One Million Time-Bandwidth Product Full-Field ... - OSA Publishing
OSA/ CLEO 2011
CTuH6.pdf
One Million Time-Bandwidth Product Full-Field Waveform Measurement using Frequency-to-Time Interferometry Nicolas K. Fontaine, Ryan P. Scott, David J. Geisler, Tingting He, J. P. Heritage, and S. J. B. Yoo Department of Electrical and Computer Engineering, University of California, Davis, One Shields Ave., Davis, California 95616 USA [email protected],[email protected]
Abstract: Time-multiplexing of a single-shot interferometric measurement technique using frequency-to-time mapping and digital coherent detection characterizes the amplitude and phase of 350-GHz bandwidth waveforms with a 3-µs record length in only 113 µs. OCIS codes: (320.7100) Ultrafast measurements; (070.6020) Continuous optical signal processing.
Amplitude and phase (i.e., full-field) measurements of complex ultrafast optical waveforms with long record lengths (> 0.1 µs) and picosecond resolution is necessary for many applications including telecommunications, physics, and chemistry. Wide-bandwidth measurement techniques, such as spectral interferometry (SI) and frequency-resolved optical gating (FROG), have sub-ns record lengths due to the direct relationship to the spectral domain resolution [1-4]. Record lengths have been increased into the ns regime by applying temporal multiplexing to SI waveform characterization [2]. Recently, Asghari et al. [1] demonstrated an all-fiber, full-field measurement technique that records the spectral interference in the time domain using a fast digitizer and an optical Fourier transform (OFT). The OFT exploits strong chromatic dispersion in a linearly-chirped fiber Bragg grating (LC-FBG) to perform frequency-to-time mapping. As an extension to this technique, our group developed single-shot frequency-to-time assisted interferometry (SS-FTI) that includes four-quadrature coherent detection (FQCD) and an exact retrieval algorithm which fully characterized waveforms with 560-GHz bandwidths and 700-ps record lengths at a 40-MHz update rate [3]. This summary presents measurements with 3-ps resolution and record lengths beyond 3 µs obtained by temporal multiplexing SS-FTI. Fig. 1(a) describes the SS-FTI technique which measures a temporal window of the signal waveform, s(t), through measuring the quantity sD(t)rD*(t) and processing it with a non-iterative retrieval algorithm. Here, sD(t) is the chromatically dispersed, or frequency-to-time mapped, s(t), and rD(t) is an equivalently dispersed reference pulse, r(t) [3]. The algorithm requires characterization of H(ω) and rD(t). The measurement process isolates a measurement window with a length of T = 2B·GVD (B is the digitization bandwidth and GVD is the group velocity dispersion) centered on r(t) and automatically rejects energy outside this measurement window, making it straightforward to time-multiplex the technique. Fig. 1(b) depicts the time-multiplexing scheme where in each frame rD(t) is delayed by a different amount from sD(t) to measure a different temporal window of s(t). In the post-processing, combining the frames together with the correct constant phase extends the record length. Frequency-to-Time Dispersed Signal Mapping sD(t) GVD H(ω)
Time (20 ps/div)
|S(ω)|
Frequency (50 GHz/div)
Frame 3
Frame 4
rD
Time
(c) 1×2
10 GHz Reference
Time
1×2
÷144
HE-MZM Time EDFA HE-MZM Delay Reference Gating
sD (t)
SD (ω) ×
1 H(ω)
IDFT
s(t)
Measuremnt Window Frame 4
Time Time
−2012 ps/nm
Circ.
DFT
1 r (t) * D
T
sD(t)
1×2
90˚ Optical Hybrid
Time S
PBS 2×1
Remove Measured GVD
Combine Frames
LC-FBG
Signal ÷16
×
Frequency-to-Time Mapping PBS
2 × 2 MZS
100 ps
Frames are combined in post processing.
M1 M2 Ch1 Ch2
Waveform Shaper
sD(t) rD*(t)
Frame 1 In each frame sD(t) is delayed a different s(t) amount from rD(t).
EAWG Switching Pattern
Signal Recovery (DSP) Remove Measured Dispersed Reference
rD(t) Dispersed Reference
Frequency (50 GHz/div)
sD 10 GHz OFCG
FourQuadrature Coherent Detection
|SD(ω)|
∂2β = − λ2 D ∂f 2 c
Frame 2
sD(t)
Time (50 GHz × GVD−1 ps/div)
(b) Time Multiplexing Frame 1
Measured Quantity
rD(t)
R
90º
S+R S-R S+jR S-jR
Balanced Photodiodes /Digitizers I Q
50 GS/s Digitizer
(a) Input Signal s(t)
Time
Fig. 1. (a) SS-FTI concept and exact retrieval algorithm. (b) Temporal multiplexing scheme. (c) Experimental implementation to generate and measure complex waveforms. OFCG, optical frequency comb generator; EAWG, electronic arbitrary waveform generator.
