva and H. Mendonça, ADC Applications, Architectures and Terminology, Dynamic Characterisation of Analogue-to Digital Converters (Kluwer Academic Publishers, 2005), Vol. 860, pp. 3–45.

]. In military applications, wideband ADCs and real-time processing are integral components in electronic surveillance and counter measure systems [4

4. J. Murphy, “Development of high performance analog-to-digital converters for defense applications,” in GaAs IC Symposium. IEEE Gallium Arsenide Integrated Circuit Symposium. 19th Annual Technical Digest 1997 (Cat. No.97CH36098), (1997), pp. 83–86.

]. Furthermore, the surge of Internet traffic has led modern optical communication networks to employ higher data rates and multi-level advanced modulation formats [5

5. M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, “Field trial of a real-time, single wavelength, coherent 100 Gbit/s PM-QPSK channel upgrade of an installed 1800 km link,” in Optical Fiber Communication (OFC), collocated National Fiber Optic Engineers Conference,2010Conference on (OFC/NFOEC), paper PDPD1.

9

9. J. H. Sinsky and P. J. Winzer, “100-Gb/s optical communications: a microwave engineer's perspective,” IEEE Microw. Mag. 10(2), 44–57 (2009). [CrossRef]

]. Here, high-performance ADCs and DSP are required at the back-end of these networks to capture, equalize, and decode the high-speed data.

In optical communication links, two detection schemes can be employed: direct detection and coherent detection [17

17. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed. (John Wiley & Sons, Inc., 2002), pp. 478–517.

]. In direct detection, a photodetector (PD) captures an optical signal and the power, proportional to the amplitude squared of the electric field, is converted to a current. Direct detection is the most straightforward receiver system and has been exclusively employed in TiSER thus far. Along with simplicity, however, come drawbacks. All phase information of the signal is lost, the non-linear squaring of the electric field by the PD leads to high-harmonic distortion, and the output signal lies at baseband where it is susceptible to interference from low frequency noise. In coherent detection receivers, the optical signal is mixed with a reference beam, termed the local oscillator (LO), before detection. The LO is designed to be stable and at a higher power than the signal. Since the PD responds to the optical electric field squared, a cross term is generated which is linearly proportional to the electric field of the signal and LO. Although more complicated to implement, coherent detection offers many advantages over direct detection. High-harmonic distortion due to squaring is avoided, amplitude and phase information can be extracted, the cross term can be upshifted away from low frequency noise, and the signal is effectively amplified by the strength of the LO. All of these benefits result in a receiver with up to 20 dB greater sensitivity [18

18. T. Okoshi, “Recent advances in coherent optical fiber communication-systems,” J. Lightwave Technol. 5(1), 44–52 (1987). [CrossRef]

]. Finally, with coherent detection, advanced phase and amplitude modulation schemes with high spectral efficiency and robustness to distortions can be employed [7

7. P. J. Winzer and R. J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. 24(12), 4711–4728 (2006). [CrossRef]

]. For all of these reasons, coherent detection has become the universal standard in modern lightwave communications.

When considering coherent detection for TiSER, a unique challenge arises because of the chirped broadband optical carrier. Here we introduce the coherent dispersive Fourier transform (cDFT), an extension of the optical dispersive Fourier transform (ODFT) [19

19. P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett. 35(19), 1661–1662 (1999). [CrossRef]

, 20

20. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013). [CrossRef]

], which enables coherent detection in TiSER. In cDFT, we interfere two chirped broadband optical pulses, one carrying the time-stretched RF signal and the other acting as an LO. A beat frequency is generated from the interference, from which we can recover the full optical phase and amplitude of the modulated signal. The full coherent TiSER (cTiSER) system promises to significantly improve bandwidth and resolution, as well as reduce power consumption. Additionally, when used in all-optical TiSER [21

21. A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett. 101(5), 051113 (2012). [CrossRef]

], this technique will enable time-stretching of advanced phase and amplitude modulated optical signals. A previous, preliminary work demonstrated phase recovery of time-stretched pulses, though at a lower bandwidth and without distortion mitigation [22

