Nonlinear optical fiber based high resolution all-optical waveform sampling

Laser & Photon. Rev. 1, No. 3, 231–248 (2007) / DOI 10.1002/lpor.200710014 231

Abstract When there is a need to accurately characterize optical

waveforms and, it is not surprising that some of the best, albeit

only recently established, techniques to do this rely on all-optical

phenomena. Some basic reasons why all-optical sampling holds

great promise as a very useful tool well into the foreseeable

future are that there are no ringing phenomena with associated

waveform distortion as in electronic sampling due to impedance

mismatch, and that the time resolution can be made extremely

high (� 1 ps) while yet also offering high sensitivity for e.g. eye

diagram (a superposition of all ‘1’ and ‘0’ in a data sequence

that is widely used in telecommunications testing) and statistical

analysis. In this paper, we review recent developments in optical

fiber-based sampling of optical waveforms. In particular, we

describe the state-of-the-art in terms of the various performance

measures as well as their trade-offs.

Sampled data pattern of a 640 Gb/s. RZ data signals using a fiber

FWM-based optical sampling system.

© 2007 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Nonlinear optical fiber based high resolution all-opticalwaveform samplingPeter A. Andrekson* and Mathias Westlund

Photonics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, Gothenburg, Sweden

Received: 5 July 2007, Revised: 25 September 2007, Accepted: 25 September 2007

Published online: 5 November 2007

Key words: all-optical sampling, nonlinear optics, parametric amplification, fiber four wave mixing, equivalent-time sampling, software

synchronization

PACS: 42.65.Yi, 42.65.Ky, 42.81.Wg

1. Introduction

There is a need for ever increasingly accurate characteri-zation of optical waveforms. The term accurate is quanti-fied, of course, by a number of measures such as rise andfall time, extinction ratio, timing jitter, signal-to-noise ra-tio etc., the relative importance of each depending on theactual application being considered. The most importantmeasure in many applications is the temporal resolution,but while being important this is not an independent quan-tity and it can be traded off among other quantitative mea-sures such as the sensitivity, i.e. the signal power needed toreach a certain SNR. The characterization requirements fornext generation lightwave systems operating at 43 Gb/s or100 Gb/s Ethernet will be significant. The accurate captureof such waveforms necessitates bandwidths well in excess

of 100 GHz with a corresponding near picosecond resolu-tion.

When considering optical waveform analysis there area few key considerations to be made such as:

– Required temporal resolution: Electronic solutions(< 70 GHz) or all-optical solutions (∼ THz)

– Waveform averaging: Promotes high sensitivity but un-acceptable for eye diagrams and statistical analysis

– Intensity waveform or full optical field analysis e.g. forconstellation diagrams

– Repetitive waveforms or unique data bursts

The technique most widely used today to monitor high-bandwidth optical communication signals is to use a con-ventional electronic sampling oscilloscope with an ultra-fast photo-diode attached to the input. The progress overthe years has led to equivalent-time electronic sampling

*Corresponding author: Prof. Dr. Peter A. Andrekson, e-mail: [email protected]

© 2007 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

232 P. A. Andrekson and M. Westlund: Nonlinear fiber based all-optical waveform sampling

systems having bandwidths of up to about 100 GHz today.A fundamental drawback with electronic sampling is theincreasing difficulty to realize a small enough impairmentcaused by impedance mismatch at higher frequencies toavoid undesired ’ringing’ features in the response. Further-more, the true available bandwidth when monitoring opticalwaveforms with electronic sampling is limited by both thebandwidth of the photodiode and of the electronic samplingsystem to approximately 50–70 GHz in today’s state-of-the-art systems. In contrast, optical sampling demonstra-tions have shown bandwidths in excess of 500 GHz withintrinsic limitation expected to be several 1000 GHz andwithout any ringing artifacts. For the accurate display ofoptical signals in next generation lightwave systems oper-ating at a data rate of 40 Gb/s, which also likely may carryerror-correcting overhead bits resulting in bit-rates of 43to 50 Gb/s and which may further be implemented withreturn-to-zero data format, the actual measurement band-width needed is certainly in the 100’s of GHz with a corre-sponding pico-second resolution requirement. While opti-cal telecommunications might be considered the main ap-plication for optical waveform monitoring, and this is cer-tainly the focus here, there are also numerous other applica-tions where accurate optical waveform measurements arerequired such as for the development of ultrafast lasers formaterial processing, imaging, and metrology or for time-resolved spectroscopy, etc.

Apart from all-optical sampling, other optical tech-niques exist to reach very high temporal resolution andto eliminate the ’ringing’ concern such as the use of streakcameras (with approximately 2 ps resolution) or intensityautocorrelators (< 0.1 ps resolution). While these instru-ments are very mature, well understood and widely used,they do also hold significant drawbacks in specific appli-cations. For example, in the case of streak cameras, theyhave a very modest sensitivity especially in the telecom-munication window around 1550 nm, precluding the studyof optical eye diagrams. In the case of autocorrelators the,by definition symmetric response function, precludes e.g.the independent study of rise and fall times or the studyof pseudo-random bit sequences (PRBS). Furthermore,both streak cameras and autocorrelators are polarization-dependent which in most cases is unacceptable. This is be-cause optical waveforms that, for example, have encoun-

tered polarization-mode dispersion (PMD), perhaps afterhaving been propagated through an optical fiber, will be-come depolarized and thus not properly visualized if thedetection system has a larger response for some polariza-tion states than for others.

In recent years, optical sampling techniques haveemerged as powerful tools to monitor optical waveformsand being useful without giving up much in terms of sen-sitivity or resolution. At the core of these techniques is anoptical nonlinearity, be it in crystals or in optical fibers. Thisnonlinearity enables the function of a gate being opened bya short optical sampling pulse. The intrinsic temporal re-sponse time of the processes utilized is often 10 fs or less,and thus other practical considerations such as the sam-pling pulse width and dispersive walk-off among signaland sampling pulses are the actual limiting factors for theresolution. The capture of the waveforms in these systemsis very similar to the technique being used in electronicsampling, but without the need for fast electronics. Ide-ally, this should be implemented with real-time samplingsuch that the sampling rate is larger than twice the highestfrequency content of the signal of interest. However, eventhe capture of a 10 Gb/s non-return-to-zero (NRZ) signalis challenging, requiring a sampling rate of about 40 Giga-samples/s. Therefore, the temporal resolution limit in realtime oscilloscopes is essentially set by the maximum possi-ble sampling rate. In practice, this resolution limit is around30 ps or longer. On the other hand, in test and measurementsituations where the sequence of interest is repetitive ratherthan a unique singular event, one can fortunately resort toequivalent-time sampling. In this case, the sampling gate isopened by a narrow sampling pulse triggered by a time basethat is typically a (arbitrarily) small sub-multiple of the in-coming signal and offset by a small frequency differencesuch that the acquired samples are slowly walking acrossthe studied repetitive waveform. Thus a cross-correlationof the sampling pulse and signal is obtained that is identicalwith the signal assuming that the sampling pulse is shortenough. This applies also when measuring eye diagrams ata fixed bit rate even if the data is random.

In Fig. 1, we compare schematically an electrical sam-pling implementation with an optical sampling implemen-tation. In the electronic case, the bandwidth is limitedmainly by the photo-diode and the electrical strobe dura-

PIN(~ 50 GHz)

PIN / APD(~ 100 MHz)

A/D

electrical strobe

A/D

optical strobeinput optical

signalinput optical

signal

Figure 1 Experimental setup of time and polarization resolved optical sampling based on FWM. PC: Polarization controller. (Left)

Conventional system for sampling optical signals: High-speed detection and electronic sampling. (Right) All-optical sampling system:

Optical sampling with short optical pulse and detection with low bandwidth photo-diode, A/D: Analog-to-digital converter.

