Technique for the measurement of picosecond optical pulses using a non-linear fiber loop mirror and an optical power meter

: A method for measuring picosecond pulse width by using only fiber components and optical power meters is presented. We have shown that the output power splitting ratio of a non-linear fiber loop mirror can be used to extract the full-width half maximum of the optical pulse, assuming a known slowly varying envelope shape and internal phase structure. Theoretical evaluation was carried out using both self-phase and cross-phase modulation approaches, with the latter showing a twofold sensitivity increase, as expected. In the experimental validation, pulses from an actively fiber mode-locked laser at the repetition rate of 10 GHz were incrementally temporally dispersed by using SMF–28 fiber, and then successfully measured over a pulse width range of 2–10 ps, with a resolution of 0.25 ps. This range can be easily extended from 0.25 to 40 ps by selecting different physical setup parameters.


Introduction
The efficient generation of ultra-short laser pulses in the picosecond regime has enabled a wide range of applications from optical communications [1] to the measurement of ultra-fast physical processes [2].In order to measure the characteristics of picosecond optical fields, a number of techniques have been developed including frequency resolved optical gating (FROG) [3][4][5], spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses (SPIDER) [6,7] and sonogram [8,9].Some modified versions of FROG have also been reported using cross phase modulation and four wave mixing for the full characterization of an optical pulse [10,11].In addition to these non-linear methods, there are a number of linear self referencing methods, for example, phase reconstruction using optical ultrafast differentiation (PROUD), that avoid the requirement of high pump powers and provide a complete pulse characterization [12][13][14].These methods allow for the full amplitude and phase reconstruction of the pulse.Compact methodologies based on on-chip technologies have also been demonstrated making use of highly non-linear optical waveguide technology [15,16].In general, ultra-short pulse measurement techniques either require high pulse energies or expensive measurement equipment such as optical spectrometers in order to operate.
All optical performance monitoring is crucial for achieving stable optical networks, in particular with regards to the effects of dispersion.There are several parameters that can alter the dispersion of an optical link, i.e. temperature, path reconfiguration or physical maintenance around the fiber site [17].Also, in some applications, for example in optical networks or in cases where well-behaved optical pulses are used as a temporal probe, it is often enough to monitor the temporal envelope of the pulse to allow compensation of any dispersion that may be induced between the laser source and the monitor point.High-speed photodetectors and sampling oscilloscopes, intensity auto-correlators or cross-correlators can be used in laboratory environments for this purpose.
In this manuscript, we present an alternative method which uses a fiber amplifier, nonlinear optical fiber loop mirror (NOLM) [18] and optical power meters.Since the system is implemented in an all-fiber configuration, with no moving parts or complex measurement equipment, it can be implemented as a simple system bolt-on, or in remote locations with the potential for distributed arrays of monitors across networks.Unlike optical sampling oscilloscopes and optical auto-correlators, this method does not monitor the shape of the optical pulses but only their temporal width; hence, it can also be used to monitor the residual dispersion of the optical link [17].
Design of the method was carried out using simulations of the non-linear Schrodinger equation(s) using well-defined split step method [19].From simulations we found that this method is compatible with well-behaved pulses with slowly varying envelopes such as sech 2  or Gaussian.The measurement range is related to the non-linear phase shift introduced by the measured signal (its peak power can be boosted by using an erbium-doped fiber amplifier (EDFA) up to its saturated output power) and to the length of the non-linear medium and its non-linear coefficient.In this work, pulse widths up to 10 ps are measured, with a resolution of 0.25 ps, assuming a sech 2 or Gaussian pulse envelope with slowly varying phase internal structure.The measurement range can be extended to cover 0.25 to 40 ps by careful selection of the physical parameters in the setup.
The remainder of this paper is organized as follows: Section 2 describes the highly nonlinear fiber (HNLF) based NOLM pulse width measurement scheme and the simulated model using the split-step method for both, self-phase and cross-phase modulation variations.Section 3 presents the experimental realization of the scheme with results and analysis presented in section 4. Device limitations and discussion are presented in section 5 and finally conclusions are presented in section 6.