22. B. W. Buckley, A. Fard, and B. Jalali, “Time-stretch analog-to-digital conversion using phase modulation and broadband coherent detection for improving resolution,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest Series (Optical Society of America,2011), paper OThW4. [CrossRef]

]. Phase recovery was also exploited in a different context to perform high-speed vibrometry [23

23. A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett. 98(10), 101107 (2011). [CrossRef]

]. Here we demonstrate a full cTiSER prototype system, with an RF bandwidth of greater than 30 GHz (limited by the intensity modulator), and with a stretch factor of 24. We take advantage of the full complex electric field information to achieve digital dispersion compensation across the full bandwidth of the system, and employ it in equalization of a time-stretched 40 gigabit per second (Gbit/s) data signal.

2. Coherent detection

In conventional coherent detection systems, a stable continuous wave (CW) LO reference beam mixes with the signal of interest. We can represent the signal and LO electric fields in the time domain as Esig(t)exp(iωsigt) and ELOexp(iωLOt) respectively, where Esig(t) carries the information, ELO is the approximately time independent electric field amplitude of the LO source, and ωsig and ωLO are the optical carrier frequencies. The physical fields are the real portions of the complex fields written here. The optical intensity, converted to a current signal at the PD, is proportional to the amplitude squared of the sum of the electric fields
I(t)|Esig(t)|2+|ELO|2±2Re{Esig(t)E*LOexp(iωIFt)}
(1)
where ωIF = ωsigLO is the intermediate frequency (IF), and the asterisk signifies complex conjugation. The last term on the right of Eq. (1) is the cross term of interest, which scales linearly with the signal and LO electric fields, and which is upshifted to the IF. In homodyne detection, the signal and LO operate at the same frequency so the IF cancels to zero, leaving only phase offsets. In heterodyne detection the signal and LO operate at different optical frequencies, and the IF is some finite RF frequency given by the difference of the two. The plus and minus signs in front of the cross term represent the complementary outputs of a 2 × 2 interferometric mixer. Balanced detection is achieved by subtracting the two complementary outputs, leaving only the cross term.

Coherent detection offers many advantages over direct detection. With a sufficiently well characterized LO beam, the phase and amplitude of the signal electric field Esig(t) can be determined in DSP. This capability has spurred the recent advances in coherent lightwave technology, in which phase and amplitude modulated signal formats are employed for improved spectral efficiency and robustness to impairments [7

7. P. J. Winzer and R. J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. 24(12), 4711–4728 (2006). [CrossRef]

]. With the full complex field information, digital back propagation can be used to mitigate distortions from chromatic dispersion, non-linear amplitude modulation, and optical nonlinearities [24

24. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008). [CrossRef] [PubMed]

26

26. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004). [CrossRef]

]. In heterodyne detection systems, the cross term is upshifted away from low frequency noise, allowing for improved resolution. Finally, with a high power LO, the signal is effectively amplified upon interference resulting in a mixing gain, which boosts the signal above the thermal noise limit without the need for additional amplifiers.

3. Coherent dispersive Fourier transformation

Developing a coherent detection system for TiSER poses a unique challenge. Unlike in conventional optical communication links, which use a narrow band CW beam as the carrier, the TiSER system uses a broadband, chirped optical pulse to carry the information. If we mix a broadband, chirped pulse with a narrowband LO, the IF of the mixing term will be chirped and span the full optical bandwidth of the pulse (>1 THz). The resulting bandwidth of the heterodyne signal will extend beyond the detection bandwidth of the backend PD and electronics.