© 2007 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.org

Laser & Photon. Rev. 1, No. 3 (2007) 233

0 20 40 60 80 100

0

1

electricalsampling

optical sampling

time (ps)

ampl

itude

Figure 2 Measured electrical and optical

impulse responses of sampling systems.

tion, while in the optical case the optical pulse (or strobe)is the main limiting factor. In essence, when using opticalsampling one transfers the high bandwidth (fast responsetime) requirement from the electronics to the optics. Anotable difference among the two approaches in Fig. 1 isthat in the optical case, the detector being used can have avery low bandwidth and as a consequence avalanche photodiodes (APDs) can readily be used. In the electronic sam-pling case, this is (at least currently at 1550 nm wavelength)not possible with high resolution since APDs are only avail-able with bandwidths up to about 10 GHz.

The analog-to-digital conversion and display of thewaveform is also an important part of the sampling sys-tem. While the bandwidth of the sampling system does notdepend on the speed of the acquisition and display, thatspeed is still important in real applications since it willdetermine the signal refresh rate and thus the perceptionof real-time information display. In principle, however, thesampling frequency can be made arbitrarily small, which isa consequence of the signal of interest being repetitive, thusallowing a slow accumulation of the complete waveform.

In electronic sampling systems there are, sometimes se-vere, concerns with impedance-mismatch induced ringingin the response. This is entirely eliminated in the opticalcase. Thus, the optical solution is very nicely scalable tovery high bandwidth and time resolution. Fig. 2 illustratesthis point. Here, experimental impulse responses are shownin electronic sampling using a commercial 50 GHz band-width pin-diode coupled directly to a 50 GHz bandwidthelectrical sampling oscilloscope, and the corresponding re-sponse using optical sampling adjusted for a time resolutionof 8 ps which is similar to the electronic case.

The optical-nonlinearity-based sampling methods canbroadly be classified as mentioned above as being basedon χ2 or on χ3. After some early work on single-shot all-optical sampling around 1970 [1] and on equivalent-timeall-optical sampling in the 1980s [2], the utilization of χ2

has been explored fairly extensively since the mid 1990sin various configurations including sum-frequency gener-ation (SFG) [3–11]. The χ3-in-optical-fiber-based optical

sampling schemes originate from the fact that the index ofrefraction in fibers is intensity dependent (nonlinear refrac-tion) which can be utilized in different ways as explainedlater. Recent work [12–14] has demonstrated the useful-ness of all-optical sampling by verifying high refresh rateeye-diagram analysis of data at several 100’s of Gb/s.

The remainder of this paper is organized as follows. Theprinciples of optical gating are introduced in Sect. 2 while inSect. 3 their performance and trade-offs are discussed. Thesomewhat independent but in this context relevant topicof software synchronized time base recovery is discussedin Sect. 4.

2. Principles of optical sampling

All-optical sampling techniques rely on the controlled andrapid temporary change of the phase, frequency, or polar-ization of the optical signal to be analyzed. The key ele-ments used to implement this are the sampling gate and theoptical pulse generator that will serve to open and closethe gate. Here, we will discuss sampling implementationsbased on nonlinear optical phenomena. The optical nonlin-earities used can be split into two main categories, namelythose based on second-order nonlinearities (χ2) and thosebased on third-order nonlinearities (χ3). In practice, mostχ2-based solutions are relying on crystals such as LithiumNiobate (LiNbO3) and KTP (KTiOPO4). Most χ3-basedsolutions use optical fibers which happen to have negligi-bly small second-order nonlinearity but strong enough χ3

to be used in sampling by utilizing cross-phase modulation(XPM) for example in nonlinear optical loop mirrors [15]or by utilizing four-wave mixing (FWM) [16]. The third-order nonlinearity is weak but the net effect of this nonlin-earity can still be significant if the fiber core is intentionallymade small and the fiber is long enough. We will here fo-cus on optical fiber-based third-order nonlinearity basedoptical sampling.

www.lpr-journal.org © 2007 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim


2.1. Third-order nonlinearity based sampling

The third-order nonlinearity in optical fibers and in semi-conductors can be used in different ways to perform all-optical sampling. The basic phenomena used include: four-wave mixing (FWM), cross-phase modulation (XPM) andnonlinear polarization rotation. The fundamental propertyof the fiber that is utilized in all of these sampling gates isthat the index of refraction increases with the optical inten-sity, which is known as nonlinear refraction or sometimesas the nonlinear Kerr effect. The presence of a single op-tical wave will cause an additional phase change (phasedelay) of the optical wave as the light propagates down thefiber. The amount of such self-phase modulation (SPM)is equal to ΔφNL = γPL where γ is a measure of thestrength of the 3rd order nonlinearity of the fiber and Pand L are the optical power and fiber length (ignoring at-tenuation), respectively. In the case of optical sampling, themore interesting case is that of two optical waves at differ-ent wavelengths; the signal and the sampling waves. In sucha case, if the sampling wave has much higher power, thesignal wave will experience a phase delay induced by thesampling wave, and the amount of such cross-phase mod-ulation (XPM) is equal to ΔφNL = 2γPL, i.e. twice theamount compared to SPM. This factor of two compared toSPM is perhaps not intuitive and is discussed further in [17].If optical pulses are considered, both SPM and XPM willresult in an optical phase change across the pulses, which, inturn, will cause spectral broadening and chirp of the pulses.

Another phenomenon that can be utilized for opticalsampling is four-wave mixing (FWM) that also requiresoptical phase matching among the involved optical wavesto be efficient, in contrast to XPM. In FWM, a new wave,the so-called idler, is generated at the frequency fi = 2fp−fs, with fp and fs being the pump and signal frequencies,respectively.

FWM-based optical sampling requires optical phasematching to be efficient and this is typically achieved by

placing the pump (i.e. sampling source) wavelength nearthe zero-dispersion wavelength of the fiber. In addition, ashorter fiber is preferable over a longer one as then phasematching is more easily satisfied over a wider range ofwavelength. This, however, comes at the expense of need-ing more pump power. In practice, higher order dispersion,polarization-mode dispersion as well as variation of thezero-dispersion wavelength along the fiber will also poten-tially limit the useful optical bandwidth of the device.

The efficiency, η, the power transfer from signal to theidler wave, of this process can be much higher than 100%.In this case, a significant amount of pump power is actu-ally transferred to the signal wave and to the idler wave viathe process known as parametric amplification [17]. In thespecial case when the pump wavelength coincides with thezero-dispersion wavelength (Δβ = 0), a particularly sim-ple expression can be found for the efficiency (i.e. gain):

η ≈ (γPpL)2 (1)

This expression, where Pp denotes the pump power, isa reasonably useful approximation for the FWM-basedsampling efficiency described here for wavelengths closeenough to the pump wavelength, see Fig. 3 below.

Fig. 3 illustrates an example of calculated FWM conver-sion efficiency, η, as a function of λs−λp for different sam-pling pulse source wavelength offsets from the zero disper-sion wavelength, λp−λ0. The product γPpL=

√2 resulting

in η = 3dB for small λs−λp. It should be pointed out whenanalyzing the efficiency spectrum in Fig. 3, only one of thetwo lobes around the pump wavelength is available as in-put signal wavelength range for sampling purposes. This isbecause the idler wave is being generated in the process asa mirrored copy if the incoming signal. The sampling pulsepeak power was Pp = 7W and the highly nonlinear fiber(HNLF) had parameter values: length L = 20m, nonlinearcoefficient γ = 10W−1 km−1, λ0 = 1542nm and disper-sion slope, S = dD/dλ = 0.03ps/nm2/km. The highestefficiency (and best phase-matching) occurs for a certain

-100 -50 0 50 100-4

-2

0

2

4

6

8

η(d

B)

λs-λp (nm)

λp=λ0

λp-λ0=2nm

bandwidth

λp-λ0=0.5, 1nm

Figure 3 Conversion efficiency spec-

trum of a sampling gate based on FWM.