Picosecond pulse width measurement using non-linear optical loop mirror
As noted in the introduction, the method presented here relies on the assumption that the optical picosecond pulses under investigation are of a simple form with typically a sech 2 or Gaussian shape and little internal phase structuring.The purpose of this method is to provide a means to monitor pulse width variation induced, for example by dispersion between the pulse origin and monitor point.We present two variations of the measurement technique, both based on a 3  χ optical non-linearity process in a NOLM (see Fig. 1).In both approaches optical pulses are coupled to the NOLM and the resulting average power at its output ports is measured using a slow optical power meters.The ratio 1 2 out out P P of the measured average output powers is a function of the optical switching induced by either self-phase or cross-phase modulation depends on the peak power of a laser pulse injected into the NOLM.For wellbehaved pulses, the peak power is simply related to average power through the envelope shape and pulse train duty cycle.In order to over-sample the measurement, the input pulses are incrementally amplified by an erbium doped fiber amplifier (EDFA) to produce a series of power splitting ratios as a function of the measured average power of the input pulse train.
The system behavior can be modelled by the non-linear Schrodinger equation, numerically solved using a split-step method [19].Input values to this numerical method were chosen to match parameter values of HNLF and are summarized in Table 1.The repetition rate of the pulse source was taken as 10 GHz, matching the erbium doped fiber mode-locked laser source used in the experiments.In this manuscript we use a non-linear fiber length of 100 m and an EDFA with a saturated power level of 17 dBm and therefore simulations are carried out to demonstrate the performance of the system under these constraints.However, the achievable pulse width measurement range of the method can be tuned by varying the setup components, discussed in more detail in section 5.

Self-phase modulation
Figure 1(a) shows the self-phase modulation (SPM) variant of the scheme.In this case, the amplified pulse train ( signal P ) is coupled in to one port of the NOLM, where the coupler ratio is unbalanced (80:20) in order to create asymmetry in the counter-propagating modes.An additional optical attenuator (10 dB) is added to the loop to give control of this imbalance.The higher power replica of the pulse undergoes SPM in the HNLF creating a phase shift between the replicas as they recombine at the output coupler.
The proportion of the total power coupled to each port is dependent on the relative phase between the two pulse replicas, and their relative powers: ) L φ includes the linear phase shift and linear loss and can be computed as , β is the propagation constant of the field in the optical fiber, α is the linear absorption loss, p is the splitting ratio of the input coupler, and HNLF L is the length of the HNLF.NL θ is the nonlinear phase shift and is proportional to the input power.The Eqs. ( 2) and (3) are modified from [21] due to the inclusion of a coarse wavelength division multiplexer (CWDM) coupler to inject the amplified pulse train into the loop mirror.The non-linear phase shift can be computed by numerically solving the non-linear Schrodinger equation(s), (4) for SPM and ( 5) and ( 6) for XPM, using the split step method where the non-linear phase shift induced by cross phase modulation (XPM) is approximately twice that accumulated through SPM [19].
Where, the subscript 'a' shows the high power signal parameters and 'b' shows the low power continuous wave probe signal.λ is the operating wavelength and α is the linear loss of the waveguide.The values of all the above parameters are summarized in Table 1.The splice loss and the absorption has already included in the experimental results; hence both are not included in the simulations.
The effect of counter propagating non-linear interactions in the NOLM can be significant when using high repetition rate signals [20], hence the total effective non-linear phase shift using SPM and XPM, by taking the counter clockwise non-linear phase shift into account, can be calculated using Eq. ( 7).  ), with the pulse width as a parameter.An optical circulator (CIR) is used for separating the input and output reflected power of the NOLM.A sech 2 pulse envelope is assumed in this case.The output powers follow sinusoidal variations as a function of the input average power for a given input pulse width, with maximum and minimum values defined by the asymmetric coupling fraction of the input/output coupler.The input average power inducing a π/2 phase-shift results switching of power between R and T ports of the NOLM and subsequently can be used to extract the pulse width from measurements of the power splitting between R and T ports as a function of in P , as shown in Fig. 2(c).The relationship between pulse widths and π/2 switching point can be adequately fitted to a second order polynomial.It is also apparent that to achieve this switching, average powers in the range of 10's of mW are required for few picosecond pulses.This limits the useful range of this method to pulses of ~5 ps with our EDFA having a saturated power of ~50 mW (17 dBm).

Cross-p
With a minor significantly e as a probe of t in to one inpu direction usin propagating m In order to av second CWDM The avera (2), and (3), w entering peak relative phase using Eq. ( 7) powers of the widths.As ex as compared setup.