To overcome this obstacle, we have developed the cDFT. To realize this coherent version of the time stretch transform, we use as the LO a second broadband chirped optical pulse, which is an unmodulated copy of the carrier pulse. When the two chirped optical pulses, relatively delayed with respect to each other, are mixed, the optical signals interfering at each point in time are offset by a constant frequency, resulting in a chirp-free IF modulation along the optical pulse [see Fig. 2
Fig. 2 Mixing of relatively delayed chirped optical pulses results in a beat frequency in the time-domain. In (a) we illustrate the linear chirp of each pulse by a straight line on a frequency vs. time plot. The signal and LO pulses are delayed with respect to each other, resulting in interference of spectral components offset by a constant intermediate frequency, ωIF. (b) The interference results in a sinusoidal modulation along the optical pulse. If the signal pulse is modulated with an RF signal, the amplitude and phase information is encoded in the IF modulation, analogous to a coherent heterodyne signal.
]. The phase and amplitude of the modulated time-stretched RF signal are encoded in the IF modulation, similar to in heterodyne detection, and can be recovered by adapting standard analog and digital techniques from coherent lightwave communications [17

17. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed. (John Wiley & Sons, Inc., 2002), pp. 478–517.

].

The cDFT technique can be made clearer by noting the similarity with Fourier transform spectral interferometry [27

27. E. Tokunaga, A. Terasaki, and T. Kobayashi, “Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy,” Opt. Lett. 17(16), 1131–1133 (1992). [CrossRef] [PubMed]

]. Indeed, cDFT is a single-shot spectral interferometer mapped to the time-domain via the ODFT. In conventional spectral interferometry, two optical pulses, relatively delayed, are mixed and the optical spectrum is measured. In the simplest case, one pulse is a well characterized LO pulse, with the goal being to ascertain the spectral amplitude and phase of the electric field of the second pulse. The optical spectral intensity measured is proportional to
I(ω)|E˜sig(ω)|2+|E˜LO(ω)|2±2Re{E˜sig(ω)E˜*LO(ω)exp(iωτ)}
(2)
where τ is the relative time delay and ω the optical frequency. The similarities between Eq. (1) and Eq. (2) can be seen, the crucial difference being that Eq. (1) is a time-domain signal and Eq. (2) is a frequency domain signal. The cross term of Eq. (2) is proportional to the signal and LO electric fields, and upshifted by an IF. If the LO spectrum is known, the phase and amplitude of the signal electric field can be determined.

In cDFT, the mixed signal is not detected by an optical spectrum analyzer, but is instead dispersed and captured with a single pixel PD. The large dispersion performs a ODFT, mapping the optical spectrum into the time domain via ω→t/(β2L), where β2 is the dispersion parameter and L is the length of the fiber [28

28. K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys. 80(4), 043821 (2009). [CrossRef]

]. The result is a transformation of the complex exponential in the cross term of Eq. (2)
exp(iωτ)exp(itβ2Lτ)exp(iωIFt)
(3)
with ωIF = τ/(β2L), the IF frequency of the now time domain signal. The optical spectra of the signal and LO pulses are also transformed into time-domain traces. Advantageously, the IF can be adjusted, even for a fixed dispersion, simply by controlling the relative time-delay τ. An example of a time-stretch pulse exhibiting an IF of 4 GHz, corresponding to a τ of 35 ps, is shown in Fig. 3(a)
Fig. 3 Interference of two broadband, chirped optical pulses results in an intermediate beat frequency along the pulse. (a) In this example, a time delay of 36 ps between the two pulses results in an intermediate frequency of 4 GHz. (b) We characterized the intermediate frequency for a range of relative delays. The measured dispersion of 1090 ps/nm, calculated from the slope, agrees with the specifications of the dispersive fibers used.
, and the IFs for various time delays are plotted in Fig. 3(b). A linear fit is well matched to the data, with a slope indicating a dispersion of 1090 ps/nm, in good agreement with the dispersion used.

In the cTiSER system, the LO pulse is an unmodulated copy of the signal pulse, and it is the RF time-stretched signal that is being characterized, not the inherent phase and amplitude of the carrier pulse electric field. The signal and LO spectral profiles from Eq. (2) after ODFT can be written as
E˜LO(ω)Eenv(t),E˜sig(ω)Eenv(t)ERF(t)
(4)
where ERF(t) is the time-stretched RF signal, and Eenv(t) is the optical spectrum of the original broadband pulse mapped to the time-domain. To be precise, we should add the time delay τ into the argument for the LO pulse, i.e. Eenv(t + τ). However, relative to the total pulse width after dispersion (~10 ns), the time delay τ (<50 ps) is negligible. Additionally, the resolution of the ODFT [28