Note that efficiencies over 100% are

achievable because of inherent paramet-

ric amplification.



λs − λp which depends on the sampling pulse power andon λp−λ0. As can be seen in the figure, the conversion effi-ciency peaks in this particular example at λs−λp ≈ 60nmfor λp−λ0 = 2nm, followed by a rapid drop in η when in-creasing the wavelength separation further. By moving thesampling pulse wavelength closer to λ0 (dashed curves) thepeak conversion efficiency occurs for increasing λs − λp.When λp = λ0 the theoretical bandwidth becomes infiniteeven though perfect phase-matching never occurs. In prac-tice, the other limitations mentioned above (but ignored inour calculations) will become important.

In order to achieve over 100 nm optical bandwidth re-quired for C- and L-band telecom wavelength range sam-pling the best approach is to minimize λp − λ0 and sac-rifice some conversion efficiency. The validity of thesesimulations depends strongly on the highly nonlinear fiber(HNLF) length and the length scale over which λ0 varies.Measurements indicate that the λ0 variation in a HNLF canbe several nanometers over a km of fiber while the variationcan be expected to be much smaller (< 0.5nm) in shorterfibers (< 20m). Thus, there exist a number of good reasonsfor implementing a FWM-based optical sampling systemwith an optical fiber that is as short as possible (assumingthat the correspondingly higher power and/or a fiber withlarger nonlinearity is available – without degrading otherfiber parameters).

2.2. Nonlinear optical fibers

A key enabling component for optical fiber-based samplingdevices is the optical fiber that together with the opticalsampling pulse source provides the sampling functionality.It is not only desirable to design the fiber specifically to havea strong nonlinearity, γ, but also to have a small, controlleddispersion. These are not independent parameters but needto carefully be considered simultaneously. Other aspects toconsider are excess losses (e.g. bending losses) and non-symmetries of the fiber that may cause significant undesiredpolarization-mode dispersion (PMD). In principle, a smallcore size is highly desired as the nonlinearity is linearlydependent on intensity (W/m2) rather than power. However,this assumes that other fiber parameters are not affected. Anexample of experimental data of nonlinear fibers used foroptical sampling can be found in [18].

The key factors to consider when using an optical fiberas a sampling gate are thus mainly:

– Nonlinearity (γ) 1/(W km)– Group-velocity dispersion (GVD) ps/km/nm– Dispersion slope (S) ps/(km nm2)– Zero-dispersion wavelength (λ0)– Polarization-mode dispersion (ps/

√km or ps/km)

– Splice losses to standard optical telecom fiber– Fiber loss (α) dB/m and corresponding effective

loss length

No general answer can be provided for the target val-ues of these parameters. The relative importance of these

also depend on the choice of sampling gate implementationprinciple (e.g. in XPM-based sampling, the variation of λ0

along the fiber may not be very critical) and on the samplingsystem target specifications; A 5 ps time resolution targetwould impose quite different requirement on the fiber thana 0.5 ps resolution requirement. However, there are cleartrade-offs to be made. For example, the design of a fiberwith a small core size will result in a higher γ, allowing forthe use of a shorter fiber (albeit not necessarily resultingin lower loss) and/or lower sampling pulse power, but islikely to increase the PMD of the fiber and will also changethe dispersive properties of the fiber and possibly cause itto significantly change along the fiber.

In general, there are trade-offs to be made when choos-ing the desired fiber characteristics at least with respect tothe following sampling device performance measures: timeresolution, sensitivity, and optical bandwidth. In Sect. 3, wewill further discuss and quantify these trade-offs. The dis-cussion in this section has so far assumed that the fiberused is a regular silica glass fiber. However, progress isbeing made in terms of so-called holey fiber containingseveral voids (air) and which can be manufactured to havea very large nonlinearity factor being hundreds of timesstronger than that in regular fibers as a result of mainly thevery tight optical mode confinement in a very small coreresulting in sometimes extremely large nonlinearities [19].In addition, there are other choices of materials suitable forultrafast nonlinear switching and sampling such as chalco-genide glass fibers [20], bismuth glass fibers [21], or Tel-lurite glass fibers [22]. A remaining problem is that thefiber loss still is quite high thus prohibiting a real trade-offamong optical power and device length (in the lossless casethe sampling peak power - fiber length product is constant).Another, sometimes even more important problem, is thematerial dispersion properties of these fibers. This can oftenresult in quite large net fiber dispersion (including waveg-uide dispersion) such that it directly limits the length offiber that in practice can be used for optical sampling with-out sacrificing optical bandwidth or temporal resolution.

3. Performance measures and trade-offs

In this section, we first define some important performancemeasures of all-optical sampling systems. Subsequently,we will quantify this by analyzing the FWM-based sam-pling system in detail.

Temporal resolution:The temporal resolution is here defined as the full-width athalf-maximum (FWHM) width of the impulse response ofthe sampling system. Since the temporal resolution of all-optical sampling systems can be very high, a short signalpulse used for evaluating the sampling gate performance isneeded. However, the overall sampling system resolutioncan thus often be limited by the sampling pulse duration it-self.



Sampling efficiency, η:The sampling efficiency, η, of an all-optical sampling gateis defined as the ratio of the power of the generated samplesat the output of the gate over the power of the input signal.A high sampling efficiency makes it possible to measureweaker input signals. This definition is independent of thesampling gate implementation. The sampling pulse powerwill influence the value ofη, but the relation will be differentfor different types of gate implementations.

Signal sensitivity:The signal sensitivity of a sampling system is a measureof how much signal power is required in order to samplea signal with a specified signal-to-noise ratio (SNR) of thesampled signal. The input signal to the system is assumedto be shot noise limited. The signal sensitivity is directlycoupled to the sampling efficiency defined above. How-ever, the signal sensitivity also accounts for the generationof excess noise and loss. We define the signal sensitivityas the amount of input signal power required to achieve20 dB sampled SNR. When using this definition the sam-pling system is considered a black box, independent of theimplementation which makes it a suitable measure for com-parisons between different techniques.

Optical bandwidth:The optical bandwidth of an optical sampling system is de-fined as the wavelength range over which the signal can bemeasured while maintaining the performance with respectto other performance measures. The definition of opticalbandwidth is not completely clear since boundary condi-tions with respect to both temporal resolution and signalsensitivity is required. When moving the signal wavelengthfurther from the sampling pulse wavelength, the samplinggate efficiency usually gradually decreases which results inreduced signal sensitivity. At the same time the dispersivewalk-off between the sampling pulse and the signal canincrease which degrades the temporal resolution.

3.1. Performance of optical fiber FWM-basedsampling systems

In this section we will discuss the performance of a fiberFWM-based all-optical sampling system in terms of three

measures: temporal resolution, optical bandwidth and sig-nal sensitivity. The investigation will include the influ-ence of the sampling pulse properties such as pulse width,peak power and amplitude noise as well as the very im-portant highly nonlinear fiber properties such as disper-sion, zero dispersion wavelength variation, nonlinearity andfiber length.