OSA/ CLEO 2011
CTuH6.pdf
Fig. 1(c) presents the experimental arrangement. The left side of Fig. 1(c) shows preparation of r(t) and s(t). A stable 37 line × 10.09 GHz optical frequency comb (OFC) generator based on strong modulation of a singlefrequency laser provides a train of slightly-chirped pulses (99.1-ps period). A time gating scheme using cascaded high-extinction Mach-Zehnder modulators (HE-MZM) and erbium-doped fiber amplifiers (EDFAs) reduces the reference repetition rate to 14.3 ns (i.e., frame rate, TF) and produces a strong r(t) in each frame. The signal waveform, s(t) is prepared by combining waveform A (the output of the OFCG) and waveform B (spectrally shaped OFC) together into a sequence lasting 3.14 µs. The period of s(t) is offset by 400 ps from 220 × TF such that r(t) scans through all of s(t). A polarization-multiplexing scheme combines r(t) and s(t) to share the same dispersion of the LC-FBG to produce rD(t) and sD(t). A 90° optical hybrid, two balanced photodiode pairs and two 50 GS/s digitizer channels record the in-phase (I) and quadrature-phase (Q) components of sD(t)rD*(t). A single 113-µs acquisition (6 MSamples) contains 7,920 SS-FTI measurement frames (each 600-ps wide and separated by 400 ps). Combining the frames produces the total 3.14 µs waveform. Intensity (a.u.)
(a) Measurement 1 Full Time Record - Waveform A Only
Intensity (a.u.)
(c) Spectrum of Measurement 1
3 μs
Frequency (25 GHz/div)
Intensity (a.u.)
Time (100 ps/div) (d) Measurement 2 Full Time Record - Waveform A and B
Intensity (10 dB/div)
Time (100 ns/div) Phase (2 rad/div)
(b) First 1000 ps of Measurement 1
Time (100 ps/div)
(f ) Waveform B Spectral Comparison Intensity (a.u.)
Intensity (a.u.)
Time (100 ns/div) (e) First 1000 ps of Measurement 2 Waveform B Waveform A
3 μs OSA Measured
Frequency (25 GHz/div)
Fig. 2. (a) Measurement of waveform A with waveform B blocked. (b) Amplitude and phase of the first ns and (c) spectrum. (d) Measurement with waveform A and B. (e) Intensity of first 1000 ps. (f) Comparison of waveform B’s spectrum with this technique and an OSA measurement.
Fig. 2 shows two 3.14-µs long measurements alternating between Waveform A and waveform B. In Measurement 1, waveform B is blocked. Fig. 2(b) shows the first 1000 ps of Measurement 1 to indicate the fullfield (i.e., phase and intensity) capability and the high-bandwidth (short temporal features). A Fourier transform of the temporal full-field determines the optical spectrum. Measurement 1’s optical spectrum [Fig. 2(c)] contains 35 clearly resolved modes indicating proper concatenation of the 7,290 separate SS-FTI measurement frames. Fig. 2(d,e) show the full-record and first 1000 ps of Measurement 2 which alternates between waveform A and waveform B. Fig. 2(f) compares waveform B’s spectrum to results from an optical spectrum analyzer (OSA). These measurements demonstrate full-field characterization of waveforms with resolution-to-record-length ratios or time-bandwidth products (TBP) exceeding 1.1 million (350 GHz bandwidth and 3.14 µs record-length). Using a digitizer with deeper memory depth (e.g., 250 MSamples) and a wider bandwidth reference signal, this technique is capable of measuring THz bandwidth waveforms with TBPs exceeding 50 million. [1] M. H. Asghari, et al., “Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry,” Opt. Express, 18, 16526-16538 (2010). [2] J. Cohen, et al., “Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry,” Opt. Express, 18, 24451-24460 (2010). [3] N. K. Fontaine, et al., “Frequency-to-time assisted interferometry for polarization-diversified, single-shot, full-field waveform measurement,” in Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), 2010 Conference on, 1-2 (2010). [4] L. Lepetit, et al., “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” JOSA B, 12, 2467-2474 (1995). This work was supported in part by DARPA DSO and SPAWAR under OAWG contract HR0011-05-C-0155. The authors thank NISTICA for the loan of the waveform shaper.