28. K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys. 80(4), 043821 (2009). [CrossRef]

] is insufficient to resolve spectral components on that scale, so indeed τ can be ignored in Eenv(t). After balanced detection, the signal is proportional to the cross term of Eq. (2), with the substitutions of Eq. (3) and Eq. (4),
IBD(t)|Eenv(t)|2Re{ERF(t)exp(iωIFt)}.
(5)
The task, finally, is to characterize the envelope trace and to employ coherent lightwave communication processing techniques to recover the full phase and amplitude information of the linear time-stretched RF signal.

4. Experimental setup

We implemented an optical fiber based cTiSER prototype system [Fig. 4
Fig. 4 Schematic of the optical portion of the cTiSER system. After photo-detection the time-stretched analog signal is digitized and processed digitally. In this demonstration, balanced detection was performed using a single PD, with the complementary pulses delayed in time to avoid overlap. Subtraction was performed digitally. D1: first dispersive fiber, D2: second dispersive fiber, OBPF: optical band-pass filter, VDL: variable delay line
]. An Erbium doped fiber mode locked laser (MLL) generates a 37MHz optical pulse train, which is band-pass filtered around 1570 nm to 10 nm 3 dB bandwidth. We pre-chirp the pulse train using a dispersive fiber of 45 ps/nm dispersive parameter, stretching the pulses to 450 ps width. An erbium doped fiber amplifier (EDFA) amplifies the pre-chirped pulse train to 20 dBm average power before a 1 × 2 splitter separates the pulses into signal and LO. The signal pulses are sent to a Mach-Zehnder modulator (MZM), which modulates the RF signal on top. The LO is sent through a variable optical attenuator (VOA), which matches the insertion loss of the MZM (~7 dB). It is important to match the powers of the signal and LO pulses at the receiver to maximize modulation depth of the interference fringes and to ensure the IF amplitude spans the full scale of the back end ADC. Analog balanced detection would obviate the need for this additional 7 dB attenuation of the LO, enabling a 3.5 dB mixing gain. The two pulse trains are counter-propagated through a second dispersive fiber of 1045 ps/nm dispersion imparting a total stretch factor of 24. Optical circulators (OC) at each end of the dispersive fiber direct the pulses into and out of the dispersive fiber accordingly. A delay line in one of the arms adds the relative time delay τ. In this demonstration we used a delay of 47 ps for an IF of 5.3 GHz. The signal and LO pulses are mixed in a 2 × 2 coupler, the two outputs being complementary. The polarizations of the two optical beams are aligned using a fiber coupled polarization controller in one of the arms [not shown in Fig. 4]. In lieu of a balanced detector (BD), we delay the complementary output pulses, staggering them in time, before combining and sending to a single pixel PD. The complementary pulses are realigned and subtracted digitally. If subtraction of complementary outputs were carried out before digitization, matching of signal and LO optical power would not be necessary and mixing gain could be achieved. Average power reaching the PD is approximately −6 dBm. A trans-impedance amplifier integrated on the PD amplifies the photocurrent, which is then digitized by an ADC sampling at 50 giga-samples per second (GS/s) and with an analog bandwidth of 16 GHz. All patch chords are single mode fiber of total length less than 10m and negligible dispersion (17 ps/nm-km).

5. Digital signal processing

DSP is implemented in MATLAB [29

29. M. A. T. L. A. B. Release, 2012a, The MathWorks, Inc., Natick, Massachusetts, United States.

] to subtract the complementary outputs, down-convert the IF signal, divide out the spectral envelope, and recover the full complex optical field of the time-stretched signal. We perform balanced detection digitally by capturing both complementary outputs from the 2 × 2 interferometer in a single PD. The complementary outputs are aligned and subtracted, removing the common mode DC portion of the optical pulses. The subtracted signal is band-pass filtered around the IF to remove out of band noise, in particular low frequency noise. We perform a discrete Hilbert transform on each pulse and extract the instantaneous frequency of the IF signal and average over 1000 pulses [30