In order to achieve efficient sampling, the FWM pro-cess requires phase matching between the interacting opti-cal fields as discussed earlier. The phase matching conditionrequires the sampling pulse wavelength to closely coincidewith the zero-dispersion wavelength of the nonlinear fiber.However, in FWM-based gates the sampling pulse wave-length must be well separated from the signal wavelengthin order to generate samples that can be extracted by op-tical filtering. Another issue is the broadening of the sam-pling pulse spectrum caused by SPM, which will increasethe minimum necessary wavelength separation between thesampling pulses and the signal. The amount of SPM is de-termined by a combination of sampling peak power, sam-pling pulse width and nonlinear interaction length and willset a boundary condition for maximum peak power, short-est pulse duration and longest interaction length. More de-tails about the content described in 3.1–3.5 can be foundin [23–25].

3.2. Experimental setup

As a starting point of this discussion we will introduce aschematic experimental setup suitable for all-optical sam-pling in highly nonlinear fiber. Fig. 4 shows the experimen-tal setup that was used to characterize the FWM samplingtechnique and achieve a good balance between differenttrade-off parameters in order to find an operating pointyielding high overall performance.

The sampling pulse source should produce short (∼1ps wide) pulses with a repetition rate which is suitablefor analog-to-digital conversion of the generated samples.Hence, a suitable repetition rate of the laser source is inthe range 10–100 MHz. In our experiments we used anactively mode-locked Erbium-doped fiber ring laser op-erating at 10 GHz repetition rate in order to achieve therequired short high quality sampling pulses. The laser gen-erated chirp-free sech2-shaped pulses with pulse widthTFWHM = 1.3ps [26]. To adapt to the available band-

samplingpulses

HNLF

O-BPF

O/EPi

Pp

Pswaveform

couplerA/D computer

Figure 4 Experimental setup. HNLF: highly nonlinear fiber, O-BPF: optical band-pass filter, O/E: optical-to-electrical conversion

using a photo detector and A/D: analog-to-digital conversion.



-10 -5 0 5 10

0

0.5

1

time (ps)

sam

pled

pow

er (

a.u.

)

-2 -1 0 1 20

.5

1

time (ps)

pow

er (

a.u.

)

Figure 5 Sampled pulse from a 10 GHz

actively mode-locked fiber ring laser with

λs = 1565nm and average power of

−5dBm. The solid line represents a fit-

ted sech2-shaped pulse with TFWHM =2.95 ps. A 10 m HNLF was used together

with a 1.3 ps wide sampling pulse with

PSPS ≈ 14W and λp = 1541nm. The in-

set illustrates the sampling gate compres-

sion due to the FWM-process. The solid

line represents a 1.3 ps sampling pulse and

the dashed line the resulting 0.9 ps sam-

pling gate duration.

width of our data acquisition system the repetition rate wasreduced to 100 MHz using an external intensity modulator.The output power of the sampling pulse source was boostedwith an EDFA in order to obtain around Pp = 100W sam-pling pulse peak power. The peak power could then be re-duced by an attenuator to the appropriate level for eachstudied case. It is recommended to avoid the use of compli-cated actively mode-locked lasers for sampling purposesand instead use less complicated sampling pulse gener-ators e.g. the much simpler passively mode-locked fiberlasers running directly at the desired repetition rate andhaving similar pulse characteristics. The sampling pulsesare then to be combined with the signal in a coupler, e.g.fused directional coupler or WDM-coupler. The combinedsignal is then launched into the HNLF where the FWM sam-pling process takes place and a sampling product (idler) atλi ≈ 2λp − λs is generated. In our experiments we useda HNLF with the following parameters: zero-dispersionwavelength 1540.8 nm, dispersion slope 0.03ps/km/nm2,γ = 10W−1 km−1, lengths 10, 20, and 50 m.

The loss in the HNLF was small enough to be negli-gible at these short lengths. Note that three different fiberlengths were used in order to test the length dependence ofthe different performance measures. At the output of theHNLF the generated idler wave containing the samples ofthe signal must be separated from the signal and samplingpulse source. In our experiment we used an optical band-pass filter (O-BPF) to extract the idler which then entereda low bandwidth pin-detector (O/E, Δf = 125MHz) inorder to enable analog-to-digital conversion (A/D) of thesamples in the electrical domain. The idler power enteringthe detector after filtering is denoted Pi. Finally, the ana-log electrical signal was electrically sampled by an A/Dconverter and fed into a computer for subsequent display.

3.3. Temporal resolution

In order to characterize the influence of the sampling pulsewidth and the FWM process on the temporal resolution westarted by measuring the resolution in a case with neg-ligible dispersive walk-off. In this case we selected theshortest possible HNLF (L = 10m) and a small wave-length offset between the sampling pulse source and thesignal (λs − λp = 24nm) yielding a negligible walk-off.The temporal resolution was determined by measuring thepulse width of a 10 GHz pulse train using both autocorrela-tion (with negligible resolution) and optical sampling. Theresolution of the sampling system can then be estimatedby de-convolving the actual pulse width (measured withthe autocorrelator) from the pulse width measured withthe optical sampling system. In our case we used 2.8 pswide sech2-shaped pulses at λs = 1565nm to characterizethe sampling system. The sampling pulse width was 1.3 pswhen entering the HNLF and the peak power was aboutPp = 14W (sampling efficiency η = (γPpL)2 = 200%,see Eq. (1)). The wavelength of the sampling pulse sourcewas λp = 1541nm. The sampled pulse is shown in Fig. 5

together with a sech2-shaped fit with TFWHM = 2.95ps.The resulting temporal resolution was then estimated,

by de-convolving the actual pulse width, to be Δτ =(2.952 − 2.802)1/2 = 0.93ps, which is smaller than theinitial sampling pulse width. The reason for this samplinggate compression is the fact that the FWM sampling effi-ciency depends on the sampling pulse power squared. Theinset in Fig. 5 shows the theoretical FWM-based samplinggate (dashed) assuming that the sampling efficiency is pro-portional to the square of the sampling pulse power (solid).The theory predicts that the sampling gate should be re-duced, relative to the sampling pulse width, from 1.3 ps to



0 20 40 60 80 1000

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(ps)

λs- λp (nm)

L=50 m

20 m

10 m

walk off

-20

-10

0

norm

. pow

er (

dB)

-10

0

λi - λp (nm)

50 m

10 m

-57 -37 -17 Figure 6 Calculated sampling temporal

resolution including FWM compression and

walk-off as a function of λs −λp for 10, 20,

and 50 m HNLF. The dispersion slope was

S = 0.03ps/nm2/km and λp = λ0 and the

sampling pulse width was 1.3 ps. The dashed

lines show only the walk-off for each case.

The inset shows the measured idler spectra

for the 10 and 50 m cases for three different

λs − λp.

0.9 ps agreeing well with the measurement. This compres-sion feature of the FWM-based sampling enables the useof wider sampling pulses with maintained temporal resolu-tion, which results in less influence from self-phase mod-ulation (SPM) in the nonlinear process due to a narrowersampling pulse spectrum. A similar gate-compression fea-ture can be observed when using cross-phase modulation(XPM) to implement the sampling gate, since the requiredwavelength shifting only takes place at the temporal over-lap between the signal and the leading or trailing edge ofthe sampling pulse which also results in compression of thesampling gate [13]. Note however, that the χ2-based gateswith sampling efficiency proportional to the sampling pulsepeak power do not experience sampling gate compression.

Until now the walk-off due to the difference in chro-matic dispersion between the sampling pulse and signalhas been neglected since it was very small in the L = 10mcase (< 0.2ps). However, the temporal resolution will de-pend on the signal wavelength, and hence be related to theoptical bandwidth of a HNLF-based sampling system. Alarge walk-off will limit the optical bandwidth over whicha specified resolution is maintained, e.g. Δτ < 1ps. Inthis section the walk-off is quantified with respect to thefiber parameters and in the next section this walk-off limita-tion is compared to the FWM bandwidth limited by phase-matching. It turns out that there is a direct trade-off thatneeds to be considered when designing the sampling sys-tem.