Effect of
The XPM sim switching poi obtained sech meaning that measurement e the π/2 previously wo results, uld allow f dths using he PriTel, source of picosecond optical pulses, referred here as the signal.The central wavelength of the signal was 1550.7 nm with a spectral bandwidth of 1.4 nm.The signal was amplified using an EDFA limited to a saturated output power of 50 mW (17 dBm).The input pulse width variation was achieved by using serially coupled lengths of SMF28 patchcord cables to disperse the signal.For the XPM setup, a low power continuous wave (CW), referred to here as the probe, was generated using Agilent 81989A tunable laser at the wavelength of 1530 nm with a power of 5 mW.A 1% power tap was introduced before the NOLM for an input average power monitoring of the signal by a temperature stable Agilent 8153A Lightwave Multimeter.The probe was then injected into the NOLM via a 50:50 optical directional coupler and the signal via CWDM 1 coupler (see Fig. 5(b)).The two polarization controllers (PC) used in the setup were set to maximize the power coupled to the reflected port in the linear regime.Once the state of PCs was set, it was not altered for any of the subsequent measurements.The passband of the CWDM 1 coupler is 1541 to 1559 nm.The signal after traveling HNLF of length ( HNLF L ) was subsequently filtered out of the loop using CWDM 2 coupler with the passband of 1542 to 1558 nm.The transmitted and reflected average power of the probe were measured at T and R ports, respectively as indicated in Fig. 5(b).The pulse width of the signal was measured using a FR-103XL optical auto-correlator before entering in to the NOLM.

NOLM based on self-phase modulation configuration
The experimental setup for optical pulse width measurements using the NOLM based on SPM is shown in Fig. 5(a).A varying length of SMF28 optical fiber was used to disperse nearly transform limited 2 ps FWHM laser pulses to 2.9 ps, 3.7 ps, and 4.5 ps, respectively.Figure 6 shows the normalized optical power obtained from measurements at R and T ports as a function of the in P , for the case of a 2 ps pulse.Since the simulated curves show sinusoidal dependence on the input average power, hence the measured transmitted and reflected data was fitted to ( 8) and ( 9), respectively, where A, B, C, and D are free parameters.This fitting then allows extraction of the π/2 point.
.sin( )  8) and ( 9) to extract the π/2 point The experimentally measured and fitted transmission and reflection powers of the NOLM obtained for up to a 50 mW of the input average optical power are shown in Figs.7(a) and 7(b), respectively.A 10 dB optical attenuator is used in the counter clockwise direction in order to suppress the power of signal hence the signal power in the 20% arm is not enough to produce the non-linearity.For wider pulses, the π/2 points were not accessible experimentally due to limited available EDFA saturated power, hence the fitting curves based on (8) and ( 9) were used to obtain the π/2 points.Figure 7(c) shows the input average power at π/2 points and the quadratic fitting.The measured curves show good agreement with the simulations and a clear dependence on the input pulse width.

NOLM based on cross phase modulation configuration
The experimental setup for optical pulse width measurements using the NOLM based on XPM configuration is shown in Fig. 5(b).Similarly, as before, five different pulse widths were generated from the initial 2 ps FWHM pulses.Again, the measured data were fitted to a sinusoidal function described by using ( 8) and ( 9).The 2ps pulse data were only fitted up to the π/2 point, as after this the switching exhibited some saturation.
The normalized transmission and reflection output powers of the XPM based NOLM are shown in Figs.8(a) and 8(b), respectively.The input average power of the signal at π/2 points and the quadratic fitting is shown in Fig. 8(c).As predicted by the theory, the sensitivity of the XPM is doubled compared with the SPM case, thus allowing more efficient pulse width measurements.We measured the input average optical power of the signal with an accuracy of ± 1 mW, that together with the R 2 = 99.88% of the quadratic fit, gives a predicted pulse width resolution of ~0.25 ps.