30. L. Cohen, Time-frequency analysis (Prentice Hall PTR, 1995), pp. 30–31.

]. We then down convert the upshifted signal to baseband. Because the RF time-stretched signal is AC coupled and uncorrelated with the laser pulses, averaging of the 1000 pulses leaves only the background envelope. We divide out the background from each pulse to recover the full complex electric field of the stretched RF signal. If a dual output MZM is used, we could alternatively implement a differential cTiSER system, in which the background envelope is recovered on a pulse-to-pulse basis by adding the two complementary modulated pulses from the MZM. Recovering the envelope in this way avoids distortions due to pulse-to-pulse variations [31

31. Y. Han and B. Jalali, “Differential photonic time-stretch analog-to-digital converter,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE Cat. No.CH37419-TBR), (2003), p. CWH2.

].

6. Dispersion compensation

In TiSER, dispersion is exploited to our advantage to map the optical spectrum into time and stretch the RF modulated signal. However, the parasitic dispersive effect still manifests itself, though with an attenuated dispersion induced phase, i.e.
exp(i12β2L2SωRF2),
(6)
where S is the stretch factor, L2 is the length of the second dispersive fiber, and ωRF is the pre-stretched frequency of the RF signal [12

12. Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003). [CrossRef]

]. Two methods exist which allow TiSER to overcome this bandwidth limiting dispersion penalty: one employs single side-band modulation to avoid the interference at the detector [12

12. Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003). [CrossRef]

, 34

34. J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett. 37(1), 67–68 (2001). [CrossRef]

], and the second, termed phase diversity, uses maximum ratio combining of two outputs from a MZM, which have inherently complementary transfer functions [35

35. Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech. 53(4), 1404–1408 (2005). [CrossRef]

]. However, these dispersion penalty mitigation techniques are not compatible with the differential TiSER system, as they require specialized MZMs, which do not offer complementary dual-outputs. Additionally, with all-optical TiSER, for which the dispersion penalty is the dominant bandwidth limitation, the above techniques are not always applicable, depending on the modulation format of the optical signal. There is as yet no general technique to mitigate the dispersion penalty for an arbitrarily modulated input.

With the full complex optical field captured using cTiSER, we are able to digitally equalize the dispersion-induced phase in Eq. (6), independent of the modulation format of the input signal. For each captured pulse we take a 576-point discrete Fourier transform and multiply by the inverse of the exponential in Eq. (6). A set of 576 samples (sample rate is 50 GS/s) spans 11.5 ns, the approximate pulse width after stretching. We characterized the transfer functions for both conventional direct detection and broadband coherent detection back-ends by capturing and time-stretching single-tone RF signals ranging from 15 GHz to 43 GHz. We performed dispersion compensation on the coherent detection data, and plotted the intensities for each frequency [Fig. 5
Fig. 5 When using direct detection, dispersion induced transfer function nulls arise, limiting the bandwidth of TiDER. Using coherent detection, we can recover the full complex field, which enables equalization of the dispersion penalty and a flat transfer function. The roll off at higher frequencies is due to limitations of the intensity modulator. Plotted along with the raw data is a sinusoidal model function fit to the un-equalized direct detection transfer function. The dispersion-induced phase was calculated from Eq. (6) and the additional chirp parameter was estimated from non-linear regression.
]. From Eq. (6) we calculate the dispersion-induced phase to be 25.6 ps2. The z-cut MZM imparted an additional chirp-induced phase to the sinusoidal transfer function, shifting the first dispersion null to a lower frequency and further limiting the RF bandwidth. A non-linear regression estimated the chirp parameter to be 0.61, and this effect was accounted for in the dispersion compensation [36

36. T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun. 195(5–6), 399–404 (2001). [CrossRef]

]. As illustrated, dispersion compensation mitigates the parasitic dispersive effects, boosting the bandwidth of TiSER.