The amount of walk-off, ΔTWO, between the samplingpulse and the signal is given by Eq. 2 and it is clear thatΔTWO is proportional to (λs − λp)2 when λp is close to

the zero-dispersion wavelength.

ΔTWO = L

λs∫

λp

D(λ)dλ = 12SL(λs − λp)2 , (2)

The walk-off also depends directly on the fiber dispersionslope (here S = 0.03ps/nm2/km) and fiber length L. Fig. 6(solid) shows the calculated temporal resolution includingboth the pulse width limited resolution (Δτ = 0.93ps forλs − λp = 0nm) and walk-off as a function of λs − λp

for L = 10, 20, and 50m HNLF. The dashed lines showonly the walk-off for each case. For the 50 m case thetemporal resolution was dominated by walk-off already atλs − λp = 40nm. The walk-off can also be estimated in-directly by measuring the spectral width of the generatedidler as shown in the inset of Fig. 6. When a large walk-offoccurs during the sampling the generated sampling gate be-comes wider resulting in a narrower idler spectrum. A clearspectrum narrowing was observed for the 50 m HNLF casewhen λs − λp increased.

If a sampling system with 100 nm optical bandwidthis required the temporal resolution using the 50 m HNLFwould be wider than 7 ps. This is not much better than fora conventional state-of-the-art electronic sampling oscil-loscope. In order to achieve high resolution over a largebandwidth the HNLF must be short enough for negligiblewalk-off to occur over the bandwidth of interest. For a 10 mfiber the temporal resolution can be kept below 1 ps overmore than 60 nm, and below 1.5 ps over 100 nm, when usinga 1.3 ps wide sampling pulse. The generated idler spectralwidth for the 10 m HNLF, shown in the inset of Fig. 6, was



0 20 40 60 80 100-8

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-2

0

2

4

6

8

10

FW

M s

ampl

ing

effic

ienc

y (d

B)

20m

λsignal - λp (nm)

1480 1520 1560 1600-50

-30

-10

Wavelength (nm)

Pow

er (

dB)

10

Idler

Pump

Signal

L=10m

50m

Figure 7 Experimentally measured FWM

sampling efficiency vs. wavelength separa-

tion between the signal and the sampling

pulse source (λs − λp) for three differ-

ent HNLF lengths, L: ◦: 10 m •: 20 m and

�: 50 m. Theoretical calculations based on

experimental input data (solid). Normalized

optical spectrum at the output of the 10 m

HNLF with λs = 1600nm and λp =1543nm (inset). The product PpL was kept

constant in order to have equal FWM effi-

ciencies for the three cases.

negligibly affected by walk-off at λs − λp = 57nm. Inorder to achieve sub-picosecond temporal resolution over100 nm either the HNLF length must be reduced to ∼7 mor the dispersion slope reduced to ∼0.02 ps/nm2/km. Notethat the walk-off limitation is linearly dependent on theproduct between the fiber length and dispersion slope, andhence the sampling temporal resolution can be improvedby a factor of two to 0.5 ps (with maintained 100 nm opticalbandwidth) e.g. by either use half the fiber length (3.5 m)or reduce the dispersion slope to 0.01 ps/nm2/km.

3.4. Optical bandwidth

We previously discussed the fact that the optical bandwidthof an optical sampling scope is related to the temporal res-olution through the walk-off. The optical bandwidth is alsodependent on the nature of the nonlinear process responsi-ble for the sampling. In the case of FWM in fiber the phasematching between the signal and the sampling pulse sourceis critical in order to have efficient sampling over a largebandwidth. Here we discuss the limitation due to FWMbandwidth and the relation to the walk-off limitation. Wewill also show that the FWM bandwidth depends stronglyon the length of the HNLF, which will result in a trade-offtowards signal sensitivity (discussed in the next section).

First we focus on the fiber length dependence of theFWM bandwidth. A fixed sampling pulse source wave-length at λp = 1543nm was used for three different HNLFlengths, L = 10, 20 and 50m, with λ0 = 1540.8nm. Thus,the sampling pulse source wavelength offset from λ0 was2.2 nm. The sampling pulse peak power was adjusted toachieve equal maximum FWM efficiencies for the three

cases. With this setup the sampling efficiency was measuredfor a signal wavelength range of 1570 nm < λs < 1615nm(limited by the available hardware). Fig. 7 shows the mea-sured and calculated FWM sampling efficiency as a func-tion of signal wavelength for the three HNLF lengths.

The inset in Fig. 7 shows the optical spectrum exitingthe HNLF for λs = 1600nm. By measuring the idler powerin the optical spectrum and comparing it with the inputsignal CW power the FWM conversion efficiency was ex-tracted by carefully considering the duty cycle of the gener-ated idler caused by the pulsed nature of the generated sam-ples (here 0.01% or −40 dB). The measured data (◦, •, and�) was also compared with calculated FWM conversionefficiencies (solid lines). All input parameters to the calcu-lations were taken from experimental measurements exceptfor λ0 which was extrapolated from Fig. 8. The experimen-tally measured sampling efficiencies in Fig. 7 were in goodagreement with the calculated ones. The 3 dB bandwidthincreases dramatically as the fiber length is reduced dueto a larger tolerance to the chromatic dispersion differencebetween λs and λp. In the case with 50 m HNLF the sam-pling efficiency decreases less rapidly at long wavelengthsthan predicted by simulations which can be accounted forby λ0 variations along the length of the fiber.

Fig. 7 showed that for a fixed wavelength offset be-tween the sampling pulse source and the zero dispersionwavelength of the HNLF it is beneficial to use a short fiberto achieve a large FWM bandwidth. However, while thefiber length is important for the FWM phase mismatch, theactual wavelength offset λp − λ0 is equally important forthe resulting bandwidth. To experimentally determine themaximum optical bandwidth we used a 10 m HNLF in thesampling system and measured the FWM efficiency as a



0 20 40 60 80 100 120-8

-6

-4

-2

0

2

4

6

FW

M s

ampl

ing

effic

ienc

y (d

B)

:1541nm:1542nm:1543nm:1544nm:1546nm:1548nm

λp

:1550nm

λsignal - λp (nm)

Figure 8 Experimentally measured (dots)

FWM sampling efficiency vs. wavelength

separation between the signal and the sam-

pling pulse source (λs − λp) in the 10 m

HNLF case for differentλp. The experiments

were compared with theoretical calculations

based on experimentally measured input pa-

rameters (solid). From the calculations the

zero-dispersion wavelength was established

to be λ0 = 1540.8nm. The dashed line rep-

resents λp = 1540.3nm.

function of λs − λp for different λp − λ0. The theory pre-dicts (neglecting λ0 variation) that the optical bandwidthwould increase as λp approaches λ0 and become infinitewhen λp = λ0. Fig. 8 shows the measured optical band-width of the sampling system for 0.2 < λp −λ0 < 9.2nm.The experimental values were also compared to theoreticalcalculations showing very good agreement.

By comparing the experimental and theoretical FWMsampling efficiency drop-off rates for the case with λp =1550nm (Δ) it can be concluded that only a small λ0 vari-ation occurs in the 10 m HNLF. When λp − λ0 approacheszero the bandwidth increases rapidly. For example, withλp = 1541nm the theory predicts an optical bandwidth fargreater than 100 nm and the theoretical agreement with theexperiments indicates that these predictions are accurate.Furthermore, a sampling pulse source wavelength toleranceof more than ±1.5 nm can be accepted while still achieving100 nm optical sampling bandwidth. For λp = 1541nm thevariation in FWM sampling efficiency is only 1 dB over thefirst 100 nm, which would result in small variation in thesampling sensitivity.