CTuH6.pdf
One Million Time-Bandwidth Product Full-Field Waveform Measurement using Frequency-to-Time Interferometry Nicolas K. Fontaine, Ryan P. Scott, David J. Geisler, Tingting He, J. P. Heritage, and S. J. B. Yoo Department of Electrical and Computer Engineering, University of California, Davis, One Shields Ave., Davis, California 95616 USA [email protected],[email protected]
Abstract: Time-multiplexing of a single-shot interferometric measurement technique using frequency-to-time mapping and digital coherent detection characterizes the amplitude and phase of 350-GHz bandwidth waveforms with a 3-µs record length in only 113 µs. OCIS codes: (320.7100) Ultrafast measurements; (070.6020) Continuous optical signal processing.
Amplitude and phase (i.e., full-field) measurements of complex ultrafast optical waveforms with long record lengths (> 0.1 µs) and picosecond resolution is necessary for many applications including telecommunications, physics, and chemistry. Wide-bandwidth measurement techniques, such as spectral interferometry (SI) and frequency-resolved optical gating (FROG), have sub-ns record lengths due to the direct relationship to the spectral domain resolution [1-4]. Record lengths have been increased into the ns regime by applying temporal multiplexing to SI waveform characterization [2]. Recently, Asghari et al. [1] demonstrated an all-fiber, full-field measurement technique that records the spectral interference in the time domain using a fast digitizer and an optical Fourier transform (OFT). The OFT exploits strong chromatic dispersion in a linearly-chirped fiber Bragg grating (LC-FBG) to perform frequency-to-time mapping. As an extension to this technique, our group developed single-shot frequency-to-time assisted interferometry (SS-FTI) that includes four-quadrature coherent detection (FQCD) and an exact retrieval algorithm which fully characterized waveforms with 560-GHz bandwidths and 700-ps record lengths at a 40-MHz update rate [3]. This summary presents measurements with 3-ps resolution and record lengths beyond 3 µs obtained by temporal multiplexing SS-FTI. Fig. 1(a) describes the SS-FTI technique which measures a temporal window of the signal waveform, s(t), through measuring the quantity sD(t)rD*(t) and processing it with a non-iterative retrieval algorithm. Here, sD(t) is the chromatically dispersed, or frequency-to-time mapped, s(t), and rD(t) is an equivalently dispersed reference pulse, r(t) [3]. The algorithm requires characterization of H(ω) and rD(t). The measurement process isolates a measurement window with a length of T = 2B·GVD (B is the digitization bandwidth and GVD is the group velocity dispersion) centered on r(t) and automatically rejects energy outside this measurement window, making it straightforward to time-multiplex the technique. Fig. 1(b) depicts the time-multiplexing scheme where in each frame rD(t) is delayed by a different amount from sD(t) to measure a different temporal window of s(t). In the post-processing, combining the frames together with the correct constant phase extends the record length. Frequency-to-Time Dispersed Signal Mapping sD(t) GVD H(ω)
Time (20 ps/div)
|S(ω)|
Frequency (50 GHz/div)
Frame 3
Frame 4
rD
Time
(c) 1×2
10 GHz Reference
Time
1×2
÷144
HE-MZM Time EDFA HE-MZM Delay Reference Gating
sD (t)
SD (ω) ×
1 H(ω)
IDFT
s(t)
Measuremnt Window Frame 4
Time Time
−2012 ps/nm
Circ.
DFT
1 r (t) * D
T
sD(t)
1×2
90˚ Optical Hybrid
Time S
PBS 2×1
Remove Measured GVD
Combine Frames
LC-FBG
Signal ÷16
×
Frequency-to-Time Mapping PBS
2 × 2 MZS
100 ps
Frames are combined in post processing.
M1 M2 Ch1 Ch2
Waveform Shaper
sD(t) rD*(t)
Frame 1 In each frame sD(t) is delayed a different s(t) amount from rD(t).
EAWG Switching Pattern
Signal Recovery (DSP) Remove Measured Dispersed Reference
rD(t) Dispersed Reference
Frequency (50 GHz/div)
sD 10 GHz OFCG
FourQuadrature Coherent Detection
|SD(ω)|
∂2β = − λ2 D ∂f 2 c
Frame 2
sD(t)
Time (50 GHz × GVD−1 ps/div)
(b) Time Multiplexing Frame 1
Measured Quantity
rD(t)
R
90º
S+R S-R S+jR S-jR
Balanced Photodiodes /Digitizers I Q
50 GS/s Digitizer
(a) Input Signal s(t)
Time
Fig. 1. (a) SS-FTI concept and exact retrieval algorithm. (b) Temporal multiplexing scheme. (c) Experimental implementation to generate and measure complex waveforms. OFCG, optical frequency comb generator; EAWG, electronic arbitrary waveform generator.