To further demonstrate the dispersion compensation capabilities, we captured a 40 Gbit/s non-return to zero (NRZ) pseudo-random binary sequence (PRBS) signal and generated eye-diagrams for both direct detection and coherent detection back-ends. With direct detection, dispersion penalty distorts the eye-diagram due to high-frequency attenuation [Fig. 6(a)
Fig. 6 40 Gbit/s NRZ PRBS data was time-stretched and detected using optical direct detection (a) and broadband coherent detection (b). A dispersion penalty transfer function, characterized in Fig. 5, imparts a frequency limitation when using direct detection, which can be equalized digitally using coherent detection. Rise/fall times, measured at 10% and 90% levels, improved from 18.5/19.1 ps to 16.1/15.8 ps upon equalization.
]. When applying dispersion compensation with the cTiSER system the distortion is mitigated [Fig. 6(b)]. As an indication of the increased bandwidth due to dispersion compensation, we recorded improvement in rise/fall times, measured at 10% and 90% levels, from 18.5/19.1 ps to 16.1/15.8 ps.

7. Conclusion

Photonic TiSER is a powerful technology that boosts the bandwidth and resolution of ADC technology, enabling many advanced applications, such as for military systems, biomedical diagnostics, and telecommunications. In this paper, we demonstrated a TiSER system with a coherent receiver back-end, which promises to offer to TiSER many of the benefits that coherent detection has brought to modern lightwave communications. In particular, we developed a fully functioning prototype cTiSER system with a stretch factor of 24 and analog bandwidth of >30 GHz, which captures the full amplitude and phase information of a time-stretched RF signal. Taking advantage of the full field information, we successfully performed digital dispersion compensation, equalizing the bandwidth reducing parasitic dispersive effect. Further studies will develop and characterize improvements in SNR from upshifting the signal away from low frequency noise, avoiding the non-linear distortion from square-law detection, and through implementing additional distortion corrections such as equalization of non-linear modulation. When combined with analog balanced detection, mixing gain can also be exploited to boost the signal power and improve sensitivity without additional optical or electrical amplifiers. Looking further ahead, application of this coherent detection technique in all-optical TiSER will extend the bandwidth beyond the dispersion penalty limit, as well as allow it to capture advanced phase and amplitude optical modulation formats. With all of the afforded benefits, we foresee broadband coherent detection to become the standard receiver system for time-stretch transformation.

Acknowledgments

The authors would like to acknowledge the partial support from National Science Foundation through CIAN NSF ERC under Grant No. EEC-0812072.

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A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. 7(2), 207–263 (2013). [CrossRef]

14.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl 48(3), 261–271 (2001).

15.

S. Gupta and B. Jalali, “Time-warp correction and calibration in photonic time-stretch analog-to-digital converter,” Opt. Lett. 33(22), 2674–2676 (2008). [CrossRef] [PubMed]

16.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. 91(16), 161105 (2007). [CrossRef]

17.

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed. (John Wiley & Sons, Inc., 2002), pp. 478–517.

18.

T. Okoshi, “Recent advances in coherent optical fiber communication-systems,” J. Lightwave Technol. 5(1), 44–52 (1987). [CrossRef]

19.

P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett. 35(19), 1661–1662 (1999). [CrossRef]

20.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013). [CrossRef]

21.

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett. 101(5), 051113 (2012). [CrossRef]

22.

B. W. Buckley, A. Fard, and B. Jalali, “Time-stretch analog-to-digital conversion using phase modulation and broadband coherent detection for improving resolution,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest Series (Optical Society of America,2011), paper OThW4. [CrossRef]

23.

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett. 98(10), 101107 (2011). [CrossRef]

24.

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008). [CrossRef] [PubMed]

25.

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

26.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004). [CrossRef]

27.

E. Tokunaga, A. Terasaki, and T. Kobayashi, “Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy,” Opt. Lett. 17(16), 1131–1133 (1992). [CrossRef] [PubMed]

28.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys. 80(4), 043821 (2009). [CrossRef]

29.

M. A. T. L. A. B. Release, 2012a, The MathWorks, Inc., Natick, Massachusetts, United States.

30.

L. Cohen, Time-frequency analysis (Prentice Hall PTR, 1995), pp. 30–31.

31.

Y. Han and B. Jalali, “Differential photonic time-stretch analog-to-digital converter,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE Cat. No.CH37419-TBR), (2003), p. CWH2.