3.5. Sampling sensitivity

We suggest that the signal sensitivity, Psens, of any typeof practical optical sampling system should be defined asthe input signal power required for achieving an SNR of20 dB. The sensitivity should always be accompanied bythe temporal resolution and optical bandwidth, since thereis a trade-off between sensitivity, resolution and opticalbandwidth. The SNR in an optical sampling system usinga PIN photodiode which is mainly limited by thermal noise,

of variance σ2t , is given by

SNR =(RPsigη (p ∗ h))2

σ2t

=R2P 2

sigη2 Δt2

Δt2+(κ/Δν)2

4kBTFnΔν/RL,

(3)where R is the detector responsivity, Psig is the input signalpower to be sampled, kB is Boltzmann’s constant, T is thetemperature, Fn is the detector amplifier noise figure, Δν isthe bandwidth of the receiver (detector plus ADC), and RL

is the detector load resistance. The factor (p∗h) representsthe peak amplitude of the convolution between the normal-ized optical sample p(t) and the impulse response h(t) ofthe receiver, where Δτ is the temporal resolution of thesampling system and the constant κ is the time-bandwidthproduct of the impulse response of the receiver. The factor(p ∗ h) determines to what extent the detected sample isbroadened or, equivalently how much its peak amplitudedecreases after detection. Depending on the exact shapeof the impulse response, the constant κ varies slightly andmust be measured for each individual system. As a theo-retical example assuming Gaussian sampling pulses withFWHM pulse width Δτ and a Gaussian detection responsewith a 3 dB bandwidth Δν, the constantκ = ln 2/π ≈ 0.22.In the experiments for the fiber FWM-based system theconstant κ was estimated to be 0.25. Note that, in general,Δν and therefore the SNR is independent of the samplingfrequency. A similar expression as Eq. (3) can be obtainedfor an APD including the multiplication factor, shot- andexcess-noise.

To investigate the validity of the theoretical analysis ofthe sampling sensitivity we conducted experiments usingthe HNLF FWM-based sampling system. In order to estab-lish the trade-off between the sampling sensitivity and the



-30 -20 -10 05

10

15

20

25

30

Signal power (dBm)

SN

R (

dB)

8 ps

1 ps

50 GHz osc.Opt. sampling

-30 -20 -10 05

10

15

20

25

30

Signal power (dBm)

18 ps

8 ps

1 ps

1/ Dn

(c)(a) PIN (b) APD

107

108

109

1010

1011

1012

-25

-20

-15

-10

-5

0

Sig

nal s

ensi

tivity

(dB

m)

at 2

0 dB

SN

RReceiver bandwidth (Hz)

1 ps

8 ps

1/ Δν

(c)

PIN

Δτ =18 ps

18 ps

Figure 9 Experimentally obtained SNR data (•) compared with theoretical predictions for different temporal resolutions for (a) PIN

receiver and (b) APD-receiver. In (c) the signal sensitivity, Psens, is shown as a function of PIN receiver bandwidth for different

resolutions. The � in (a) show electronically sampled SNR with 50 GHz bandwidth.

temporal resolution, Δτ , that is predicted by Eq. (3) the res-olution was varied by changing the sampling pulse widthby means of dispersion. Three different temporal resolu-tions were investigated (1, 8, and 18 ps) and for each casethe peak FWM sampling efficiency (η = (γPpL)2) wasmaintained close to 100% by adjusting the sampling pulsepeak power (5–20 W) and the HNLF length (10 or 50 m).Two different receivers were investigated in order to showthe potential benefit of using an APD.

Fig. 9a shows the experimentally obtained SNR datafor the PIN photodiode, which are in excellent agreementwith the theoretical predictions based on Eq. (3), where theSNR scales as∝ P 2

sig and∝ Δτ2. The results are also com-pared to a 50 GHz electrical sampling oscilloscope with ahigh-speed (50 GHz) photodiode front end, and the sen-sitivity was Psens = −3dBm, which is nearly equal toour sampling system but at 1 ps resolution. At 8 ps resolu-tion, which is more comparable to the 50 GHz oscilloscope,the sensitivity was −12 dBm, an improvement by 9 dB, ascan be expected from Eq. (3), since the signal sensitivityscales as ∝ 1/Δτ in this region where Δτ � κ/Δν. For18 ps resolution the sensitivity was improved even furtherto −16 dBm. By using an APD the SNR can be increasedfurther. Fig. 9b shows the corresponding measurements forthe APD case, which are compared to theory (Eq. (3) modi-fied to include APD multiplication, shot- and excess-noise)with good agreement. The sensitivity was further improvednearly by a factor equal to the APD multiplication factorM = 9, to Psens = −11dBm, −18dBm, and −22dBm,respectively.

Fig. 9c shows the signal sensitivity as a function of thereceiver bandwidth, which is compared with the experi-

mentally obtained points at Δν = 125MHz for the differ-ent temporal resolutions. In this region where Δτ � κ/Δνthe signal sensitivity can be improved by increasing the re-

ceiver bandwidth since it scales as Psens ∝ 1/√

Δν. Therealso exists an optimum receiver bandwidth Δνopt = κ/Δτ ,which is, however not reasonable to reach in optical sam-pling systems with very high resolution, since avoiding fastelectronics is a key point of all-optical sampling.

In order to compare different sampling systems to eachother in terms of sampling sensitivity and temporal resolu-tion it is relevant to define a figure-of-merit as:

FOM = 1/(Δτ · Psens) (4)

With this definition different sampling systems (also elec-trical) can be compared in a fair way. Basically, in order toachieve a good FOM the sampling system should be ableto measure small sample energies ΔτPsens. In the mea-surements for the fiber FWM-based sampling system theFOM was equal to 2 ps−1 mW−1 (or equally 2 fJ−1) in allPIN cases (0.2 for the 50 GHz oscilloscope) and around10 ps−1 mW−1 for the APD case.

3.6. Techniques for polarization-independentsampling

When using an all-optical sampling oscilloscope to monitora data signal in a transmission system it is critical that thesampling efficiency is constant irrespective of the signalstate-of-polarization (SOP). Otherwise an SOP drift will



combiner

SPSPC

PM-fiber

HNLF

O-BPFComputer

& DAQ

y

x

combiner

SPSPC

HNLF

PBS

PC

O-BPF

Computer& DAQ

a)

b)

signalinput

signalinput

PIN

PIN

Figure 10 Schematic setup of

three polarization-independent

optical sampling gates.

(a) Single-path fiber based

gate [27], (b) dual-path fiber

based gate [28]. SPS: sampling

pulse source, PC: polarization

controller, HNLF: highly non-

linear fiber, O-BPF: optical

band-pass filter, DAQ: data

acquisition card, PBS: polar-

ization beam splitter.

cause amplitude variation of the sampled signal. Further-more, polarization-dependent sampling systems cannot beused to evaluate polarization-dependent effects on a pulse,such as polarization-mode dispersion (PMD) in fiber. Un-fortunately every optical process used in the literature toimplement a switch suitable for sampling is inherently po-larization dependent. These processes can be completelypolarization dependent as with FWM in fibers where thesampling efficiency equals zero when the polarization statesof the signal and sampling pulse are orthogonal.