OSA/ CLEO 2011
CTuH6.pdf
Fig. 1(c) presents the experimental arrangement. The left side of Fig. 1(c) shows preparation of r(t) and s(t). A stable 37 line × 10.09 GHz optical frequency comb (OFC) generator based on strong modulation of a singlefrequency laser provides a train of slightly-chirped pulses (99.1-ps period). A time gating scheme using cascaded high-extinction Mach-Zehnder modulators (HE-MZM) and erbium-doped fiber amplifiers (EDFAs) reduces the reference repetition rate to 14.3 ns (i.e., frame rate, TF) and produces a strong r(t) in each frame. The signal waveform, s(t) is prepared by combining waveform A (the output of the OFCG) and waveform B (spectrally shaped OFC) together into a sequence lasting 3.14 µs. The period of s(t) is offset by 400 ps from 220 × TF such that r(t) scans through all of s(t). A polarization-multiplexing scheme combines r(t) and s(t) to share the same dispersion of the LC-FBG to produce rD(t) and sD(t). A 90° optical hybrid, two balanced photodiode pairs and two 50 GS/s digitizer channels record the in-phase (I) and quadrature-phase (Q) components of sD(t)rD*(t). A single 113-µs acquisition (6 MSamples) contains 7,920 SS-FTI measurement frames (each 600-ps wide and separated by 400 ps). Combining the frames produces the total 3.14 µs waveform. Intensity (a.u.)
(a) Measurement 1 Full Time Record - Waveform A Only
Intensity (a.u.)
(c) Spectrum of Measurement 1
3 μs
Frequency (25 GHz/div)
Intensity (a.u.)
Time (100 ps/div) (d) Measurement 2 Full Time Record - Waveform A and B
Intensity (10 dB/div)
Time (100 ns/div) Phase (2 rad/div)
(b) First 1000 ps of Measurement 1
Time (100 ps/div)
(f ) Waveform B Spectral Comparison Intensity (a.u.)
Intensity (a.u.)
Time (100 ns/div) (e) First 1000 ps of Measurement 2 Waveform B Waveform A
3 μs OSA Measured
Frequency (25 GHz/div)
Fig. 2. (a) Measurement of waveform A with waveform B blocked. (b) Amplitude and phase of the first ns and (c) spectrum. (d) Measurement with waveform A and B. (e) Intensity of first 1000 ps. (f) Comparison of waveform B’s spectrum with this technique and an OSA measurement.
Fig. 2 shows two 3.14-µs long measurements alternating between Waveform A and waveform B. In Measurement 1, waveform B is blocked. Fig. 2(b) shows the first 1000 ps of Measurement 1 to indicate the fullfield (i.e., phase and intensity) capability and the high-bandwidth (short temporal features). A Fourier transform of the temporal full-field determines the optical spectrum. Measurement 1’s optical spectrum [Fig. 2(c)] contains 35 clearly resolved modes indicating proper concatenation of the 7,290 separate SS-FTI measurement frames. Fig. 2(d,e) show the full-record and first 1000 ps of Measurement 2 which alternates between waveform A and waveform B. Fig. 2(f) compares waveform B’s spectrum to results from an optical spectrum analyzer (OSA). These measurements demonstrate full-field characterization of waveforms with resolution-to-record-length ratios or time-bandwidth products (TBP) exceeding 1.1 million (350 GHz bandwidth and 3.14 µs record-length). Using a digitizer with deeper memory depth (e.g., 250 MSamples) and a wider bandwidth reference signal, this technique is capable of measuring THz bandwidth waveforms with TBPs exceeding 50 million. [1] M. H. Asghari, et al., “Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry,” Opt. Express, 18, 16526-16538 (2010). [2] J. Cohen, et al., “Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry,” Opt. Express, 18, 24451-24460 (2010). [3] N. K. Fontaine, et al., “Frequency-to-time assisted interferometry for polarization-diversified, single-shot, full-field waveform measurement,” in Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), 2010 Conference on, 1-2 (2010). [4] L. Lepetit, et al., “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” JOSA B, 12, 2467-2474 (1995). This work was supported in part by DARPA DSO and SPAWAR under OAWG contract HR0011-05-C-0155. The authors thank NISTICA for the loan of the waveform shaper.