32.

G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Academic Press, 2007), pp. 51–78.

33.

H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett. 31(21), 1848–1849 (1995). [CrossRef]

34.

J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett. 37(1), 67–68 (2001). [CrossRef]

35.

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech. 53(4), 1404–1408 (2005). [CrossRef]

36.

T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun. 195(5–6), 399–404 (2001). [CrossRef]

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2310) Fiber optics and optical communications : Fiber optics
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(140.4050) Lasers and laser optics : Mode-locked lasers
(260.2030) Physical optics : Dispersion
(320.1590) Ultrafast optics : Chirping

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 17, 2013
Revised Manuscript: August 28, 2013
Manuscript Accepted: August 29, 2013
Published: September 6, 2013

Citation
Brandon W. Buckley, Asad M. Madni, and Bahram Jalali, "Coherent time-stretch transformation for real-time capture of wideband signals," Opt. Express 21, 21618-21627 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21618


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  4. J. Murphy, “Development of high performance analog-to-digital converters for defense applications,” in GaAs IC Symposium. IEEE Gallium Arsenide Integrated Circuit Symposium. 19th Annual Technical Digest 1997 (Cat. No.97CH36098), (1997), pp. 83–86.
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  9. J. H. Sinsky and P. J. Winzer, “100-Gb/s optical communications: a microwave engineer's perspective,” IEEE Microw. Mag.10(2), 44–57 (2009). [CrossRef]
  10. A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analague-to-digital conversion,” Electron. Lett.34(11), 1081–1083 (1998). [CrossRef]
  11. B. Jalali and F. M. A. Coppinger, “Data conversion using time manipulation,” US Patent 6,288,659 (2001).
  12. Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol.21(12), 3085–3103 (2003). [CrossRef]
  13. A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev.7(2), 207–263 (2013). [CrossRef]
  14. N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl48(3), 261–271 (2001).
  15. S. Gupta and B. Jalali, “Time-warp correction and calibration in photonic time-stretch analog-to-digital converter,” Opt. Lett.33(22), 2674–2676 (2008). [CrossRef] [PubMed]
  16. J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007). [CrossRef]
  17. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed. (John Wiley & Sons, Inc., 2002), pp. 478–517.
  18. T. Okoshi, “Recent advances in coherent optical fiber communication-systems,” J. Lightwave Technol.5(1), 44–52 (1987). [CrossRef]
  19. P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett.35(19), 1661–1662 (1999). [CrossRef]
  20. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics7(2), 102–112 (2013). [CrossRef]
  21. A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012). [CrossRef]
  22. B. W. Buckley, A. Fard, and B. Jalali, “Time-stretch analog-to-digital conversion using phase modulation and broadband coherent detection for improving resolution,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest Series (Optical Society of America,2011), paper OThW4. [CrossRef]
  23. A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011). [CrossRef]
  24. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008). [CrossRef] [PubMed]
  25. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol.26(20), 3416–3425 (2008). [CrossRef]
  26. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004). [CrossRef]
  27. E. Tokunaga, A. Terasaki, and T. Kobayashi, “Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy,” Opt. Lett.17(16), 1131–1133 (1992). [CrossRef] [PubMed]
  28. K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys.80(4), 043821 (2009). [CrossRef]
  29. M. A. T. L. A. B. Release, 2012a, The MathWorks, Inc., Natick, Massachusetts, United States.
  30. L. Cohen, Time-frequency analysis (Prentice Hall PTR, 1995), pp. 30–31.
  31. Y. Han and B. Jalali, “Differential photonic time-stretch analog-to-digital converter,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE Cat. No.CH37419-TBR), (2003), p. CWH2.
  32. G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Academic Press, 2007), pp. 51–78.
  33. H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett.31(21), 1848–1849 (1995). [CrossRef]
  34. J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett.37(1), 67–68 (2001). [CrossRef]
  35. Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech.53(4), 1404–1408 (2005). [CrossRef]
  36. T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun.195(5–6), 399–404 (2001). [CrossRef]

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