Two optical fiber-based implementation examples ofpolarization-independent sampling gates are describedhere. Fig. 10a shows a single optical path polarization-independent sampling gate utilizing FWM in fiber [27]. Thesampling pulses from the SPS were combined with the sig-nal in a WDM-coupler. A polarization-maintaining (PM)fiber with differential group delay (DGD) larger than thesampling pulse width was then used to split each samplingpulse into two equal and orthogonal pulses by aligning thesampling pulses at 45◦ relative to the birefringence axesof the PM-fiber. Note that the DGD of the PM-fiber wasalso added to the signal, which is critical in order to samplethe signal at the same position in time for both polariza-tion axes. After the PM-fiber, the FWM based samplingtook place in a 50 m HNLF. As a result of the strong po-larization dependence of the FWM process, two indepen-dent polarization sampling channels were created withinthe same optical path. After the sampling process in theHNLF the samples were filtered out by an optical band-pass filter (O-BPF). For each sampling point two samplesarrived at the low bandwidth detector, separated in time bythe DGD of the PM-fiber, and represented the amplitudeof the two polarization states of the signal. Note, however,

that the DGD of the PM-fiber was much smaller than theimpulse response time of the detector, and thus, the peakpower of the impulse response corresponded to the com-bined energy of the two samples. Hence, the amplitude ofthe impulse response was independent of the signal polar-ization state. The maximum polarization dependence wasmeasured to be 0.3 dB (7%). This small residual value wasbelieved to be limited by the alignment of the samplingpulses into the PM-fiber.

Fig. 10b shows another fiber-based polarization-independent sampling gate based on FWM [28]. The oper-ation is very similar to the single-path method apart fromthe method used to implement independent sampling of thetwo polarization axes. In this case, the sampling pulses andthe signal were split by a polarization beam splitter (PBS)into parts co-and counter-propagating through the HNLF.The sampling pulse polarization state was aligned into thePBS such that equally efficient sampling took place in thetwo directions in the HNLF. The generated samples exit thePBS through the same port the signal entered, and hencea circulator was required in order to filter out the samples.The resulting polarization dependence was 0.7 dB whichwas claimed to arise from loss asymmetry in the loop [28].

The performance in terms of polarization dependenceof the three techniques for polarization-independent all-optical sampling presented here are very similar. The smalldifferences in the measured values depend rather on the par-ticular equipment used than on the principle of operationof the techniques. In order to maintain the same sensitivityas in the polarization dependent case the sampling pulsesource power must be increased by a factor of two in bothtechniques described here. Other performance measuressuch as optical bandwidth, temporal resolution, etc. are not



input signal

3 dB

polarimeter

PC1sampling pulses

HNLF O-BPF

A/D

50 m

O/E

PC2

f153 f1f2=

99%

1%

computer

Figure 11 Experimental setup of time and polarization

resolved optical sampling based on FWM. PC: Polariza-

tion controller.

s1

s2

s3 0.50.650.58

0 25 50 75 100 125 150

-.5

0

.5

1

Sto

kes

para

met

er v

alue

time (ps) Poincaré sphere

Figure 12 State-of-polarization of a 160 Gb/s polarization multiplexed data signal vs. time. The Stokes parameter is shown as circles

while the total optical power is illustrated by the solid line (left). The SOP of the data visualized on the Poincaré sphere (right).

expected to suffer due to the techniques for polarization-independence. Taking into account the large differences inthe added amount of hardware and cost between the dif-ferent solutions, compared with the polarization dependentcase, the single-path solution appears advantageous.

3.7. Time-resolved state-of-polarizationsampling

Polarization related detrimental effects on optical transmis-sion systems such as polarization mode dispersion (PMD)and nonlinear polarization rotation will become increas-ingly problematic to handle as the channel bit-rates in-crease. In addition, modulation formats relying on control-ling the state-of-polarization (SOP) is attracting increasinginterest, for example, to potentially increase the spectral ef-ficiency in DWDM systems. Hence, monitoring of the SOPof optical signals is expected to become increasingly im-portant, including perhaps also more detailed informationsuch as the time-resolved SOP evolution.

All-optical SOP sampling systems with high time res-olution were recently demonstrated [29, 30]. The setupfrom [29] is schematically shown in Fig. 11 and utilizesa polarization rotation FWM-based concept. This setup issimilar to the one described in Fig. 4 with the major dif-ference in that the sampling pulses were here polarizationmodulated at two different frequencies.

Since the FWM process is strongly polarization depen-dent, only signal power that has the same SOP as the sam-pling pulses will be sampled at any given time.

The capability of the SOP sampling method was eval-uated with a 160 Gb/s optically time-division and polariza-tion multiplexed (i.e. all neighbouring bits nominally be-ing orthogonally polarized) data signal. Fig. 12 shows theSOP of the first 24 bits of the 160 Gb/s waveform. Notethat neighbouring bits have orthogonal SOPs, as expected.The figure also visualizes the SOPs of the signal on thePoincaré sphere. The solid line indicates the average SOPof the 160 Gb/s signal and the small angular spread of thesamples indicates that only a small amount of PMD hasaffected the signal.



Figure 13 Sampled eye-diagrams of a

640 Gb/s RZ data signals using a fiber

FWM-based optical sampling system.

Figure 14 Sampled data pattern of a 640 Gb/s RZ data signals using a fiber FWM-based optical sampling system.

3.8. Experimental performance withpseudo-random digital data

In Fig. 13 we present typical experimental return-to-zero(RZ) data eye-diagrams at the very high bit rate of 640 Gb/s.The temporal resolution was 1.0 ps and the sampling sensi-tivity was 2 mW. Furthermore, the polarization dependencewas less than 0.5 dB. The data displayed shows very cleareye openings suggesting error-free performance. The dif-ference in amplitudes among the different eye diagrams iscaused by imperfect condition in the optical multiplexerused to generate the data and is not an artifact of the sam-pling system.

Fig. 14 shows the same data with the word repetitionrate as time base (in this case 127 bits of data). Only afraction of the data bits are shown here. The lack of in-terference noise among neighboring one-bits suggests thatthe actual optical pulse duration is much shorter than 1 ps.

The displayed waveform is thus resolution limited by thesampling system.

4. Software synchronized time-base recovery

In this section, we briefly describe a technique that we havefound useful for time-base reconstruction for optically sam-pled high-speed communication signals. A major problemwhen dealing with very high speed signal is the clock re-covery. Not only do the complexity and the required per-formance increase at higher bit-rates or higher resolutionneeds, but such hardware also tends to be specific for eachparticular line rate or repetition frequency. Here we de-scribe a technique which enables synchronization of theacquired samples without the presence of a hardware trig-ger. The technique is based on a software algorithm thatcalculates the position in time of each acquired sample byusing the Fourier transform of a set of samples. The soft-



randomstartingpoint 1/fS = M.TB + Δt

(here M = 2)

1

2

3

4

5

6

7

8

910 111213 1415

TB equivalent time

pow

er

randomstartingpoint

Δt1

47

10 13

2

3

5

6

8

9

TB

15

pow

er

0 equivalent time

0

0

0 11 12 14

K = 3 (pattern)

K = 1 (eye)

Figure 15 Principle of the software based sampling time-base. The first sample is acquired at a random starting time indicated by the

bold arrow. Consecutive samples are separated by 1/fs which can be divided into an integer number of signal bit-slots M and a small

time-step Δt using the relation 1/fs = MTB + Δt. The build up of a three bit waveform is demonstrated by the acquisition of 15

samples with M = 2 and Δt ∼ TB/19. Either the data pattern waveform with K = 3 (top) or the eye-diagram with K = 1 (bottom)

can be visualized.

ware synchronization technique is compared to the trigger-based sampling schemes and some fundamental differencesare identified. This approach in addition to eliminating theneed for a hardware clock recovery and traditional triggercircuitry, also can significantly simplify the performancerequirements on the pulsed laser that serves as samplingpulse source.