Device limitations and discussion
In order to characterize the temporal width of an optical pulse, the setup described above is required to define the π/2 switching point with respect to the average power of the signal.This therefore puts a limitation on the measurement range of the system that depends on the available saturation power of the EDFA and the length of non-linear fiber in the loop.As stated above, the accuracy of the measurement is limited by the accuracy of measuring the input average power from power meter and the linearity of the fitted calibration curve.Assuming the dispersion length is higher than the non-linear length, the non-linear phase shift for XPM is given as: where γ is the non-linear coefficient, av P is the input average power, T is the laser repetition period, τ is the pulse width of the laser signal, and eff L is the effective length of the HNLF fiber given as  [19].Considering (10), it is clear that the operation range for measuring an optical pulse width can be extended by maximizing any or all of listed parameters.By using XPM simulations the dynamic range of the measurement system was estimated for practically achievable lower and upper limits for the following parameters.HNLF lengths were considered with the lower limit as HNLF L = 20 m and HNLF L = 1 km as the upper limit.We also considered a maximum available EDFA saturated output power ~40 dBm.The results of these simulations are summarized in Fig. 9.
From Fig. 9(a) we can see that the minimum pulse width that could be measured with the hardware is 250 fs and can be achieved using HNLF L = 50 m and 15 dBm EDFA.As mentioned above, the resolution of this method is 0.25 ps, hence by using this hardware, the minimum possible pulse width can be measured as 250 fs.However, the device range can be extended to measure optical pulse widths well beyond 10 ps FWHM.If using HNLF L = 20 m and 38 dBm EDFA or HNLF L = 1 km and 21 dBm EDFA the device can be used to measure an optical pulse within the region of 10 -40 ps as shown in Figs.9(b) and 9(c), respectively.For pulses longer than 40 ps, the accumulated non-linear phase on the counter-propagating signal is significant, limiting the measureable effective non-linear phase shift of the system, highlighting the significant role of the repetition rate in this scheme.The device can be also easily reconfigured for pulse width measurements beyond a 40 ps range, by lowering the repetition rate, however for this regime, high speed electronics may be a more attractive option.

Conclusion
We have presented an all-fiber non-linear interferometric method for determining optical pulse widths using measurements of average power using slow detectors.The approach is applicable where Gaussian or sech 2 pulse envelopes can be assumed and the internal phase structure is slowly varying (for example in dispersive communications links).Pulses in the range of 2-10ps were successfully characterized experimentally.The dynamic range of the proposed method is limited by available hardware, with realistic limits of 250 fs to 40 ps.The method may find its use in distributed networks or as a bolt-on to optical systems using ultrashort pulse sources.This fiber device can be also implemented as an integrated non-linear Sagnac or Mach-Zehnder interferometer using integrated optical platforms, including silicon on insulator (SOI), where mode volumes can be small and non-linear coefficients can be very high, i.e. 307 (Wm) −1 , potentially leading to improvements in device miniaturization, stability and power [22].

A
is the slowly varying amplitude of the pulse envelope, 2( , ) a b β is the group velocity dispersion, ( ) , a b γ is the non-linear coefficient, ( , ) a b

Δ
is the total effective phase shift, _ cw NL θ is the non-linear phase shift produced in the clockwise direction and _ ccw NL θ is the non-linear phase shift produced in counter-clockwise direction due to XPM.

Fig. 1 .
Fig. 1.Non-linear optical loop mirror (a) in self phase modulation configuration; (b) in cross phase modulation configuration using CWDM couplers for injecting and filtering out the pulsed signal.Where OA -optical attenuator, CWDM -course wavelength division multiplexing/de-multiplexer, CIR -optical circulator, and HNLF -highly non-linear fiber Figures 2(a) and 2(b) shows the normalized reflected power ( 1 out P ) at the reflected port (R) and transmitted power ( 2 out P ) at transmitted port (T) of NOLM plotted as a function of the input average power ( in P), with the pulse width as a parameter.An optical circulator (CIR) is used for separating the input and output reflected power of the NOLM.A sech 2 pulse envelope is assumed in this case.The output powers follow sinusoidal variations as a function of the input average power for a given input pulse width, with maximum and minimum values defined by the asymmetric coupling fraction of the input/output coupler.The input average power inducing a π/2 phase-shift results switching of power between R and T ports of the NOLM and subsequently can be used to extract the pulse width from measurements of the power splitting between R and T ports as a function of in P , as shown in Fig.2(c).The relationship between pulse widths and π/2 switching point can be adequately fitted to a second order polynomial.It is also apparent that to achieve this switching, average powers in the range of 10's of mW are required for few picosecond pulses.This limits the useful range of this method to pulses of ~5 ps with our EDFA having a saturated power of ~50 mW (17 dBm).
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Fig. 6 .
Fig.6.The normalized reflected and transmitted NOLM output power based on SPM measurements showing a sinusoidal fit using (8) and (9) to extract the π/2 point

Fig. 7 .
Fig. 7. Measured: (a) reflected, (b) transmitted output power of the NOLM in SPM configuration as a function of the input average power of the signal obtained for different pulse

Fig. 8 .
Fig. 8. Measured: (a) reflected, (b) transmitted output power of the NOLM on XPM configuration as a function of the input average power of the signal obtained for different pulse widths values.(c) Input average power at π/2 points as a function of the signal pulse showing quadratic fitting.