In this scheme, a software algorithm is applied to thegenerated samples in order to extract the synchronizationinformation directly from a set of asynchronously acquiredsamples and use the information to reconstruct the originalinput waveform [31–33]. The technique utilizes a samplingstrobe source with a certain sampling rate, fS, which isasynchronous to the repetitive waveform to be measured.With this technique, no trigger event is necessary and thetotal number of samples, N , required for waveform recon-struction is collected in a single sequence with N sam-ples separated by 1/fS. Fig. 15 illustrates the principle ofthe waveform build-up as more and more samples are col-lected for a three bits sequence. The relationship betweenthe sampling pulse separation, 1/fS, and the bit slot, TB ,is described by

1/fS = MTB + Δt , (5)

where M represents the number of bit slots skipped be-tween two consecutive sampling instances and Δt rep-

resents a smaller time-step (< ±TB/2) responsible forscanning the bit slot. The position of the ith sample ina K bit long repetitive waveform is calculated as ti =rem[t1 + i/fS, KTB ], where t1 is the random position ofthe first sample (marked by an arrow) and rem[x, y] repre-sents the remainder of x after division by y. As an examplethe first 15 samples in a sampling sequence with M = 2and Δt ≈ TB/19 is shown in Fig. 15 as filled grey circles.In Fig. 15 (top) the sample acquisition is shown for thetime scale representing the complete pattern of three bits(K = 3). In order to visualize a one bit slot eye-diagram tiare calculated using K = 1. The time-step Δt is indicatedin Fig. 15 as the time difference between two consecutivesamples in the eye-diagram mode with K = 1.

With the software synchronized time-base it is alsostraightforward (in contrast to traditionally triggered sys-tems) to select the correct pattern length in the software andsimply extend the timeline to include all bits separated, thusdisplaying the actual bit pattern and not the eye diagram.

There are a few drawbacks with the software synchro-nized time-base compared to the traditional hardware trig-ger based techniques. For example, it is straightforward tounderstand that a certain minimum signal amplitude mod-ulation is required in order for the algorithm to pick up theaccurate Fourier component representing the correct Δt.Hence, there is a minimum power level required for syn-



0 25 50 75 100time (ps)

0 25 50 75 100time (ps)

0 25 50 75 100time (ps)

9000 m8200 m

3900 m

7000 m

5800 m5000 m

3200 m2300 m0 m SMF

Figure 16 Software synchronized eye-diagram of a 40 Gb/s NRZ data signal for an increasing amount of chromatic dispersion. The

signal was transmitted through different lengths of standard single-mode fiber (SMF) ranging from 0–9 km corresponding to 0–150 ps/nm

of dispersion.

chronization as well as a minimum signal to noise ratio(SNR), but the absolute requirements are not obvious andwill depend on the implementation of both hardware andsoftware. However, in [34] synchronization of signals withless than 10 dB SNR and severe timing jitter is success-fully demonstrated.

Fig. 16 shows an experimental result of the softwaresynchronization robustness towards chromatic dispersion.A 40 Gb/s NRZ data signal was transmitted through differ-ent lengths of SMF which corresponded to 0–150 ps/nm ofchromatic dispersion. When testing larger dispersion valuesthe algorithm lost precision and additional drift appearedin the eye-diagrams. The robustness shown by the softwarealgorithm is comparable to conventional hardware clockrecovery circuits.

5. Discussions and conclusions

In terms of performance when characterizing multi-levelformat signals such as DQPSK or QAM signals, it will beincreasingly important that the sensitivity and the linearity

of the measurement system are very high. Therefore theFOM introduced earlier (the inverse of the sensitivity timestemporal resolution product) is very important as it clearlyquantifies the trade-off always present and allows a faircomparison among different solutions. In the context ofintrinsic time resolution, essentially none of the systemsdiscussed here are close to any fundamental limits. Thus,in principle, the sampling system presented here is scalableto bandwidths well over 1 THz, should this be needed. Theresolution is mainly limited by the sampling pulse widthand dispersive effects and the resulting resolution limitationneeds to be traded against other performance criteria. Newmaterials will likely emerge that can improve the FOM andthe trade-offs. These include engineered materials such asphotonic crystal fibers (PCF) that can have very uniqueproperties. One such property is that they can be designedand fabricated to have the zero-dispersion wavelength in thevisible wavelength range which allows them to be used e.g.for optical waveform sampling of visible light. While this isnot a telecom wavelength window, it illustrates that some ofthe high speed waveform sampling techniques discussed inthis chapter may find applications where the tools of choice



today include autocorrelators, streak cameras, and pump-probe setups.

While performance is a key aspect of the solutions dis-cussed here, most techniques are typically fairly complexand thus expensive. Therefore, it is important to find morecost effective and robust solutions without sacrificing toomuch performance. The most expensive component in highresolution optical sampling systems is by far the opticalpulse source. Frequently, passively mode-locked lasers arebeing used and while this certainly represents a much lessexpensive solution than actively mode-locked lasers, sim-pler pulse sources with sufficient performance are neededto reduce cost.

Acknowledgements The Swedish Foundation for Strategic Re-

search (SSF) provided funding this research project. We ac-

knowledge fruitful discussions with Dr. Henrik Sunnerud and

Dr. Magnus Karlsson. The Knut and Alice Wallenberg Foundation

is acknowledged for funding significant equipment used for ex-

periments conducted. In addition, Picosolve Inc. is acknowledged

for lending us their optical sampling oscilloscope to generating

some of the data presented here.

Peter Andrekson received his Ph. D.from Chalmers University of Tech-nology, Sweden, in 1988. After threeyears with AT&T Bell Laborato-ries, Murray Hill, USA, he returnedto Chalmers where he is now afull professor at the Department ofMicrotechnology and Nanoscience.He was Director of Research at

CENiX Inc., Allentown, USA, and worked at the newlyestablished Center for Optical Technologies at LehighUniversity, Bethlehem, USA. His research interests in-clude nearly all aspects of high speed and high capacityfiber communications such as optical amplifiers, non-linear pulse propagation, all-optical functionalities, andvery high speed transmission.

Andrekson is a Fellow of the Optical Society ofAmerica and a Fellow of the IEEE. He is the author andco-author of over three hundred scientific publicationsand conference papers in the area of optical communi-cations, more than sixty of which were invited papers atleading international conferences and journals. He is orhas served on several technical program committees andas international project and candidate evaluator, and hasalso served as an expert for the evaluation of the NobelPrize in Physics in 1996 and in 2007. He also holds sev-eral patents. In 1993 he was awarded a price from theSwedish government research committee for outstand-ing work performed by young scientists, and in 2000 hewas awarded the Telenor Nordic research award for hiscontribution to optical technologies.

Mathias Westlund received theM. Sc. degree in engineering physicsand the Ph. D. degree in electrical en-gineering from Chalmers Universityof Technology, Göteborg, Sweden,in 1999 and 2004, respectively. Thetitle of his Ph. D. dissertation was“Fiber-based all-optical samplingfor ultrafast waveform monitoring”

which summarizes his main research activity.Since the Ph. D. defense Dr. Westlund has, in excess

of continued research at Chalmers, founded PicoSolveInc., a company which has put the first fiber-based alloptical sampling system on the market.

He is currently also part time employed as a Re-searcher with the Photonics Laboratory at ChalmersUniversity of Technology. He has authored and coau-thored approximately 40 journal papers and conferencecontributions. In addition to all-optical sampling, his re-search interests focus on high-speed transmission, noveldata modulation formats, fiber lasers, and fiber opticalparametric amplifiers. Dr. Westlund is a Member of theOptical Society of America (OSA).

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Nonlinear optical fiber based high resolution all-optical waveform sampling